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Diagnostics of a See-Through Hollow Cathode Discharge by Emission, Absorption, and Fluorescence Spectroscopy

Permanent Link: http://ufdc.ufl.edu/UFE0021604/00001

Material Information

Title: Diagnostics of a See-Through Hollow Cathode Discharge by Emission, Absorption, and Fluorescence Spectroscopy
Physical Description: 1 online resource (153 p.)
Language: english
Creator: Taylor, Nicholas Roger
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: absorption, emission, interferometry, lifetime, time
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Atomic line filters have been suggested to be attractive in areas of Doppler velocimetry, resonance fluorescence detection, and resonance ionization detection. They are based on the resonant absorption of photons by an atomic vapor, and allow all other radiation to pass. This allows the detection of very low levels of light superimposed on a large optical background. Several elements have been studied for use as atomic line filters, such as the alkali metals, alkaline earths, and thallium. As previously recognized, thallium is especially attractive since the 535.046 nm metastable transition overlaps with the second harmonic output of an Nd:La sub 2 Be sub two O sub 5 (BEL) laser (1070 nm). This makes thallium ideal for certain applications as an atomic line filter. Recently a see-through hollow cathode lamp, or galvatron (Hamamatsu), was made commercially available. The galvatron geometry is unique compared to traditional hollow cathode lamps since the cathode and cell are oriented in a T-shape, with the cathode bored completely through to allow the propagation of a light source through the cathode. This allows multi-step excitation of the atomic vapor, not easily accomplished with a traditional hollow cathode lamp. The advantages that a galvatron offers over conventional atomic reservoirs make it an attractive candidate for the application as an atomic line filter; however, little spectroscopic data have been found in the literature. For this reason, Doppler temperatures, number densities, quantum efficiencies, and lifetimes have been determined in order to characterize this atomic reservoir as a potential atomic line filter. These parameters are determined by use of various spectroscopic techniques which include emission, absorption, time-resolved fluorescence, and time-resolved laser-induced saturated fluorescence spectroscopy. From these measurements, it has been demonstrated that a galvatron is an attractive atomic reservoir for applications as an atomic line filter. The spectral resolution of this atomic line filter was found to be superior to that of a traditional hollow cathode lamp and electrodeless discharge lamp. A desired number density can be rapidly produced by applying the appropriate current and can be reproduced from one experiment to the next. In addition, the quantum efficiency of this system was found to be limited only by the competing radiative pathways of the particular energy level arrangement which allows it to be a very efficient detector. This system has the potential to be simple, compact, and portable which makes it an ideal atomic line filter.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nicholas Roger Taylor.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Winefordner, James D.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021604:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021604/00001

Material Information

Title: Diagnostics of a See-Through Hollow Cathode Discharge by Emission, Absorption, and Fluorescence Spectroscopy
Physical Description: 1 online resource (153 p.)
Language: english
Creator: Taylor, Nicholas Roger
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: absorption, emission, interferometry, lifetime, time
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Atomic line filters have been suggested to be attractive in areas of Doppler velocimetry, resonance fluorescence detection, and resonance ionization detection. They are based on the resonant absorption of photons by an atomic vapor, and allow all other radiation to pass. This allows the detection of very low levels of light superimposed on a large optical background. Several elements have been studied for use as atomic line filters, such as the alkali metals, alkaline earths, and thallium. As previously recognized, thallium is especially attractive since the 535.046 nm metastable transition overlaps with the second harmonic output of an Nd:La sub 2 Be sub two O sub 5 (BEL) laser (1070 nm). This makes thallium ideal for certain applications as an atomic line filter. Recently a see-through hollow cathode lamp, or galvatron (Hamamatsu), was made commercially available. The galvatron geometry is unique compared to traditional hollow cathode lamps since the cathode and cell are oriented in a T-shape, with the cathode bored completely through to allow the propagation of a light source through the cathode. This allows multi-step excitation of the atomic vapor, not easily accomplished with a traditional hollow cathode lamp. The advantages that a galvatron offers over conventional atomic reservoirs make it an attractive candidate for the application as an atomic line filter; however, little spectroscopic data have been found in the literature. For this reason, Doppler temperatures, number densities, quantum efficiencies, and lifetimes have been determined in order to characterize this atomic reservoir as a potential atomic line filter. These parameters are determined by use of various spectroscopic techniques which include emission, absorption, time-resolved fluorescence, and time-resolved laser-induced saturated fluorescence spectroscopy. From these measurements, it has been demonstrated that a galvatron is an attractive atomic reservoir for applications as an atomic line filter. The spectral resolution of this atomic line filter was found to be superior to that of a traditional hollow cathode lamp and electrodeless discharge lamp. A desired number density can be rapidly produced by applying the appropriate current and can be reproduced from one experiment to the next. In addition, the quantum efficiency of this system was found to be limited only by the competing radiative pathways of the particular energy level arrangement which allows it to be a very efficient detector. This system has the potential to be simple, compact, and portable which makes it an ideal atomic line filter.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nicholas Roger Taylor.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Winefordner, James D.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021604:00001


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5f7700d141769e0d38335e94611deb4e17d2e15a







DIAGNOSTICS OF A SEE-THROUGH HOLLOW CATHODE DISCHARGE BY EMISSION,
ABSORPTION, AND FLUORESCENCE SPECTROSCOPY

















By

NICHOLAS TAYLOR


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2007

































2007 Nicholas Taylor









ACKNOWLEDGMENTS


I want to start off by thanking my advisor, mentor, and friend, Dr. James D.

Winefordner. His persistent enthusiasm and guidance for each of his students is truly

inspiring. His passion and encouragement were a fuel that helped to drive much of my

understanding of scientific research, learning, and life. I consider myself extremely

fortunate that I was given the opportunity to be a member of his research group and

looking back, I can't imagine my life without this experience.

I give a special thanks to Dr. Nicol6 Omenetto for his seemingly endless patience.

His door is always open and the stimulating conversations that we had really helped my

understanding of the many conceptual, theoretical, and experimental aspects of

spectroscopy. I would also like to thank Dr. Benjamin Smith, whose advice and many

insightful suggestions were much appreciated. He always makes it a point to daily pass

through the lab to see if anything is needed or questions need answering.

I thank Jeanne Karably for all she has done. She is always willing to help in any

way and is a true asset to the analytical division. I also thank the electronic and machine

shop. They do an amazing job based on the dismal descriptions that we provide, and are

always willing to work with us in order to provide exactly what is needed.

Lastly I thank my family and friends for their constant support throughout

undergraduate and graduate studies.









TABLE OF CONTENTS

page

A CK N O W LED G M EN T S ........................................................ ....................................... 3

L IST O F TA B L E S .......... .... .............. ................................................................... 7

LIST OF FIGU RE S ................................................................. 8

ABSTRAC T ................................................... ............... 12

CHAPTER

1 IN TEN T AN D SCOPE OF STUD Y ......................................................................... .............14

Introduction to A tom ic Line Filters ................................................................. 14
A tom ic R eserv oirs ................................................................15
The Glow Discharge ..................................................................... ......... 18
The Cathode Dark Space ................................. .......................... ... .......19
The Negative Glow ............................. .. ...... ... .................. 20
T h e F araday D ark Sp ace ........................................................................................... 2 1

2 HIGH RESOLUTION EMISSION SPECTROSCOPY OF A SEE-THROUGH
HOLLOW CATHODE DISCHARGE BY A SCANNING FABRY-PEROT
SP E C T R O M E T E R .............. ......... .......................................................................22

Introdu action ................. .......... .................................................................................22
Interferom eter Concept ................... ................................ .......... .......... .... 24
F inesse C considerations ......................................................................................... 27
Reflection Finesse, FR ................ ... ....................... .... ............ 27
Flatness and Parallelism Finesse, FF ........................................................... ...............28
A perture F inesse, F A ............................................................ ................29
Experimentally Determined Finesse........................................ 30
Broadening M mechanism s ............................................................... ................ ........ 31
N natural B roadening ................................................................................ ..................... 3 1
Collisional Broadening ..................................... ....... ................. ...... ......... 32
H oltzm ark Broadening .......................................... ...................... ..... 33
Instrument Function Broadening ............. ....................... 33
Doppler Broadening ..................................... ......................... 34
Self-A absorption Broadening............................................ ............... ............... 34
O their B roadening M mechanism s ............................................................................... ..... 35
Evaluation of Broadening M echanisms........... ................................. .. ..............35
Experim ent ................................. ................................................ 36
Results .................................... ... .. ................. 39
Discussion .................. ...... ............ ........................ 43
Conclusion ....................................... .......... ................ 5 ...... 1 5



4









3 NUMBER DENSITY MEASUREMENTS IN A SEE-THROUGH HOLLOW
CATHODE DISCHARGES WITH A HIGH RESOLUTION FABRY-PEROT
SPECTROMETER ............ .......... ................................... 53

In tro d u ctio n ........................ ............................................................................................... 5 3
E x p e rim e n ta l ................................ ......... .....................................................5 7
Results and Discussion ...................................... .. ......... ....... ..... 59
C onclu sions.......... .........................................................63

4 NUMBER DENSITY OF A SEE-THROUGH HOLLOW CATHODE
DISCHARGE BY CONVENTIONAL ABSORPTION SPECTROSCOPY .......................65

Intro du action ......... ............................................................................... 6 5
E xperim mental ............. .. ............ ................................................. 66
N um ber D density M easurem ents ..................................................................... ..................68
P ath L ength M easurem ents........................................................................... ....................69
L ine Source M easurem ents........................................................................... ....................70
C on clu sion ........ .. ........ ......... ......... ............................................... 72

5 TIME-RESOLVED LASER-INDUCED SATURATED FLUORESCENCE
MEASUREMENTS: EVALUATION OF NUMBER DENSITY AND
Q U A N T U M E FFIC IE N C Y ......................................................................... .....................74

In tro d u ctio n ................... ...................7...................4..........
T h eory ...................................... ...................7.........6
Rate Equation Approach Versus Density Matrix Approach .......................................76
Ideal Two-Level Saturation Curve Under Steady State Conditions..............................78
Two-Level Saturation Curve Under Transient Conditions ..........................................80
Three-Level Saturation Curve in the Presence of a Trap .............................................82
Number Density Under Steady-State Saturation Conditions .......................................85
E x p erim en tal ................................................... ....................... ................ 8 7
L a ser S y stem .......................................................................... 8 7
Detection System ............................................................................... ...... ........ ......... 89
Vacuum Photodiode Calibration .................................. .....................................89
Spectrom eter C alibration ........................................................................ ...................90
Evaluation of Dye Laser Parameters .................. ..................................... 92
S p ectral P profile ................................................................92
S p atial P ro file ................................................................9 4
Tem poral profile ......... .. .......... ...... .. .......................... ... 96
R results and D discussion ............................. .......... ........... ....... .......... .. ...... ... 97
Saturation Curve Measurement: Evaluation of the Quantum Efficiency ...................97
Number Density M easurement........ .................... ................. .... ............... 103
C o n c lu sio n .......... .... .............. ...................................... ..............................10 6

6 LIFETIME MEASUREMENTS OF SEVERAL S, P, AND Dj STATES IN A
THALLIUM SEE-THROUGH HOLLOW CATHODE DISCHARGE ...........................108









In tro d u ctio n .......................................1.............................8
E x p erim mental ............................................................................... 1 10
L asers and O ptics .............. ............................................ .......... ........... 110
D etectio n ............................................................................... 1 12
Results and D discussion ................... ... ........... ... ................. ........... ....... ..... 112
6 2D3/2 and 6 2D5/2 Lifetime Measurements .............. ............................................112
7 2S 1/2 L ifetim e M easurem ent.......................................................................... .... 115
6 2P3/20 Lifetim e M easurem ent ......................................................... .............. 117
Collisional Deexcitation Rate Constant........................... ............................ 125
C on clu sion ......................................................... ............................................... 12 6

7 FINAL CONCLUSIONS AND FUTURE WORK .............................................................128

C o n clu d in g R em ark s .................................................................................. ................ .. 12 8
H yperfine Structure Considerations ........................................ ......................... 128
Absorption M easurem ents ............................................................................. 129
Saturated Fluorescence M easurem ents.................................. ..................................... 131
L ifetim e M easurem ents ........................................................................ ........ ........... 132
F u tu re W o rk .................................................................................................. ...............1 3 3
Signal-to-N oise Ratio Considerations ........................................................................ 133
A tom ic R reservoir Elem ent ................................... ................................................... 134
Pulsed D ischarge M easurem ents ........................................................ ............. ..135

APPENDIX

A CURVE-OF-GROWTH CALCULATION-LINE SOURCE
A P P R O X IM A T IO N .............................................................................. ......................... 137

B SPONTANEOUS TRANSITION PROBABILITY CALCULATION FOR THE
377.572 NM HYPERFINE STRUCTURE...................................... ......................... 140

C LIST OF SYMBOLS USED THROUGHOUT THIS WORK WITH
DESCRIPTIONS AND UNITS GIVEN.. ........................... .....................143

L IST O F R E FE R E N C E S ......... .. ............. .........................................................................147

B IO G R A PH IC A L SK E T C H ............ ........................................................... .......................... 153









LIST OF TABLES


Table page

2-1 Calculated broadening components for thallium and lead that would be expected in a
galvatron based on known parameters and an assumed temperature of 1000 K..............36

5-1 Values used for fluorescence radiance calculation with symbols and descriptions
provided ........................................................ ..................................9 1

5-2 Previously reported saturation parameter values for various elements under various
experim mental conditions. ......................... ............................ ...... .... ...........101

6-1 Transition probabilities obtained from the National Institute of Standards and
T technology ......... ..... .... ............... .........................................113

6-2 Comparison of previously reported values on the spontaneous lifetime of the 6 2D3/2
state ......................................... ................................................... 1 14

6-3 Comparison of previously reported values on the spontaneous lifetime of the 6 2D5/2
state ......................................... ................................................... 1 1 5

6-4 Comparison of previously reported values on the spontaneous lifetime of the 7 2S1/2
state ......................................... ................................................... 1 16

6-5 Comparison of previously reported values on the effective lifetime of the 6 2P3/20
m etastable state ...................................... ................................. .......... 124









LIST OF FIGURES


Figure page

1-1 Cross sectional view of A) hollow cathode lamp and B) galvatron. .................................18

1-2 A) Illustration of a simple planar glow discharge and B) the voltage distribution.
Here Vo represents the ground voltage and Vb is the breakdown voltage [18]..................19

2-1 Partial energy level diagram of the hyperfine structure of A) 535.046 nm transition
of thallium and B) 405.7807 nm transition of lead. Both thallium and lead odd
isotopes have a nuclear spin quantum number I = 1/2. Not drawn to scale.....................23

2-2 Simple illustration of A) a Fabry-Perot interferometer and B) a Michelson
interferom eter .................................... ........................... ....... ......... 26

2-3 Experimental determination of the finesse of the interferometer using a helium-neon
laser at 632.8 nm. The variations in the intensity between the 3 orders are due to
slight intensity variations in the HeNe source ....................................... ............... 30

2-4 Experimental set-up for the measurement of the lead and thallium emission profiles
from a laser galvatron, hollow cathode lamp, and an electrodeless discharge lamp.........37

2-5 Experimental profiles of the 535.046 nm transition of thallium from A) galvatron and
B) hollow cathode lamp. ......................... ........ .. .. ..... .. .............40

2-6 Experimental profiles of the 405.7807 nm transition of lead from A) galvatron and
B) hollow cathode lamp. Both sources were measured under the same experimental
setup. ..................... ........................................ 40

2-7 Comparison between a thallium galvatron and a thallium hollow cathode lamp
profiles operated at the same current. All profiles are normalized................................41

2-8 Comparison between a lead galvatron and a lead hollow cathode lamp profiles
operated at the same currents. All profiles are normalized .............................................42

2-9 Experimental profiles of the 535.046 nm transition of thallium from an electrodeless
discharge lam p. ............................................................................43

2-10 Calculated profiles fitted to the experimental profiles of a thallium galvatron at
currents of 10, 15, 20, and 30 m A ........................................................... ............... 45

2-11 Calculated profiles fitted to the experimental profiles of a lead hollow cathode lamp
for currents of 6, 10, 15, and 20 m A ........................................ ............................ 46

2-12 Doppler temperature values obtained from the fit of the calculated two layer model
for A) 535.046 nm transition of thallium and B) 405.7807 nm transition of lead from
a galvatron, hollow cathode lamp, and electrodeless discharge lamp. ...........................47









2-13 Calculated resolving powers for A) thallium galvatron and hollow cathode lamp and
B) lead galvatron and hollow cathode lamp. ........................................ ............... 47

2-14 Optical depth values obtained from the fit of the calculated two layer model for A)
535.046 nm transition of thallium and B) 405.7807 nm transition of lead for a
galvatron, hollow cathode lamp, and electrodeless discharge lamp. ................................48

2-15 Number density values obtained from optical depths obtained from the application of
the two layer model for A) thallium and B) lead using equation 2-17. ..........................50

3-1 Illustration of a Fabry Perot interferometer and a monochromator used as a cross
dispersion system for two monochromatic wavelengths. .............................................55

3-2 Tutorial for the method of using a continuum source. A) Represents the use of a
monochromator with a large spectral bandpass. B) Represents the use of a
monochromator with a small spectral bandpass. .................................... .................55

3-3 Illustration of the production of a quasi-continuum source from two line sources for
the measurement of high resolution absorption measurements....................................57

3-4 Experimental setup used for high resolution absorption profile measurements ...............59

3-5 A) Scan of the EDL profile self-reversed. B) Scan of the HCL profile self-absorbed.
C) Resulting profile of the combined profiles yielding a quasi-continuum source
over the absorption profile. ....................................................................... ....................59

3-6 Resulting absorption profiles of the thallium 6 2P3/20 metastable state of thallium due
to various currents applied to the see-through hollow cathode discharge. The blue
wing on the quasi-continuum profile is cut off due to a small amount of order overlap
from an adjacent order. This order overlap did not cause distortion of the observed
absorption profiles ................. ............ ...................... ........... 60

3-7 Hyperfine structure for the thallium 535.046 nm transition with relative intensities,
Iij. ( -) thallium 203 isotope, ( -) thallium 205 isotope. Not drawn to scale............62

3-8 Number density measurement of the 6 2P3/20 metastable state of thallium by
absorption and emission measurements.................... ..... ... .. ................ ..63

4-1 Illustration of the absorption profile (red) of the galvatron and the emission profile
(blue) of the HCL ................ .......... .... ........... ......................... 66

4-2 Experimental arrangement for absorption measurements. Lens 1 and lens 2 are both
fused silica with focal lengths of 10 cm. Both irises had a diameter of 2 mm. Not
draw n to scale. .......................................................... ................. 67

4-3 Number density measurements by conventional absorption. The results from
saturated fluorescence and high resolution emission data are also plotted. For the
absorption number density calculation, temperature values were obtained from high









resolution emission measurements [40]. The emission source (HC1) current was
fi xed at 2 .0 m A ......................................................... ................. 69

4-4 Absorption measurements as the cathode was translated through the emission beam.
The HC1 emission source was held constant at 10 mA throughout this experiment. ........70

4-5 High resolution emission measurements of the lead 405.7807 nm and the thallium
535.046 nm transitions in a galvatron and hollow cathode lamp at similar currents.........71

5-1 Partial energy level diagrams for thallium and lead displaying the possible transitions
involved with wavelengths and oscillator strengths labeled. Collision constants
betw een levels 1 and 2 are neglected ........................................ ........................... 75

5-2 Experimental set-up used for all saturation curve and number density measurements.....88

5-3 Representation of the losses that would be encountered in the collection optics. Not
draw n to scale. .......................................................... ................. 9 1

5-4 Experimentally measured dye laser spectral profile with FWHM of 6.63 pm. Also
shown is the calculated mode structure obtained from a cavity length of 35 cm.
Intensities shown are arbitrary and do not represent any physical quantity ....................92

5-5 A) A three dimensional spatial profile obtained by translating photodiode with a 100
|tm pinhole through the Scanmate 1 dye laser beam. B) A two dimensional view of
the same profile demonstrating the fairly homogenous profile. ....................................95

5-6 A) Scanmate 1 dye laser temporal profile for the thallium 377.572 nm transition.
Recorded with a photodiode (rise time of 200 ps) and 500 MHz oscilloscope. ................96

5-7 Experimentally measured saturation curve from a thallium galvatron with 10.0 mA
applied. This data was modeled with time dependent two-level saturation curves for
laser pulse durations of 1, 10, and 100 ns. Y21 = 1 was used for all three theoretical
cu rv es ......................................................... ....................................99

5-8 Experimentally measured saturation curve from a thallium galvatron with 10.0 mA
applied. This data was modeled to a time dependent three-level saturation curves in
the presence of a trap for pulse durations of 1, 10, and 100 ns. For all three plots, the
collisional de-excitation rate constants were assumed to be zero..................................100

5-9 Experimentally measured saturation curve from a lead galvatron with 10.0 mA
applied. This data was modeled to a time dependent three-level saturation curve in
the presence of a trap for a pulse duration of 4 ns. All collisional de-excitation rate
constants w ere set to zero. ..................................................................... ....................102

5-10 Plot of the ground state number density as a function of current. ..................................103

5-11 Plot of the metastable state number density of thallium as a function of current............ 105









5-12 Plot of the metastable state number density of lead as a function of current.
Saturated fluorescence values are compared to results obtained from conventional
absorption and high resolution emission measurements.................... ...............106

6-1 Partial energy level diagram for thallium ............................................ ............... 109

6-2 Experimental setup used for both single-step and two-step laser excited fluorescence
measurements. IF is an interference filter used to remove laser scatter. Mirrors 1-4
are used for laser beam height and orientation alignment. PD-1 and PD-2 are
photodiodes used to monitor the time delay between the two pulses for two step
fluorescence measurements. PD-3 is a photodiode used to trigger the signal
acquisition ........................................................ ......... ............ ..........111

6-3 Measured fluorescence curve for the thallium 6 2D3/2 state ...........................................113

6-4 Measured fluorescence curve for the thallium 6 2D5/2 state ............................................115

6-5 Measured fluorescence curve for the thallium 7 2S1/2 state. ...........................................116

6-6 Measured lifetime curves for the thallium 6 2P3/20 metastable state. .............................118

6-7 Measured fluorescence waveform at 377.572 nm due to 276.787 nm excitation ..........119

6-8 Plot of the lifetimes, T, and calculated deexcitation rate constant, k21, at various
currents for the thallium 6 2P3/20 metastable state. .................... ......................... 125

A-1 Theoretical curve of growth plot for a purely Doppler broadened absorption profile
assuming a line source. The number density in this plot was converted to atoms cm
3, where as the calculation above defined the number density as atoms m-3 .................139

B-l Energy level diagram for the hyperfine structure of the thallium 377.572 nm
transition. Units in this figure are given in frequency; however, wavelength units are
u sed in the text. .......................................................... ............... 142









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



DIAGNOSTICS OF A SEE-THROUGH HOLLOW CATHODE DISCHARGE BY EMISSION,
ABSORPTION, AND FLUORESCENCE SPECTROSCOPY

By

Nicholas Taylor

December 2007



Chair: James D. Winefordner
Major: Chemistry

Atomic line filters have been suggested to be attractive in areas of Doppler velocimetry,

resonance fluorescence detection, and resonance ionization detection. They are based on the

resonant absorption of photons by an atomic vapor, and allow all other radiation to pass. This

allows the detection of very low levels of light superimposed on a large optical background.

Several elements have been studied for use as atomic line filters, such as the alkali metals,

alkaline earths, and thallium. As previously recognized, thallium is especially attractive since

the 535.046 nm metastable transition overlaps with the second harmonic output of an

Nd:La2Be205 (BEL) laser (1070 nm). This makes thallium ideal for certain applications as an

atomic line filter.

Recently a see-through hollow cathode lamp, or galvatron (Hamamatsu), was made

commercially available. The galvatron geometry is unique compared to traditional hollow

cathode lamps since the cathode and cell are oriented in a T-shape, with the cathode bored

completely through to allow the propagation of a light source through the cathode. This allows









multi-step excitation of the atomic vapor, not easily accomplished with a traditional hollow

cathode lamp.

The advantages that a galvatron offers over conventional atomic reservoirs make it an

attractive candidate for the application as an atomic line filter; however, little spectroscopic data

have been found in the literature. For this reason, Doppler temperatures, number densities,

quantum efficiencies, and lifetimes have been determined in order to characterize this atomic

reservoir as a potential atomic line filter. These parameters are determined by use of various

spectroscopic techniques which include emission, absorption, time-resolved fluorescence, and

time-resolved laser-induced saturated fluorescence spectroscopy. From these measurements, it

has been demonstrated that a galvatron is an attractive atomic reservoir for applications as an

atomic line filter. The spectral resolution of this atomic line filter was found to be superior to

that of a traditional hollow cathode lamp and electrodeless discharge lamp. A desired number

density can be rapidly produced by applying the appropriate current and can be reproduced from

one experiment to the next. In addition, the quantum efficiency of this system was found to be

limited only by the competing radiative pathways of the particular energy level arrangement

which allows it to be a very efficient detector. This system has the potential to be simple,

compact, and portable which makes it an ideal atomic line filter.









CHAPTER 1
INTENT AND SCOPE OF STUDY

Introduction to Atomic Line Filters


Interest in atomic line filters continues to grow and spread to a wide range of

research. They have found an array of applications including Doppler velocimetry [1],

resonance fluorescence detection [2-6], and resonance ionization detection [7,8] to only

name a few. They are based on the absorption of signal photons resonant with an

electronic transition of the atomic system and allow all other radiation to pass. This type

of high background rejection makes atomic line filters very attractive for the detection of

a weak optical signal superimposed on a large solar environment. Detection by other

spectroscopic methods would require filtering of the background radiation by means of

narrow glass filters or the use of a dispersive system such as a grating or prism

spectrometer. These ultra-narrow band filters have an incredible advantage in high

background applications such as in atmospheric backscatter lidar or space

communications.

Atomic line filters have the potential of achieving spectral bandwidths as narrow

as a few GHz to MHz without a loss in luminosity. Therefore, atomic line filters can

achieve very high resolving powers, where the resolving power is defined as the ratio of

the wavelength being measured, X (nm), to the resolution of the system, AX (nm). For an

atomic line filter, the resolution is determined by the FWHM of the absorption profile of

the atomic vapor, thus, they can achieve very high resolving powers, depending on the

temperature and collisional environment. Since they are based on an atomic vapor, their

collection solid angle is limited only by the geometric design of the atomic reservoir,

which allows an enhanced luminosity when compared to other systems. Luminosity here









is defined as the product of the acceptance solid angle (sr) and the projected area (cm2).

In conventional dispersive systems like a grating monochromator, the resolving power

and luminosity are controlled by the slit widths. Decreasing the slit widths reduces the

bandpass observed by the detector and results in an increase in the resolving power of the

monochromator; however, this restricts the throughput of light accepted by the

monochromator and reduces the luminosity of the system. Of course, the inverse would

be true if the slits were increased. The luminosity-resolving power product can be

thought of as being constant in this case. It is considered one of the most important

figures of merit when comparing spectroscopic systems. An atomic line filter, however,

does not have a constant luminosity-resolving power product. The resolving power,

based on the width of the absorption profile of the metal vapor, and the luminosity, based

on the geometric design of the atomic reservoir; are independent of one another.

Reducing the line width by cooling the vapor would result in a narrower absorption

profile and thus increase the resolving power of the system; however, the system retains

the same collection solid angle and projected area. The luminosity-resolving power

product of atomic line filters have been discussed theoretically by Matveev et. al. [9] and

were found to be superior to interferometer and heterodyne systems.

Atomic Reservoirs

One of the requirements of an atomic line filter is the atomic vapor should be easy

to produce and stable in number density. Sealed cells are commonly used atomic

reservoirs; however, since many metals have relatively low vapor pressures, elevated

temperatures from elaborate heating systems are needed in order to produce an

appropriate, controllable, and stable number density. Currently, there are about 23

elements that can produce a suitable atomic vapor with moderate heating of









approximately 500 C [10]. If they are laboratory constructed cells, then elaborate

vacuum and flushing procedures may be needed in order to remove the presence of

molecular species. There may also be a need to distill the metal from its oxide form [11].

The presence of molecular species is important in terms of the quantum efficiency of the

atomic system and translates into the overall detection efficiency of the atomic filter. If

the cell is not heated uniformly, condensation of the metal vapor can build up on the

windows of the cell which can impair its performance as an effective atomic line filter.

Attempts with flames as an atomic reservoir have also been made. Smith et al.

[12] successfully used a magnesium seeded flame to detect Stokes Raman photons from

carbon tetrachloride by laser enhanced ionization. While this is a simple and convenient

system, it suffers from many disadvantages. Since flames require the use of combustible

gases there are inherent safety concerns. In addition, an appropriate ventilation system is

needed when dealing with toxic metals such as lead and thallium. The use of a flame also

requires large quantities of a high concentration of the metal salt solution to produce a

continuous supply of the metal vapor. There is also an issue with portability, since an

ideal atomic line filter should be capable of moving to the location of interest as well as

be able to operate in harsh environments. Flames would be difficult to deal with in

windy environments, under water, or in space. Perhaps the largest disadvantage

associated with flames would be the quantum efficiency of an atomic vapor in a

combustion environment. Poor quantum efficiency values, on the order of 0.03 to 0.001

have been reported [13, 14], depending on flame composition. This is due to the flame

being a high temperature, high quenching environment with a large concentration of

molecular species. One must also consider that the elevated temperature and pressure









causes a broadening of the absorption profile resulting in an inferior spectral resolution.

It is apparent that the simplicity and convenience is outweighed by many disadvantages

associated with a flame and would not make it an ideal atomic reservoir.

Hollow cathode lamps are also capable of producing an atomic vapor. This is

achieved by the well known sputtering process that occurs from the hollow cathode effect

and can be applied to nearly every metal. These are simple systems capable of producing

a stable atomic vapor from refractory metals that would otherwise require extreme

temperatures. Unlike sealed cells, hollow cathode lamps are capable of producing an

atomic vapor from 63 elements, compared to 23 from sealed cells. These discharges can

be easily controlled with a stable current source and sustained for long periods of time

with negligible fluctuations or drift. They operate in very pure, low pressure buffer gases

typically in the range of 1-20 torr, with Doppler temperatures on the order of 350-750 K

[15-17]. This results in narrow absorption profiles, therefore, very high spectral

resolution, limited only by Doppler broadening. Unlike sealed cells and flames, hollow

cathode lamps have limited optical access, with only one access window for multistep

excitation. The combination of two or three lasers would be difficult and can reduce the

acceptance solid angle, therefore, reducing the luminosity of the reservoir.

Recently a see-through hollow cathode lamp, or galvatron (Hamamatsu), was

made commercially available. The galvatron and hollow cathode lamp both operate by

the hollow cathode effect; however the cathode of a galvatron is oriented in a T-shape

and the cathode is hollowed completely through so it is open on both ends as shown in

figure 1-1. This allows optical access at both ends of the cathode. This geometry also

permits the use of a second laser to counter-propagate through the filter for fluorescence,









ionization, or opto-galvanic detection which would be difficult to obtain with traditional

hollow cathode lamps. The use of multi-step excitation for the detection of the signal

radiation can have an advantageous in the selectivity of the detection signal.


A) Cathode B) Cathode

Anode




Anode A




Figure 1-1. Cross sectional view of A) hollow cathode lamp and B) galvatron.


Since these see-through hollow cathode lamps are relatively new, little

spectroscopic information is available on them. Therefore, in order to evaluate the

potential of this hollow cathode discharge as an atomic line filter, one must measure

several spectroscopic parameters of the discharge including Doppler temperatures,

number densities, quantum efficiencies, and lifetimes of these systems at various applied

currents in order to evaluate the potential such a filter would possess.

The Glow Discharge

Since the purpose of this research is the spectroscopic diagnostics of several

parameters of the discharge for use as an atomic line filter, the anatomy and processes of

the discharge will only be briefly discussed here. A typical glow discharge consists of

two electrodes sealed in a low pressure gaseous medium, typically argon or neon. If a

potential is dropped across these electrodes, a discharge can be created and sustained with

various dark and luminous areas as depicted in figure 1-2. Although figure 1-2 represents








a planar electrode configuration, it equally applies to a hollow cathode discharge were the

cathode is a hollowed out cylinder rather than a flat surface. Each region will be briefly

discussed below.



Dark Cathode Negative Glow Faraday Dark
Space Space

A)

Cathode Anode







Vo
B)

Vb

Figure 1-2. A) Illustration of a simple planar glow discharge and B) the voltage
distribution. Here Vo represents the ground voltage and Vb is the breakdown
voltage [18].

The Cathode Dark Space

The cathode dark space is the region directly adjacent to the cathode surface. It is

a region of low luminosity, hence the name dark space. Due to the negative potential that

is applied to the cathode, electrons generated in this region are repelled away from this

area and are accelerated towards the anode. This region is also referred to as the cathode

fall region due to the repulsion of electrons from this region. These repelled electrons are

of such high energy that they are incapable of exciting atoms within this region, which









accounts for the low luminosity of this region. These high energy electrons are, however,

responsible for the ionization of the buffer gas. These positively charged buffer gas ions

are attracted to the negative potential applied to the cathode and are accelerated towards

the cathode surface. These accelerated buffer gas ions eventually collide with the

cathode surface and, if sufficient energy has been transferred, will result in the removal of

an atom of the cathode material. This process is referred to as sputtering, and accounts

for the atomization of the cathode material. Therefore, the cathode dark space is very

important in sustaining the discharge.

The Negative Glow

The negative glow region is easily identified as the bright luminous glow region

of the discharge. There are two types of electrons that exist in this region, fast high

energy electrons and slower thermal electrons. The fast high energy electrons are the

result of electrons that have escaped the dark cathode space without a loss in energy due

to collisions. This class of electrons typically has electron temperatures on the order of

20 25 eV and number densities on the order of 106 cm-3 [18,19] As mentioned

previously, these electrons are of such high energy that they are only capable of

ionization of the buffer gas, as well as sputtered species.

The second class of electrons is slow thermal electrons. These thermal electrons

have two separate origins; therefore, can be divided into two groups. The first group

originates as the product of gas phase ionization collisions with the buffer gas or

sputtered species. They typically have electron temperatures on the order of 2 10 eV

and number densities on the order of 107 108 cm-3 [18,19] The second group originates

from both fast high energy electrons from the dark cathode space and electrons from gas

phase collisions. These electrons have undergone several elastic and inelastic collisions









in the discharge yielding electron temperatures on the order of 0.05 0.6 eV and number

densities on the order of 109 1011 cm3 [18,19] In addition, the number density of

electrons is essentially equivalent to the number density of ions present in the negative

glow region, which yields a nearly field free region, as shown in figure 1-2. These slow

thermal electrons are responsible for the excitation of atoms present and accounts for the

high luminous nature of the region. For this reason, the negative glow region is the most

analytically useful and has been extensively investigated by many authors.

The Faraday Dark Space

The faraday dark space is a region between the anode edge of the negative glow

region and the anode of the discharge. Electrons that have diffused into this region have

lost most of their energy by collisions in the negative glow region and are typically not

capable of further excitation or ionization. For this reason, the faraday dark space region

is not very luminous, and if the distance between the cathode and anode is small, as is the

case of a hollow cathode lamp, then this region may not be very prominent.









CHAPTER 2
HIGH RESOLUTION EMISSION SPECTROSCOPY OF A SEE-THROUGH
HOLLOW CATHODE DISCHARGE BY A SCANNING FABRY-PEROT
SPECTROMETER

Introduction

The luminosity-resolving power product is one of the most important figure of

merit when comparing spectroscopic systems. For an atomic line filter, the resolving

power is governed by the absorption profile of the atomic vapor. Therefore, in order to

evaluate the potential of a see-through hollow cathode discharge as an atomic line filter,

one must measure the spectral profiles of this discharge at various applied currents in

order to evaluate the spectral resolution and Doppler temperature that such a filter would

possess. Typically, the absorption profile of the atomic vapor would be evaluated by

direct measurements with a narrow band diode laser. This would be possible, due to the

unique design of the discharge lamp; however, diode lasers at the transitions of interest

were not available. The Doppler temperatures can also be evaluated by measurement of

the emission profile of the discharge. This type of high resolution measurement has

traditionally been achieved by either long focal length spectrographs, or with an

interferometer. A high resolution scanning Fabry-Perot interferometer was available,

with mirrors capable of obtaining an acceptable resolving power at the transitions of

interest. Therefore, focus of this work was on the measurement of the emission profiles

from the hyperfine structure of the 535.046 nm transition of thallium and the 405.7807

nm transition of lead in a see-through hollow cathode discharge by means of a scanning

Fabry-Perot spectrometer. Partial energy level diagrams of thallium and lead is shown in

figure 2-1.










205T1 (70.5 %)


F=l


g=3


2 -
2S1/2 -






535.046 nm





2P3 o
P3/2 -


F=


13.32 GHz
0.45 GHz
0.45 GI-z


F=0


g=5


1.32 GHz


F=


0.53 GHz


g=3


20Pb (22.1 %)
a= 9/15 b = 5/15 c = 1/15

g = 4 F = 3/2


208Pb (52.4 %)


206pb (24.1 %)


g=3


g=3


24pb (1.4 %)




g=3








g 5


g =4 F = 3/2


.= 405.7807 nm .= 405.7820 nm


S= 405.7832 nm


Figure 2-1. Partial energy level diagram of the hyperfine structure of A) 535.046 nm
transition of thallium and B) 405.7807 nm transition of lead. Both thallium
and lead odd isotopes have a nuclear spin quantum number I = /2. Not drawn
to scale.


F=


g=3


12.17 GHz

g=1


g=5



).52 GHz
g=3


3P o


405.7805 nm
405.7842 nm
405.7770 nm


203TI (29.5 %)









Interferometer Concept

Perhaps the earliest conception of interferometry can date as early as 1831, when

George Airy mathematically described the coherent addition of light from multiple

reflections between two plane surfaces. This became known as the Airy distribution and

is shown as [20],


TI() = 2 4Ro sin 2 (2- a)
(1 -Ro)2 I R)2

A = 2/d cos (2-1b)


=1 (2-1c)


where ois the wavenumber (cm-1), I(o) is the wavenumber dependent transmission

intensity, Tis the transmission coefficient, Ro is the reflection coefficient, r is the

refractive index of the medium between the mirrors, d is the mirror separation (mm), and

0 is the angle of incidence of the radiation. Equation 2-la can be evaluated by

considering the following condition; if n = A, where n is an integer, then equation 2-la

reduces to,

Tmax (-R)2 11-R (2-2a)

A = 1- R T (2-2b)

where Tmax is the peak transmission of the incident radiation that is injected into the

cavity, A is the absorption coefficient, Tis the transmission coefficient, and Ro is the

reflection coefficient. It is clear from equation 2-la that Tmax can be achieved by varying

the wavelength, the refractive index, or the distance between two mirrors if the light is

collimated (0 = 0) and monochromatic. If the radiation is not truly collimated, then









various angles of the incident radiation that satisfy equation 2-2a will result in the

characteristic circular fringe pattern. This is due to the fact that at these angles, the

incident radiation takes a path length that results in constructive interference, yielding the

maximum transmission of the incident light.

As mentioned, if the condition nX = A is met, a maximum transmission will be

observed for every integer value of n, known as the order of interference. The separation

between one interference maximum to an adjacent maximum is defined as the free

spectral range. From equations 2-la and 2-1b, the free spectral range is mathematically

shown to be,

AAFSR (2-3a)


A FSR = (2-3b)


Ao FsR (2-3c)


where 2 is the wavelength of the radiation (m), r is the refractive index of the medium

between the two mirrors (1.001 for air), AIFSR is the free spectral range in wavelength

units (m), AvFSR is the free spectral range in frequency units (Hz), Ao-FSR is the free

spectral range in wavenumber units (m-1), c is the speed of light constant (2.9979 x 108 m

s-1), and dis the separation between the faces of the two mirrors (m). One should be

aware of units for a correct calculation of the free spectral range.

Many interferometers have been developed throughout the years; the two most

commonly encountered are the Michelson interferometer and the Fabry-Perot

interferometer. The Michelson interferometer, developed by Albert Abraham Michelson,

had significant historical importance. This was the device that was used in the famous









Michelson-Morley experiment, which proved that the medium that composed the

universe was not ether, a commonly accepted theory at the time [21]. In 1899, Marie

Fabry and Jean A. Perot developed the Fabry-Perot interferometer. A significant

improvement over the Michelson interferometer, the Fabry-Perot design incorporates

multiple rays of light folded back onto each other by two plane parallel surfaces, as

opposed to a Michelson interferometer which is based on a single pass as shown in figure

2-2.


A) Mirror Mirror B)
Mirror

Mirror








d Beam splitter




Figure 2-2. Simple illustration of A) a Fabry-Perot interferometer and B) a Michelson
interferometer.

In 1954, Pierre Jacquinot demonstrated that for a given resolving power, a Fabry-

Perot etalon demonstrated superiority over gratings or prisms of similar area [22].

Interferometers have been a very valuable tool in the analysis atomic spectral lines;

however, in order to obtain the resolution necessary for these measurements, certain

theoretical considerations need to be evaluated in order to determine if the measurement

apparatus contributes to the overall observed profile.









Finesse Considerations

The finesse of an interferometer is a parameter that measures of the number of

spectral lines that can be resolved in a single free spectral range and is used to evaluate

the resolving power of the interferometer. The ultimate finesse of an interferometer is

defined as the ratio of the free spectral range to the instrument function of the

interferometer. Since the finesse is a constant, varying the free spectral range will affect

the instrument function. The ultimate finesse of a scanning interferometer is composed

of three basic components, the reflection finesse (FR), surface flatness and parallelism

finesse (FF), and the aperture finesse (FA), sometimes referred to the scanning aperture

finesse. Chabbal [23] discusses in detail the convolution of these finesse components,

however, a good approximation is given by:

1 1 1 1
++ + 2 (2-4)
F F F F

where F, is the ultimate finesse of the system. Each one will be discussed individually

with regards to their contribution to the system used in this work.

Reflection Finesse, FR

The reflection finesse component is dependent on the reflection coefficient of the

mirrors as seen from the relation in equation 2-5. The high reflective mirrors used for the

thallium study where from a copper vapor laser (CVI). These mirrors have a fairly

uniform reflection from 520 nm to 670 nm with a reflection coefficient of approximately

99 % at 535.0 nm. The high reflective mirrors used for the lead study were obtained

from Bristrol and have a reflection coefficient of 98.5 % at 405.8 nm. Therefore, from

equation 2-5, the reflection finesse for the high reflection mirrors is calculated to be 312.6

and 207.9 for the thallium and lead mirrors, respectively.










FR = (2-5)
R
(1 Ro)

Flatness and Parallelism Finesse, FF

The flatness finesse component is dependent on the degree of flatness and surface

imperfection of the mirrors [24]. The mirrors used for thallium are polished to a flatness

of /20 and from equation 2-6, results in flatness finesse of only 10. For this reason, a

restricting iris is used prior to the radiation entering the interferometer. The mirrors have

a global flatness of /20 over the 2 inch diameter of the mirror; however, if the limit of

the diameter exposed is only a few millimeters, the local surface flatness that the

radiation is exposed to can be on the order of /200 or greater, however, the exact local

flatness is not known.


FF = (2-6)
2

The mirror flatness is given by X/Mwhere Mis defined as the degree of flatness of the

mirror. From equation 2-6, a surface flatness from 100 to 200 or better can be obtained

for the thallium mirrors, depending on the surface area to which the radiation is exposed.

The mirrors used for the lead study were polished to a flatness of /200 giving a flatness

finesse of 100; however, the use of a restricting iris prior to the interferometer will yield a

flatness finesse greater than this, and can be as high as 200 300. Although it is difficult

to know the exact finesse of this component, it is not expected to be the limiting finesse

based on experimental observations. The parallelism component of this finesse refers to

the degree of parallelism between the two mirrors. A lack of parallelism between the two

mirrors will result in different path lengths for different areas of the mirror. As a result, a

distortion of the interference pattern will be observed. Since extremely fine tuning can be









achieved from the piezoelectric mounts on the static mirror, the degree of flatness of the

mirrors becomes the limiting finesse in this case.

Aperture Finesse, FA

A finesse component is also associated with the aperture of the system [24]. As

one of the mirrors is translated, or scanned, the transmitted fringe pattern collapses on the

aperture. The aperture only allows the central portion of the fringe system to reach the

detection system at a time, so the detection system integrates what it "sees" at any given

time. Therefore, if a small aperture is used, a small portion of the fringe system is

detected at a time and a high aperture finesse is obtained. If a large aperture is used, a

larger portion of the ring system is detected at any given time, which results in a

distortion of the measured profile and a decrease in the aperture finesse. This is

analogous to the slit width of a monochromator. From equation 2-7, the aperture finesse

can be calculated from known parameters,

FA (AAFR)(8)(f)2 (2-7)
(B2)(/)

where the parameters are: fis the focal length of the lens (20 cm), B is the diameter of

the aperture (300 tm for thallium and 100 tm for lead), A)FSR is the free spectral range

(22.0 pm for thallium and 12.0 pm for lead), 2 is the wavelength (535.046 nm for

thallium and 405.7807 nm for lead), and FA is the aperture finesse. From the parameters

and optics used in this study, the aperture finesse is calculated to be 146 for thallium and

286 for lead. This finesse can be increased by reducing the aperture diameter; however,

the trade-off is a reduction in the throughput of the system and can affect the

measurement of lower current profiles.











Experimentally Determined Finesse

The ultimate finesse of the system is limited to the lowest finesse component. To


experimentally determine this, a helium-neon laser at 632.8 nm was used for the thallium

mirrors. The results can be seen in figure 2-3. The finesse can be determined by taking

the ratio of the FWHM of any order to that of the distance between two adjacent orders.

From this ratio, an experimental finesse of 130 was measured, which agrees well with the

lowest calculated finesse of 146. For a free spectral range of 22.0 pm, and instrumental

FWHM of 0.17 pm is obtained.


AXFSR AIF= 130.34
8-1
7-
6-
5
S4-
3-

1-

3 Orders

Figure 2-3. Experimental determination of the finesse of the interferometer using a
helium-neon laser at 632.8 nm. The variations in the intensity between the 3 orders are
due to slight intensity variations in the HeNe source.


It should be noted however, that this finesse was measured at 632.8 nm and the

thallium transition studied occurs at 535.046 nm. To truly know the finesse of the

interferometer at this transition, a line source would be needed at, or very near this

wavelength. Use of the second harmonic from an Nd: YAG laser at 532 nm could be

used, however, the laser would need to operate in a single mode in order for it to be

considered a line source and such a source was not available. An Ar+ laser lasing at

514.5 nm would not give an accurate representation of the finesse at 535 nm since the









reflection curve drops rapidly below 520 nm. In addition, a suitable source was not

available at 405.8 nm for lead; however, based on a calculated ultimate finesse 134 along

with a free spectral range of 12.0 pm, an adequate instrumental FWHM of 0.09 pm will

be sufficient for accurate profile measurements.

Broadening Mechanisms

The sputtering process in a hollow cathode discharge results in the promotion of

atoms to excited energy levels. The excited atoms then relax to the ground state resulting

in the emission of photons with wavelengths characteristic of the cathode material. There

is a well known relationship between the emission profile and the Doppler temperature of

the system, if the profile is dominated by Doppler broadening and has been observed in

past works [15-17]. In order to verify this for the present systems, several broadening

mechanisms are evaluated for thallium and lead to determine the extent each component

will contribute to the overall shape of the measured profiles.

Natural Broadening

Natural broadening is based on the Heisenberg Uncertainty Principle which

relates the lifetime of an excited state to the precision of the energy measurement, as seen

from equation 2-8a,

h
AEAt -- (2-8a)
2xr

Av 1- (2-8b)
I2 At

where At is the lifetime of the excited state (s), h is Planck's constant (6.626 x 10-34 J's),

and Av is the FWHM of the profile measured (Hz). From equation 2-8b it can be seen

that the longer the lifetime of the transition, the more time one has to measure the energy

and results in greater precision of the measurement, thus, a narrower observed profile.









Since the spontaneous lifetime of the thallium 2S1/2 state and the lead 3P10 state have been

calculated to be 7.52 ns and 5.50 ns, respectively. The spontaneous lifetimes of these

states are calculated from transition probabilities obtained from the Nation Institute of

Standards and Technology (NIST). From these lifetimes, an obtained natural broadening

contribution of 0.020 pm for thallium and 0.016 pm for lead is calculated from equation

2-8b.

Collisional Broadening

Collisional broadening, also called pressure broadening, results in a change in

phase of the atomic oscillator when collisions occur between the emitting atom of interest

and a foreign gas atom. This can be characterized by a correlation time, which can be

interpreted as the average time between two phase-changing collisions. According to the

Lorentz theory, the broadening contribution due to collisions in the galvatron can be

described by [16],


AL= -- L no 2 .. R T .- + (2-9)
IT Mi M2

where oL is the collision cross section between thallium/lead and neon atoms (thallium:

~ 3.0 x 10-17 cm2 [25]; lead: 3.0 x 10-17 cm2 [25]), R is the molar gas constant (8314.51

mJ mol-1 K-1), M1 and M2 are the atomic mass of thallium/lead (thallium: 204.383 g mol-

1; lead: 207.241 g mol-1) and neon (20.179 g mol-1), respectively, Tis the temperature of

the system (1000 K), and no is the number density of the neon filler gas (4.51 x 1017 cm

3). It should be noted that a temperature of 1000 K was used for all temperature

dependent calculations. From equation 2-9, a collisional broadening FWHM can be

calculated to be 1.39 x 10-5 pm for thallium and 7.98 x 10-6 pm for lead.









Holtzmark Broadening

Holtzmark broadening, also called resonance broadening, results by the same

mechanism as collisional broadening, however, Holtzmark broadening results from

collisions between two atoms of the same kind, in this case between two thallium or lead

atoms.

4 xi- R-T
A4 =-- rR-n T (2-10)


In equation 2-10 [16], oHis the collision cross section between two thallium/lead atoms

(thallium: 1.20 x 10-12 cm2 [26]; lead: 5.13 x 10-13 cm2 [27]), no is the number density of

thallium/lead and is assumed to be 1012 atoms cm-3. It can be seen that the resonance

collision cross sections are approximately five orders of magnitude larger than the

Lorentz collision cross sections; however, the number density of thallium/lead atoms

present is approximately five orders of magnitude smaller than number density of neon.

From equation 2-10, a Holtzmark broadening FWHM can be calculated to be 5.21 x 10-7

pm and 9.01 x 10-8 pm for thallium and lead, respectively.

Instrument Function Broadening

In any measurement system there is some inherent contribution of the

measurement system to the profile being measured. It is always desirable to reduce this

contribution as much as possible to the point were its contribution becomes negligible. In

an interferometric system, the finesse and free spectral range will dictate the instrument

function of the interferometer. For thallium measurements, an experimental finesse of

130 was measured with a free spectral range of 22.0 pm as shown in figure 2-3. For lead,

an ultimate finesse of 134 was calculated, and a free spectral range of 12.0 pm was used









for profile measurements. From these values, the instrument function was calculated as

follows,

A A, SR (2-11)
F


where F is the finesse of the system and AXFSR is the free spectral range of the

interferometer as calculated by equation 2-3a. From equation 2-11, an instrumental

FWHM of 0.17 pm is calculated for thallium and 0.09 pm is calculated for lead.

Doppler Broadening

Doppler broadening is the result of a statistical distribution of velocities of the

emitting atoms along the observation path. Since atoms are in motion with respect to the

observation line, the Doppler Effect causes a statistical distribution in the frequencies

observed that is directly related to the velocity distribution and is temperature dependent.

The Doppler broadening contribution can be calculated as



2,1n2 2RT (2-12)
c M


where Vo is the frequency of the transition being observed (thallium: 5.60 x 1014 Hz; lead:

7.388 x 1014 Hz). From equation 2-12, a Doppler broadening FWHM can be calculated

to be 0.85 pm for thallium and 0.64 pm for lead.

Self-Absorption Broadening

Self-absorption broadening occurs when the system has an emitting layer

followed by an absorbing layer with both layers in similar thermal environments. If both

layers are optically dense, the measured emission from the system will appear broadened.

This is due to the preferential absorption at the kernel of the profile, where the frequency









dependent absorption coefficient is large, as compared to the wings of the profile where

the absorption coefficient is smaller. This results in an apparent broadening of the profile

with a non-Gaussian shape [28,29]. There is no simple equation to predict the

contribution of self-absorption; however, previous works have shown that self-absorption

does contribute to the broadening of the profile, especially at high currents [15-17].

Other Broadening Mechanisms

Other broadening mechanisms to consider are Stark broadening (Avs), molecular

quenching broadening (AVMQ), and broadening due to unresolved isotopic shifts or

hyperfine structure. Most atoms emit in the negative glow region of the discharge, and

since this region is known to be a nearly field free region, Stark broadening is expected to

be negligible. The present systems are filled with a very high purity of neon, with

molecular concentrations less than 1 ppm [30], therefore, broadening due to molecular

quenching will be negligible. Broadening due to unresolved hyperfine structure is

expected to occur due to small unresolved transitions within the envelope of larger peaks,

which will contribute slightly to the overall observed profile, however, the amount this

will contribute can only be evaluated using an appropriate model.

Evaluation of Broadening Mechanisms

From the calculations made on each of the broadening mechanisms, which are

based on known parameters and a temperature of 1000 K, it can be concluded that the

dominating broadening mechanism is Doppler broadening, which has also been observed

in past works [15-17]. The next largest contributing factor comes from the instrument

function; however, since it is approximately five times narrower than the expected

Doppler width, it is not expected to significantly contribute to the width of the profile.

All other contributions are several orders of magnitude narrower than the expected









Doppler profile and therefore can be considered negligible. A summary of all broadening

contributions considered for both thallium and lead is shown in table 2-1.

Table 2-1. Calculated broadening components for thallium and lead that would be
expected in a galvatron based on known parameters and an assumed
temperature of 1000 K.
T1 Pb
AVN (AXN) 21.2 MHz (0.020 pm) 28.9 MHz (0.016 pm)
Avc (Abc) 0.014 MHz (1.39 x 10-5 pm) 0.014 MHz (7.98 x 10-6 pm)
AVH (AXH) 546 Hz (5.21 x 10-7 pm) 164 Hz (9.01 x 10-8 pm)
AVD (AXD) 890 MHz (0.85 pm) 1.16 GHz (0.64 pm)
AVIF (AXIF) 177 MHz (0.17 pm) 164 MHz (0.09 pm)
Avs (Aks) negligible negligible
AvMQ (AXMQ) negligible negligible


Experiment

The experimental apparatus used can be seen in figure 2-4. It consists of a

galvatron, hollow cathode lamp, or an electrodeless discharge lamp. The emission is

collected with a 1 inch diameter glass lens with a focal length of 15 cm. The lens was

placed at 15 cm (If) from the face of the cathode in order to collimate the emission. Due

to optical table size constraints, the collimated emission was reflected 900 using a one

inch diameter aluminum coated mirror towards the Fabry-Perot interferometer and

detection system.

As mentioned previously, a restricting iris was used prior to the interferometer.

This was used to restrict the surface area incident on the mirrors in an attempt to increase

the flatness finesse. An optimal restricting iris diameter of 2.5 mm was found to result in

a maximum resolving power and throughput for both lead and thallium measurements. A

larger diameter would reduce the flatness finesse, making it the limiting finesse,









therefore, reduce the resolving power. A smaller diameter would not result in an increase

in resolving power and would only reduce the signal intensity. Since the galvatron is not

a well defined point source, some of the collected emission will be slightly divergent.

Consequently, a restricting iris is advantageous in that it also spatially filters the emission

into a more highly collimated beam of emission.



Restricting Scanning Fabry-Perot
Iris Interferometer Lens Monochromator


Mirror I T
Scanning
Aperture
Lens o

Trigger a

Thallium
Galvatron



Figure 2-4. Experimental set-up for the measurement of the lead and thallium emission
profiles from a laser galvatron, hollow cathode lamp, and an electrodeless
discharge lamp.

The Fabry-Perot interferometer used in this study involves piezoelectric scanning.

A high voltage ramp generator (EXFO Burleigh) applies a saw-tooth voltage to the

piezoelectric crystal, translating one of the mirrors linearly. The expansion of a

piezoelectric crystal is not linear with voltage; however, a first order polynomial can be

applied to the ramp voltage waveform in order to provide a linear translation with

voltage. This calibration was accomplished by observing several orders from a HeNe

laser and adjustments were made to the voltage waveform until the temporal spacing

between adjacent transmission peaks were the same for all orders observed. The linearity









of the mirror translation in time results in evenly spaced orders, which is extremely

important in the conversion of the x-axis from time to wavelength. The ramp generator

offers a variable scan rate which determines the time taken to complete one scan; varing

from 20 ms to 10 s. This permits the rapid scanning of emission profiles and allows real

time adjustments of mirror parallelism for rapid optimization of the signal. In addition, a

signal-to-noise advantage can be gained by averaging several scanned profiles. The

voltage amplitude can also be varied from 0 V to 1000 V, which determines the distance

the translating mirror travels, thus, the number of orders that are observed on the

oscilloscope for a single scan. The ramp generator also provides a trigger output. This

allowed the oscilloscope to be triggered when the voltage ramp is initiated. The second

Fabry-Perot mirror is static and is attached to two piezoelectric crystals. Applying a D.C.

voltage individually to these crystals allows fine tuning of the parallelism between the

two mirrors with respect to one another.

The light transmitted through the Fabry-Perot is collected with a 20 cm focal length lens

and is imaged onto an aperture. The aperture is simply a metal plate with a pinhole

drilled in the center. As the Fabry-Perot scans, the fringe system collapses onto this

aperture so that only a very small portion of the profile is allowed to be transmitted and

be detected at any given time during the scan.

The emission that is transmitted through the aperture is collected using a 500 mm

focal length monochromator (Acton 500i) with 2400 grooves mm-1 grating and entrance

and exit slit widths of 1 mm. The monochromator acts as a spectral filter so that only the

emission line of interest is detected and filters out neighboring emission lines. Detection

is made with the use of a photomultiplier tube (R928 Hamamatsu) with -1000 V applied









from a high voltage power supply. The signal is sent to a low-noise current amplifier

(Stanford Research Systems model SR570) which allows the signal to be amplified and

filtered. The amplified signal is observed with a 100 MHz oscilloscope (Tektronix model

TDS 3012B) which was set to average 512 waveforms in order to obtain the best signal to

noise ratio prior to recording the profile.

Results

Since the scanning mirror translates towards the static mirror during the voltage

ramp, the profile is scanned from higher wavelength to lower wavelength when read from

left to right. To view the profile in terms of wavelength, the profile is flipped 1800 on the

x-axis. In order to convert the x-axis from time to wavelength, the free spectral range

must be known. This is done by using a metric caliper and measuring the plate

separation, d, and using equation 2-3a. The width of the hyperfine structure is

approximately 13 pm wide for thallium and 7 pm for lead from center of the first

component to the center of the last component. In order to obtain the highest resolving

power possible without order overlap, the free spectral range of the interferometer is set

to 22.0 pm for thallium measurements and 12.0 pm for lead measurement. The distance

from any point on one order to the same point on an adjacent order is defined as the free

spectral range, and since the plate translation is linear, time can be converted into relative

wavelength shift. By setting the most intense peak to zero, every evenly spaced time

point is converted into a wavelength shift relative to the zero peak. All profile intensities

are then normalized, allowing the measurement of emission profiles in the form of

normalized intensity versus wavelength.













10- -300mA 10- -50mA
20 0 mA -80mA
09- -150mA 09- 10 0mA
I08A1 5 08mA
08- 10 0 mA 08- -15 0 mA
Theoretical shifts 2 0 mA
07- and intensity es 07- A
d 06- 06- -40 0 mA
d Theoretical shifts
0 5 \ 05 and intensities
04 04-
5 03- 03-
02- 02-
01- 0 1-
00 00-
4 2 0 2 4 6 8 10 12 14 16 4 16
AX (pm) A% (pm)


Figure 2-5. Experimental profiles of the 535.046 nm transition of thallium from A)
galvatron and B) hollow cathode lamp.


Once experimental parameters were optimized and adjustments made to obtain


the highest resolving power possible, the profiles of several currents were recorded from


the thallium and lead galvatrons. The final profiles were plotted and normalized to one.


The results of the thallium galvatron can be seen in figure 2-5 and the results from the


lead measurements can be seen in figure 2-6. As mentioned previously, galvatrons


operate in a similar manner as hollow cathode lamps. Therefore, profiles from a neon-


filled Jarrell Ash thallium hollow cathode lamp and neon-filled Fisher lead hollow


cathode lamp were recorded for comparison.



3 0 mA
A) 50mA B) 60A
1 0 80mA 10 -- 00mA
00-0 mA 5- 0 mA

-20 0 mA 25 0 mA
08 T- heortcal Shifts 0 mA
30 0 mA
07 -and Intensites 07 35 0 mA
40 0 mA
06 06- Theortical Shifts
0 5 s and Inte nsites
05 1 505
04- r 04-
S03- 03
02- 02-
01- 01-
00 00 0 .
5 4 3 2 1 0 1 2 3 45 4 3 2 1 0 1 2 3 4 5
&A (pm) a (pm)


Figure 2-6. Experimental profiles of the 405.7807 nm transition of lead from A)
galvatron and B) hollow cathode lamp. Both sources were measured under
the same experimental setup.












A comparison of the thallium hollow cathode lamp and thallium galvatron


operated at similar currents is shown in figure 2-7. As can be seen, the hollow cathode


lamp displays a much broader and more highly self-absorbed profile than that of the


hollow cathode lamp. The reason for this may be related to the pressure inside the two


discharge lamps. By reducing the pressure inside the hollow cathode discharge tube, a


larger mean free path results, therefore, an increase in kinetic energy transfer from the


ionized neon atom to the cathode surface [19]. The direct result is an increase in


sputtering efficiency which yields higher number densities than for a higher pressure


discharge operated at a similar current. An increase in the number density of sputtered


species yields emission profiles that are more susceptible to self-absorption. It should be


noted, however, that not knowing the pressure of neon inside the hollow cathode lamp


makes it difficult to make any direct comparison between the two emission sources.

10- 0-
09- Current= 10 0 Cur t 100 A Current = 15 0 mA
Galvatron 0 9 Galvatron
08 Hollow cathode lamp 08- Hollow cathode lamp
07- Theoretical Shifts Theoretical shifts
06- = 06-
05-
03- 00 3
02- 02
0 1- 0 1-

4 2 0 2 4 6 8 10 12 14 16 0 4 6 8 10 12 14 16
AX (pm) AA, (pm)


10- Current 20 0 mA 10- Current= 30 0 mA
09 Galvatron 09 Galvatron
0 Hollow cathode lamp 08 -Hollow cathode lamp
Theoretical shifts Theoretical shifts
0 7- 0 7
= 06- = 06-
i \05
0 04- 04
0 3 0 3
02 02
01- 01 1

4 2 0 2 4 6 8 10 12 14 12 14 16
AA (pm) AA (pm)



Figure 2-7. Comparison between a thallium galvatron and a thallium hollow cathode
lamp profiles operated at the same current. All profiles are normalized.













Comparing the results between the lead galvatron and lead hollow cathode lamp


in figure 2-8 clearly demonstrates the opposite is observed. The profiles obtained from


the lead galvatron clearly show a broader profile with a great amount of observed self-


absorption. As mention previously, this may be explained by the different pressures


present in the discharge. Since the pressure in either lamp is unknown, it is difficult to


draw any direct conclusions; however, it would stand to reason that the pressure in the


lead galvatron may be less than the lead hollow cathode lamp.



Current= 10 0 mA Current= 15 0 mA
1o- -Galvatron Profile -Galvatron Profile
Hollow Cathode Profile 10- Hollow Cathode Profile
09 --Theoretical Shifts --Theoretical Shfts
and Intensites 09 and Intensities
08- 08-

060
S06
05 05
04- 04
03 o 0 3-
02- 02-
01- / J 01A

5 4 3 2 1 0 1 2 3 4 5 4 3 1 1 2 3 4 5
AX (pm) AX. (pm)
Current= 20 0 mA
Galvatron Profile
1 Hollow Cathode Profile
Theoretical Shifts
o 9 and Intensities





= 04




5 4 3 2 1 o) 1 2 3 4 5
AX (pm)


Figure 2-8. Comparison between a lead galvatron and a lead hollow cathode lamp
profiles operated at the same currents. All profiles are normalized.


The profiles of a thallium electrodeless discharge lamp were also studied and are


shown in figure 2-9. It can clearly be seen that the electrodeless discharge lamp displays


a larger susceptibility to self-absorption, and self-reversal at higher powers. Profiles at


powers larger than 20 W could not be measured with a free spectral range of 22.0 pm due











to distortions in the wings of the profiles from two adjacent orders. This is known as


order overlap, where the profile broadens to a point larger than the free spectral range.


This results in the wings of two adjacent orders overlapping with each other causing


distortion of the profiles. Order overlap can be corrected by increasing the free spectral


range; however, this also results in an increase in the instrumental FWHM of the


interferometer.


13W
10- -14W
16W
09- 18W
20W
08- Theoretical shifts
.07-
06-
05
04
03-
02-
01-
00J
6 4 2 0 2 4 6 8 10 12 14 16 18
AX (pm)

Figure 2-9. Experimental profiles of the 535.046 nm transition of thallium from an
electrodeless discharge lamp.

Discussion

Analysis of the experimental profiles was performed using the two-layer model


described by Braun et al. [31]. The model describes the discharge in terms of two layers,


an emitting and absorbing layer followed by a non-emitting absorbing layer. For the


emitting and absorbing layer, the intensity, Ii, is given by


I, (v) oc exp[-or(v)- n 1 ] (2-13)


The parameters are o (v) is the frequency dependent absorption cross section (cm2), nl is


the number density of absorbing atoms (cm-3), and 11 is the optical path length of the


emitting and absorbing layer (cm). The frequency dependent absorption cross section for


a Doppler line can be expressed as:









{~2}
o(v) = ao .-exp v ]V (2-14)


The parameters are: ao is the peak cross section, (v-Vo) is the radiation frequency relative

to the center of the line, and AvD is the Doppler width. The absorbing layer that directly

follows the emitting layer transmits the emission and can be described as

I2(v) oc I,(v) exp[- o(v) n2, 2] (2-15)

where the subscripts 1 and 2 denotes the emitting and absorbing layer and the non-

emitting absorbing layer, respectively. By combining equations 2-13, 2-14, 2-15,

introducing equation 2-16a as the optical depth of the respective layer, and taking into

account a multi-component system, the following expression is derived for the measured

emission from the second absorbing layer:

TOD = o 1n

I, (v) c 1- exp C TOD1 (i)exp- Xexp C. rOD(i) exp- V(2-16b)


where the summations are taken over i components. Both thallium and lead transitions

studied here contain six components as shown in figure 2-1. A constant, C, is added to

give each component a weight in order to correct for intensity due to the natural

abundance of each isotope and degeneracy of each hyperfine component.

Analysis of the galvatron profiles was done by calculating the profile with the

model described above using MathCAD. The calculated profiles were then normalized

and plotted with the experimental profiles in Origin. As can be seen from equation 2-

16b, there are three parameters that can be varied, TODI, TOD2, and AvD which is controlled

through the Doppler temperature. All three parameters were adjusted appropriately until











the best fit to the experimental profiles was obtained. Results of some calculated

emission profiles for the thallium galvatron and lead hollow cathode lamp can be seen in

figures 2-10 and 2-11.


8 6 4 2 0 2 4 6 8 10 12 14 16 18 20
Ak (pm)


Current = 20 mA
Experimental Profile
Calculated Profile
(T1 0.60, '-2 -0.80, T = 565 K)
Theortical Shifts and intensity






kk -


S06
054
S04


A (pm)


10 12 14 16 18 20


A (pm)


Figure 2-10. Calculated profiles fitted to the experimental profiles of a thallium
galvatron at currents of 10, 15, 20, and 30 mA.


A (pm)


1.0-
0.9-
0.8-
0.7-
S0.6-
0.5
S0.4-
0.3-
0.2-
0.1-


6 4 2 0


v.V . .. . .












Current = 6 0 mA
Expenmental Profile
- Calculated Profile
T=02 2=025 T=320K
--Theorttcal Shifts
and Intensities


00 ., , 4 ,


5 4 3 2 1 0
AX (p


1 2 3 4 5
m)
Current =15 0 mA
Experimental Profile
Calculated Profile
S0 45 = 0 58 T 385K
Theoretical Shifts
and Intensities









ki-r


5 4 3 2


Current 10 0 mA
Expenmental Profile
- Calculated Profile
S=025 2=035 T=350K
- Theoretical Shifts
and Intensities


0 1 2 3 4 5
A. (pm)
Current = 20 0mA
Experimental Profile
Calculated Profile
=070 0 =095 T=405K
Theoretical Shifts
and Intensities


5 4 3 2 1 0 1 2 3 4 5 5 4 3 2 1 0 1 2 3 4 5
A; (pm) A; (pm)

Figure 2-11. Calculated profiles fitted to the experimental profiles of a lead hollow
cathode lamp for currents of 6, 10, 15, and 20 mA.


The fit of the calculated profiles to that of the experimental profiles in figures 2-


10 and 2-11 shows a fairly adequate fit. The region where it fails slightly is in the wings


of the higher current profiles. This discrepancy is a result of the model using a Gaussian


function; however, the presence of self-absorption is known to result in a non-Gaussian


profile [28,29]. Despite the minor discrepancies between the experimental results and the


model, an adequate fit is obtained and the information from it is still valid. Therefore, the


model was applied to all thallium and lead emission profiles.


10-
09-
08-
07-
06-
. 05-
04-
03-
02-
01-














A) Applied Power (W)
125 130 135 140 145 150 155 160 165 170 175 180 185 190
1100 .
1050- --Galvatron
1000- Hollow cathode lamp
S950- Electrodeless discharge lamp
900-
850-
800-
750-
700-
650o
S600
EL 550-
500- .
450-
400 . .


B)
650-
625 -
S600
575
S550
525
500-
475-
S450 /
425 -
S400 -

S350 // Hollow Cathode Lamp
325- / Galvatron
300


4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 0 5 10 15 20 25 30 35 40 45

Applied Current (mA) Applied Current (mA)


Figure 2-12. Doppler temperature values obtained from the fit of the calculated two layer

model for A) 535.046 nm transition of thallium and B) 405.7807 nm transition

of lead from a galvatron, hollow cathode lamp, and electrodeless discharge

lamp.


Doppler temperature values for the thallium and lead galvatron, hollow cathode


lamp, and thallium electrodeless discharge lamp obtained from the fit of the two-layer


model can be seen in figure 2-12. These values are in reasonable agreement with


previously reported Doppler temperature values [15-17] for hollow cathode lamps. The


precision of all calculated emission profiles measured was found to be + 15 K.







92000 A) Galvatron 1200000 B) Galvatron
920000Hollow cathode lamp 1150000- Hollow cathode lamp
0000- 1150000
880000- b 1 0
0000-100000
860000 0
840000- ~ 1050000-
820000




720000 \ 850000 -
700000 \800000
680000 -
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 0 5 10 15 20 25 30 35 40 45
Current (mA) Current (mA)




Figure 2-13. Calculated resolving powers for A) thallium galvatron and hollow cathode

lamp and B) lead galvatron and hollow cathode lamp.












From the Doppler temperatures obtained, the resolving power for the thallium and


lead galvatron and hollow cathode lamp can be calculated by Rpower = X/AX, where X is the


wavelength of the transition (thallium: 535.046 nm; lead: 405.7807 nm) and AX is the


FWHM of the Doppler broadened absorption profile, calculated from Doppler


temperatures shown in figure 2-13. The FWHM of an absorption profile from a flame


can be approximately 1 to 5 pm, depending on flame type and composition, which results


in resolving powers on the order of 100,000 to 500,000. As for commercially available


spectrometers, resolving powers of 10,000 to 50,000 are typically obtained. Higher


resolving powers can be obtained; however, cost and size can be considerably increased


and is often accompanied with a loss of throughput. Resolving powers for sealed cells


can be similar to those found for the galvatrons and hollow cathode lamps; however, they


are dependent on the temperature applied as well as the type and pressure of buffer gas


used.



A) B)


Applied Power (W)
125 130 135 140 145 150 155 160 165 170 175 18 0 18 5 190
275
Galvatron emitting layer
S2 50 o Galvatron absorbing layer
A 225- -- HCL emittig layer
HCL absorbing layer
. 200- EDL emitting layer
S75 --EDL absorbmg layer
175-
1 75

, 125
100 <
075
I 050- *
a o5 0


28.
26


18 / 18
- 1 6

^ 12- .
S08-
S06 / ---HCL EmittingLayer
04 --HCL Absorbing Layer
S- Galvatron Emitting Layer
O -2 Galvatron Absorbing Layer


2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 00 5 10 5 25 30 35 40 45
1 5 l 20 25 30 35 40 45
Applied Current (mA) Applied Current (mA)

Figure 2-14. Optical depth values obtained from the fit of the calculated two layer model
for A) 535.046 nm transition of thallium and B) 405.7807 nm transition of
lead for a galvatron, hollow cathode lamp, and electrodeless discharge lamp.









Figure 2-14 shows that as the current, or power, increases, the optical depth of

both layers also increase. This is expected, since the number density, n, increases with

increasing current or power. If it is assumed that all atoms in the system can be found in

either the emitting layer or absorbing layer, then equation 2-16a can be rearranged to

calculate the number density of the thallium and lead metastable state if the absorption

cross section and path length of the system are know.


n, = OD1 +OD2 (2-17)
o-o 1

Using an absorption cross section [11] of 5.2 x 10-12 cm2 for the thallium 535.046 nm

transition, assuming a path length of 2 cm, and using optical depth values of 0.32

(emitting layer) and 0.40 (absorbing layer) obtained from the model for the two layers of

the thallium galvatron at 10.0 mA, a calculated a number density of 6.93 x 1010 cm-3 is

obtained for the 6 2P3/20 state. This value is further validated by comparing it to values

obtained by saturated fluorescence [32] and high resolution absorption measurements

[33]. For an applied current of 10.0 mA, number density values of 5.30 x 1010 cm-3 and

4.24 x 1010 cm-3 were obtained from saturated fluorescence and high resolution

absorption measurements, respectively, and are in fair agreement with the value obtained

from the analysis of the emission profiles. A path length of 2 cm, which is the length of

the cathode bore, was used for the number density calculations for all methods. These

are reasonable values obtained for this metastable level; however, these are approximate

values since the path length of the two layers is not known with a high degree of

accuracy. If equation 2-17 is applied to all the emission profiles, the resulting plot of

number density for the metastable state of the galvatron for the four currents measured

results in figure 2-15














A) B)
2 6x10 1x10 -
2 4x10 910"-
2 2210"- I
7x10 -
1 8x 10 7x10"
18x ~6x1010
1 6x10 -
1 4x10 5x1010
1 2x101- 4x1010
101011 O T1
,0 3xx101- Pb
8 Ox1010 2x1010
2x6 Ox10
Z 6 0x101- Z .
1x1010
10 12 14 16 18 20 22 24 26 28 30 32 2 4 6 8 10 12 14 16 18 20 22
Current (mA) Current (mA)



Figure 2-15. Number density values obtained from optical depths obtained from the
application of the two layer model for A) thallium and B) lead using equation
2-17.

Similarly, equation 2-17 was applied to the optical depths obtained from analysis


of the lead emission profiles in order to calculate the number density for each applied


current. Using a calculated absorption cross section* of 2.45 x 10-11 cm2 and a path


length of 2 cm was used for this calculation and results can be seen in figure 2-15. These


results are verified by comparison with saturated fluorescence measurements and


conventional absorption measurements. Values of 6.90 x 1010 cm-3 and 5.42 x 1010 cm-3


were obtained from saturated fluorescence and conventional absorption measurements,


respectively. These values agree well with a number density of 5.20 x 1010 cm-3 obtained


from emission results for an applied current of 10.0 mA. Values obtained from saturated


fluorescence and conventional absorption measurements will be discussed in greater


detail in following chapters.






* Absorption cross section was calculated using an average number density value obtained from saturated
fluorescence and conventional absorption measurements, assuming a path length of 2 cm, and using
equation 2-17.









Conclusion

Measurement of the hyperfine structure of the 535.046 nm transition of thallium

and the 405.7807 nm transition of lead in a see-through hollow cathode discharge was

accurately measured with a Fabry-Perot spectrometer to investigate its potential as a

narrow band atomic line filter. The data obtained from the two-layer model has shown

that the thallium hollow cathode lamp and electrodeless discharge lamp both show larger

amounts of self-absorption, higher Doppler temperatures, and larger optical depths than

the thallium galvatron when compared to similar applied currents. However, the opposite

was observed from the lead analysis. The two-layer model used to analyze the profiles of

the three emission sources was quite successful in view of its simplicity; however, it

failed to accurately model the self-reversed profiles of the hollow cathode lamp and

electrodeless discharge lamp. This is expected to be due to the presence of a temperature

gradient, therefore, at least two Doppler temperatures should be used in the modeling of

the experimentally obtained profiles, one for each layer. The addition of this parameter

would make it difficult to obtain reliable values and should be done with a curving fitting

program for best results.

The spectral resolution of the thallium galvatron was found to be superior to that

of a traditional hollow cathode lamp and electrodeless discharge lamp, however, the

spectral resolution of the lead galvatron was found to be less than a traditional hollow

cathode lamp. Despite these differences, both the galvatron and hollow cathode lamp

still yield superior resolving powers when compared to other atom reservoirs and

spectrometers. Number densities were also obtained for both thallium and lead

galvatrons by use of the optical depth values obtained from analysis of emission profiles.

These number density values were verified by fluorescence and absorption methods and









agree well with values obtained from emission results. These are simple systems capable

of producing an acceptable number density that is both stable and reproducible. They are

atomic reservoirs that are not plagued by problems such as those associated with sealed

cells, flames, and ICP torches.









CHAPTER 3
NUMBER DENSITY MEASUREMENTS IN A SEE-THROUGH HOLLOW
CATHODE DISCHARGES WITH A HIGH RESOLUTION FABRY-PEROT
SPECTROMETER

Introduction


In order to evaluate the resolving power of this atomic line filter, high resolution

absorption measurements are needed. High resolution absorption measurements on

atomic vapors are typically done with narrow band diode lasers capable of scanning

across the absorption profile. However, most atomic transitions of interest are in the UV

region not easily accessible by diode lasers. Another common approach is the use of a

continuum source with a high resolution monochromator; however, typical conventional

grating and echelle monochromators [34,35] have been shown to give inadequate

resolution and throughput, necessary for these measurements.

Fabry-Perot interferometers have also been used in conjunction with continuum

sources. In this method, radiation from a continuum source is sent through an absorbing

medium and then to a Fabry-Perot spectrometer. In order to better understand how this

occurs, it is best to begin with a simple system containing only two monochromatic

wavelengths as shown in figure 3-1. It can be seen that the interferometer produces the

characteristic circular fringe pattern for each wavelength with its multiple orders. If this

interference pattern is imaged onto the slit of a monochromator, the result will be sections

of the dispersed radiation separated vertically. The grating of the monochromator then

disperses the radiation horizontally according to the wavelength. The final result imaged

onto the exit slit of the monochromator is the two wavelengths cross dispersed. If this

idea is expanded to a continuum source, the result will be many wavelengths

constructively interfered and cross dispersed onto the exit slit of the monochromator. As









the Fabry-Perot is tuned, or scanned, the result will be a line source capable of scanning

across the absorption profile of interest; however, several problems are associated with

this approach. Kirkbright et al. [36] applied this method to the measurement of calcium

in a flame using a monochromator with a spectral bandpass of 2 nm. In those

measurements, the monochromator had such a poor resolution that absorption

measurements were only possible with an extremely high concentration of the salt

solution. The weak absorption signal was due to a large and unknown number of non-

absorbing channels being detected simultaneously with the resonant absorbing channels,

which resulted in a very weak, or diluted, absorption signal and was only overcome by

averaging multiple data along with a very high absorber concentration. Figure 3-2 A

clearly demonstrates how the use of a low resolution monochromator results in a very

weak, or diluted, absorption signal. Wagenaar et al. [37] also applied this method to the

measurement of calcium, but with a high resolution monochromator capable of resolving

one free spectral range. This approach also required a high concentration of calcium in

order to obtain absorption profiles. The profiles that were obtained yielded a poorly

defined baseline due to the monochromator bandpass which resulted in a loss in the

wings of the profile as shown in figure 3-2 B. The lack of a well defined baseline makes

it difficult for accurate absorption coefficients and Doppler widths to be assigned.

Another problem encountered was the limited temperature stability of the

monochromator, which caused the selected bandpass of the monochromator to slowly

drift away from the absorption profile. Some of these problems were alleviated by

synchronizing the tuning of the Fabry-Perot with the grating of the monochromator. This

allowed the detection of a single order as it scanned across the absorption profile;









however, this approach required careful synchronization of the two components as well

as special grating components capable of achieving the slow scan rate.


k i2
AA rm
.J m+2
+ In m+2
A-m2
AAJ m

Interference pattern imaged onto the Interference pattern Interference pattern imaged onto
entrance slit of a monochromator behind entrance slit the exit slit of the monochromator

Figure 3-1. Illustration of a Fabry Perot interferometer and a monochromator used as a
cross dispersion system for two monochromatic wavelengths.

absorption
order profile monochromator
A) m J bandpass



m+2


absorption 4 monochromator
order profile bandpass

B) m MMM J_
m+1 JaJJa J JJ4

m+2 aMJIJmJI


Figure 3-2. Tutorial for the method of using a continuum source. A) Represents the use
of a monochromator with a large spectral bandpass. B) Represents the use of
a monochromator with a small spectral bandpass.

In 1970, Bazhov and Zherebenko [38] introduced a method using two

electrodeless discharge lamps to create a quasi-continuum source over the absorption









profile of interest. This was achieved by setting one emission source to be self-reversed

and another emission source to be self-absorbed. These two emission sources

superimposed onto one another resulted in a broadened, flat topped emission profile

centered over the absorption profile as shown in figure 3-3. Using this approach retains

the resolving power of a Fabry-Perot interferometer and greatly relaxes the restrictions of

the monochromator, only needing the resolution capable of isolating the broad quasi-

continuum from neighboring spectral lines which can be easily achieved with

commercially available monochromators. Passing the combined emission profiles

through an absorbing medium will result in absorption of the emission and will be

characteristic of the absorption profile of the atomic vapor. If the resulting emission

profile is obtained by the scanning Fabry-Perot spectrometer, the result should be the

emission profile containing the absorption profile, as shown in figure 3-3. Since line

sources are used, the combined emission profile will be centered directly over the

absorption profile and provides excellent wavelength stability without the need to worry

about wavelength tuning, fluctuations, or drift. There was no need for unrealistically

high absorber concentrations and the thermal stability of the monochromator was

unimportant. The relaxation of the slit width restrictions of the monochromator greatly

improved the throughput of the system and allowed for a much higher signal to noise

ratio. In addition, the signal to noise ratio will be further enhanced by the use of an

electrodeless discharge lamp and hollow cathode lamp rather than a Xe-arc lamp. Xe-arc

lamps have significant low frequency flicker noise due to arc wander, and since the noise

is generated from the source, the use of a lock-in will have no effect. The use of the

approach proposed by Bazhov and Zherebenko [38], described above, allows both the









determination of the resolving power of the atomic line filter, as well as number density

measurements, if the profile can be well resolved with an acceptable baseline and signal -

to noise ratio.

Self-reversed Self-absorbed Combined Emission Absorption Measured Absorption
profile profile profile profile profile



++




Figure 3-3. Illustration of the production of a quasi-continuum source from two line
sources for the measurement of high resolution absorption measurements.

Experimental

The 535.046 nm light from a thallium EDL (Perkin Elmer) and thallium hollow

cathode lamp (Jarrell Ash) was collimated and combined with a 50/50 beam splitter as

shown in figure 3-4. The light is focused through the bore of the see-through hollow

cathode discharge followed by a lens to re-collimate the light. Due to the dimensions of

the optical table, the light is reflected 900 with a mirror and sent to the interferometer.

The interferometer (Coherent Optics Inc. 370) is composed of a static mirror and

a translating mirror. A high voltage ramp generator (EXFO RG-91) applies a voltage

from 0-1000 V in a saw tooth waveform. As the voltage is ramped, the piezo-electric

crystal linearly translates the mirror and therefore, scans across the profile. The resulting

interference pattern is collected and focused onto an aperture placed in front of the

monochromator (Acton 500i). The aperture has a 300 |tm diameter and allows the

passing of only the central portion of the interference pattern. Therefore, as the mirror

translates, the circular interference pattern collapses onto the aperture and the transmitted

light is filtered by the monochromator tuned to the 535.046 nm transition. The scanning









Fabry-Perot was found to have an experimentally determined finesse of 130. A mirror

separation of 6.50 mm resulted in a free spectral range of 22.0 pm. This arrangement

yielded an instrument FWHM of 0.17 pm, which should be more than capable of

resolving the absorption profiles. Alignment of the interferometer was accomplished

with a HeNe laser.

Since the see-through hollow cathode discharge is also a thallium emission

source, it will produce 535.0 nm emission. For this reason, a mechanical chopper is used

to modulate the combined line sources. The resulting signal from the photomultiplier

tube (Hamamatsu R928) is then amplified with a current amplifier (Stanford Reseach

Systems model SR570) and sent to a lock-in amplifier (EG&G) for phase sensitive

detection. Since the shortest time constant of the lock-in is 1 ms, the scanning of the

interferometer must be considerably slower, otherwise a distortion of the true signal will

result. For this reason, a function generator is used to control the ramp generator. A

Tektronix function generator capable of producing a triangle waveform with a 2 x 10-4 Hz

frequency is used. Scanning the profile at this frequency allowed the use of a 1 s time

constant on the lock-in amplifier. This resulted in the best signal to noise ratio without

distortion of the recorded profile.









50/50 BS


Figure 3-4. Experimental setup used for high resolution absorption profile measurements.

Results and Discussion

The combination of the two line sources results in a quasi-continuum source for

the thallium 535.046 nm transition as shown in figure 3-5. The profiles of the EDL and

HCL are also measured individually.




A) B) C)











Figure 3-5. A) Scan of the EDL profile self-reversed. B) Scan of the HCL profile self-
absorbed. C) Resulting profile of the combined profiles yielding a quasi-
continuum source over the absorption profile.


Function
Generator











20.0 mA 25.0 mA


Figure 3-6. Resulting absorption profiles of the thallium 6 2P3/20 metastable state of
thallium due to various currents applied to the see-through hollow cathode
discharge. The blue wing on the quasi-continuum profile is cut off due to a
small amount of order overlap from an adjacent order. This order overlap did
not cause distortion of the observed absorption profiles.

Figure 3-6 show the results of spectral scans at four currents applied to the

galvatron. The results obtained are similar to those obtained by Wagenaar et al. [37],

with a poorly defined baseline. An improved baseline could be obtained by broadening

each profile; however, the width of the profile is already slightly too broad for the

selected free spectral range of the interferometer. Increasing the emission profile would

result in severe order overlap which would distort the true profile. The free spectral

range could be adjusted to accommodate for order overlap but would also result in a

broader instrument FWHM, resulting in an unacceptable resolution for these

measurements.


0.0 mA 10.0 mA


15.0 mA









The measurements in figure 3-6 are the result of absorption from the F2 -* Fi

transition for the two isotopes, 203Tl and 205T1, as shown in figure 7. The number density

of each isotope can be calculated using the peak absorption coefficient. This method

assumes that the spectral line is fully resolved which is a good approximation considering

an instrument FWHM of 0.17 pm was used. Calculation of the number density by

measurement of the peak absorption coefficient can be done using the following

equations [39],


k
N=
7(: 1(3-la)
(0.4697). 2 -.(2.65 x 10-2). (/2)


Av =7.16x107 V (3-lb)

-In
k ln (3-1c)


where Io is the intensity of incident light and I is the intensity after absorption. The

absorption path length, 1, is assumed to be 2 cm, the length of the cathode bore. The

FWHM of the Doppler broadened absorption profile, AvD (Hz), can be calculated from

equation 3-lb, where Vo is the central frequency of the transition (5.603 x 1014 Hz), Tis

the Doppler temperature (K), and Mis the atomic mass (204.383 g mol-1). The Doppler

temperature values used for this calculation were obtained by high resolution emission

measurements [40]. Since the hyperfine structure was measured, the oscillator strengths

(fj) in equation 3-la must be determined for each hyperfine component. This is

accomplished by the following relationship and is calculated as follows [41],









ki = fkl 2Fk +1 (3-2)
inn fn 2F+1

fI + 21 + otal (3-3)
fot, = 0.15

I,, / [(2 x 1) + 1] 0.20 5
I21 f2 [(2x2)+1] f21 1 4
I,, [(2x1)+1] (_0.20 (4)
110 fo [(2x1)+1] f \0.40 \4
121 _21 [(2x2)+1] f2 = 1 Y5
,10 fo [(2x1)+1] fo 0.40 4

f = 0.0214 f2 = 0.0955 f0 = 0.0331



F2 F1 Fi
121 7 2S1/2 F

F1 21 FFo
F, Fo
F1 F1 Io = 0.40
I1 = 0.20
lI IF2
6 2P3/2


Figure 3-7. Hyperfine structure for the thallium 535.046 nm transition with relative
intensities, ij. ( -) thallium 203 isotope, ( -) thallium 205 isotope. Not
drawn to scale.

If all calculated values are combined and substituted into equation 3-la, the number

densities for each isotope are determined.


205 + 203 = total (3-4)

From equation 3-4, the total number density of the 6 2P3/20 metastable state can be

calculated by high resolution absorption measurements. The results obtained from the










calculation of the number density are in fair agreement with values obtained by high

resolution emission measurements [40] shown in figure 3-8. The discrepancy between

the two methods may be attributed to the poorly defined baseline of the profiles obtained

in figure 3-6. As explained previously, the lack of a well defined baseline makes it

difficult to accurately determine the Doppler widths, as well as calculate the peak

absorption coefficient, equation 3-1c, and can yield an inaccurate number density values.



1012
10



o 0o



'a
10





SHigh resolution absorption

10 0





Figure 3-8. Number density measurement of the 6 2p3/20 metastable state of thallium by
absorption and emission measurements.


Conclusions

It has been shown that the combination of two line sources to generate a quasi-

continuum source is capable of measuring the absorption profile of a hollow cathode

discharge. The results obtained are similar to these obtained by Wagenaar et al. [37],

who had a poorly defined baseline; however, in these measurements a poor resolution

monochromator was used which greatly relaxed the slit width requirement. This

increased the throughput of the system resulting in a higher signal to noise ratio. Also,









the use of two stable line sources, EDL and HCL, greatly reduced the low frequency

flicker noise commonly associated with Xe-arc lamps.

It should be noted here that the quasi-continuum source could potentially be

generated by another approach. If the EDL were subjected to a magnetic field, then the

Zeeman effect would split these levels, with a separation dependent on the magnitude of

the applied magnetic field. If an appropriate polarizer is used, the combination of this

source with a self-absorbed profile should result in a similar flat-topped quasi-continuum

source for high resolution measurements. To this author's knowledge, the Zeeman

approach has never been attempted. In fact, the only paper found that applied the

combination of two line sources to create a quasi-continuum source was by Bazhov and

Zherebenko [38] in 1970 and no follow up papers or any variation of this method towards

the application of absorption measurements could be found.

Measurement of the absorption profile yielded number densities that are

comparable to those obtained from high resolution emission measurements. The direct

measurement of the absorption profile width would not yield an accurate Doppler

temperature due to the presence of unresolved hyperfine structure components. In

addition, it would be difficult to determine the true FWHM due to the poorly defined

baseline resulting in inaccurate values. Despite these broadening components, the profile

still appears to be Doppler limited and therefore, has a resolving power superior to a

flame and ICP plasma, and comparable to sealed cells.









CHAPTER 4
NUMBER DENSITY OF A SEE-THROUGH HOLLOW CATHODE DISCHARGE BY
CONVENTIONAL ABSORPTION SPECTROSCOPY

Introduction

Conventional absorption spectroscopy can also be applied to the present system

for number density measurements. It is well known that as the current applied to a

hollow cathode lamp (HCL) is increased, the width of the emission profile is also

increased [15-17,40]. If an HCL is held fixed at a low current relative to that applied to

the galvatron, then the emission from the HCL can be roughly approximated as a line

source. In the line source approximation, the source is assumed to have an infinitely

narrow width, or delta function, so the frequency dependence on the absorption

coefficient is removed. It is also assumed the line source is centered on the transition,

k(v) = ko. Since both lamps are low pressure discharges, the profiles are limited by

Doppler broadening and therefore, there will be no shifting in the peaks of the emission

or absorption profiles. Therefore, it can be assumed that the emission profile from the

hollow cathode lamp will be centered on the absorption profile of the galvatron.

If the line source approximation holds true, the absorption measurements can be

directly related to the number density of the atomic vapor created, if the path length,

absorption profile width, and oscillator strength are known [33,39] as was shown in

equations 3-la 3-1c. In this work, the 276.787 nm thallium transition will be used to

determine the ground state number density of the thallium galvatron and the 405.7807 nm

transition will be used to determine the number density of the lead metastable state.























Figure 4-1. Illustration of the absorption profile (red) of the galvatron and the emission
profile (blue) of the HCL.

Experimental

Absorption measurements are carried out using neon filled, thallium (Jarrell Ash)

and lead (Fisher) hollow cathode lamps both set at a fixed current of 2.0 mA and

modulated with a mechanical chopper (EG&G 5207) at a frequency of 625 Hz. Neon

filled thallium and lead galvatrons (Hamamatsu) are used as the see-through hollow

cathode discharges. All lenses used are fused silica with one inch diameters. A

monochromator (Thermo Jarrell Ash) is used with a 500 mm focal length, 1200 grooves

mm- grating, and slit widths of 0.5 mm. The detector is a photomultiplier tube (R928

Hamamatsu) with -1000 V applied from a high voltage power supply (Bertan model

342A). The anode current was sent to a low-noise current preamplifier (Stanford

Research model SR570) with a gain of 200 nA V-1 and a 6 dB high pass filter at 10 kHz.

The amplified signal is sent to a lock-in amplifier (EG&G) for phase sensitive detection

with a gain of 50 mV V-1, a time constant of 1 s, and a phase of 153.40. The demodulated

signal is monitored on a 100 MHz oscilloscope (Tektronix TDS 3012B) and recorded

with a strip chart recorder.











Thermo Jarrell Ash



Lens I H.V.
I I I si
Iris
of 2 Lens 2



Lead/Thallium
u Galvatron Lock-in Scople
AH.. amplifier
Reference

I Iris Strip Chart
Recorder


Mirror --------------------------- Mirror


Figure 4-2. Experimental arrangement for absorption measurements. Lens 1 and lens 2
are both fused silica with focal lengths of 10 cm. Both irises had a diameter
of 2 mm. Not drawn to scale.

The experimental design used for the collection of absorption data is shown in

figure 4-2. Since the galvatron is also a spectral line emission source, reduction of

background emission is required. This is accomplished by using a lens placed 10 cm

from the cathode face of the HCL to collimate the emission. The emission was spatially

filtered with an iris having a diameter of 2 mm. The collection lens used to focus the

emission onto the slits of the monochromator is placed approximately one meter from the

galvatron. This is done in order to remove as much of the emission from the galvatron as

possible, since the galvatron emission is diverging and the HCL emission was collimated.

The galvatron emission is further reduced with a 2 mm iris placed before the collection









lens. The monochromator is tuned to the 276.787 nm emission line of thallium and 405.8

nm emission line of lead.

It is important to note that by placing the galvatron with the anode facing the

HCL, rather than facing the detector (see figure 4-2) less emission from the galvatron is

observed. Orientation in this manner aided with the reduction of background emission

noise.

Number Density Measurements

The results obtained from the strip chart recorder were used to calculate the

ground state number density for each current using equations 3-la-c. Temperature values

used to calculate the Doppler width of the absorption profiles were obtained from results

obtained by high resolution emission measurements [40]. Figure 4-3 shows that the

absorption data obtained for thallium are not in agreement with values obtained from

saturated fluorescence measurements [32], whereas the lead data shows excellent

agreement with saturated fluorescence values, as well as high resolution emission values.

In order to explain this discrepancy, our assumptions must be reviewed. Two major

assumptions are made; the hollow cathode lamp acts as a line source and that the

absorption path length is a constant. The method for calculating the number density is

based on the assumption that an infinitely narrow line source is used; however, this is

known to not be true since the emission of the hollow cathode lamp will have some

inherent width due to Doppler broadening and possibly a small amount of broadening due

to self-absorption. This will result in number density errors at lower galvatron currents.

Therefore, one must know what the relative widths of the absorption and emission

profiles are in order to accurately apply the line source approximation. In addition,

because the galvatron is also a line source the detector detects the D.C. emission from the











galvatron. At low currents, the background emission noise will be reduced by the lock-in


amplifier; however, as the galvatron current is increased the background emission noise


will grow to the point where the signal becomes buried in noise.


10,
101 Thallium Lead


1S .'t u fo
S10 101


S 101 _
1 10
010'
S 10' A;
SGal Absorption (A Saturated fluorescence
10 Time-Resolved Laser-Induced A Absorption
Saturated Fluorescence Emission
10. 101 10 101. 10 .
10 101 10 10 101 10 101
Galvatron Current (mA) Galvatron Current (mA)

Figure 4-3. Number density measurements by conventional absorption. The results from
saturated fluorescence and high resolution emission data are also plotted. For
the absorption number density calculation, temperature values were obtained
from high resolution emission measurements [40]. The emission source (HC1)
current was fixed at 2.0 mA.

Path Length Measurements

Throughout the diagnostics of the thallium and lead galvatrons, it was noticed that


the discharge extended beyond the ends of the cathode. Therefore, the optical path length


is no longer constant with current or spatially uniform. In equation 3-1c, the path length,


1, is assumed to be constant and not to vary with current. In order to validate this


assumption, the absorbance was measured across the face of the cathode as a function of


distance from the face of the cathode. The experimental arrangement is similar to that


shown in figure 4 except the galvatron is rotated 900 and placed on a translating stage in


order to translate the cathode away from the intersecting beam.












0 12-


0 10
Galvatron Current
S1.0 mA
0 08
08 3.0 mA
S 5.0mA
Z 006- 7.0mA
o < 10.0 mA

004-
V


I,
002- 4

000- V f! -1- --.. -

24 22 20 18 16 14 12 10 8 6 4 2 0
Distance (mm)


Figure 4-4. Absorption measurements as the cathode was translated through the emission
beam. The HC1 emission source was held constant at 10 mA throughout this
experiment.

A quartz shield surrounds the outer cylinder of the cathode in order to prevent


sputtering process on the cathode. As a result of sputtering on the face of the cathode, a


small amount of metal vapor was deposited on this quartz shield. Therefore, a current of


10 mA was used in order to obtain a measurable signal. Figure 4-4 clearly shows that


absorption occurs beyond the face of the cathode; however, it is only noticeable at higher


currents. Even at higher currents it can be seen that the absorption drops off dramatically


past the face of the cathode and only extends out a few mm. This validates the


assumption of a single value for the absorption path length with changing current.

Line Source Measurements

In order to validate that the HCL can be approximated as a line source, emission


profiles of the HCL and galvatron were measured at similar currents. This was done by


use of a scanning Fabry-Perot interferometer as described in reference [40]. Because of


the spectral range of the interferometer mirrors, a thallium ground state transition could













not be selected; however, the 535.046 nm transition was accessible and allowed relative


conclusions to be drawn about the emission and absorption profiles of the ground state.


Measurement of the emission profiles from the thallium and lead hollow cathode


lamps and galvatrons are shown in figure 4-5. It can be seen that when applying similar


currents to the HCL and the galvatron yields profiles of different widths. The thallium


galvatron exhibits a slightly narrower profile than the HCL with noticeably less



10. Thallium ,10 Thallium
09- 09-
Current = 15 0 mA
08- Current = 10 0 mA o8- Galvatron
0 rGalvatron 07- Hollow Cathode Lamp
SHollow Cathode Lamp
06- 06-


04 04
03- 03-
02- 02-
01- 01-
00- 00-
2 0 2 4 6 8 10 12 14 16 4 2 0 2 4 6 8 10 12 14 16
AA (pm) A (pm)




Current 15 0 mA
S Lead Crent=100mA Lead Galvatron
SLeaGalvatron LeaHollow Cathode Lamp
09- Hollow Cathode Lamp 09-
08- 08-
07- 07
06- 06-
05- b05-
04- 04-
03- 03-
02- 02-
01- \ 01

5 4 3 2 1 0 1 2 3 4 5 5 4 3 2 1 0 1 2 3 4 5
AX (pm) AX (pm)


Figure 4-5. High resolution emission measurements of the lead 405.7807 nm and the
thallium 535.046 nm transitions in a galvatron and hollow cathode lamp at
similar currents.


self-absorption. It is also important to note that the absorption profile is expected to be


narrower than the emission profile observed in figure 4-5 due to the absence of the self-


absorption broadening component. From the results in figure 4-5, it cannot be concluded









with any degree of certainty the assumption that a line source was used in the

measurement of the number density for the thallium galvatron and would reflect in an

error in the calculation. This explains the discrepancy between the fluorescence

measurements and absorption measurements observed in figure 4-3. From the results of

the lead emission profiles in figure 4-5, it can be seen that the lead galvatron produces a

much broader emission profile than the lead hollow cathode lamp at similar currents.

Therefore, it can be concluded that the lead hollow cathode lamp can be approximated as

a line source relative to the absorption profile of the lead galvatron when operated at a

low current, which explains the agreement in number density between the absorption

measurements and fluorescence measurements.

It assumed that the major reason the two galvatrons behaved so differently is due

to the pressure of the buffer gas used in each lamp. Since the galvatrons are

manufactured by Hamamatsu, the Pb HCL by Fisher, and the Tl HCL by Jarrell Ash, it is

expected that each lamp will contain a different buffer gas pressure. This can affect the

sputtering efficiency, number density, and Doppler temperature of each lamp operated at

similar currents.

Conclusion

Number density measurements of the thallium and lead galvatrons by

conventional absorption method yielded conflicting results when compared to the results

obtained by saturated fluorescence. As shown in figure 4-3, thallium shows a very poor

agreement to the saturated fluorescence measurements, whereas lead showed excellent

agreement between the fluorescence and emission methods. It was found that the poor

agreement for the thallium galvatron and excellent agreement of the lead galvatron was

due to the relative spectral widths of the emission source and absorbing medium. The









thallium galvatron produced a narrower emission profile relative to the emission profile

of the hollow cathode lamp at similar currents, whereas the lead galvatron produced

broader emission profile relative to the emission profile of the lead hollow cathode lamp.

From this, it can be concluded that the lead hollow cathode lamp behaved as a line source

and in turn resulted in more accurate measurements. The thallium hollow cathode lamp

did not satisfy the line source approximation and thus resulted in erroneous results, as

was demonstrated. The difference in the observed emission profiles is expected to be due

to the different construction of each lamp. Each lamp would likely contain a different

buffer gas pressure since each HCL came from a different manufacture than the

galvatrons.

It has been shown that the use of a hollow cathode lamp can be applied to the

measurement of number densities by absorption; however, the relative widths of the

emission source and absorption profile should be known in order to correctly apply the

line source approximation.









CHAPTER 5
TIME-RESOLVED LASER-INDUCED SATURATED FLUORESCENCE
MEASUREMENTS: EVALUATION OF NUMBER DENSITY AND QUANTUM
EFFICIENCY

Introduction

As previously mentioned, the luminosity-resolving power product is an important

figure of merit when comparing different spectroscopic systems; however, other

parameters must also be evaluated in order to properly assess the effectiveness of an

atomic filter. One of these parameters is the number density of the metal vapor. An

effective filter should be able to easily produce, and reproduce, a desired number density

for extended periods of time with little to no fluctuations or drift. An ideal system would

be simple, compact, and portable if possible. If the system is not able to generate an

acceptable number density, the result will be much of the signal radiation transmitted

through the filter, thus, will not be detected.

The quantum efficiency of the system is another important parameter. Under a

high collision, high quenching environment, the atoms that resonantly absorb the signal

photons must compete with non-radiative pathways. Atoms that collisionally de-excited

prior to fluorescing or ionizing result in a loss of the signal. Quantum efficiencies as low

as 0.03 0.001 have been reported for flames [13,14], and values as low as 0.1 have been

found for sealed cells [39]. Therefore, the quantum efficiency of the atomic system is

directly related to the overall detection efficiency of the filter and is very important for

sensitive fluorescence and ionization detection [42-44].

The advantages that a galvatron offers over conventional atomic reservoirs makes

it an attractive candidate for the application as an atomic line filter, however, little

spectroscopic data has been found in the literature. Therefore, time-resolved laser-








induced saturated fluorescence was used to determine number density and quantum

efficiency of the metal vapor produced in a thallium and lead galvatron. Thallium and

lead were chosen as the atomic vapor for their three level schemes shown in figure 5-1.

The relatively strong transition probabilities make these transitions promising for

fluorescence and ionization detection.


1 2-

B12 Pv
B21 Pv

377.572 nm (0.13)
1


Pb


i A

k23
.yk32
Yi


3.283 eV
535.046 nm (0.15)




0.966 eV


k31 i kl3


k32 A23

k23 j


7 2S1/2





6 23/20
6 2Pl/2


4.373 eV 7 3pI
405.7807 nm (0.13)
B32 Pv
SB23 Pv


283.3053 nm (0.21) 3 1.32 eV 6 3P2
S _k31 k13 63P0

Figure 5-1. Partial energy level diagrams for thallium and lead displaying the possible
transitions involved with wavelengths and oscillator strengths labeled.
Collision constants between levels 1 and 2 are neglected.









Theory

Rate Equation Approach Versus Density Matrix Approach

In general, there are three approaches to treat the interaction of light with an

atomic (molecular) system; the classical, semi-classical, and the full quantum mechanical

approach. The rate equation (RE) approach is a classical approach which treats both the

incident light and the atomic system in a classical way. The populations of the various

levels involved are described by use of the Einstein coefficients for stimulated emission

and absorption (Bjk and Bkj, respectively), Einstein coefficients for spontaneous emission

(Ajk), and collisional excitation and de-excitation rate constants (kkj and kjk, respectively).

The RE approach considers the source to be incoherent with a smooth featureless

structure over the absorption profile of the atomic vapor. Therefore, in order for the RE

formalism to be valid, the bandwidth of the incident laser must be much broader than the

absorption profile of the atomic vapor, even under very high laser intensities where

power broadening could dominate the width of the absorption profile [45,46]. There

must also be several closely spaced longitudinal modes present under the absorption

profile in order for the source to be considered smooth and featureless. In addition, the

rate of dephasing collisions in the atomic vapor must be high in order to destroy any

coherence created by the monochromatic laser field [47]. A convenient way to check if

the use of the RE approach is valid is if the following condition is fulfilled; AViaser >>

B12pv [45,47]. The RE approach is a commonly used method by laser spectroscopists due

to its simplicity, versatility, and accuracy when the aforementioned condition is met.

Laser spectroscopists may often find themselves with a laser spectral profile that

does not meet the condition validating the RE approach. Under these high resolution

conditions, coherence phenomena, such as the well known Rabi oscillation frequency and









Stark splitting effects can be observed. These effects can not be explained quantitatively,

or even qualitatively, by use of the RE approach and are only realized by use of the

density matrix (DM) formalism. The DM approach is a semi-classical approach, which

treats the incident light classically and the atomic system quantum mechanically [45-48].

Even though it provides a more accurate description of the light/atom interaction under

intense monochromatic radiation, it is, however, mathematically a great deal more

complicated compared to the RE approach. The RE approach only produces m

differential equations; one for each energy level considered. The DM approach,

however, produces m2 coupled differential equations since the phase of the wave function

must also be considered. In addition, each degenerate energy level is also treated as an

individual state; therefore, the mathematics becomes increasingly cumbersome with

every energy level that is considered. If the DM approach were applied to the limiting

case were a broad-band pulsed laser is used, with a pulse duration much longer than the

inverse of the laser bandwidth (Aviaser-), then the Rabi oscillations quickly damp out,

resulting in the DM approach mathematically reducing to the RE approach [46-48].

Therefore, in this broad-band limit, it would be unreasonable to use the DM approach

when the much simpler RE approach could be used with equal accuracy.

Taking into consideration values used for the thallium measurements, the FWHM

of the laser profile, Aviaser, was found to be 14.0 GHz and from the maximum laser

output, a stimulated absorption rate, B12pvmax, was found to be 2.3 GHz. Therefore, with

the present laser system and atomic reservoir, the use of the rate equation for the

description of this atomic vapor is validated by fulfilling the condition Avaser >> B12Pv

and therefore, the RE approach will be the only approach considered.









Of course, the most complete theoretical description of the light/atom interaction

would necessitate a full quantum mechanical treatment. This would require the quantum

mechanical nature of light to be included, where creation and annihilation operators are

used to describe the interaction between light and matter. This is known as the quantum-

electrodynamical (QED) approach and has been applied to two and three level systems

[49-51]; however, this approach lies beyond the scope of this research and will not be

discussed further.

Ideal Two-Level Saturation Curve Under Steady State Conditions

Figure 5-1 shows a partial energy level diagram of thallium and lead with the

transitions labeled. It should be noted here that the theoretical section of this paper will

make use of the laser spectral energy density, po (J cm-3 Hz-1), however, the laser

spectral irradiance, E (J s-1 cm-2 nm-1) will be used throughout the rest of the paper.

They are related to one another through the speed of light constant, c (2.9979 x 1010 cm

s-1) by


S= (5-1)
C

One should be aware of the units used here. Equation 5-1 is in the form of frequency,

Hz; however, results in this paper are reported in units of wavelength, nm.

To begin with the simplest case, the thallium and lead atom will be assumed to

behave as a two-level atom. If these atomic systems are excited with a broad band,

spatially uniform, step-like laser pulse having duration much longer than the effective

lifetime of the excited state, a steady state fluorescence waveform will result. The

intensity of the resulting fluorescence signal is dependent on the population of the excited

state, n2, and is a function of the laser spectral energy density. Using the RE approach









and neglecting collisional excitation (k2 = k32 = 0), we have the general rate equation for

n2(t) [45-47],

dn = B 12,p (t)n {B21p, (t)+ A21 + k21 2 (5-2a)
dt
n, + n2 =nT (5-2b)

where A21 (s1) is the Einstein coefficient of spontaneous emission, B21 (1 cm3 s-1 Hz) is

the Einstein coefficient for stimulated emission, B12 (J1 cm3 s-1 Hz) is the Einstein

coefficient for stimulated absorption, k21 (s-1) is the collisional de-excitation rate constant,

and nj (cm-3) represents the number density of the level indicated by the subscript.

Combining equations 5-2a, and 5-2b, and assuming steady state conditions, dn2ldt = 0,

yields the following equation [47],


n= n2s) m Sp,) (5-3)
1+ o
pvo

where p, (J cm-3 Hz-) is the spectral energy density, ps (J cm-3 Hz-1) is the saturation

spectral energy density, or saturation parameter, and S( po ) is defined as the ideal

saturation function [47]. The plateau value for po -* oo is given by


n2 = gax Smax (5-4)
nJ gl + g2

where gj are the statistical weights of the state indicated by the subscript. The saturation

parameter, p is give by



S 91+ g,) c 21










21 A21 (5-5b)
A21 + k21

where h (6.626 x 10-34 J s) is Planck's constant, Vo (Hz) is the central frequency of the

transition, and Y21 is the defined as the quantum efficiency of the transition. Evaluation

of equation 5-3 can be carried out by considering three limits. First, if p, >> ps then

the equation reduces to (n2/nT) max which is the plateau value of the saturation curve. In

this region, the number density of the excited state, n2, becomes independent of the laser

energy density and has a value equal to half of the total population of the system (if gi =

g2). The second limit is the point at which po = ps When this condition is met, the

population of the excited state has reached half of its plateau value and a quarter of the

total population of the system (if gi = g2). At this point, the combined stimulated

emission and absorption rate constants (B12 + B21) po are equivalent to the combined

spontaneous emission and collisional de-excitation rate constants (A21 + k21). The last

limit is the region when py << ps This region becomes linear with laser energy density

and has a slope of (n/2/lT) max1/

Two-Level Saturation Curve Under Transient Conditions

The ideal case described above dealt with a laser pulse width much longer than

the effective lifetime of the excited state. This allows the system to achieve a steady state

even at low spectral energy densities. However, if the laser pulse duration is equivalent

to, or less than, the effective lifetime of the excited state, then the atomic system will not

be able to respond fast enough to the rapidly changing laser energy density. If the system

is subjected to a broad band, spatially uniform, step-like excitation function, then the

resulting population of the excited level as a function of time can be given by [52],










n2(t)= nf 1-exp- (5-6)


where n2SS is the steady state population of the excited level and tr is defined as the

response time of the system [53]. It can be seen that in the limit t o, equation 5-6

reduces to the steady state condition, as would be expected.

1
tr = (5-7a)
+ B12 v + A21 + k21


S = nBpt, (5-7b)
n2

Equation 5-7a clearly demonstrates that the response time of the atomic system is

dependent on the laser energy density. Therefore, under complete saturation, the

response time of the system will be very fast and dominated by stimulated processes.

This implies that levels 1 and 2 become "lock" together by the laser, with the atoms

rapidly circulating between the two levels; each level having population determined by

their statistical weights. Therefore, under complete saturation the peak of the

fluorescence waveform can be described as a two level system under steady state

conditions despite the presence of a third intermediate level. Thus, a two level steady

state fluorescence waveform can be achieved with a short laser pulse if the transition is

completely saturated. If po is attenuated to where B12 pv becomes negligible, then the

response time simply reduces to the effective lifetime of the atomic system. This also

implies that the two levels are no longer "locked" together by the laser and therefore, can

no longer be considered a two level system due to the branching of the fluorescence into

the laser locked level and into the third intermediate level. In addition, if a short laser

pulse is used at these lower energy densities, the response time of the atomic system will









not be sufficient to achieve a steady state resulting in a distortion of the measured

saturation curve. This distortion also produces an "apparent" saturation parameter whose

value will be higher than the true saturation parameter and is dependent on the pulse

duration. This type of non-steady state response has been previously described and

modeled by Omenetto et al. [52].

Three-Level Saturation Curve in the Presence of a Trap

The previous two sections approximated thallium and lead as a two-level system,

however, the atomic systems shown in figure one is a three-level system. Here, the laser

is coupled to levels one and two, with level two radiativly connected to a third metastable

level. This metastable state is long lived in a low collision environment (k31 ~ 0), as is

the present case. If this metastable level acts as a true trap, or loss-less sink, then all

atoms fluorescing into this level will be taken out of circulation, or trapped, during the

pulse duration and will not further contribute to the fluorescence signal. The presence of

this third level is important in both the linear portion of the saturation curve as well as in

the saturation region. In the linear region, the fluorescence quantum efficiency for both

radiative pathways, A21 and A23, will affect the overall detected saturation curve. Thus,

the resulting signal will be affected by the spontaneous decay, A23, into this third level

and must be taken into account. This third level becomes especially important under

saturation conditions. As mentioned previously, under saturation conditions, the

response time of the system (equation 5-7a) is dominated by stimulated processes

between the two laser "locked" levels [52,53]. Therefore, if complete saturation has been

achieved, then the system can initially be considered a two-level system. However, as

the pulse increases in duration, a significant number of atoms will accumulate in this

third level trap, resulting in fewer atoms circulating in the two laser coupled levels. This









is observed as a loss in the population of level 2 and results in a decrease in the observed

fluorescence signal. In order to properly apply this metastable trap level to the thallium

and lead atomic systems, the time dependent rate equations must be used to determine the

temporal behavior of atoms in each of the three states. Therefore, the time dependent rate

equations for the three levels can be written as [47,54]

dn,
d = -nB12 + n2(A21 + B21 v + k21)
dt (5-8a)
dn
2--= n112P -n 2(A21 + B21 + k21 + A23 +k23) (5-8b)

n3 2 (A23 + k23) (5-8c)
dt
n, = nT n2 n3 (5-8d)

where all variables have been previously defined and all transitions correspond to those

for thallium in figure 5-1. These equations can easily be rearranged to take into account

the excitation of lead from the metastable level. Equation 5-8d implies that the system is

closed and no losses occur. To simplify the mathematics, let

a= B12 v f = B21Pv + A21 + k21
Y = A23 o = A23 + k23

It is assumed that at t = 0 all atoms can be found in the ground state resulting in the initial

condition n = nT and n2= n3 = 0. Solving equations 5-8a-c yields [54],


n, (t)= -n, r 1- exp(- l .t)+ n a 1- exp(-2 t) (5-9a)
2 p1 -41 t-2 e31 ] 2b

n2 (t)= n, T [exp(- t)- exp(- 2 t)] (5-9b)

3y -T o exp(- t)+ n, T y exp(- 2 .t)+ nT aoy (5-9c)
31 (2 --31 ) 32 (2 1- 1 1)1 2









with t being the instantaneous point at which the fluorescence value is measured. 4i and

2 are defined as [54]


a ++Y a+P+ y + (5-10a)
2 2


2= a+6y+ + a +6 + + o (5-10b)
2 2

If a time-integrated, or time averaged, method of detection is used i.e. a boxcar, then the

total number of photons emitted with a frequency v23 within a pulse duration, zaser (s), can

be given as [54]


I = fl A23 n2(t)dt (5-11 la)

Sn T I_2 exp(-, aer)- exp(- 2 ) (5-1 b)r
7o .2 1-

Another potential trap often considered is the ionization continuum, where the

recombination of ions and electrons can be a long process [55] compared to a pulse

duration of a few nanoseconds. As can be seen for thallium in figure 5-1, level 2 is 3.283

eV above the ground state. If this excited atom were to absorb another photon at 377.572

nm, it would promote the atom 6.566 eV above the ground state. This would put the

atom into the ionization continuum since the ionization potential for thallium is 6.11 eV.

As for lead, the 405.7807 nm laser promotes an atom to an energy level 4.373 eV above

the ground state. A second photon at 405.7807 nm would only promote the atom to an

energy level 6.106 eV above the ground state, and since lead has an ionization energy of

7.42 eV, this second photon would not have sufficient energy for ionization of the lead

system and could only be achieved by a multi-photon process or by some collisional

process. Therefore, the potential of the ionization continuum acting as a possible trap









does exist for thallium and lead, however, this type of photo-ionization typically have

low photo-ionization cross sections and would only become a factor if very intense laser

energies were used, well in excess of the saturation parameter and above what was

achievable with the current experimental set-up. In addition, since the system is a low

pressure environment, ionization due to collisional processes is expected to be negligible.

Thus, the ionization continuum will not be considered here.

Number Density Under Steady-State Saturation Conditions

One advantage of saturated fluorescence spectroscopy over traditional

fluorescence is the independence of the signal on the source intensity. In other words,

fluctuations that occur in the source will not translate to the observed fluorescence signal

under saturation conditions. This results in a higher signal to noise ratio, especially if

direct-line fluorescence measurements are made. Also, in special situations where

absolute measurements are required, the achievement of saturation allows one to obtain

the number density of a species without the tedious need to measure accurately the

spectral energy density of the source. As mentioned previously, under complete

saturation the system initially can be considered a quasi-two level system after which the

presence of a trap influences the fluorescence intensity. If the fluorescence is measured

in absolute units at this peak value, then quasi-two level steady state conditions are

achieved, and the number density can be calculated from a simple two level approach if

the transition probabilities, statistical weights, and the path length are known. The

fluorescence radiance equation for a basic two level system can be written as [45,56]











B, =( h v21A21nT 1 (5-12)
1+ 1 1+ P



where / (cm) is the path length and p is the modified saturation spectral energy density

which is given by [56]

A21 (5-13)
B21 Y21

with Y21 is the quantum efficiency of the system (equation 5-5b). The saturation spectral

energy density is defined as the energy density required to produce half of the maximum

fluorescence radiance, BF, which occurs at complete saturation and is related to p,, by


S= 2 P* (5-14)
gl + g2


As can be seen, if complete saturation has occurred, (po >> p, *), then equation 5-12

reduces to [45,56]


BF-x hv21A21n T (5-15)
T ) g, + g 2

Equation 5-15 shows the simplification of the number density calculation in the

saturation region due to the removal of the source dependence. Therefore, ifBFax is

measured in absolute units and the fundamental parameters are known, then the number

density of the ground state can easily be determined.

In the introduction, it was mentioned that the atomic reservoir needs to be able to

produce an appropriate number density to be an effective atomic line filter. Of course









this raises the question as to what is an appropriate number density. This is a question

not easily answered since little information is known about the spectral profile of the

signal and how it compares to the absorption profile of the atomic vapor. However, if we

take the limit of the signal to be a line source, then a curve of growth calculation will

provide information as to the number density needed to absorb a desired fraction of light.

For this calculation, the absorption profile for thallium and lead was assumed to be purely

Doppler broadened, i.e. a damping parameter equal to zero, with a path length of 2 cm

and a Doppler temperature of 500 K. These are typical values commonly associated with

hollow cathode discharges [15-17]. A more detail description of the calculation for this

curve of growth can be seen in Appendix A. Based on this calculation, with appropriate

parameters used, a number density of 8.90 x 1011 cm-3, 5.44 x 1011 cm-3, and 8.10 x 101

cm-3 would be needed for 99.9 % of the signal radiation to be absorbed by the thallium

ground state transition, thallium metastable state transition, and lead metastable state

transition, respectively. Therefore, it needs to be determined what current applied to the

galvatron will produce this number density.

Experimental

Laser System

The experimental system for the measurements in this paper can be found in

figure 5-2. The laser system consisted of a Lambda Physik LPX 200 XeCl excimer laser

used to pump a Lambda Physik Scanmate 1 dye laser with a 20 mm cuvette. The excimer

operated at 10 Hz with an output energy of approximately 75 mJ/pulse. The dye used to

achieve the 377.572 nm thallium resonance line was BBQ (Exciton) at a concentration of

5 x 10-3 M in ACS grade cyclohexane. The dye used to achieve the 535.046 nm thallium

transition was Coumarine 540A (Exciton) at a concentration of 8 x 10-3 M in ACS grade










methanol. The dye used to achieve the 405.7807 nm lead transition was DPS (Exciton) at

a concentration of 1 x 10-3 M in ACS grade p-dioxane. Two irises were used to isolate

the central portion of the laser beam. This helped to reduce laser scatter, as well as make

the beam more homogenous. The diameters were set to 2 mm so that the beam just filled

the bore of the cathode. The see-through hollow cathode discharge used was a thallium

galvatron (Hamamatsu) with neon filler gas at a pressure of 14 torr [57] and a lead

galvatron (Hamamatsu) with neon filler gas with an unknown pressure. The applied

current was accurately measured with a home made pick-off circuit and monitored on a

Fluke 29 series II multimeter.




Photodiode
Mirror Trigger
H.V.
Supply


Neutral density filter etan
Iris Vacuum Photodiode

Glass slide

50 ~
Thallium
Galvatron ,g



Lens 50 Q
Pierced -- --------- PMT
M irror 1 I' a. i,,, .ii ..,, I


Beam Interference i[
Trap Lens filter u Uil l.


Figure 5-2. Experimental set-up used for all saturation curve and number density
measurements.









Detection System

The monochromator was a McPherson model 218 with criss-cross Czerny-Turner

geometry, a grating of 1200 grooves mm-1, blazed at 300 nm, reciprocal linear dispersion

of 2.6 nm mm-1, ruled grating area of 50 x 50 mm, focal length of 300 mm, and an f-

number of 5.3. The entrance and exit slits were set to 1 mm. Glass color filters were

placed directly in front of the entrance slit to allow the fluorescence radiation to pass and

to block any stray laser light. Fluorescence was detected with a photomultiplier tube

(Hamamatsu R1414) with -1000 V applied and a measured rise time of 1.0 ns.

Triggering was accomplished with a photodiode from a small portion of the excimer

radiation.

Laser irradiance was determined using a Fisherbrand plain microscope slide and

reflecting a small portion of the laser beam to a Hamamatsu R1328U-03 vacuum

photodiode. The vacuum photodiode was supplied with +300 V from a Bertan series

105, 1 kW high voltage power supply. The signal was detected on a 400 MHz Tektronix

oscilloscope.

Vacuum Photodiode Calibration

Calibration of the vacuum photodiode was accomplished by removing the lamp

and inserting a Melles Griot broad band power/energy meter type 13PEM001 with an

AOSK0032 sampling head. The photodiode was checked for linearity over a wide range

of energies with calibrated neutral density filters and was found to be linear over the

entire energy range reported in this paper. Equation 5-16 shows the calculation used to

obtain the conversion factor, PA (J s-1 cm-2 nm-1 mV-1),










PZ = ser (. ) (5-16)
SAser. (cm2) x Atlser (s) x AA r (nm) x S,, (m V) (5-16)


where Qiaser (J) is the energy/pulse measured on the energy meter, Alaser (cm2) is the cross

sectional area of the laser beam filtered by the two irises, Atlaser (s) is the FWHM of the

laser temporal profile, A1,aser (nm) is the FWHM of the spectral profile, and Smv (mV) is

the voltage signal obtained on the oscilloscope for a given energy. Multiplying PA by the

signal obtained on the oscilloscope yields the spectral irradiance of the laser at any given

attenuation. Values for the laser parameters used in this calculation will be discussed

later.

Spectrometer Calibration

Calibration of the spectrometer was accomplished by use of a calibrated Oriel

instruments 1000 W quartz tungsten halogen irradiance standard (serial # 7-1121).

Linearity of the detector was checked to ensure the proper conversion factor. Equation 5-

17a shows the conversion of the measured fluorescence voltage into a fluorescence

radiance. The spectrometer was calibrated with the same optics, filters, and settings as

the fluorescence measurements.

B=F ImV xF xSg x x 10-6

Alens -Apiercmg (5-17b)
f2

Here Imv (mV) is the peak voltage measured, sg (nm) is the geometric spectral bandpass

of the monochromator determined by a slit width of 1 mm, and Q (sr) is the collection

solid angle of the lens. Since a pierced mirror was used to collect the fluorescence, a

small portion of the fluorescence is loss due to this piercing. This loss can be corrected










for by subtracting the resulting solid angle that is lost and is illustrated in figure 5-3. The

parameter F (J s-1 cm-2 nm-1 mV-1) is the conversion factor for measured voltage to

irradiance at 535.046, 377.572, and 283.3 nm. This was obtained by relating the

measured signal from the spectral irradiance lamp to the calibrated spectral irradiance

value supplied by the manufacture. Table 5-1 displays all values used in the calculation

of the fluorescence radiance of thallium. All values are the same for lead as well with the

exception of the fluorescence radiance conversion factor.

Pierced mirror
Lens (f= 12 cm)



0.4 cm 2.54 cm





Figure 5-3. Representation of the losses that would be encountered in the collection
optics. Not drawn to scale.

Table 5-1. Values used for fluorescence radiance calculation with symbols and
descriptions provided.
Symbol Description Value
BF fluorescence radiance (W cm2 sr')
1mv measured signal intensity (mV)
EA reported value for the irradiance standard @ 535.0 nm 9.4986 pW cm2 nm1
Rd reciprocal linear dispersion 2.6 nm mm1
W entrance and exit slit widths 1 mm
Sg geometric spectral bandpass 2.6 nm
Alens fluorescence collection lens area (d = 2.54 cm) 5.07 cm2
Apercing piercing area (d = 0.40 cm) 0.1257 cm2
f focal length of the fluorescence collection lens 12 cm
FA calibration factor 5.8282 pW cm2 nm' mV-1
0 collection solid angle (corrected) 0.0312 sr
10-6 conversion from pW to W










Evaluation of Dye Laser Parameters


Spectral Profile

An assumption made in the theoretical section assumed that the laser source is

broadband. This is to validated the use of the RE approach and to ensure that each atom

is subjected to the same spectral irradiance regardless of its velocity. For this assumption

to be valid, the spectral profile of the laser needs to be determined. The laser beam was

diverged with a concave lens and passed through an air-spaced Fabry-Perot etalon with a

spacer of 3.011 mm and a finesse greater than 30 (instrumental FWHM = 0.79 pm). The

fringe pattern created was projected onto the vacuum photodiode. In front of the

photodiode was a 100 |pm pinhole which was used to isolate a small portion of the central

fringe. The laser was scanned from 377.60 nm to 377.70 nm at a rate of 1 pm/s and a

repetition rate of 30 Hz. The signal was detected with a boxcar and recorded on a strip

chart recorder (Picoscope).


F1 --F1
I1 = 0.577 -- Calculated absorption profile,
1.0 T 500Ka-0
0.9/ '- ------ Measured laser spectral profile
0.8
0.7-
A=0 6.63 pm / F1 Fo
S0.6 Fo Fi Iio= 0.250
S0.5- Io = 0.173
0 /Longitudinal
0.4 mode structure
0.3
0.2
0.1 -
0.0
14 12 10 8 6 4 2 0 2 4 6 8 10 12 14
Ak (pm)
Figure 5-4. Experimentally measured dye laser spectral profile with FWHM of 6.63 pm.
Also shown is the calculated mode structure obtained from a cavity length of
35 cm. Intensities shown are arbitrary and do not represent any physical
quantity.









Determination of the spectral profile measured can be achieved by making use of

the free spectral range of the etalon from equation 5-18,

22
AFSR = = 23.6 pm (5-18)


with A = 377.572 nm, 7 being the refractive index of the medium between the etalon

plates (= 1.001 for air), and d= 3.011 mm being the separation between the mirrors. This

free spectral range value is equal to the peak separation of two adjacent orders on the

strip chart recorder, therefore, providing a spectral ruler and allowing the calibration of

the x-axis. From figure 5-4, it can be seen that the FWHM of the dye laser output was

determined to be 6.63 pm. The mode spacing calculated from equation 5-19 shows that

the FWHM output of the dye laser contains approximately 32 longitudinal modes. Here c

is the speed of light (2.9979 x 1010 cm s-1), L is the length of the cavity (- 35 cm), and the

factor 2 represents one round trip in the cavity. It should be noted that this equation

represents the spacing between two adjacent modes in Hz and that figure 5-4 displays it

in terms of wavelength.

C
Av = (5-19)
2L

In order to verify that the laser source behaves as a quasi-continuum, the number

of longitudinal modes present within the absorption profile of the transition needs to be

determined. In order to verify this, the absorption profile for the 377.572 nm transition

was calculated. A value of 500 K was used for the Doppler temperature and a value of 3

x 10-3 was used for the damping parameter, which are values commonly associated with

hollow cathode discharges [15-17]. It was found from figure 5-4 that the central

transitions contain approximately 10 modes which justifies the assumption of a quasi-









continuum source. It can also be seen that the laser intensity does not change

significantly across the absorption profile. This results in a fairly smooth spectral

irradiance over the absorption profile; therefore, every velocity class will be subjected to

approximately the same spectral irradiance. Similar results were obtained for the

thallium 535.046 nm and 405.7807 nm laser profiles.

It can be seen from figure 5-4 that the red wing of the laser profile, when tuned to

the central transition, slightly overlaps the Fo -> Fi hyperfine component resulting in a

slight excitation of this transition. Thus, as the spectral irradiance increases, the central

transition will become saturated, however, the hyperfine component under the red wing

of the laser will not experience the irradiance necessary for saturation. This will result in

a distortion of the saturation curve in which a high irradiance plateau will never be

practically achieved. However, by inspection of figure 5-4, it can be seen that the

spectral irradiance observed by the Fo -> Fi hyperfine component is about an order of

magnitude less than that experienced by the central transition and should not significantly

contribute to the signal.

It is important to note here that the laser profile only encompasses the central two

transitions. These two transitions are a result of the Fi -- Fi hyperfine transition of the

two thallium isotopes, thallium 205 (70.5 % natural abundance) and thallium 203 (29.5 %

natural abundance). Therefore, for an accurate calculation of the number density, the

transition probability, AF1,F1, for this transition needs to be determined. A more detailed

description of this calculation can be found in appendix B.

Spatial Profile

In order to avoid unnecessary distortion in the saturation curve, the spatial beam

profile must be homogenous. This ensures that every atom in the analytical volume is









subjected to the same spectral irradiance. A distortion in the measured saturation curve

will result if this requirement is not met [47,58,59]. For this reason, a spatial beam

profile measurement was done.


A) B)












Figure 5-5. A) A three dimensional spatial profile obtained by translating photodiode
with a 100 |tm pinhole through the Scanmate 1 dye laser beam. B) A two
dimensional view of the same profile demonstrating the fairly homogenous
profile.

A certified 100 |tm pinhole (Melles Griot) was inserted onto the face of a

photodiode and was secured to an x-z translational stage. The laser beam was sent

through the two irises for spatial filtering and then to the face of the photodiode with the

pinhole so that only a small portion of the beam was detected. The output from the

photodiode was detected with a boxcar average and the resulting averaged output was

measured with a Keithley 182 sensitive digital voltmeter. The result from translating the

photodiode through the spatially filtered laser beam can be seen in the three dimensional

plot in figure 5-5. The laser beam was measured to have an area, Aaser, of 0.0314 cm2

which is the area of the two irises and cathode bore. It can be seen then that the beam

quality after spatial filtering is satisfactory and can be considered fairly homogenous.











Therefore, no distortions of the saturation curve are to be expected as a result of spatial


heterogeneity.


Temporal profile

Determination of the dye laser temporal profile is of great importance for several


reasons. A time-resolved measurement of the laser pulse can determine the temporal


mode structure of the dye laser, the pulse duration necessary for the laser spectral


irradiance calculations, and help to verify if steady-state conditions apply.


The profile was obtained with an ET 2000 photodiode (Electro-Optics


Technology, Inc.) with a 200 ps rise time and was measured with a 500 MHz


oscilloscope (Tektronix TDS 520D). Neutral density filters were inserted into the path of


the beam to assure the profile remained the same regardless of intensity and that the


photodiode was not saturated. The photodiode was also placed at different positions of


the beam to verify that the temporal response did not vary within the beam. The temporal


profile of the dye laser output can be seen in figure 5-6. It was found that the dye laser


used for thallium had a pulse FWHM of 7.0 ns and lead was found to have a FWHM of

4.0 ns.


10-
09-
08-
07-
06-
5 05
04 At l 70ns
03-
02-
01-
00- '
30 25 20 15 10 5 0 5 10 15 20 25 30 35

Figure 5-6. A) Scanmate 1 dye laser temporal profile for the thallium 377.572 nm
transition. Recorded with a photodiode (rise time of 200 ps) and 500 MHz
oscilloscope.









It should be noted, however, that the idea of pulse duration may be confusing

when applying it to real situations. The value used for calculation of theoretical

saturation curves comes from time zero to the point where the fluorescence

measurements are recorded, in this case the peak of the fluorescence pulse. If a

theoretical square pulse is considered, then this would correspond to the pulse width.

However, in real optical systems, pulses take on more of a Gaussian profile at best.

Therefore, time zero is the instant the laser pulse begins and the pulse duration as

described in the theoretical section is the time at which the fluorescence signal is

measured. For the measurements thallium 377.572 nm transition, fluorescence values

were taken at a time of 10 ns and for the lead 405.7807 nm transition, fluorescence values

were taken at a time of 4 ns. Therefore, the correct pulse duration for theoretical

calculations is a value of 10 ns for thallium and 4 ns for lead.

Results and Discussion

Saturation Curve Measurement: Evaluation of the Quantum Efficiency

Having measured the optical parameters of the laser system and calibrated the

laser spectral irradiance and fluorescence radiance detectors, a saturation curve for the

thallium see-through hollow cathode lamp can be generated for the excitation with the

377.572 nm line and observing the direct line fluorescence at 535.046 nm. Similarly, the

lead galvatron can be generated for the excitation with the 405.7807 nm line and

observing the direct line fluorescence at 283.3 nm. Measurement of the saturation curve

was done by inserting neutral density filters into the path of the beam. The

photomultiplier tube linearity was checked periodically by inserting a 0.3 neutral density

filter. Considering that thallium fluorescence values were recorded at 10 ns and that the

effective lifetime of the 7 2S1/2 state has been measured to be 7.7 ns [60], it would not be









expected that steady state conditions apply. Similarly, the 7 3P10 lead state has a

calculated lifetime of 5.50 ns; therefore, a pulse duration of 4 ns would not be expected to

produce a steady state. Therefore, modeling the data obtained was done with a two-level

time dependent model as well as a three-level time dependent model in the presence of a

trap.

A collisional de-excitation rate constant between the 6 2P3/20 metastable state and

the 6 2P1/2 ground state of thallium has been found by Taylor et al. [60] to be on the

order of 105 s-. This value is quite reasonable for a low pressure discharge and is

expected to be on the same order of magnitude, or less, between the 6 2P1/2 and 7 2S1/2

state of thallium and is expected to be similar for the lead galvatron. This suggests that

all collisional rate constants can be considered negligible (kij 0). Initially, a time

dependent two-level model was used and the saturation curves can be seen in figure 5-7.

It should also be noted that the 100 ns theoretical curve in figure 5-7 also represents a

two-level steady state theoretical curve since this time is much longer than the response

time of the system (see equation 5-7a).

As mentioned previously, due to the presence of an intermediate level, a time

dependent two-level model does not accurately represent the thallium atomic system in

the linear region of the saturation curve. This has been demonstrated in figure 5-7 where

the 10 ns curve, which should give the most accurate results due to the experimental

parameters used, somewhat lacks agreement with the experimental data.












10



S10





Experimental Data
10 ------------- 1.0 ns
S,-10.0 ns
------ 100.0 ns

10,"
10' 102 103 10 105 10
Spectral Irradiance (J s-1 cm-2 nm ')

Figure 5-7. Experimentally measured saturation curve from a thallium galvatron with
10.0 mA applied. This data was modeled with time dependent two-level
saturation curves for laser pulse durations of 1, 10, and 100 ns. Y21 = 1 was
used for all three theoretical curves.

For a more accurate analysis of the data, a three-level time dependent saturation

curve in the presence of a trap needs to be considered. The thallium 6 2P3/20 metastable

state has a radiative lifetime of 250 ms [11], and a measured effective lifetime of a few

microseconds [60]. Since these lifetimes are much longer than the pulse duration, the

metastable state will act as a trap, or loss-less sink. It can be seen in figure 5-8 that the 10

ns theoretical curve shows excellent agreement with the experimentally measured

saturation curve. From the intersection of the linear and plateau asymptotes of the

experimentally measured saturation curve, a saturation parameter of 2.06 x 104 J s-1 cm-2

nm is obtained. This is in good agreement with the theoretical value of 1.84 x 104 J S-1

cm-2 nm 1. It should be mentioned that the saturation parameter calculated and

experimentally determined for time-dependent theory under non-steady state conditions

are "apparent" values due to distortion of the saturation curve. The theoretical value for a

two-level system under steady state conditions is calculated to be 9.75 x 103 J s-1 cm-2










nm-1, which is lower than the experimental value as expected. A table of saturation

parameter values obtained by previous authors is listed in table 5-2.





102


107






experimental data
-- 10- ---------1.0 ns
.. .. 10.0 ns
-------100.0 ns

10
10' 102 103 104 105 106
Spectral Irradiance (J s1 cm2 nm )


Figure 5-8. Experimentally measured saturation curve from a thallium galvatron with
10.0 mA applied. This data was modeled to a time dependent three-level
saturation curves in the presence of a trap for pulse durations of 1, 10, and 100
ns. For all three plots, the collisional de-excitation rate constants were
assumed to be zero.

The theoretical saturation curve in figure 5-8 was calculated with collisional rate

constants equal to zero. Since this curve shows excellent agreement with the

experimentally measured saturation curve, it can be concluded that the quantum

efficiency of this atomic system is limited only to the transition probabilities and that any

collisional rate constants are to be considered negligible (kij << Ai). This conclusion is

quit reasonable based on the fit of the model and is further supported by the collisional

rate constant value of 105 s-1 [60] reported by Taylor et al. [60], when compared to the

spontaneous transition probability of 6.08 x 107 s-1 for the 7 2S1/2 6 2P1/20 transition.










Table 5-2. Previously reported saturation parameter values for various elements under
various experimental conditions.
Source Element Transition EQs Method
(nm) (J s'1 cm-2 nm-1)

-done in a low pressure system (assumed
Bolshov et. al. k's -0) with a Nd:YAG pumped dye laser
[54]' Pb 283.3053 3.33 x 105 (doubled with KDP crystal)
Olivares and -done in an air-hydrogen flame with a N2
Hieftje [58] Tl 377.572 5.90 x 104 pumped dye laser
-same as previous (both used 377 nm
Olivares and excitation and observed the fl of each
Hieftje [58] Tl 535.046 6.33 x 104 wavelength)
-done in an air-acetylene flame w/ an
argon shield with a cw Ar+ pumped dye
Smith et al. [61]2 Na 589.5924 8.0 x 105 laser
Calcar and -done in an Hydrogen-oxygen-argon
Alkemade [60] Na 589.5924 2.3 x 104 flame with a flash lamp pumped dye laser
-done in a low pressure system with
Taylor et al. [32] Tl 377.572 2.06 x 104 Excimer pumped dye laser
Taylor [present -done in a low pressure system with
work] Pb 405.7807 8.91 x 103 Excimer pumped dye laser
1Measurements in this work were time-integrated rather than time-resolved which accounts for the high
value despite the low pressure system.

2The high value obtained in this work is due to the use of an air-acetylene flame which results in a high
quenching environment.

Similar measurements are also applied to the lead metastable state. In this case,

the 405.7807 nm transition is excited and direct line fluorescence is measured at

283.3053 nm. The reason this transition was chosen was due to the fact that sufficient

energy was not available to achieve saturation of the ground state transition of 283.3053

nm. This is due to the great loss in energy from the frequency doubling crystal used to

achieve the 283.3053 nm transition. Even though the metastable state is excited, rather

than the ground state, the same concept can be applied. In this particular case, the ground

state behaves as the trap, were collisional excitation from the ground state is considered

negligible, thus, atoms fluorescing into this state are taken out of circulation. Therefore,

the same theory that was applied to the thallium ground state can be appropriately applied

to the lead metastable state. An experimentally obtained saturation curve for the










405.7807 nm transition of a lead galvatron at an applied current of 10.0 mA can be seen

in figure 5-9. This curve is shown in figure 5-9 with a theoretical time dependent three

level saturation curve in the presence of a trap. This curve is calculated with appropriate

parameters, a pulse duration of 4 ns, and collisional rate constants equal to zero. The

saturation parameter measured by experiment was found to be 8.91 x 103 J s-1 cm-2 nm-1,

which is in good agreement with a theoretical value of 8.50 x 103 J s-1 cm-2 nm-'. From

the excellent fit of the theoretical curve to the experimental data, it can be concluded that

the quantum efficiency of the lead galvatron is limited only by spontaneous emission

rates, as was found from the thallium results.









101

10-1
C


o 10 -.
O Experimental Data
Theoretical Curve

10-
102 103 104 105 106
Spectral Irradiance (J s' cm2 nm')


Figure 5-9. Experimentally measured saturation curve from a lead galvatron with 10.0
mA applied. This data was modeled to a time dependent three-level saturation
curve in the presence of a trap for a pulse duration of 4 ns. All collisional de-
excitation rate constants were set to zero.










Number Density Measurement

Based on the measurement of the saturation curves obtained for thallium and lead,

the maximum laser spectral irradiance produces nearly complete saturation of the

selected transition. Therefore, operating in this region results in fluorescence values

equivalent to the maximum fluorescence achievable, BFmax, which are directly related to

the ground state number density. Converting this fluorescence signal into absolute units

allows calculation of the number density for each current applied. Smith et. al. [62]

preformed a similar measurement on a lead hollow cathode lamp and their results agree

well with the results found in the present work. A direct comparison can not be made due

to differences in the lamp design and cathode geometry, the cathode element, sputtering

efficiency, as well as the pressure of the filler gas; however, the relative relationship

between the current applied and number density agrees well with the results found here.


1013
16.0 mA

1012
~ 10o


10




10




100
S
a


-D S



10-2 10-1 10 101

Galvatron Current (mA)

Figure 5-10. Plot of the ground state number density as a function of current.









Based on the curve of growth calculation in appendix A, a number density of 8.90

x 1011 cm-3 is needed for 99.9 % absorption of a line source signal. From the results in

figure 5-10, an applied current of 16.0 mA produces a number density of 9.52 x 1011 cm

3, therefore, a current of 16.0 mA or higher provides an appropriate number density to

absorb nearly all signal photons incident on the detector. It was also observed that

number densities measured at applied currents higher than 16.0 mA began to deviate

from linearity. This is assumed to be due to post-filter effects, which is a result of the

metal vapor becoming optically thick. Therefore, fluorescent photons created from the

metal vapor will be reabsorbed by atoms between the emitting atom and the detector and

translates into a distortion of the true number density present. This observation is in

agreement with the curve of growth calculation, in which the bend in the calculated curve

is a result of the metal vapor moving from the optically thin region into the optically thick

region.

Applying this method for the measurement of the thallium metastable state can

also be accomplished. The same procedures and calculations are applied, the only

difference being the laser wavelength tuned to the 535.046 nm transition and the

spectrometer must be recalibrated for the direct line fluorescence at 377.572 nm. A

complete saturation curve does not necessarily need to be generated in order to evaluate if

complete saturation is achieved. If the peak fluorescence signal does not change after the

laser beam has been sufficiently attenuated, then saturation has been achieved and BFmax

can be measured for various currents. Since the thallium metastable state has been

measured previously by high resolution emission and high resolution absorption

measurement, it can be compared to values obtained with the saturated fluorescence










method. The results of this analysis combined with previous measurements can be seen

in figure 5-11.





1012

ol a

o 1010 .

109
j : o



107 a Laser-Induced Saturated Fluorescence
a Emission
106 Absorption
+ 10 .

10-1 100 101
Galvatron Current (mA)

Figure 5-11. Plot of the metastable state number density of thallium as a function of
current.

From the values obtained for the thallium metastable state, a maximum number

density of 2.29 x 1011 cm3 is found for an applied current of 30.0 mA. From a curve of

growth calculation, this number density is capable of absorbing only 95 % of the signal

radiation. In order to obtain a number density of 5.44 x 1011 cm3 pumping of this

metastable state would be needed in order to absorb 99.9 % of the signal radiation.

For a final analysis, the number density of the lead metastable state was also

measured by excitation of the 405.7807 nm transition and observing the direct line

fluorescence at 283.3053 nm. The same parameters were used as in table 5-1, with the

exception of the calibration factor, FA = 5.0723 [tW cm-2 nm-1 mV-1, which was measured

for 283.3053 nm. From measured values and using equation 5-15, number densities are










obtained for this metastable state and are shown in figure 5-12. These values are also in

agreement from conventional absorption and high resolution emission values.


1012





10
E :






10 Saturated Fluorescence
10 ,
e Conventional Absorption
17High Resolution Emission
10
101 100 101
Galvatron Current (mA)

Figure 5-12. Plot of the metastable state number density of lead as a function of current.
Saturated fluorescence values are compared to results obtained from
conventional absorption and high resolution emission measurements.

Conclusion

A thallium see-through hollow cathode discharge, or galvatron, has been

investigated as a potential atomic line filter. Number density values for the thallium

galvatron have been obtained at various applied currents by time-resolved laser-induced

saturated fluorescence and are reasonable compared to previous studies [62]. Results

obtained show that the galvatron is easily able to produce number densities capable of

99.9 % absorption of a line source when a current of 16.0 mA or higher is applied.

However, applied currents greater than 16.0 mA begin to demonstrate post-filter affects

as seen by the deviation from linearity in the measured number density values in figure 5-









10. This is a result of the metal vapor becoming optically thick which is reasonable

based on the curve-of-growth calculation (see appendix A).

The quantum efficiency of the system was also evaluated. A theoretical

saturation curve calculated for a three-level atom in the presence of a trap showed

excellent agreement with the experimental saturation curve. All theoretical curves were

calculated with all collisional de-excitation rate constants equal to zero (kij = 0) and,

therefore, only the spontaneous transition probabilities, Ai, need to be considered in

calculating the quantum efficiency of any allowed transition. This is a perfectly

reasonable conclusion since the galvatron is relatively low pressure system with virtually

no molecular species present.

In conclusion, it has been demonstrated that a galvatron is an attractive atomic

reservoir for applications as an atomic line filter. A desired number density can be

rapidly produced by applying the appropriate current and can be reproduced from one

experiment to the next. In addition, the quantum efficiency of this system is limited only

by the competing radiative pathways of the particular energy level arrangement which

allows it to be a very efficient detector. This system has the potential to be simple,

compact, and portable which makes it an ideal atomic line filter.









CHAPTER 6
LIFETIME MEASUREMENTS OF SEVERAL S, P, AND Dj STATES IN A
THALLIUM SEE-THROUGH HOLLOW CATHODE DISCHARGE

Introduction

Several elements have been studied for the use as atomic line filters, such as the

alkali metals [63,64], alkaline earths [65,66], and thallium [67]. As previously

recognized by Liu et al. [67], thallium is especially attractive since the 535.046 nm

metastable transition overlaps with the second harmonic output of a Nd:La2Be205 (BEL)

laser (1070 nm). This makes the 535.046 nm thallium metastable state transition ideal for

certain applications as an atomic line filter. Oehry et al. [68] have also reported use of

the thallium metastable state as an atomic line filter. In this report, a hollow cathode

lamp was used to pump the metastable state of a thallium atomic vapor in a heated sealed

cell. With appropriate cell dimensions and buffer gas pressure, the lifetime of the

metastable state could last for several ms. This allows the detection of a weak signal well

after the state has been initially pumped.

The idea proposed by Oehry et al. [68] is expanded upon with the use of a see-

through hollow cathode discharge, or galvatron (Hamamatsu), as an alternative atomic

reservoir. The advantage of a galvatron is that they may be used continuously over long

periods of time without need to remove any molecular impurities such as oxygen, a major

contributor to the quenching of the thallium metastable state [11,69]. This is a simple

system, capable of easily producing an acceptable and stable number density of both

ground state and metastable state number densities. If the signal were to be enhanced by

pumping the metastable state, the effective lifetime of this state would need to be

determined. The lifetimes of all states radiatively coupled to the 6 2P3/20 metastable state

are also determined.










N



S62D3/2 \ I 6 D5/2
7 i 7 P3/2t Ia
7--I/20- + 0 119 eV
ex = 276.787 nm 1 = 351.924 nm
s = 1301.32 nm = 1151.28nm

s2 probe = 535.046 nm in tesop a pb
7 S1/2 k I = 352.943 nm


k = 377.572 nm

6 2P3/2
S= 1.28 pm 6 Pi/20


Figure 6-1. Partial energy level diagram for thallium.

In this chapter, the lifetimes of the 7 2S1/2, 6 2D3/2, and 6 2D5/2 states are

determined by time-resolved single-step fluorescence shown by the partial energy level

diagram in figure 6-1. However, the 6 2P3/20 metastable state could not be analyzed by a

single-step fluorescence approach. The direct magnetic-dipole transition at 1.28 tim is

extremely weak and observing the resulting fluorescence would be very difficult. In

order to determine the lifetime of such a long lived state, a two-step fluorescence method

is used [69,70]. This two-step method involves the use of pump and probe laser pulses.

The pump laser pulse transfers ground state atoms into the state of interest directly or

indirectly by fluorescence or collisional processes. The temporally delayed probe pulse

interrogates the population of the pumped state by either observing the resulting

fluorescence or opto-galvanic signal. A plot of the resulting signal as a function of time

delay results in the decay waveform for the metastable state. From the lifetime values

obtained, collisional deexcitation rate constants for each current applied are also derived.









Experimental


Lasers and Optics

The experimental setup used for this work was the same for both the single step

and two-step fluorescence measurements (figure 6-2). For single step excitation of the 6

2D3/2 and 6 2D5/2 states, a XeCl excimer (Lambda Physiks LPX 200) pumped dye laser

(Lambda Physiks Scanmate 1) was used. Coumarin 540A (Exciton) dissolved in

methanol was used at a concentration of 8 x 10-3 M. The dye laser output was sent to a

second harmonic generation unit (Lambda Physiks) for frequency doubling to obtain the

276.787 nm ground state thallium transition. To obtain the 535.046 nm transition, a

nitrogen (Laser Science Inc. model VSL-337ND) pumped dye laser (Photochemical

Research Associates Inc. model LN102) was used. The dye for this transition was the

same as that for the generation of the fundamental of the 276.787 nm transition. Mirrors

1-4 are UV enhanced aluminum coated and are used in order to obtain the appropriate

beam height and orientation. A pierced mirror directed the collected fluorescence

towards the monochromator and allows both the 276.787 nm and 535.046 nm laser

beams to pass. Fused silica lenses collected the fluorescence and imaged it onto the slit

of the monochromator. In order to filter stray laser scatter, a glass slide was placed in

front of the entrance slit of the monochromator when the 276.787 nm laser was used and

a color glass filter when the 535.046 nm laser was used.













Excimer Fast Scope
Laser

PM
Iye i i Nitrogen Laser
Dye


Frequency IF Dye Laser
doubling unit Lens
Ln ----Glan
kex = 276.787 nm PD-3 Glass
Thallium 7 robe = 535.046 rm
Mirror-1 probe = 535.046 nm

.Mirror-4

Pierced Mirror r
SMirror-2 Mirror-3
PD-1 i __ PD-2
Scope


Figure 6-2. Experimental setup used for both single-step and two-step laser excited
fluorescence measurements. IF is an interference filter used to remove laser
scatter. Mirrors 1-4 are used for laser beam height and orientation alignment.
PD-1 and PD-2 are photodiodes used to monitor the time delay between the
two pulses for two step fluorescence measurements. PD-3 is a photodiode
used to trigger the signal acquisition.

For the two-step fluorescence measurements, the two laser systems had to operate

in temporal synchrony. This was done by adopting a method used by Omenetto et al.

[69]. In this scheme, pulse generator-1 (Wavetek model 802) is used to trigger the

excimer laser while the synchronous output is used to trigger a boxcar (Stanford Research

Systems model SR250). The temporally adjustable gate output of the boxcar is used to

trigger pulse generator-2 (Systron Donner model 101). The output of pulse generator-2

triggers the nitrogen laser system, which is used to generate the 535.046 nm laser beam.









The boxcar in this arrangement acts as a convenient delay generator. The jitter between

the two laser pulses was approximately 10 ns, acceptable for the present measurement.

Detection

The monochromator used was a McPherson model 218 with crossed Czerny-

Turner geometry, a grating of 1200 grooves mm-1, blazed at 300 nm, reciprocal linear

dispersion of 2.6 nm mm-1, ruled grating area of 50 x 50 mm, focal length of 300 mm,

and an f-number of 5.3. The entrance and exit slits were set at 200 utm giving a

geometric spectral bandpass of 0.52 nm. This was more than sufficient to resolve the

351.924 nm fluorescence from the 352.943 nm fluorescence. Detection was

accomplished with a high speed photomultiplier tube (Hamamatsu R3091) having a rise

time of 400 ps, a spectral response 300 to 850 nm, and -2500 V applied. The resulting

fluorescence waveform was observed on a 500 MHz oscilloscope (Tektronix TDS 520D).

Results and Discussion

6 D3/2 and 6 D5/2 Lifetime Measurements

Lifetime measurements on the 6 2D3/2 and 6 2D5/2 thallium states were done by

single-step laser-induced fluorescence. The population of the 6 2D3/2 state was pumped

by the 276.787 nm ground state transition. The 6 2D3/2 state was measured by tuning the

monochromator to the 352.943 nm transition and observing the resulting direct line

fluorescence waveform. Calculated values were also obtained from equation 1,


= 1 (1)
2Ajk

where Ajk (S-1) are the transition probabilities for all radiative de-excitation pathways of

the state of interest. Values for all transition probabilities covered in this work were










obtained from the National Institute of Standards and Technology website

(http://physics.nist.gov/PhysRefData/ASD/linesform.html) and are shown in table 6-1.

Table 6-1. Transition probabilities obtained from the National Institute of Standards and
Technology
Transition Transition Probability, Aik (S1)
7 2S1/2 6 2P1/20 6.25 x 107 s-1
7 2S1/2 6 2P3/20 7.05 x 107 s1
6 2D3/2 6 2P3/20 2.20 x 107 s1
6 2D3/2 -6 2P1/20 1.26 x 10 sl8
6 2D5/2 6 2P3/20 1.24 x 10s s-



The resulting waveform for the 6 2D3/2 state can be seen in figure 6-3. The experimental

data was fitted with a nonlinear least squares fit in order to obtain the lifetime for the

fluorescence waveform. From figure 6-3, a value of 6.4 + 0.1 ns was found and agrees

fairly well with the calculated value, as well as values obtained from previous works

shown in table 6-2. The lifetime for this state was independent of the applied current, as

expected, since this is a low pressure inert gas system where quenching effects are

expected to be negligible.


Experimental Data (14.0 mA)
0.022- Non-linear least squares fit
0.020 x -w
0.020- y co + cle
0.018- -=6.4 0.1 ns
0.016-
0.014-
0.012-
S0.010-
S0.008-
0.006-
0.004-
0.002
0 2 4 6 8 10 12 14 16 18 20 22
Time (ns)

Figure 6-3. Measured fluorescence curve for the thallium 6 2D3/2 state.











Table 6-2. Comparison of previously reported values on the spontaneous lifetime of the 6
2D3/2 state
Source Reported value
Gough and Series [71] 5.2 0.8 ns
Gallagher and Lurio [72] 6.2 1 ns
Anderson and Sorensen [73] 6.8 0.5 ns
Cunningham and Link [74] 6.9 0.4 ns
Shimon and Erdevdi [75] 6.9 0.5 ns
Lindgird et al. [76] 6.1 0.7 ns
Biemont etal. [77] 8.5 0.5 ns
Calculated 6.76 ns
Present work 6.4 0.1 ns


The same approach was applied to the measurement of the 6 2D5/2 state, the only

difference being that the monochromator was tuned to the 351.924 nm transition. This is

not a direct excitation, however, and involves the transfer of atoms through collisional

coupling into this higher lying energy level. Figure 6-4 clearly shows that the resulting

signal was much weaker, with a greatly reduced signal-to-noise ratio. Omenetto and

Matveev [78] observed comparable fluorescence waveforms using a similar energy level

scheme for gold with comparable signal-to-noise ratio. Despite the poor signal-to-noise

ratio obtained with the present results, a lifetime of 7.5 + 1.1 ns is obtained for the 6 2D5/2

state. Despite an uncertainty of 14.7 %, the value obtained agrees fairly well with the

calculated value, as well as values obtained from previous authors shown in table 6-3. As

in the case of the 2D3/2 state, the 6 2D5/2 state showed no dependence on the applied

current. For a more precise lifetime measurement of the 6 2D5/2 state, a more direct

excitation transition should be used.











Experimental Data (Current = 14.0 mA
0.0018- Non-linear least squares fit
0.0016- y = + cle
0.0014- T 7.5 .lns
..\
0.0012- *
S0.0010- 0
I 0.0008
0.0006-
0.0004- .. '-
0.0002-
0.0000
0 2 4 6 8 10 12 14 16
Time (ns)



Figure 6-4. Measured fluorescence curve for the thallium 6 2D5/2 state.

Table 6-3. Comparison of previously reported values on the spontaneous lifetime of the 6
2D5/2 state
Source Reported value
Shimon and Erdevdi [75] 7.2 0.6 ns
Lindgird et al. [76] 6.5 0.7 ns
Gough and Griffiths [79] 6.8 0.4 ns
Anderson and Sorensen [73] 7.6 0.5 ns
Calculated 8.06 ns
Present Work 7.5 1.1 ns


7 S1/2 Lifetime Measurement

The lifetime of the 7 2S1/2 state was also measured by single-step laser-induced

fluorescence. The 535.046 nm output of the nitrogen pumped dye laser was used to

populate the 7 2S1/2 state. The fluorescence was collected by tuning the monochromator

to the 377.572 nm transition. As can be seen in figure 6-5, an experimental lifetime for

this state, 7.7 0.2 ns, is in good agreement with the calculated value of 7.52 ns, as well

as previously reported values shown in table 6-4. As with the 2Dj states, since the

lifetime of this transition is only 7.7 ns, the excited atoms do not have sufficient time to









interact with their environment; therefore, no current dependence was observed. This

suggest that the collisional rate constants, kij, for the S and 2Dj states are much less than

that of the spontaneous transition probabilities, yielding a high quantum efficiency and

low quenching environment.


Experimental Data (Current = 18.0 mA)
0.025- Non-linear least squares fit

y = co + ce-t
0.020
7.7 + 0.2 ns


0.015


0.010- %


0.005 *


0.000
0 5 10 15 20 25 30 35
Time (ns)

Figure 6-5. Measured fluorescence curve for the thallium 7 2S1/2 state.

Table 6-4. Comparison of previously reported values on the spontaneous lifetime of the 7
2S1/2 state
Source Reported value
Demtroder [80] 8.7 0.3 ns
Gallagher and Lurio [72] 7.6 0.2 and 7.4 + 0.3 ns
Penkin and Shabanova [81] 8.25 0.6 ns
Lawrence et al. [82] 8.1 0.8 ns
Norton and Gallagher [83] 7.45 0.2 ns
Cunningham and Link [74] 7.65 0.2
Anderson and Sorensen [73] 7.7 0.5 ns
Shimon and Erdevdi [75] 7.4 0.5 ns
Harvey et al. [84] 7.8 0.3 ns
Lindgird et al. [76] 6.9 1.0 and 6.3 + 0.7 ns









Table 6-4. Continued
Hsieh and Baird [85] 7.55 0.08 ns
Rebolledo etal. [86] 7.61 0.16 ns
Biemont et al. [77] 7.3 0.4 ns
Calculated 7.52 ns
Present work 7.7 0.2 ns

6 2P3/2" Lifetime Measurement

The thallium 6 2P3/20 state is a metastable state 0.996 eV above the ground state.

Since the 6 2P3/20 6 2P1/20 transition is forbidden, it will be very weak and long lived,

having a reported spontaneous lifetime of 250 ms [11]. Since this is a weak transition

observation of the 1.28 |tm fluorescence from the 6 2P3/20 6 2P1/20 transition would be

difficult. A diode laser at 535.046 nm could be used to monitor the lifetime of the

metastable state by relating the observed absorption to the population of the metastable

state as a function of time; however, such a diode laser was not available. For this

reason, a two-step laser-induced fluorescence measurement was used to determine the

effective lifetime of the 6 2P3/20 metastable state. This was done by pumping the

metastable state with a 276.787 nm laser pulse. Pumping of the metastable state could

also have been accomplished using a 377.572 nm laser pulse, but since a 276.787 nm

laser was already available from the previous measurements, it was used as the excitation

source. To avoid losses due to photo-ionization from the pump laser beam, the pulse

energy was held to approximately 1 p.J per pulse. In a low pressure system, this pulse

energy approaches the saturation spectral irradiance for this transition; therefore,

maximum population enhancement is nearly achieved. The direct line fluorescence into

the 6 2P3/20 metastable state allowed indirect pumping of this state, and since the lifetime

of the 6 2D3/2 state was found to be only 6.4 + 0.1 ns, there should be no distortion of the









measured lifetime. The 276.787 nm laser pulse is followed by the 535.046 nm laser

pulsed, which is temporally controlled by the boxcar. The 535.046 nm laser pulse probes

the population of this metastable state and the resulting fluorescence is observed at

377.572 nm. The intensity of the resulting fluorescence is directly related to the

population of the probed state; therefore, measuring the fluorescence intensities at

different time delays with respect to the pump pulse allowed the determination of the

effective lifetime of the 6 2P3/20 state.


Experimental Data
1* 6.0 mA
A 8.0 mA
S10.0 mA
12.0mA
< 14.0 mA

-e
N


0.1 -.








0.01
0 2 4 6 8 10 12 14 16
Time Delay (ps)

Figure 6-6. Measured lifetime curves for the thallium 6 2P3/20 metastable state.

The resulting lifetime curves were fitted with a nonlinear least squares method to

obtain the lifetimes of the metastable state for the different currents applied. The values

of the experimental and fitted curves were normalized shown in figure 6-6. Values from

0 to 100 ns time delays could not be taken due to the collisional transfer of atoms into the

7 2P1/20 and the 7 2P3/20 states, which also result in 377.572 nm fluorescence as shown in











figure 6-7. The long rise time and decay is due to the spontaneous lifetimes [87] of 61.9


1.7 ns and 48.4 1.3 ns for the 7 2P120 and 7 2P3/20 states, respectively. Since the atoms


must decay through many states, their final observed fluorescence waveform becomes


stretched, thus resulting in the observed fluorescence waveform. Therefore, in order to


avoid distortion to the measured lifetime curves for the metastable level, values prior to


100 ns time delay were not recorded. This is acceptable for the present two-step


fluorescence approach since the measured lifetimes are on the order of a few |ts. If a


highly quenching atomic reservoir were to be used, such as an air-acetylene flame, where


the effective lifetime of the 6 2P3/20 state has been reported to be only 81 ns [69], this


fluorescence approach could not be used.


10-
09 Current= 140mA
08-
07-
06-
05-
04
03-
02-
01-
00-
-20 0 20 40 60 80 100 120 140 160
Time (ns)

Figure 6-7. Measured fluorescence waveform at 377.572 nm due to 276.787 nm
excitation.

To explain the observed lifetimes for this metastable state, the different


deexcitation factors need to be considered. As described by Magerl et al. [11], effective


lifetimes are dependent on four factors, the natural lifetime, natural, the lifetime due to


collisions with the buffer gas, r .. the lifetime due to collisions with ground state


thallium atoms, ., and the lifetime due to collisions with the walls of the container, Twall,


as shown in equation 6-1.









1 1 1 1 1
+ +- + (6-1)
The contribution fue to6tZtka uralZ'fffPontapjas, lieitme is the result of an

isolated atom, unperturbed by its environment, naturally decaying. In the present system,

the natural lifetime of the 6 2P3/20 metastable state has been reported to be 0.250 ms [11].

The expected lifetime of the thallium metastable state due to collisions with the

buffer gas, r .. can be calculated by the following equation [11],

1
7 = (6-2)
'TI-Ne nNe Urelative

where o-r-Ne (3 x 10-24 cm2) is the collision cross section [88] between metastable state

thallium atoms and neon atoms, and n (4.51 x 1017 cm-3) is the number density of neon

atoms at a pressure of 14 torr. The parameter Vrelative is the relative velocity between the

thallium metastable state and the neon buffer gas and is calculated [70] by equation 6-3,

8"-k T
Relative (- T 6-3)


where kb (1.38 x 10-20 mJ K-') is the Boltzmann constant, T(495 K) is the Doppler

temperature [40] of the system at an applied current of 10.0 mA, and p is the reduced

mass of the system,

m *nm2 (6-4)
mi + m2

where mi and m2 are the masses of neon (3.531 x 10-23 g) and thallium (3.394 x 10-22 g),

respectively, and is calculated to be 3.198 x 10-23 g. When these values are substituted

into equation 6-2, a calculated lifetime value of 10.02 s is obtained for the 6 2P3/20 state

due to collisions with the neon buffer gas. This long calculated lifetime is due to the









extremely small collisional cross section between the thallium metastable state and neon

atoms.

The expected lifetime of the thallium metastable state due to collisions with

ground state thallium atoms, T ., is calculated [11] in a similar fashion to that in equation

6-2, and is shown in equation 6-5,

1
self (6-5)
'TI-Tl T' iT Urelative

where crn-rI (5 x 10-16 cm2) is the collisional cross section [11] between the metastable

state thallium atoms and ground state thallium atoms. The parameter nrU (3.4 x 1011 cm-3)

is the number density [32] of ground state thallium atoms and Vrelative (3.20 x 104 cm S-1) is

the relative velocity between the two thallium atoms calculated from equation 6-3 for an

applied current of 10.0 mA. If these values are substituted into equation 6-5, a value of

0.180 s is obtained for the quenching lifetime of the thallium metastable state due to

collisions with ground state thallium atoms. Despite the higher collisional cross section,

the lifetime is relatively long due to the small ground state number density for an applied

current of 10.0 mA.

It is generally accepted that the presence of oxygen, 02, is the main contributor

for the quenching of the thallium metastable state in oxygen rich environments such as a

flame [11,69] due to its high quenching cross section [89] of 2.8 x 1015 cm2. If this were

the case here, the resulting lifetime at a current of 10.0 mA would correspond to an

oxygen partial pressure of approximately 10-2 torr. It is known, however, that the

concentration of oxygen in the present atomic reservoir does not exceed 1 ppm (6 x 10-4

torr) [30]. In the present work, the lifetime measurements were carried out in a low









pressure, very pure neon buffer gas with negligible molecular species present so the

quenching contribution due to oxygen, nitrogen, hydrocarbons, water, or any other

molecular species is expected to be negligible. This would also negate any losses due to

chemical reactions.

The lifetime due to collisions with the walls of the cell [11] is given by equation

6-6a and 6-6b,

1
Twall Do p (6-6a)
geometry
Pbuffer

2.geomet r 05 f (6-6b)


where Fgeometry is the geometry factor of the first diffusion mode, r is the radius (0.1 cm)

and I is the length (2 cm) of the cylinder, Do is the diffusion constant (0.7 cm2 s-1) [11] of

thallium metastables in neon at a reference gas pressurepo (75 torr) [11], andp .. is the

pressure of the neon buffer gas (14 torr) [57] in the discharge. From these values, an

effective lifetime value of 4.59 x 10-4 s is calculated. Therefore, based on equation 6-1,

the lifetime for this system is expected to be dominated by deexcitation with the walls of

the cathode. However, the calculated value does not agree with the lifetime values

experimentally observed.

Since the present study was done in a low pressure steady state glow discharge

rather than in the afterglow of a pulsed discharge or a static sealed cell, certain

considerations need to be made. Magerl et al. [11] explain that by increasing the buffer

gas pressure, the lifetime of the metastable state also increases. This is due to collisions

with the buffer gas reducing the mean free path of the thallium metastable and therefore,

diffusion of thallium atoms to the walls of the container is reduced. However, in the









present atomic reservoir, thallium atoms are generated at the walls of the cathode and

diffusion into the negative glow region is reduced with increasing buffer gas pressure due

to a shorter mean free path. Bruhn and Harrison [90] reported that as high as 90 % of the

metal atoms that are sputtered redeposit back on the cathode surface through back-

diffusion. Taking this into account, most of the sputtered thallium atoms would reside

between the cathode surface and the mean free path of the sputtered atom. It is also

known that the Doppler temperature of the sputtered atoms is higher close to the surface

of the cathode and decreases as the distance is increased [91,92]. High resolution

emission measurements [40] have found a Doppler temperature of 495 15 K for an

applied current of 10.0 mA; however, this is predominately a Doppler temperature

measurement of the negative glow region where most of the emission occurs. If a

Doppler temperature of 1000 K were used with a pressure of 14 torr of neon for this

region, a mean free path of 82.6 |tm is calculated. If this mean free path is used as the

radius in equation 6-6b, then a calculated lifetime, due to collisions with the cathode

surface, of 3.2 |ts is obtained, in good agreement with the experimental value of 3.1 + 0.3

|ts for an applied current of 10.0 mA. For a more accurate calculation, the Doppler

temperature of this region would need to be determined for various applied currents.

Since the lifetimes were measured in a D.C. discharge, other factors need to be

considered as well, such as the presence of ions and electrons. It has been observed by

Turk and Omenetto [55] that increasing the concentration of electrons in an air acetylene

flame, by the addition of cesium, affected the slow decay rate of ion-electron

recombination of strontium atoms with lifetimes on the order of a few microseconds. It

was also observed by Axner et al. [70] that the addition of cesium resulted in a slightly









































Sourc

Omenett
Axner et
Magerl e
Aleksand
Pickett a
Lurio an
Lurio an
Present


shorter effective lifetime of a lead metastable state in an air acetylene flame. Taking into

account these observations along with the results found in the present study would

suggest a lifetime contribution due to electron-thallium collisions. It is also known that

the highest concentration of electrons in a glow discharge is found in the region between

the cathode dark space and negative glow region, due to electron multiplication from fast

high energy electrons and the production of slow thermal electrons. The contribution of

electrons along with wall quenching collisions would explain the observed lifetime

dependence on the applied current; however, further analysis would be needed before any

direct conclusions can be made. Such studies would include determination of quenching

cross sections, number densities, and relative velocities. A comparison of the effective

lifetime values obtained in the present study to those obtained from previous work is

shown in table 6-5.

Table 6-5. Comparison of previously reported values on the effective lifetime of the 6
2P3/20 metastable state

e Reported Value Atomic Reservoir
o et al. [69] 81 ns Air-Acetylene flame (-2500 K, -760 torr)
al. [70] 2 ps Graphite furnace (in pure N2 buffer gas, -2500 K, -760 ton
't al. [11] 48 ms Sealed cell (5 cm long and 3 cm diameter, 723 K, 75 torr A
drov et al.[88] 20 ms Sealed cell (18 cm long and 5.8 cm diameter, 668 K, 10 tor
nd Anderson [93] 12.7 ps Sealed cell (15 cm long and 5 cm diameter, 1089 K, no buf
d Gallagher [94] 30 ps Sealed cell (In vacuum)
d Gallagher [94] 1 ms Sealed cell (low pressure Ar)
York 4.8 0.6 ps Galvatron (6.0 mA, 467 K, 14 torr Ne)
3.8 0.4 ps Galvatron (8.0 mA, 481 K, 14 torr Ne)
3.1 0.3 ps Galvatron (10.0 mA, 495 K, 14 torr Ne)
2.8 0.1 ps Galvatron (12.0 mA, 509 K, 14 torr Ne)
2.1 0.2 sts Galvatron (14.0 mA, 523 K, 14 torr Ne)


r)
r)
rNe)
fer gas)











Collisional Deexcitation Rate Constant

Since the lifetime of the metastable state has been measured, the collisional


deexcitation rate constant between this level and the ground state can also be calculated


by the following relationship,


1 (6-7)
A21 + k21

where A21 is the spontaneous emission transition probability (s1) and k21 is the collisional


deexcitation rate constant (s-1). If k21 is assumed to be much greater than A21 (k21 >> A21),


then equation 6-7 reduces to,


1
k21 (6-8)


which is a safe assumption since A21 is calculated to be 4 s-1 due to a spontaneous lifetime


of 250 ms. Results from these calculations can be seen in figure 6-8. The lifetime and


collisional deexcitation rate constant both show a linear relationship with current, further


suggesting a contribution of electron-thallium collisions to the observed effective lifetime


of the thallium metastable state.


Lifetime
5 0- Collision Deexcitation Constant
S 50x1 05
45-
S45x105
40-
40x05 O0
35- .
S3 5x10 0
30- 330x105

25- 25x105

20- 20x10
5 6 7 8 9 10 11 12 13 14 15
Galvatron Current (mA)



Figure 6-8. Plot of the lifetimes, T, and calculated deexcitation rate constant, k21, at
various currents for the thallium 6 2P3/20 metastable state.









Conclusion

The lifetimes of several S, P, and D states of a thallium see-through hollow

cathode discharge have been determined by time-resolved single-step and two-step laser

excited fluorescence. The lifetime values obtained for the S and D states agree well with

calculated values, as well as values obtained from previous work. It can therefore be

concluded that these are high quantum efficiency transitions and collisional de-excitation

is considered negligible for these transitions.

The lifetime of the 6 2P3/20 metastable state was found to be in the low

microsecond region and is expected to be due to collisions with wall of the cathode. In

order to more accurately explain the results obtained, temperature measurements in the

dark cathode region of the discharge are needed. In addition, before any direct

conclusion is made, diagnostic measurements are needed in order to better understand the

contribution that electrons have on the lifetime of the thallium metastable.

In conclusion, the use of this atomic reservoir as an atomic line filter for the

detection of input radiation at 535.046 nm from sources such as the second harmonic of a

Nd:BEL laser would not be as efficient as a sealed cell due to the relatively low effective

lifetime of the metastable state. This reservoir does have the advantage in that it is a D.C.

discharge and so the metastable state will be thermally populated without the need for an

external pumping source. If pumping is desired for signal enhancement, it would be best

if the metastable state were continuously pumped by use of a cw diode laser. Future

studies should also involve effective lifetime measurements with the galvatron operating

in pulsed mode. Working in pulsed mode would effectively populate the metastable

state, remove any resonant background radiation generated by the galvatron, and increase

the signal-to-background ratio. The use of this atomic line filter in combination with a









frequency doubled Nd:BEL laser could prove to be a superior detection system for

applications involving a high optical background.









CHAPTER 7
FINAL CONCLUSIONS AND FUTURE WORK

Concluding Remarks

Several parameters of a see-through hollow cathode discharge, or galvatron, were

measured in order to evaluate its potential as an atomic line filter. Among these

parameters was the resolving power that such an atomic reservoir would yield for various

applied currents. Resolving power measurements were accomplished by obtaining high

resolution emission profiles for thallium and lead at various applied currents. The profiles

obtained were analyzed with a two-layer model from which Doppler temperatures were

determined. Based on these results, resolving powers were found to be similar to sealed

cells and hollow cathode lamps, and superior to flames, ICP, and conventional

spectrometers. Number densities were also determined for both thallium and lead from

the optical depths acquired from the two-layer model, and values are in fair agreement

with measurements from other methods.

Hyperfine Structure Considerations

To achieve a high resolving power in an atomic line filter, a narrow absorption

profile must be obtained. However, one must also consider the width of the hyperfine

structure. If the thallium and lead systems are considered, both of which have a mildly

broad hyperfine structure, then the width of the hyperfine structure must be taken into

account when considering the resolving power of the entire atomic system. These atomic

systems have relatively wide hyperfine structure, which results in a lower effective

resolving power. This problem may be alleviated by use of a mono-isotopic cathode of

the element. If lead is considered, then a cathode compose purely of 208Pb would result in

a single line, with no hyperfine splitting of the state. A single absorption line dominated









purely by Doppler broadening will result in resolving powers reported in this work. As

for thallium, the two naturally occurring isotopes both have hyperfine components and

can not be narrowed by a mono-isotopic cathode. However, thallium was specifically

chosen for its 535.046 nm metastable transition which conveniently overlaps with the

second harmonic of a Nd:BEL laser. The spectral output of this laser may be as broad as

30 pm, assuming the laser is not operated in single mode. In this particular case, the

signal is much broader than the absorption profile of the atomic reservoir; therefore,

much of the signal will be transmitted without detection. Therefore, it would be

beneficial if the absorption profile of the atomic vapor were broader, with a broad

hyperfine structure, in order to absorb as much of the signal as possible. This could

enhance the sensitivity and possibly increase the signal-to-noise ratio of the filter and still

retain a high background rejection.

Absorption Measurements

High resolution absorption measurements were made on the thallium discharge by

combining a self-reversed profile from a thallium electrodeless discharge lamp and a self-

absorbed profile from a thallium hollow cathode lamp. The combination of these two

line sources produces a quasi-continuum source over the absorption of the atomic vapor.

This quasi-continuum source, after passed through the atomic vapor, can be reconstructed

using a scanning Fabry-Perot interferometer, with the resulting emission profile

containing the absorption profile of the atomic vapor. Unfortunately, due to the

complicated hyperfine structure of thallium, and the resolution of the interferometer, a

poorly defined baseline was obtained for all currents measured. The poor baseline makes

it difficult to assign the 100 % transmission value, therefore, inaccurate Doppler widths

and inaccurate peak absorption coefficients would be obtained. This would result in









slightly inaccurate number densities; however, the results obtained are in fair agreement

with number densities obtained from high resolution emission profile analysis. For

improvement of the baseline, a broader quasi-continuum would be needed in order to

improve the baseline, however, the profile used already fills the free spectral range and an

increase would result in the emission profile spilling into adjacent orders and would

result in distortion of the measured absorption profiles despite the gain in baseline

improvement. The free spectral range could be increased in order to compensate for this

profile broadening; unfortunately, this also decreases the resolution of the interferometer

and results in an unacceptable instrumental FWHM. Despite these difficulties, it has

been shown that high resolution absorption profiles can be obtained by use of a scanning

Fabry-Perot interferometer and can be used as an alternative to diode lasers if such a laser

at the transition of interest does not exist. The mirrors of the interferometer can cover a

larger spectral range than a diode laser, and therefore, can be applied to several

transitions of various elements. The enhanced spectral scanning ability allows one to

measure absorption profiles that may be too broad for the scanning capabilities of a

narrow band diode laser.

Conventional absorption measurements were also done on the thallium and lead

galvatrons by use of a hollow cathode lamp with a fixed low current. Results obtained

for thallium were not in agreement with results from saturated fluorescence

measurements. This discrepancy was attributed to the relative width of the emission

profile from the hollow cathode lamp to the absorption profile of the thallium galvatron.

As for the lead metastable state, good agreement was found from conventional absorption

measurements compared to results obtained from saturated fluorescence and high









resolution emission measurements. This agreement was due to the relative widths of the

emission from a hollow cathode lamp and the absorption profile of the galvatron. It has

been shown that a hollow cathode lamp can be used for accurate absorption

measurements in a low pressure glow discharge; however, the relative widths of the

absorption profile of the discharge and the emission profile of the hollow cathode lamp

need to be known in order for accurate measurements to be made.

Saturated Fluorescence Measurements

Analysis of the quantum efficiency and number density of the atomic system was

evaluated by use of time-resolved laser-induced saturated fluorescence spectroscopy.

Saturation curves were obtained for thallium and lead by measuring the peak of the

fluorescence waveform at various attenuated laser spectral irradiances. These saturation

curves were fitted with a time dependent three-level theoretical curve in the presence of a

trap, or loss less sink. From known parameters and setting collisional rate constants to

zero, an excellent fit was obtained for both thallium and lead. This translates into

quantum efficiencies that were limited only by spontaneous emission rates. This is

advantageous over high quenching reservoirs such as flames, ICP plasma, or sealed cells,

depending on buffer gas and pressure.

Number density values were also obtained and are compared to values obtained

from other spectroscopic methods. It was found that the thallium and lead galvatrons

produce an acceptable number density based on curve-of-growth calculations; however,

pumping of the thallium and lead metastable states may be needed in order to enhance the

population of these levels and therefore, enhance the fraction of signal radiation that is

absorbed by the atomic vapor. The present discharge has an advantage over other atomic









reservoirs, since the atomic vapor is easily produced, and reproduced, by simply applying

a stable current and can be sustained for extended periods of time.

Lifetime Measurements

The lifetimes of several S, P, and D states were measured by single step and two

step laser excited fluorescence. The single step measurements of the S and D states were

found to be in good agreement with values obtained from previous works as well as

calculated values. Since the thallium metastable state is a very weak and long lived, with

a spontaneous lifetime of 250 ms, a pump and probe method was used for this

measurement. Lifetimes on the order of a few microseconds was found for the discharge

when operated at various currents in D.C. mode. If the thallium metastable state were

pumped, a window of a few microseconds exists before the state needs to be re-pumped.

The metastable state could be directly pumped by a cw diode laser at 1.28 |tm in order to

achieve an increased number density for signal enhancement. The lifetimes reported here

are superior compared to high quenching environments such as flames, where a lifetime

of 81 ns has been reported; however, sealed cells do offer an advantage in this case,

where lifetimes of several milliseconds can be obtained with the appropriate cell

dimensions and buffer gas pressure. In the sealed cell reservoir, however, the population

of the metastable state is extremely low, and therefore, pumping of this metastable state is

required for this reservoir. For hollow cathode discharges, the metastables state is

already thermally populated due to collisions with thermal electrons, ions, metastables,

and buffer gas atoms. Therefore, this metastable state will only need mild pumping from

the ground state.









Collisional rate constants are obtained from the lifetimes of the thallium

metastable state. These values were found to be on the order of 105 s. These values

are several orders of magnitude less than spontaneous transition rates, 107 s1, making

collisional quenching negligible for this atomic system at various currents. These results

are further supported by the results obtained from analysis of the saturation curves

obtained for both thallium and lead, which concluded that the collisional rate constants

are considered negligible.

A see-through hollow cathode discharge has been extensively studied by several

spectroscopic methods as a potential atomic reservoir for use as an atomic line filter.

Each method used provided valuable data on the characterization of this discharge and

was evaluated in terms of its application as an atomic line filter. It has been found that

this reservoir is a high quantum efficiency system and is capable of producing an

acceptable number density for use as an atomic line filter. Resolving powers have been

found to be superior to flames, plasmas, and conventional spectrometers, and are

comparable to sealed cells. The see-through hollow cathode is a simple, compact, and

portable system which can be applied to a number of applications.

Future Work

Signal-to-Noise Ratio Considerations

Future work on the characterization of a see through hollow cathode discharge

would involve analysis of the signal to noise ratio of the discharge as an atomic line

filter. Many of the parameters evaluated in this work were in an attempt to find optimal

operating currents for this reservoir. As previously discussed, there are trade-offs that

must be considered in choosing an optimal operating current, such as number density and

resolving power. The signal-to-noise ratio must also be considered. For example, it has









been reported by Pertucci [95] that the optimal signal-to-noise ratio was found to be at

low currents applied to a hollow cathode lamp when opto-galvanic detection was

employed. If opto-galvanic detection is used, then an optimal resolving power would

also be found at these lower currents; however, the trade-off is a drastic reduction in

number density of the atomic vapor. As it is known from curve-of-growth theory, a low

number density would result in a large portion of the signal radiation to pass through the

atomic vapor, resulting in a loss of the signal. This could reduce the sensitivity of the

filter and limit its applications. Therefore, optimal signal-to-noise ratios for detection by

fluorescence, ionization, and opto-galvanic detection would need to be determined in

order to evaluate its effectiveness in certain applications.

Atomic Reservoir Element

In the present study, thallium and lead were chosen as the two elements for the

atomic vapor. The reasons these two elements were chosen is due to their three energy

level system, the relatively strong oscillator strengths at these transitions, the overlap of

an atomic transition with the output of an efficient solid state laser (thallium), and for the

mass of the two elements. The mass is a factor since the absorption profiles are Doppler

broadened, therefore, heavier elements will have a slower relative velocity compared to

lighter elements in a similar thermal environment. The result is a narrower absorption

profile and higher resolving power. In addition, it has already been mentioned that the

hyperfine structure of the transition is important in the resolving power of the atomic

vapor. If a very high resolving power is required, then an atomic system that is

composed of a single line would be desired, such as calcium or a cathode composed of a

mono-isotopic element. In contrast, mercury has a complicated hyperfine structure

approximately 45 pm wide [28]; therefore, much of the resolving power is lost with this









element; however, this broad hyperfine structure will increase the fraction of absorbed

signal and could possibly enhance the sensitivity. In terms of oscillator strength for

ground state transitions, cesium, barium, and magnesium have very high values of

0.7131, 1.64, and 1.80, respectively (obtained from NIST). In addition, these ground

state transitions occur at 852.113 nm, 553.5481 nm, and 283.2127 nm for Cs, Ba, and

Mg, respectively, so transitions in the UV, Visible, and near-IR can be achieved

depending on the specific application. High oscillator strengths are also important in the

number density required for the desired fraction of signal absorbed. Therefore, high

oscillator strengths relax the number density requirements for the atomic reservoir. If

ionization is the method of detection, then an atom with a relatively low ionization

potential may be desired. For example, cesium has an ionization potential of only 3.8939

eV compared to mercury, which has an ionization potentials of 10.4375 eV. Since

virtually any metal can be chosen, many elements possess attractive features. Clearly,

there are many factors that must be considered before selecting an element for the atomic

reservoir, and the detection method and specific application must be taken into account.

Consequently, it would benefit if the measurements taken in the present work are

repeated for other cathode elements of see-through hollow cathode discharges for

potential application as atomic line filters.

Pulsed Discharge Measurements

Presently, all the work that was performed on the thallium and lead see-through

hollow cathode discharge had been done by operating the discharge in D.C. mode.

However, the discharge can also be operated in pulsed mode. Operation in pulsed mode

would be beneficial in terms of signal-to-background ratio if fluorescence detection is

performed. The reason for this is due to the fact that the lamp also emits at the detection









wavelength. By delaying the signal input until the emission has been removed could

enhance the sensitivity of detection. However, this would really only be applicable for

measurements that include the ground state, since excited states will radiatively de-excite

to the ground state, leaving an unacceptable number density. In addition, there would be

an optimal window in which the number density of the ground state is acceptable for

measurements, since the atomic vapor will diffuse out of the analytical volume or re-

deposit back onto the cathode surface. There are many parameters that would need to be

considered such as pulse amplitude, duration, and frequency. Operation in pulsed mode

could provide a valuable method of detection; however, work on this is needed in order to

confirm or refute this approach.

The main intent and scope of this research is based on the evaluation of a see-

through hollow cathode discharge as a potential atomic line filter. Based on the results

obtained in this work, this discharge does offer several advantages over other atomic

reservoirs, however, applications of this discharge is not limited solely to atomic line

filters. This discharge has demonstrated quantum efficiencies, number densities, and

lifetimes that could be attractive for other types of research, pure and applied that may

necessitate a simple and controllable atomic reservoir.









APPENDIX A
CURVE-OF-GROWTH CALCULATION-LINE SOURCE APPROXIMATION

In atomic absorption, the fraction of light absorbed can be described by [95],

a=- (A-l)


where (o is the incident radiant power and ( is the transmitted radiant power. The

transmitted spectral radiant power at a given wavelength is given by Beer's law as [95],

,z = (0), exp- (k(A) 1) (A-2)

The total radiant power transmitted is given by [95],

o = f (,)odA (A-3)

Thus, a can be expressed as [95],

S(QZ), (- exp-(k(A)- 1))d (A-4)


where k(2) is the wavelength dependent absorption coefficient (m-1) and / is the path

length (m). The integral in equation A-3 extends over the entire wavelength interval for

which the incident spectral radiant power is measured. If a line source approximation is

used, then the wavelength dependent absorption coefficient becomes constant over the

source profile. This means that the wavelength dependence is removed and is equal to

the maximum, or peak absorption coefficient, ko. Therefore, for the limit of a line source,

equation A-4 now becomes [95, 96],

aL = 1-exp-(ko .) (A-5)

where ko is defined as,

k e2 2 n f (A-6)
4-so -m, -AAD









Here e is the charge of an electron (1.602 x 10-19 C), o0 is the wavelength at the peak of

the transition (377.572 x 10-9 m), n is the number density of the absorber (m'3, f is the

oscillator strength of the transition (0.13 unitless), so is the permittivity of a vacuum

(8.854 x 10-12 C2 J-1 m-1), me is the electron rest mass (9.109 x 10-31 kg), c is the speed of

light (2.9979 x 108 m s-1), and AAD is the FWHM of a Doppler broadened absorption

profile (4.228 x 10-13 m for a temperature of 500 K). Substitution of equation A-6 into

equation A-5 yields the expression for the fraction of light absorbed as function of

number density,


aL = 1- exp- e .o n (A-7)
4-so-m,-c -AAD

Therefore, a plot of fraction of light absorbed as a function of number density results in

figure A-1. By rearrangement of equation A-7, the number density can be calculated for

any desired fraction of light absorption for this atomic system and is given by,


n = -4 me 2 AAD ln(1- a) (A-8)
e2 202 */, f

Therefore, if 99.9 % of incident radiation is to be absorbed, then setting aL to 0.999 yields

a number density of 8.90 x 1011 cm-3












100-



10-_











10 108 109 10o 101 1012 1013 101
Number Density (atoms cm3)


Figure A-1. Theoretical curve of growth plot for a purely Doppler broadened absorption
profile assuming a line source. The number density in this plot was converted
to atoms cm-3, where as the calculation above defined the number density as
atoms m-3
atoms m








APPENDIX B
SPONTANEOUS TRANSITION PROBABILITY CALCULATION FOR THE 377.572
NM HYPERFINE STRUCTURE

As can be seen in figure 5-4, the laser spectral profile only probed thallium atoms

residing in the Fi ground level. The two transitions excited are from the two naturally

occurring isotopes of the same transition, Fi Fi; therefore the transition probability

will be the same for each isotope. In order to calculate the total number density of the

system, the transition probability needs to be calculated in order to properly evaluate

equation 5-15. The relative intensities of the three hyperfine components of each isotope

allows the oscillator strength for each transition to be calculated by the following

relationship [41],

Iki f kl 2Fk- (B-1)
In., fnn 2F +1

fl + f0 + Af = total (B-2)
foto =0.13

where fotat is the oscillator strength for the entire hyperfine structure. By applying

equation B-1 and intensities found in figure 5-4, the oscillator strength ratios can be

determined and is calculated as follows,

I f, [(2 x )+1] f, I 0.577 .( 1
I01 f1 [(2x0)+1] f,0 \0.173) 3)
Sf, [(2 x 1)+1] f,/ _0.577. (3)
I, f,10 [(2x1)+1] f,0 0.25) J3)
,10 flo [(2x1)+1] fi ( 0.25 (1
01 fo1 [(2 x0)+1] fo, 0.173) 3)

By substituting these ratios into equation B-2, the oscillator strength for each hyperfine

component is obtained. For the thallium 377.572 nm transition, the oscillator strengths

were found to be,









f,= 0.0557 fo = 0.0501 f = 0.0242

and from the relationship between the oscillator strength and spontaneous emission

transition probability [95],

6.67 x10 -5 g, f (B-3)
A2 =
g, ",o2

the transition probability for each hyperfine component can be calculated and were found

to be,

Al = 2.61x107 s1
A10 =3.77x 106 s1
A01 = 2.35 x 107 s1

Therefore, in this work a value of 2.61 x 107 s-1 was used to calculate the number density

of the thallium galvatron for each current applied.

An important point should be made here. In equation 5-15, the number density is

also dependent of the statistical weights of the lower and upper levels. In general,

statistical weights are found by the relationship,

g, = 2J, +1 Eq. 31

however, using the Jvalue from the spectroscopic terms in figure 5-1 yields an average

statistical weight of the state. Since this work involved the excitation of a selected

hyperfine component, and not the entire hyperfine structure, the statistical weights of the

lower and upper level of the hyperfine transition, shown in figure B-l, need to be applied

in equation 5-15. In this particular work the average statistical weights of the lower and

upper level are the same (gi = 2 and g2 = 2), as are the statistical weights of the selected

hyperfine transition that was excited (gi = 3 and g2 = 3); therefore, in this particular case











the statistical weight factor, g2/(gl+g2), still yields a value of 0.5. If a different hyperfine

transition were excited, then the statistical weights of that transition would need to be

applied along with the appropriate transition probability.


81T1 205 (70.5 %)


F=l


81T1 203 (29.5 %)


g=3


7 2S1/2






377.572 nm





6 2P1/2


F=0


13.32 GHz
0.45 GHz
0.45 G1-z


F=l


F=0


g=3


F=1 g=3
S1

1.21 GHz 3 21.11 GHz
F=0 g=----------
F=0 gi


21.31 GHz


Figure B-1. Energy level diagram for the hyperfine structure of the thallium 377.572 nm
transition [11]. Units in this figure are given in frequency; however,
wavelength units are used in the text.


g= 3

12.17 GHz











APPENDIX C
LIST OF SYMBOLS USED THROUGHOUT THIS WORK WITH DESCRIPTIONS
AND UNITS GIVEN


Description


Symbol



a

AX

Xo

Vo

AVL

AVH

AVIF

AVD

Avs

AVMQ

AVlaser

A4FSR, AVFSR, AGFSR
F.

FR

FF

FA

GL

GH

o(v)
Go
T

Tmax

Ro


d
0

M

f
B

AE


Units


Wavelength

wavenumber

resolution

peak wavelength

peak frequency

collisional broadening FWHM

Holtzmark broadening FWHM

Instrumental FWHM

Doppler broadening FWHM

Stark broadening FWHM

molecular quenching broadening FWHM

laser spectral FWHM

free spectral range

ultimate finesse

reflection finesse

flatness and parallelism finesse

aperture finesse

collisional broadening cross section

Holtzmark broadening cross section

frequency dependent absorption cross section

peak absorption cross section

transmission coefficient

maximum transmission

reflection coefficient

refractive index

mirror separation distance

angle of incidence

degree of flatness

lens focal length

diameter of the aperture

energy difference between two states


nm

cm'

nm

nm

Hz

Hz

Hz

Hz

Hz

Hz

Hz

Hz

nm, Hz, cm1

unit less

unit less

unit less

unit less

cm2

cm2

cm2

cm2

unit less

unit less

unit less

unit less

mm

degrees

unit less

cm

cm

J











Description


Symbol

T

M

Vo

Vb

n,

I,(v)
1

TOD

Power

k(v)

k.

fk
Io
F

J

Bk,

Bjk

Ajk

kjk

gj

Y3k
t

t,
njss

Ex

Exs

Pvo

p*

Pvo
BF
BFmax

Qlaser
A laser

Atlaser


temperature

atomic molar mass

ground voltage

breakdown voltage

number density of the respective state

frequency dependent intensity

path length

optical depth

resolving power

frequency dependent absorption coefficient

peak absorption coefficient

absorption oscillator strength

incident intensity

total angular momentum quantum number

total electronic angular momentum quantum number

stimulated absorption coefficient

stimulated emission coefficient

spontaneous emission transition probability

collisional de-excitation rate constant

degeneracy

quantum efficiency

time

response time

steady state population

spectral irradiance

saturation spectral irradiance

spectral energy density

modified spectral energy density

saturation spectral energy density

fluorescence radiance

fluorescence radiance under saturation

laser energy per pulse

cross section laser beam area

temporal FWHM of the laser pulse


Units

K

g mol-1

V

V

cm3

unit less

cm

unit less

unit less

cm-1

cm-1

unit less

unit less

unit less

unit less

J1 cm3 s-1 Hz

J-1 cm3 s-1 Hz

S-1

S-1

unit less

unit less

s

s

cm3

J s-' cm2 nm-1

J s-1 cm-2 nm1

J cm-3 Hz-1

J cm-3 Hz-1

J cm-3 Hz-'

J s-1 cm-2 sr-

J s-1 cm-2 sr-

J

cm2





Symbol

A)laser

SmV

P)

F,

S,
K2

ImV

Alens

Apiercmg

W

Rd

L

T

Natural

Tbuffer

Itself

Twall

)relative

m,



Do

Po

Pbuffer
r

Fgeometry

a



Oo

0)o



e

F0

me

c


Description

spectral FWHM of the laser

peak voltage signal produced from laser pulse

laser spectral irradiance conversion factor

conversion factor for irradiance to radiance

geometric spectral bandpass

collection solid angle

peak voltage from fluorescence signal

area of collection lens

area of piercing on collection mirror

slit widths

reciprocal linear dispersion

cavity length

effective (spontaneous) lifetime of an excited state

natural (or spontaneous) lifetime of an excited state

effective lifetime due to collisions with buffer gas

effective lifetime due to collisions with atoms of the same kind

effective lifetime due to collisions with the walls of the container

relative velocity between two species

atomic mass

reduced mass

diffusion constant

reference gas pressure

buffer gas pressure

radius

geometry factor

fraction of light absorbed

transmitted radiant power

incident radiant power

total radiant power at a given wavelength

radiant power at a given wavelength

charge of an electron

permittivity of a vacuum

electron rest mass

speed of light constant


Units

nm

mV

J s-1 cm-2 nmn1 mV1

J s-1 cm-2 sr-1 mV1

nm

sr

mV

cm2

cm2

mm

nm mm-1

cm

ns

ns

ns

ns

ns

cm s'
cm S-1

g

g

cm2 s-1

torr

torr

cm

cm-2

unit less

unit less

unit less

unit less

unit less

1.602 x 1019 C

8.854 x 10-12 C2 F1 m

9.109 x 10-31 kg

2.99.7 x 1010 cm s-1











Description


Units


Boltzmann constant
gas constant
Planck's constant


23 1


1.38 x 10-23 J K-
8314.51 mJ mol' K-1
6.626 x 10-4 J s


Symbol









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BIOGRAPHICAL SKETCH

Nicholas Roger Taylor was born in the small town of Bloomington, Wisconsin, on July 7,

1979. Upon graduating from River Ridge high school in 1998, he attended Winona State

University in Winona, Minnesota. In May of 2003, Nick graduated with a Bachelor of Science

in chemistry and a minor in biochemistry. In August 2003, Nick began his graduate studies in

analytical chemistry at the University of Florida. Under the supervision of Dr. James D.

Winefordner, he completed his doctoral research in October 2007. In July 2007, he accepted a

post-doctoral position with Dr. Paul Farnsworth at Brigham Young University, located in Provo,

Utah.





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1 DIAGNOSTICS OF A SEE-THROUGH HOLLO W CATHODE DISCHARGE BY EMISSION, ABSORPTION, AND FLUORESCENCE SPECTROSCOPY By NICHOLAS TAYLOR A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007

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2 2007 Nicholas Taylor

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3 ACKNOWLEDGMENTS I want to start off by thanking my advi sor, mentor, and friend, Dr. James D. Winefordner. His persistent enthusiasm a nd guidance for each of his students is truly inspiring. His passion and encouragement were a fuel that helped to drive much of my understanding of scientific re search, learning, and life. I consider myself extremely fortunate that I was given the opportunity to be a member of his research group and looking back, I cant imagine my life without this experience. I give a special thanks to Dr. Nicol Omenetto for his seemingly endless patience. His door is always open and the stimulating c onversations that we had really helped my understanding of the many conceptual, theo retical, and experimental aspects of spectroscopy. I would also lik e to thank Dr. Benjamin Smith, whose advice and many insightful suggestions were much appreciated. He always makes it a point to daily pass through the lab to see if anything is n eeded or questions need answering. I thank Jeanne Karably for all she has done She is always willing to help in any way and is a true asset to the analytical di vision. I also thank th e electronic and machine shop. They do an amazing job based on the dism al descriptions that we provide, and are always willing to work with us in or der to provide exactly what is needed. Lastly I thank my family and friends for their constant support throughout undergraduate and graduate studies.

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4 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................3 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........8 ABSTRACT....................................................................................................................... ............12 CHAPTER 1 INTENT AND SCOPE OF STUDY......................................................................................14 Introduction to Atomic Line Filters........................................................................................14 Atomic Reservoirs.............................................................................................................. ....15 The Glow Discharge............................................................................................................. ..18 The Cathode Dark Space.................................................................................................19 The Negative Glow..........................................................................................................20 The Faraday Dark Space.................................................................................................21 2 HIGH RESOLUTION EMISSION SPECT ROSCOPY OF A SEE-THROUGH HOLLOW CATHODE DISCHARGE BY A SCANNING FABRY-PEROT SPECTROMETER.................................................................................................................22 Introduction................................................................................................................... ..........22 Interferometer Concept......................................................................................................... ..24 Finesse Considerations......................................................................................................... ..27 Reflection Finesse, FR.....................................................................................................27 Flatness and Parallelism Finesse, FF................................................................................28 Aperture Finesse, FA........................................................................................................29 Experimentally Determined Finesse................................................................................30 Broadening Mechanisms........................................................................................................31 Natural Broadening.........................................................................................................31 Collisional Broadening....................................................................................................32 Holtzmark Broadening....................................................................................................33 Instrument Function Broadening.....................................................................................33 Doppler Broadening........................................................................................................34 Self-Absorption Broadening............................................................................................34 Other Broadening Mechanisms.......................................................................................35 Evaluation of Broadening Mechanisms...........................................................................35 Experiment..................................................................................................................... .........36 Results........................................................................................................................ .............39 Discussion..................................................................................................................... ..........43 Conclusion..................................................................................................................... .........51

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5 3 NUMBER DENSITY MEASUREMENTS IN A SEE-TH ROUGH HOLLOW CATHODE DISCHARGES WITH A HIGH RESOLUTION FABRY-PEROT SPECTROMETER.................................................................................................................53 Introduction................................................................................................................... ..........53 Experimental................................................................................................................... ........57 Results and Discussion......................................................................................................... ..59 Conclusions.................................................................................................................... .........63 4 NUMBER DENSITY OF A SEE-THROUGH HOLLOW CATHODE DISCHARGE BY CONVENTIONAL ABSORPTION SPECTROSCOPY.........................65 Introduction................................................................................................................... ..........65 Experimental................................................................................................................... ........66 Number Density Measurements.............................................................................................68 Path Length M easurements.....................................................................................................69 Line Source M easurements.....................................................................................................70 Conclusion..................................................................................................................... .........72 5 TIME-RESOLVED LASER-INDUCED SATURATED FLUORESCENCE MEASUREMENTS: EVALUATION OF NUMBER DENSITY AND QUANTUM EFFICIENCY....................................................................................................74 Introduction................................................................................................................... ..........74 Theory......................................................................................................................... ............76 Rate Equation Approach Versus Density Matrix Approach...........................................76 Ideal Two-Level Saturation Curv e Under Steady State Conditions................................78 Two-Level Saturation Curve Under Transient Conditions.............................................80 Three-Level Saturation Curve in the Presence of a Trap................................................82 Number Density Under SteadyState Saturation Conditions..........................................85 Experimental................................................................................................................... ........87 Laser System...................................................................................................................87 Detection System.............................................................................................................89 Vacuum Photodiode Calibration.....................................................................................89 Spectrometer Calibration.................................................................................................90 Evaluation of Dye Laser Parameters......................................................................................92 Spectral Profile............................................................................................................... .92 Spatial Profile................................................................................................................ ..94 Temporal profile..............................................................................................................96 Results and Discussion......................................................................................................... ..97 Saturation Curve Measurement: Evaluation of the Quantum Efficiency........................97 Number Density Measurement......................................................................................103 Conclusion..................................................................................................................... .......106 6 LIFETIME MEASUREMENTS OF SEVERAL S, P, AND DJ STATES IN A THALLIUM SEE-THROUGH HO LLOW CATHODE DISCHARGE..............................108

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6Introduction................................................................................................................... ........108 Experimental................................................................................................................... ......110 Lasers and Optics..........................................................................................................110 Detection...................................................................................................................... ..112 Results and Discussion.........................................................................................................112 6 2D3/2 and 6 2D5/2 Lifetime Measurements...................................................................112 7 2S1/2 Lifetime Measurement........................................................................................115 6 2P3/2 o Lifetime Measurement......................................................................................117 Collisional Deexcitation Rate Constant.........................................................................125 Conclusion..................................................................................................................... .......126 7 FINAL CONCLUSIONS AND FUTURE WORK..............................................................128 Concluding Remarks............................................................................................................128 Hyperfine Structure Considerations..............................................................................128 Absorption Measurements.............................................................................................129 Saturated Fluorescence Measurements..........................................................................131 Lifetime Measurements.................................................................................................132 Future Work.................................................................................................................... ......133 Signal-to-Noise Ratio Considerations...........................................................................133 Atomic Reservoir Element............................................................................................134 Pulsed Discharge Measurements...................................................................................135 APPENDIX A CURVE-OF-GROWTH CALCULATION-LINE SOURCE APPROXIMATION.............................................................................................................137 B SPONTANEOUS TRANSITION PROBABILITY CALCULATION FOR THE 377.572 NM HYPERFINE STRUCTURE...........................................................................140 C LIST OF SYMBOLS USED THROUGHOUT THIS WORK WITH DESCRIPTIONS AND UNITS GIVEN..............................................................................143 LIST OF REFERENCES.............................................................................................................147 BIOGRAPHICAL SKETCH.......................................................................................................153

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7 LIST OF TABLES Table page 2-1 Calculated broadening components for thalliu m and lead that would be expected in a galvatron based on known parameters and an assumed temperature of 1000 K...............36 5-1 Values used for fluorescence radiance calculation with symbols and descriptions provided....................................................................................................................... ......91 5-2 Previously reported saturation parameter values for various elements under various experimental conditions...................................................................................................101 6-1 Transition probabilities obtained from the National Institute of Standards and Technology..................................................................................................................... .113 6-2 Comparison of previously reported valu es on the spontaneous lifetime of the 6 2D3/2 state.......................................................................................................................... ........114 6-3 Comparison of previously reported valu es on the spontaneous lifetime of the 6 2D5/2 state.......................................................................................................................... ........115 6-4 Comparison of previously reported valu es on the spontaneous lifetime of the 7 2S1/2 state.......................................................................................................................... ........116 6-5 Comparison of previously reported va lues on the effective lifetime of the 6 2P3/2 o metastable state............................................................................................................... .124

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8 LIST OF FIGURES Figure page 1-1 Cross sectional view of A) hollow cathode lamp and B) galvatron..................................18 1-2 A) Illustration of a simple planar glow discharge and B) the voltage distribution. Here Vo represents the ground voltage and Vb is the breakdown voltage [18]..................19 2-1 Partial energy level diagram of the hyperfine structure of A) 535.046 nm transition of thallium and B) 405.7807 nm transition of lead. Both thallium and lead odd isotopes have a nuclear spin quantum number I = Not drawn to scale........................23 2-2 Simple illustration of A) a Fabry-Perot interferometer and B) a Michelson interferometer................................................................................................................. ....26 2-3 Experimental determination of the finesse of the interferometer using a helium-neon laser at 632.8 nm. The variations in the intensity between the 3 orders are due to slight intensity variations in the HeNe source...................................................................30 2-4 Experimental set-up for the measurement of the lead and thallium emission profiles from a laser galvatron, hollow cathode lam p, and an electrodeless discharge lamp.........37 2-5 Experimental profiles of the 535.046 nm tran sition of thallium from A) galvatron and B) hollow cathode lamp.....................................................................................................40 2-6 Experimental profiles of the 405.7807 nm tr ansition of lead from A) galvatron and B) hollow cathode lamp. Both sources we re measured under the same experimental setup.......................................................................................................................... .........40 2-7 Comparison between a thallium galvat ron and a thallium hollow cathode lamp profiles operated at the same current. All profiles are normalized...................................41 2-8 Comparison between a lead galvatron and a lead hollow cathode lamp profiles operated at the same currents. All profiles are normalized...............................................42 2-9 Experimental profiles of the 535.046 nm tr ansition of thallium from an electrodeless discharge lamp................................................................................................................. ..43 2-10 Calculated profiles fitted to the experi mental profiles of a thallium galvatron at currents of 10, 15, 20, and 30 mA......................................................................................45 2-11 Calculated profiles fitted to the experime ntal profiles of a lead hollow cathode lamp for currents of 6, 10, 15, and 20 mA..................................................................................46 2-12 Doppler temperature values obtained from the fit of the calculated two layer model for A) 535.046 nm transition of thallium a nd B) 405.7807 nm transition of lead from a galvatron, hollow cathode lamp, a nd electrodeless discharge lamp...............................47

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92-13 Calculated resolving powers for A) th allium galvatron and hollow cathode lamp and B) lead galvatron and hollow cathode lamp......................................................................47 2-14 Optical depth values obtained from the fit of the calculated two layer model for A) 535.046 nm transition of thallium and B) 405.7807 nm transition of lead for a galvatron, hollow cathode lamp, a nd electrodeless discharge lamp..................................48 2-15 Number density values obtained from opti cal depths obtained from the application of the two layer model for A) thallium and B) lead using equation 2-17..............................50 3-1 Illustration of a Fabry Perot interferom eter and a monochromator used as a cross dispersion system for two m onochromatic wavelengths...................................................55 3-2 Tutorial for the method of using a conti nuum source. A) Represents the use of a monochromator with a large spectral ba ndpass. B) Represents the use of a monochromator with a small spectral bandpass................................................................55 3-3 Illustration of the production of a quasicontinuum source from two line sources for the measurement of high resolution absorption measurements.........................................57 3-4 Experimental setup used for high reso lution absorption profile measurements................59 3-5 A) Scan of the EDL profile self-reversed. B) Scan of the HCL profile self-absorbed. C) Resulting profile of the combined profiles yielding a quasi-continuum source over the absorption profile.................................................................................................59 3-6 Resulting absorption profiles of the thallium 6 2P3/2 o metastable state of thallium due to various currents applied to the see-th rough hollow cathode disc harge. The blue wing on the quasi-continuum prof ile is cut off due to a small amount of order overlap from an adjacent order. This order overlap did not cause distortion of the observed absorption profiles............................................................................................................ .60 3-7 Hyperfine structure for the thallium 535.046 nm transition with rela tive intensities, Iij. ( ) thallium 203 isotope, ( ) thallium 205 isotope. Not drawn to scale............62 3-8 Number density measurement of the 6 2P3/2 o metastable state of thallium by absorption and emission measurements.............................................................................63 4-1 Illustration of the absorption profile (red) of the galvatron an d the emission profile (blue) of the HCL.............................................................................................................. .66 4-2 Experimental arrangement for absorption measurements. Lens 1 and lens 2 are both fused silica with focal lengths of 10 cm. Both irises had a diameter of 2 mm. Not drawn to scale................................................................................................................. ...67 4-3 Number density measurements by conve ntional absorption. The results from saturated fluorescence and hi gh resolution emission data ar e also plotted. For the absorption number density calculation, temp erature values were obtained from high

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10 resolution emission measurements [40]. The emission source (HCl) current was fixed at 2.0 mA................................................................................................................ ..69 4-4 Absorption measurements as the cathode was translated through the emission beam. The HCl emission source was held constant at 10 mA throughout this experiment.........70 4-5 High resolution emission measurements of the lead 405.7807 nm and the thallium 535.046 nm transitions in a galvatron and ho llow cathode lamp at similar currents.........71 5-1 Partial energy level diagrams for thallium and lead displaying the possible transitions involved with wavelengths and oscillator strengths labeled. Collision constants between levels 1 and 2 are neglected.................................................................................75 5-2 Experimental set-up used for all satura tion curve and number density measurements.....88 5-3 Representation of the losses that would be encountered in the collection optics. Not drawn to scale................................................................................................................. ...91 5-4 Experimentally measured dye laser spect ral profile with FWHM of 6.63 pm. Also shown is the calculated mode structure obt ained from a cavity length of 35 cm. Intensities shown are arb itrary and do not represen t any physical quantity......................92 5-5 A) A three dimensional spatial profile obtained by translatin g photodiode with a 100 m pinhole through the Scanmate 1 dye laser beam. B) A two dimensional view of the same profile demonstrating the fairly homogenous profile.........................................95 5-6 A) Scanmate 1 dye laser temporal pr ofile for the thallium 377.572 nm transition. Recorded with a photodiode (rise time of 200 ps) and 500 MHz oscilloscope.................96 5-7 Experimentally measured saturation cu rve from a thallium galvatron with 10.0 mA applied. This data was modeled with time dependent two-level sa turation curves for laser pulse durations of 1, 10, and 100 ns. Y21 = 1 was used for all three theoretical curves......................................................................................................................... ........99 5-8 Experimentally measured saturation cu rve from a thallium galvatron with 10.0 mA applied. This data was modeled to a time dependent three-level saturation curves in the presence of a trap for pulse durations of 1, 10, and 100 ns. For all three plots, the collisional de-excitation rate cons tants were assumed to be zero....................................100 5-9 Experimentally measured saturation cu rve from a lead galvatron with 10.0 mA applied. This data was modeled to a time dependent three-level saturation curve in the presence of a trap for a pulse duration of 4 ns. All collisio nal de-excitation rate constants were set to zero................................................................................................102 5-10 Plot of the ground state number density as a function of current....................................103 5-11 Plot of the metastable state number dens ity of thallium as a function of current............105

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115-12 Plot of the metastable state number de nsity of lead as a function of current. Saturated fluorescence values are compared to results obtained from conventional absorption and high resolution emission measurements..................................................106 6-1 Partial energy level diagram for thallium........................................................................109 6-2 Experimental setup used for both single-s tep and two-step laser excited fluorescence measurements. IF is an inte rference filter used to remove laser scatter. Mirrors 1-4 are used for laser beam height and orie ntation alignment. PD-1 and PD-2 are photodiodes used to monitor the time dela y between the two pulses for two step fluorescence measurements. PD-3 is a photodiode used to trigger the signal acquisition.................................................................................................................... ....111 6-3 Measured fluorescence curve for the thallium 6 2D3/2 state.............................................113 6-4 Measured fluorescence curve for the thallium 6 2D5/2 state.............................................115 6-5 Measured fluorescence curve for the thallium 7 2S1/2 state.............................................116 6-6 Measured lifetime curves for the thallium 6 2P3/2 o metastable state................................118 6-7 Measured fluorescence waveform at 377.572 nm due to 276.787 nm excitation............119 6-8 Plot of the lifetimes, and calculated deexcitation rate constant, k21, at various currents for the thallium 6 2P3/2 o metastable state............................................................125 A-1 Theoretical curve of growth plot for a purely Doppler broadened absorption profile assuming a line source. The number density in this plot was converted to atoms cm3, where as the calculation above de fined the number density as atoms m-3...................139 B-1 Energy level diagram for the hyperf ine structure of the thallium 377.572 nm transition. Units in this figure are given in frequency; however, wavelength units are used in the text............................................................................................................... ..142

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12 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DIAGNOSTICS OF A SEE-THROUGH HOLLO W CATHODE DISCHARGE BY EMISSION, ABSORPTION, AND FLUORESCENCE SPECTROSCOPY By Nicholas Taylor December 2007 Chair: James D. Winefordner Major: Chemistry Atomic line filters have been suggested to be attractive in areas of Doppler velocimetry, resonance fluorescence detection, and resonance ionization detec tion. They are based on the resonant absorption of photons by an atomic vapor and allow all other radiation to pass. This allows the detection of very low levels of light superimposed on a large optical background. Several elements have been studied for use as atomic line filters, such as the alkali metals, alkaline earths, and thallium. As previously r ecognized, thallium is especially attractive since the 535.046 nm metastable transition overlaps with the second harmonic output of an Nd:La2Be2O5 (BEL) laser (1070 nm). This makes thalliu m ideal for certain applications as an atomic line filter. Recently a see-through hollow cathode lamp, or galvatron (Hamamatsu), was made commercially available. The galvatron geometry is unique compared to traditional hollow cathode lamps since the cathode and cell are orie nted in a T-shape, with the cathode bored completely through to allow the propagation of a light source through the cathode. This allows

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13 multi-step excitation of the atomic vapor, not easily accomplished with a traditional hollow cathode lamp. The advantages that a galvatron offers ove r conventional atomic reservoirs make it an attractive candidate for the application as an atom ic line filter; however, little spectroscopic data have been found in the literature. For this reason, Doppler temperatur es, number densities, quantum efficiencies, and lifetimes have been determined in order to characterize this atomic reservoir as a potential atomic line filter. Th ese parameters are determined by use of various spectroscopic techniques which include emissi on, absorption, time-resolved fluorescence, and time-resolved laser-induced saturated fluorescen ce spectroscopy. From these measurements, it has been demonstrated that a galv atron is an attractive atomic re servoir for applications as an atomic line filter. The spectral resolution of this atomic line filter was f ound to be superior to that of a traditional hollow cathode lamp and elect rodeless discharge lamp. A desired number density can be rapidly produced by applying the appropriate current and can be reproduced from one experiment to the next. In addition, the quant um efficiency of this system was found to be limited only by the competing radiative pathways of the particular en ergy level arrangement which allows it to be a very efficient detector. This system has the potential to be simple, compact, and portable which makes it an ideal atomic line filter.

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14 CHAPTER 1 INTENT AND SCOPE OF STUDY Introduction to Atomic Line Filters Interest in atomic line filters continues to grow and spread to a wide range of research. They have found an array of app lications including Doppler velocimetry [1], resonance fluorescence detection [2-6], and re sonance ionization det ection [7,8] to only name a few. They are based on the absorp tion of signal photons resonant with an electronic transition of the atomic system and al low all other radiation to pass. This type of high background rejection makes atomic line f ilters very attractive for the detection of a weak optical signal superimposed on a la rge solar environment. Detection by other spectroscopic methods would require filtering of the background radiation by means of narrow glass filters or the use of a dispersive system such as a grating or prism spectrometer. These ultra-narrow band filters have an incredible advantage in high background applications such as in a tmospheric backscatter lidar or space communications. Atomic line filters have the potential of achieving spectral bandwidths as narrow as a few GHz to MHz without a loss in lumi nosity. Therefore, atomic line filters can achieve very high resolving powers, where the resolving power is defined as the ratio of the wavelength being measured, (nm), to the resolution of the system, (nm). For an atomic line filter, the resolution is determin ed by the FWHM of the absorption profile of the atomic vapor, thus, they can achieve ve ry high resolving powers, depending on the temperature and collisional environment. Si nce they are based on an atomic vapor, their collection solid angle is limited only by the geometric design of the atomic reservoir, which allows an enhanced luminosity when co mpared to other systems. Luminosity here

PAGE 15

15 is defined as the product of the acceptance so lid angle (sr) and the projected area (cm2). In conventional dispersive systems like a grating monochromator, the resolving power and luminosity are controlled by the slit widths Decreasing the slit widths reduces the bandpass observed by the detector and results in an increase in the re solving power of the monochromator; however, this restricts the throughput of light accepted by the monochromator and reduces the luminosity of the system. Of course, the inverse would be true if the slits were increased. The luminosity-re solving power product can be thought of as being constant in this case. It is consider ed one of the most important figures of merit when comparing spectroscopi c systems. An atomic line filter, however, does not have a constant luminosity-resol ving power product. The resolving power, based on the width of the absorption profile of the metal vapor, and the luminosity, based on the geometric design of the atomic reser voir; are independent of one another. Reducing the line width by cooling the vapor would result in a narrower absorption profile and thus increase the resolving power of the system ; however, the system retains the same collection solid angle and projec ted area. The luminosity-resolving power product of atomic line filters have be en discussed theoretically by Matveev et. al. [9] and were found to be superior to inte rferometer and heterodyne systems. Atomic Reservoirs One of the requirements of an atomic line filter is the atomic vapor should be easy to produce and stable in number density. Sealed cells are commonly used atomic reservoirs; however, since many metals have relatively low vapor pressures, elevated temperatures from elaborate heating systems are needed in order to produce an appropriate, controllable, a nd stable number density. Currently, there are about 23 elements that can produce a suitable at omic vapor with moderate heating of

PAGE 16

16 approximately 500 C [10]. If they are la boratory constructed cells, then elaborate vacuum and flushing procedures may be need ed in order to remove the presence of molecular species. There may also be a need to distill the metal from its oxide form [11]. The presence of molecular species is important in terms of the quantum efficiency of the atomic system and translates into the overall de tection efficiency of the atomic filter. If the cell is not heated uniformly, condensat ion of the metal vapor can build up on the windows of the cell which can impa ir its performance as an eff ective atomic line filter. Attempts with flames as an atomic reservoir have also been made. Smith et al. [12] successfully used a magne sium seeded flame to detect Stokes Raman photons from carbon tetrachloride by laser enhanced ionizatio n. While this is a simple and convenient system, it suffers from many disadvantages. Si nce flames require the use of combustible gases there are inherent safety concerns. In addition, an appropriate ventilation system is needed when dealing with toxic metals such as lead and thallium. The use of a flame also requires large quantities of a high concentration of the me tal salt solution to produce a continuous supply of the metal vapor. There is also an issue with portability, since an ideal atomic line filter should be capable of moving to the loca tion of interest as well as be able to operate in harsh environments. Flames would be difficult to deal with in windy environments, under water, or in space. Perhaps the largest disadvantage associated with flames would be the quant um efficiency of an atomic vapor in a combustion environment. Poor quantum ef ficiency values, on the order of 0.03 to 0.001 have been reported [13, 14], depending on flame composition. This is due to the flame being a high temperature, high quenching e nvironment with a larg e concentration of molecular species. One must also consider that the elevated temperature and pressure

PAGE 17

17 causes a broadening of the absorption profile re sulting in an inferior spectral resolution. It is apparent that the s implicity and convenience is out weighed by many disadvantages associated with a flame and would not make it an ideal atomic reservoir. Hollow cathode lamps are also capable of producing an atomic vapor. This is achieved by the well known sputtering process th at occurs from the hollow cathode effect and can be applied to nearly every metal. These are simple systems capable of producing a stable atomic vapor from refractory meta ls that would otherw ise require extreme temperatures. Unlike sealed cells, hollow cathode lamps are capable of producing an atomic vapor from 63 elements, compared to 23 from sealed cells. These discharges can be easily controlled with a st able current source and sustai ned for long periods of time with negligible fluctuations or drift. They operate in very pure, low pressure buffer gases typically in the range of 1-20 torr, with Doppler temperatures on the order of 350-750 K [15-17]. This results in na rrow absorption profiles, therefore, very high spectral resolution, limited only by Doppler broadening. Unlike sealed cells and flames, hollow cathode lamps have limited optical access, with only one access window for multistep excitation. The combination of two or three lasers would be difficult and can reduce the acceptance solid angle, therefore, redu cing the luminosity of the reservoir. Recently a see-through hollow cathode lamp, or galvatron (Hamamatsu), was made commercially available. The galvatr on and hollow cathode lamp both operate by the hollow cathode effect; however the cathode of a galvatron is oriented in a T-shape and the cathode is hollowed co mpletely through so it is ope n on both ends as shown in figure 1-1. This allows optical access at bot h ends of the cathode. This geometry also permits the use of a second lase r to counter-propagate through the filter for fluorescence,

PAGE 18

18 ionization, or opto-galvanic detection which w ould be difficult to obta in with traditional hollow cathode lamps. The use of multi-step excitation for the detection of the signal radiation can have an advantageous in the selectivity of the detection signal. Figure 1-1 Cross sectional view of A) ho llow cathode lamp and B) galvatron. Since these see-through hollow cathode lamps are relatively new, little spectroscopic information is available on them Therefore, in order to evaluate the potential of this hollow cathode discharge as an atomic line filter, one must measure several spectroscopic parameters of the discharge including D oppler temperatures, number densities, quantum efficiencies, and lif etimes of these systems at various applied currents in order to evaluate the potential such a filter would possess. The Glow Discharge Since the purpose of this research is the spectroscopic dia gnostics of several parameters of the discharge for use as an atom ic line filter, the anatomy and processes of the discharge will only be briefly discussed here. A typical glow discharge consists of two electrodes sealed in a low pressure gaseous medium, typically argon or neon. If a potential is dropped across these electrodes, a discharge can be created and sustained with various dark and luminous areas as depicted in figure 1-2. Although figure 1-2 represents A) B) Cathode Cathode Anode Anode

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19 a planar electrode configurat ion, it equally applies to a hol low cathode discharge were the cathode is a hollowed out cylinder rather than a flat surface. Each region will be briefly discussed below. Figure 1-2. A) Illustration of a simple pl anar glow discharge and B) the voltage distribution. Here Vo represents the ground voltage and Vb is the breakdown voltage [18]. The Cathode Dark Space The cathode dark space is the region directly adjacent to the cathode surface. It is a region of low luminosity, hence the name dark space. Due to the negative potential that is applied to the cathode, electrons generated in this region are repelled away from this area and are accelerated towards the anode. This region is also referred to as the cathode fall region due to the repulsion of electrons fr om this region. These repelled electrons are of such high energy that they are incapable of exciting at oms within this region, which (-) Vb Vo Negative Glow Faraday Dark Space Dark Cathode Space Cathode Anode A) B)

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20 accounts for the low luminosity of this region. These high energy elec trons are, however, responsible for the ionization of the buffer ga s. These positively charged buffer gas ions are attracted to the negative potential applied to the cathode and are accelerated towards the cathode surface. These accelerated buffe r gas ions eventually collide with the cathode surface and, if sufficient energy has been transferred, will result in the removal of an atom of the cathode material. This proce ss is referred to as sputtering, and accounts for the atomization of the cathode material. Therefore, the cathode dark space is very important in sustaining the discharge. The Negative Glow The negative glow region is easily identified as the bright luminous glow region of the discharge. There are two types of el ectrons that exist in this region, fast high energy electrons and slower thermal electrons The fast high energy electrons are the result of electrons that have escaped the dark cathode space without a loss in energy due to collisions. This class of electrons typically has electr on temperatures on the order of 20 25 eV and number dens ities on the order of 106 cm-3 [18,19] As mentioned previously, these electrons are of such hi gh energy that they are only capable of ionization of the buffer gas, as well as sputtered species. The second class of electrons is slow th ermal electrons. These thermal electrons have two separate origins; therefore, can be divided in to two groups. The first group originates as the product of gas phase i onization collisions with the buffer gas or sputtered species. They typi cally have electron temperatur es on the order of 2 10 eV and number densities on the order of 107 108 cm-3 [18,19] The second group originates from both fast high energy electrons from th e dark cathode space and electrons from gas phase collisions. These electr ons have undergone several elas tic and inelasti c collisions

PAGE 21

21 in the discharge yielding elec tron temperatures on the order of 0.05 0.6 eV and number densities on the order of 109 1011 cm-3 [18,19] In addition, the number density of electrons is essentially equiva lent to the number density of ions present in the negative glow region, which yields a nearly field fr ee region, as shown in figure 1-2. These slow thermal electrons are responsible for the exc itation of atoms present and accounts for the high luminous nature of the region. For this reason, the negative glow region is the most analytically useful and has been extensively inve stigated by many authors. The Faraday Dark Space The faraday dark space is a region betw een the anode edge of the negative glow region and the anode of the discharge. Electr ons that have diffused into this region have lost most of their energy by co llisions in the negative glow region and are typically not capable of further excitation or ionization. For this reason, the faraday dark space region is not very luminous, and if the distance between the cathode and anode is small, as is the case of a hollow cathode lamp, then this region may not be very prominent.

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22 CHAPTER 2 HIGH RESOLUTION EMISSION SPECT ROSCOPY OF A SEE-THROUGH HOLLOW CATHODE DISCHARGE BY A SCANNING FABRY-PEROT SPECTROMETER Introduction The luminosity-resolving power product is one of the most important figure of merit when comparing spectroscopic systems. For an atomic line filter, the resolving power is governed by the absorp tion profile of the atomic va por. Therefore, in order to evaluate the potential of a s ee-through hollow cathode discharge as an atomic line filter, one must measure the spectral profiles of this discharge at various applied currents in order to evaluate the spectral resolution and Doppler temperature that such a filter would possess. Typically, the absorption profile of the atomic vapor would be evaluated by direct measurements with a narrow band diode la ser. This would be possible, due to the unique design of the discharge lamp; however, di ode lasers at the transitions of interest were not available. The Doppler temperatur es can also be evaluated by measurement of the emission profile of the discharge. This type of high resolution measurement has traditionally been achieved by either long focal length spectrographs, or with an interferometer. A high resolution scanning Fabry-Perot interferometer was available, with mirrors capable of obtaining an acceptabl e resolving power at the transitions of interest. Therefore, focus of this work wa s on the measurement of the emission profiles from the hyperfine structure of the 535.046 nm transition of thallium and the 405.7807 nm transition of lead in a see-through hollow cathode discharge by means of a scanning Fabry-Perot spectrometer. Partial energy level diagrams of thallium and lead is shown in figure 2-1.

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23 Figure 2-1. Partial energy level diagram of the hyperfine structure of A) 535.046 nm transition of thallium and B) 405.7807 nm transition of lead. Both thallium and lead odd isotopes have a nuclear sp in quantum number I = Not drawn to scale. 0.52 GHz 12.17 GHz 2S1/2 2P3/2 o g = 3 g = 3 g = 1 g = 1 g = 3 g = 3 g = 5 g = 5 13.32 GHz 1 3 0.45 GHz 1.32 GHz 5 3 1 3 3 5 0.53 GHz F = 1 F = 0 F = 1 F = 0 F = 2 F = 1 F = 1 F = 2 535.046 nm 207Pb (22.1 %) a = 9/15 b = 5/15 c = 1/15 208Pb (52.4 %) 206Pb (24.1 %) 204Pb (1.4 %) 3P1 o 3P2 a = 405.7805 nm b = 405.7842 nm c = 405.7770 nm = 405.7807 nm = 405.7820 nm = 405.7832 nm a b c g = 3 g = 3 g = 3 g = 5 g = 5 g = 5 F = 3/2 F = 1/2 F = 5/2 F = 3/2 2.6008 GHz 8.8020 GHz g = 4 g = 2 g = 6 g = 4 205Tl (70.5 %) 203Tl (29.5 %) B) A)

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24 Interferometer Concept Perhaps the earliest concepti on of interferometry can date as early as 1831, when George Airy mathematically described the coherent addition of light from multiple reflections between two plane su rfaces. This became known as the Airy distribution and is shown as [20], = 2 d cos 1 where is the wavenumber (cm-1), I() is the wavenumber dependent transmission intensity, T is the transmission coefficient, Ro is the reflection coefficient, is the refractive index of the medium between the mi rrors, d is the mirror separation (mm), and is the angle of incidence of the radiat ion. Equation 2-1a can be evaluated by considering the following condition; if n = where n is an intege r, then equation 2-1a reduces to, where Tmax is the peak transmission of the incident radiation that is injected into the cavity, A is the absorption coefficient, T is the transmission coefficient, and Ro is the reflection coefficient. It is clear from equation 2-1a that Tmax can be achieved by varying the wavelength, the refractive index, or the distance between two mirrors if the light is collimated ( = 0) and monochromatic. If the radi ation is not truly collimated, then 1 2 2 2 2sin ) 1 ( 4 1 ) 1 ( ) ( o o oR R R T I T R A R A R T T 1 1 1 ) 1 (2 2 2 max (2-1a) (2-1b) (2-2a) (2-1c) (2-2b)

PAGE 25

25 various angles of the incident radiation th at satisfy equation 2-2a will result in the characteristic circular fringe pattern. This is due to the fact that at these angles, the incident radiation takes a path length that re sults in constructive in terference, yielding the maximum transmission of the incident light. As mentioned, if the condition n = is met, a maximum transmission will be observed for every integer value of n, known as the order of interfer ence. The separation between one interferen ce maximum to an adjacent maximum is defined as the free spectral range. From equations 2-1a and 2-1b, the free spectr al range is mathematically shown to be, where is the wavelength of the radiation (m), is the refractive index of the medium between the two mirrors (1.001 for air), FSR is the free spectral range in wavelength units (m), FSR is the free spectral range in frequency units (Hz), FSR is the free spectral range in wavenumber units (m-1), c is the speed of light constant (2.9979 x 108 m s-1), and d is the separation between the faces of the two mirrors (m). One should be aware of units for a correct calcul ation of the free spectral range. Many interferometers have been devel oped throughout the year s; the two most commonly encountered are th e Michelson interferometer and the Fabry-Perot interferometer. The Michelson interferomet er, developed by Albert Abraham Michelson, had significant historical importance. This was the device that was used in the famous d d c dFSR FSR FSR 2 1 2 22 (2-3a) (2-3b) (2-3c)

PAGE 26

26 Michelson-Morley experiment, which proved that the medium that composed the universe was not ether, a commonly accepted th eory at the time [21]. In 1899, Marie Fabry and Jean A. Perot developed the Fa bry-Perot interferometer. A significant improvement over the Michelson interferomet er, the Fabry-Perot design incorporates multiple rays of light folded back onto each other by two plane parallel surfaces, as opposed to a Michelson interferometer which is based on a single pass as shown in figure 2-2. Figure 2-2. Simple illustration of A) a Fabr y-Perot interferometer and B) a Michelson interferometer. In 1954, Pierre Jacquinot demonstrated that for a given resolving power, a FabryPerot etalon demonstrated supe riority over gratings or pris ms of similar area [22]. Interferometers have been a very valuable tool in the analysis atomic spectral lines; however, in order to obtain the resolution necessary for these m easurements, certain theoretical considerations need to be evaluated in order to determine if the measurement apparatus contributes to th e overall observed profile. d Beam splitter Mirror Mirror Mirror Mirror A) B)

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27Finesse Considerations The finesse of an interferometer is a parameter that measures of the number of spectral lines that can be resolv ed in a single free spectral ra nge and is used to evaluate the resolving power of the interferometer. The ultimate finesse of an interferometer is defined as the ratio of the free spectral range to the instrume nt function of the interferometer. Since the finesse is a consta nt, varying the free spectral range will affect the instrument function. The ultimate finesse of a scanning interferometer is composed of three basic components, the reflection finesse (FR), surface flatness and parallelism finesse (FF), and the aperture finesse (FA), sometimes referred to the scanning aperture finesse. Chabbal [23] discusses in detail the convolution of these finesse components, however, a good approximation is given by: where Fu is the ultimate finesse of the system. Each one will be discussed individually with regards to their contribution to the system used in this work. Reflection Finesse, FR The reflection finesse component is depende nt on the reflection coefficient of the mirrors as seen from the relation in equation 2-5. The high reflective mirrors used for the thallium study where from a copper vapor lase r (CVI). These mirrors have a fairly uniform reflection from 520 nm to 670 nm with a reflection coefficient of approximately 99 % at 535.0 nm. The high reflective mirrors used for the lead study were obtained from Bristrol and have a reflection coeffici ent of 98.5 % at 405.8 nm. Therefore, from equation 2-5, the reflection finesse for the high reflection mirrors is calculated to be 312.6 and 207.9 for the thallium and lead mirrors, respectively. 2 2 2 21 1 1 1A F R uF F F F (2-4)

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28 Flatness and Parallelism Finesse, FF The flatness finesse component is depe ndent on the degree of flatness and surface imperfection of the mirrors [24] The mirrors used for thallium are polished to a flatness of /20 and from equation 2-6, results in flatne ss finesse of only 10. For this reason, a restricting iris is used prior to the radiati on entering the interferometer. The mirrors have a global flatness of /20 over the 2 inch diameter of th e mirror; however, if the limit of the diameter exposed is only a few millimet ers, the local surface flatness that the radiation is exposed to can be on the order of /200 or greater, however, the exact local flatness is not known. The mirror flatness is given by /M where M is defined as the de gree of flatness of the mirror. From equation 2-6, a surface flat ness from 100 to 200 or be tter can be obtained for the thallium mirrors, depending on the surf ace area to which the radiation is exposed. The mirrors used for the lead st udy were polished to a flatness of /200 giving a flatness finesse of 100; however, the use of a restricting iris prior to the interferometer will yield a flatness finesse greater than this, and can be as high as 200 300. Although it is difficult to know the exact finesse of this component, it is not expected to be the limiting finesse based on experimental observations. The parall elism component of this finesse refers to the degree of parallelism between the two mirrors A lack of parallelism between the two mirrors will result in different path lengths for different areas of the mirror. As a result, a distortion of the interference pattern will be obs erved. Since extremely fine tuning can be ) 1 (o o RR R F 2 M FF (2-5) (2-6)

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29 achieved from the piezoelectric mounts on the st atic mirror, the degr ee of flatness of the mirrors becomes the limiting finesse in this case. Aperture Finesse, FA A finesse component is also associated w ith the aperture of the system [24]. As one of the mirrors is translated, or scanned, the transmitted fringe pattern collapses on the aperture. The aperture only allows the central portion of the fringe system to reach the detection system at a time, so the detection sy stem integrates what it sees at any given time. Therefore, if a small aperture is used, a small portion of the fringe system is detected at a time and a high aperture finesse is obtained. If a large aperture is used, a larger portion of the ring system is detect ed at any given time, which results in a distortion of the measured profile and a decrease in the aperture finesse. This is analogous to the slit width of a monochromator. From equation 2-7, the aperture finesse can be calculated from known parameters, where the parameters are: f is the focal length of the lens (20 cm), B is the diameter of the aperture (300 m for thallium and 100 m for lead), FSR is the free spectral range (22.0 pm for thallium and 12.0 pm for lead), is the wavelength (535.046 nm for thallium and 405.7807 nm for lead), and FA is the aperture finesse. From the parameters and optics used in this study, the aperture fi nesse is calculated to be 146 for thallium and 286 for lead. This finesse can be increased by reducing the aperture diameter; however, the trade-off is a reduction in the thr oughput of the system and can affect the measurement of lower current profiles. ) )( ( ) )( 8 )( (2 2 B f FFSR A (2-7)

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30Experimentally Determined Finesse The ultimate finesse of the system is limited to the lowest finesse component. To experimentally determine this, a helium-neon la ser at 632.8 nm was used for the thallium mirrors. The results can be seen in figure 2-3. The finesse can be determined by taking the ratio of the FWHM of any order to that of the distance between two adjacent orders. From this ratio, an experimental finesse of 130 was measured, which agrees well with the lowest calculated finesse of 146. For a free spectral range of 22.0 pm, and instrumental FWHM of 0.17 pm is obtained. 0 1 2 3 4 5 6 7 8 Intensity (a.u.)3 Orders FSR/IF = 130.34 Figure 2-3. Experimental determination of the finesse of the interferometer using a helium-neon laser at 632.8 nm. The variations in the intens ity between the 3 orders are due to slight intensity variations in the HeNe source. It should be noted however, that this finesse was measured at 632.8 nm and the thallium transition studied occurs at 535.046 nm. To truly know the finesse of the interferometer at this transition, a line s ource would be needed at, or very near this wavelength. Use of the second harmonic fr om an Nd: YAG laser at 532 nm could be used, however, the laser would need to operate in a single mode in order for it to be considered a line source and such a source was not available. An Ar+ laser lasing at 514.5 nm would not give an accurate representation of the finesse at 535 nm since the

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31 reflection curve drops rapidl y below 520 nm. In addition, a suitable source was not available at 405.8 nm for lead; however, ba sed on a calculated ultimate finesse 134 along with a free spectral range of 12.0 pm, an ad equate instrumental FWHM of 0.09 pm will be sufficient for accurate profile measurements. Broadening Mechanisms The sputtering process in a hollow cathode discharge results in the promotion of atoms to excited energy levels. The excited at oms then relax to the ground state resulting in the emission of photons with wavelengths ch aracteristic of the cathode material. There is a well known relationship between the emi ssion profile and the D oppler temperature of the system, if the profile is dominated by D oppler broadening and has been observed in past works [15-17]. In order to verify this for the present systems, several broadening mechanisms are evaluated for thallium and lead to determine the extent each component will contribute to the overall sh ape of the measured profiles. Natural Broadening Natural broadening is based on the Heisenberg Uncertainty Principle which relates the lifetime of an excited state to th e precision of the energy measurement, as seen from equation 2-8a, where t is the lifetime of the ex cited state (s), h is Plan cks constant (6.626 x 10-34 Js), and is the FWHM of the profile measured (H z). From equation 2-8b it can be seen that the longer the lifetime of the transition, the more time one has to measure the energy and results in greater precision of the meas urement, thus, a narrower observed profile. t h t E 2 1 2 (2-8a) (2-8b)

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32 Since the spontaneous li fetime of the thallium 2S1/2 state and the lead 3P1 o state have been calculated to be 7.52 ns and 5.50 ns, respectively. The spontaneous lifetimes of these states are calculated from transition probabil ities obtained from the Nation Institute of Standards and Technology (NIST). From thes e lifetimes, an obtained natural broadening contribution of 0.020 pm for thallium and 0. 016 pm for lead is calculated from equation 2-8b. Collisional Broadening Collisional broadening, also called pressu re broadening, results in a change in phase of the atomic oscillator when collisions occur between the emitting atom of interest and a foreign gas atom. This can be charac terized by a correlation time, which can be interpreted as the average time between two pha se-changing collisions. According to the Lorentz theory, the broadening contribution due to collisions in the galvatron can be described by [16], where L is the collision cross section between thallium/lead and neon atoms (thallium: ~ 3.0 x 10-17 cm2 [25]; lead: ~ 3.0 x 10-17 cm2 [25]), R is the molar gas constant (8314.51 mJ mol-1 K-1), M1 and M2 are the atomic mass of thal lium/lead (thallium: 204.383 g mol1; lead: 207.241 g mol-1) and neon (20.179 g mol-1), respectively, T is the temperature of the system (1000 K), and no is the number density of the neon filler gas (4.51 x 1017 cm3). It should be noted that a temperat ure of 1000 K was used for all temperature dependent calculations. From equation 29, a collisional broadening FWHM can be calculated to be 1.39 x 10-5 pm for thallium and 7.98 x 10-6 pm for lead. 2 11 1 2 2 M M T R no L L (2-9)

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33Holtzmark Broadening Holtzmark broadening, also called res onance broadening, results by the same mechanism as collisional br oadening, however, Holtzmark broadening results from collisions between two atoms of the same kind, in this case between two thallium or lead atoms. In equation 2-10 [16], H is the collision cross section between two thallium/lead atoms (thallium: 1.20 x 10-12 cm2 [26]; lead: 5.13 x 10-13 cm2 [27]), no is the number density of thallium/lead and is assumed to be 1012 atoms cm-3. It can be seen that the resonance collision cross sections are approximately fi ve orders of magnitude larger than the Lorentz collision cross sections; however, the number density of thallium/lead atoms present is approximately five orders of magnitude smaller th an number density of neon. From equation 2-10, a Holtzmark broadening FWHM can be calculated to be 5.21 x 10-7 pm and 9.01 x 10-8 pm for thallium and lead, respectively. Instrument Function Broadening In any measurement system there is some inherent contribution of the measurement system to the profile being measur ed. It is always desirable to reduce this contribution as much as possible to the point were its contribution becomes negligible. In an interferometric system, the finesse and fr ee spectral range will dictate the instrument function of the interferometer. For thallium measurements, an experimental finesse of 130 was measured with a free spec tral range of 22.0 pm as shown in figure 2-3. For lead, an ultimate finesse of 134 was calculated, a nd a free spectral range of 12.0 pm was used (2-10) M T R no H H 4

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34 for profile measurements. From these values the instrument function was calculated as follows, where F is the finesse of the system and FSR is the free spectral range of the interferometer as calculated by equation 23a. From equation 2-11, an instrumental FWHM of 0.17 pm is calculated for thallium and 0.09 pm is calculated for lead. Doppler Broadening Doppler broadening is the result of a st atistical distribution of velocities of the emitting atoms along the observation path. Sinc e atoms are in motion with respect to the observation line, the Doppler Effect causes a statistical distributi on in the frequencies observed that is directly related to the veloci ty distribution and is temperature dependent. The Doppler broadening contribu tion can be calculated as where o is the frequency of the transition being observed (thallium: 5.60 x 1014 Hz; lead: 7.388 x 1014 Hz). From equation 2-12, a Doppler broadening FWHM can be calculated to be 0.85 pm for thallium and 0.64 pm for lead. Self-Absorption Broadening Self-absorption broadening occurs when the system has an emitting layer followed by an absorbing layer with both layers in similar thermal environments. If both layers are optically dense, the measured emission from the system will appear broadened. This is due to the preferential absorption at the kernel of the profile, where the frequency FFSR IF M RT co D2 2 ln 2 (2-11) (2-12)

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35 dependent absorption coefficient is large, as compared to th e wings of the profile where the absorption coefficient is smaller. This re sults in an apparent br oadening of the profile with a non-Gaussian shape [28,29]. Ther e is no simple equation to predict the contribution of self-absorption; however, prev ious works have shown that self-absorption does contribute to the broadening of the profil e, especially at high currents [15-17]. Other Broadening Mechanisms Other broadening mechanisms to consider are Stark broadening ( S), molecular quenching broadening ( MQ), and broadening due to unres olved isotopic shifts or hyperfine structure. Most atoms emit in the negative glow region of the discharge, and since this region is known to be a nearly fiel d free region, Stark broadening is expected to be negligible. The present systems are fill ed with a very high purity of neon, with molecular concentrations less than 1 ppm [3 0], therefore, broadening due to molecular quenching will be negligible. Broadening due to unresolved hyperfine structure is expected to occur due to small unresolved transitions within th e envelope of larger peaks, which will contribute slightly to the overall observed profile, however, the amount this will contribute can only be evaluated using an appropriate model. Evaluation of Broadening Mechanisms From the calculations made on each of the broadening mechanisms, which are based on known parameters and a temperatur e of 1000 K, it can be concluded that the dominating broadening mechanism is Doppler broadening, which has also been observed in past works [15-17]. The next largest co ntributing factor comes from the instrument function; however, since it is approximately five times narrower than the expected Doppler width, it is not expected to significantly contribute to the width of the profile. All other contributions are several orders of magnit ude narrower than the expected

PAGE 36

36 Doppler profile and therefore can be consider ed negligible. A summ ary of all broadening contributions considered for both thallium and lead is shown in table 2-1. Table 2-1. Calculated broadening component s for thallium and lead that would be expected in a galvatron based on known parameters and an assumed temperature of 1000 K. Tl Pb N ( N) 21.2 MHz (0.020 pm) 28.9 MHz (0.016 pm) C ( C) 0.014 MHz (1.39 x 10-5 pm) 0.014 MHz (7.98 x 10-6 pm) H ( H) 546 Hz (5.21 x 10-7 pm) 164 Hz (9.01 x 10-8 pm) D ( D) 890 MHz (0.85 pm) 1.16 GHz (0.64 pm) IF ( IF) 177 MHz (0.17 pm) 164 MHz (0.09 pm) S ( S) negligible negligible MQ ( MQ) negligible negligible Experiment The experimental apparatus used can be seen in figure 2-4. It consists of a galvatron, hollow cathode lamp, or an elec trodeless discharge lamp. The emission is collected with a 1 inch diameter glass lens with a focal length of 15 cm. The lens was placed at 15 cm (1f) from the face of the cathode in or der to collimate the emission. Due to optical table size constraints, the collim ated emission was reflected 90 using a one inch diameter aluminum coated mirror to wards the Fabry-Perot interferometer and detection system. As mentioned previously, a restricting iris was used prior to the interferometer. This was used to restrict the surface area inci dent on the mirrors in an attempt to increase the flatness finesse. An optimal restricting ir is diameter of 2.5 mm was found to result in a maximum resolving power and throughput for both lead and thallium measurments. A larger diameter would reduce the flat ness finesse, making it the limiting finesse,

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37 therefore, reduce the resolving power. A sma ller diameter would not result in an increase in resolving power and would only reduce the si gnal intensity. Since the galvatron is not a well defined point source, some of the collected emission will be slightly divergent. Consequently, a restricting iris is advantageous in that it also spatially filters the emission into a more highly collimated beam of emission. Figure 2-4. Experimental set-up for the meas urement of the lead and thallium emission profiles from a laser galvatron, ho llow cathode lamp, and an electrodeless discharge lamp. The Fabry-Perot interferomet er used in this study invol ves piezoelectric scanning. A high voltage ramp generator (EXFO Burlei gh) applies a saw-tooth voltage to the piezoelectric crystal, translating one of th e mirrors linearly. The expansion of a piezoelectric crystal is not linear with voltage ; however, a first orde r polynomial can be applied to the ramp voltage waveform in or der to provide a lin ear translation with voltage. This calibration was accomplished by observing several orders from a HeNe laser and adjustments were made to the voltage waveform until the temporal spacing between adjacent transmission peak s were the same for all orde rs observed. The linearity Scanning Fabry-Perot Interferometer X Y Z Ramp VoltagRamp Time PMT Monochromator Current Amplifier Trigger 0.350 1 5 Mirror Restricting Iris Lens LensScanning ApertureThallium Galvatron

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38 of the mirror translation in time results in evenly spaced orders, which is extremely important in the conversion of the x-axis from time to wavelength. The ramp generator offers a variable scan rate which determines the time taken to complete one scan; varing from 20 ms to 10 s. This permits the rapid scanning of emission prof iles and allows real time adjustments of mirror parallelism for rapi d optimization of the signal. In addition, a signal-to-noise advantage can be gained by averaging several scanned profiles. The voltage amplitude can also be varied from 0 V to 1000 V, which determines the distance the translating mirror travels, thus, the number of orders that are observed on the oscilloscope for a single scan. The ramp ge nerator also provides a trigger output. This allowed the oscilloscope to be triggered when the voltage ramp is initiated. The second Fabry-Perot mirror is static a nd is attached to two piezoelect ric crystals. Applying a D.C. voltage individually to these crystals allows fine tuning of the parallelism between the two mirrors with respect to one another. The light transmitted through the Fabry-Perot is collected with a 20 cm focal length lens and is imaged onto an aperture. The apertu re is simply a metal plate with a pinhole drilled in the center. As the Fabry-Perot scans, the fringe system collapses onto this aperture so that only a very small portion of the profile is allowed to be transmitted and be detected at any given time during the scan. The emission that is transmitted through th e aperture is collected using a 500 mm focal length monochromator (A cton 500i) with 2400 grooves mm-1 grating and entrance and exit slit widths of 1 mm. The monochromator acts as a spect ral filter so that only the emission line of interest is de tected and filters out neighbor ing emission lines. Detection is made with the use of a photomultiplier t ube (R928 Hamamatsu) with -1000 V applied

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39 from a high voltage power supply. The signal is sent to a low-noi se current amplifier (Stanford Research Systems m odel SR570) which allows the signal to be amplified and filtered. The amplified signal is observed with a 100 MHz oscilloscope (Tektronix model TDS 3012B) which was set to average 512 waveform s in order to obtain the best signal to noise ratio prior to recording the profile. Results Since the scanning mirror translates towa rds the static mirror during the voltage ramp, the profile is scanned from higher wave length to lower wavelength when read from left to right. To view the profile in terms of wavelength, the profile is flipped 180 on the x-axis. In order to convert the x-axis from time to wavelength, the free spectral range must be known. This is done by using a metric caliper and measuring the plate separation, d, and using equation 2-3a. The wi dth of the hyperfine structure is approximately 13 pm wide for thallium and 7 pm for lead from center of the first component to the center of the last component. In order to obtain the highest resolving power possible without order ove rlap, the free spectral range of the interferometer is set to 22.0 pm for thallium measurements and 12.0 pm for lead measurement. The distance from any point on one order to the same point on an adjacent order is defined as the free spectral range, and since the plat e translation is linear, time can be converted into relative wavelength shift. By setting the most inte nse peak to zero, every evenly spaced time point is converted into a wavelength shift relati ve to the zero peak. All profile intensities are then normalized, allowing the measuremen t of emission profiles in the form of normalized intensity versus wavelength.

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40420246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) 30.0 mA 20.0 mA 15.0 mA 10.0 mA Theoretical shifts and intensities420246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) 5.0 mA 8.0 mA 10.0 mA 15.0 mA 25.0 mA 30.0 mA 35.0 mA 40.0 mA Theoretical shifts and intensities Figure 2-5. Experimental profiles of th e 535.046 nm transition of thallium from A) galvatron and B) hollow cathode lamp. Once experimental parameters were optimized and adjustments made to obtain the highest resolving power possible, the profil es of several currents were recorded from the thallium and lead galvatrons. The final profiles were plotted and normalized to one. The results of the thallium galvatron can be seen in figure 2-5 and the results from the lead measurements can be seen in figure 26. As mentioned previously, galvatrons operate in a similar manner as hollow cathode lamps. Therefore, profiles from a neonfilled Jarrell Ash thallium hollow cathode la mp and neon-filled Fisher lead hollow cathode lamp were recorded for comparison. 54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) 3.0 mA 5.0 mA 8.0 mA 10.0 mA 15.0 mA 20.0 mA Theortical Shifts and Intensities54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) 6.0 mA 10.0 mA 15.0 mA 20.0 mA 25.0 mA 30.0 mA 35.0 mA 40.0 mA Theortical Shifts and Intensities Figure 2-6. Experimental profiles of th e 405.7807 nm transition of lead from A) galvatron and B) hollow cathode lamp. Both sources were measured under the same experimental setup. B) A)

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41 A comparison of the thallium hollow cathode lamp and thallium galvatron operated at similar currents is shown in figur e 2-7. As can be seen, the hollow cathode lamp displays a much broader and more highl y self-absorbed profile than that of the hollow cathode lamp. The reason for this may be related to the pressure inside the two discharge lamps. By reducing the pressure inside the hollow cat hode discharge tube, a larger mean free path results, therefore, an increase in kinetic energy transfer from the ionized neon atom to the cathode surface [19] The direct result is an increase in sputtering efficiency which yields higher number densities than for a higher pressure discharge operated at a similar current. An increase in the number density of sputtered species yields emission profiles th at are more susceptible to se lf-absorption. It should be noted, however, that not knowing the pressure of neon inside the hollow cathode lamp makes it difficult to make any direct co mparison between the two emission sources. Figure 2-7. Comparison between a thallium galvatron and a thallium hollow cathode lamp profiles operated at the same cu rrent. All profiles are normalized. 420246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 10.0 mA Galvatron Hollow cathode lamp Theoretical Shifts420246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 15.0 mA Galvatron Hollow cathode lamp Theoretical shifts420246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 20.0 mA Galvatron Hollow cathode lamp Theoretical shifts420246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 30.0 mA Galvatron Hollow cathode lamp Theoretical shifts

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42 Comparing the results between the lead galvatron and lead hollow cathode lamp in figure 2-8 clearly demonstr ates the opposite is observed. The profiles obtained from the lead galvatron clearly show a broader pr ofile with a great amount of observed selfabsorption. As mention previously, this may be explained by the different pressures present in the discharge. Si nce the pressure in either lamp is unknown, it is difficult to draw any direct conclusions; however, it would stand to reason that the pressure in the lead galvatron may be less than the lead hollow cathode lamp. Figure 2-8. Comparison between a lead ga lvatron and a lead hollow cathode lamp profiles operated at the same current s. All profiles are normalized. The profiles of a thallium electrodeless discharge lamp were also studied and are shown in figure 2-9. It can clearly be seen that the electrodeless discharge lamp displays a larger susceptibility to self-absorption, a nd self-reversal at higher powers. Profiles at powers larger than 20 W could not be measured with a free spectral range of 22.0 pm due 54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 10.0 mA Galvatron Profile Hollow Cathode Profile Theoretical Shifts and Intensities54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 15.0 mA Galvatron Profile Hollow Cathode Profile Theoretical Shifts and Intensities54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 20.0 mA Galvatron Profile Hollow Cathode Profile Theoretical Shifts and Intensities

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43 to distortions in the wings of the profiles from two adjacent orders. This is known as order overlap, where the profile broadens to a point larger than the free spectral range. This results in the wings of two adjacen t orders overlapping with each other causing distortion of the profiles. Order overlap can be corrected by increasing the free spectral range; however, this also results in an in crease in the instrumental FWHM of the interferometer. 642024681012141618 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) 13 W 14 W 16 W 18 W 20 W Theoretical shifts Figure 2-9. Experimental profiles of th e 535.046 nm transition of thallium from an electrodeless discharge lamp. Discussion Analysis of the experimental profiles was performed using the two-layer model described by Braun et al. [31]. The model describes the di scharge in terms of two layers, an emitting and absorbing layer followed by a non-emitting absorbing layer. For the emitting and absorbing layer, the intensity, I1, is given by ] ) ( exp[ 1 ) (1 1 1l n I The parameters are () is the frequency dependent absorption cross section (cm2), n1 is the number density of absorbing atoms (cm-3), and l1 is the optical path length of the emitting and absorbing layer (cm). The frequency dependent absorption cross section for a Doppler line can be expressed as: (2-13)

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44 2exp ) (D o o The parameters are: o is the peak cross section, ( o) is the radiation frequency relative to the center of the line, and D is the Doppler width. The absorbing layer that directly follows the emitting layer transmits the emission and can be described as 2 2 1 2) ( exp ) ( ) ( l n I I where the subscripts 1 and 2 denotes th e emitting and absorbing layer and the nonemitting absorbing layer, respectively. By combining equations 2-13, 2-14, 2-15, introducing equation 2-16a as the optical dept h of the respective la yer, and taking into account a multi-component system, the following expression is derived for the measured emission from the second absorbing layer: l no OD i D o OD i D o ODi C i C I2 2 2 1 2exp ) ( exp exp ) ( exp 1 ) ( where the summations are taken over i components. Both thallium and lead transitions studied here contain six components as shown in figure 2-1. A constant, C, is added to give each component a weight in order to correct for intensity due to the natural abundance of each isotope and degeneracy of each hyperfine component. Analysis of the galvatron profiles wa s done by calculating the profile with the model described above using MathCAD. Th e calculated profiles were then normalized and plotted with the experimental profiles in Origin. As can be seen from equation 216b, there are three paramete rs that can be varied, OD1, OD2, and D which is controlled through the Doppler temperature. All three para meters were adjusted appropriately until (2-14) (2-15) (2-16b)

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45 the best fit to the experimental profiles was obtained. Results of some calculated emission profiles for the thallium galvatron and lead hollow cathode lamp can be seen in figures 2-10 and 2-11. Figure 2-10. Calculated profiles fitted to the experimental profiles of a thallium galvatron at currents of 10, 15, 20, and 30 mA. 864202468101214161820 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) Current = 10.0 mA Experimental Profile Calculated Profile (1 = 0.32, 2 = 0.40, T = 495 K) Theoretical Shifts and intensity864202468101214161820 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) Current = 15.0 mA Experimental Profile Calculated Profile (1 = 0.50, 2 = 0.58, T = 530 K) Theoretical Shifts and intensity864202468101214161820 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) Current = 20 mA Experimental Profile Calculated Profile (1 = 0.60, 2 = 0.80, T = 565 K) Theortical Shifts and intensity8642024681012141618200.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) Current = 30 mA Experimental Profile Calculated Profile (1 = 0.98, 2 = 1.4, T = 630 K) Theortical Shifts and intensity

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46 Figure 2-11. Calculated profiles fitted to the experimental profiles of a lead hollow cathode lamp for currents of 6, 10, 15, and 20 mA. The fit of the calculated profiles to that of the experimental profiles in figures 210 and 2-11 shows a fairly adequate fit. The region where it fails slightly is in the wings of the higher current profiles. This discrepanc y is a result of the model using a Gaussian function; however, the presence of self-abs orption is known to result in a non-Gaussian profile [28,29]. Despite the minor discrepanc ies between the experimental results and the model, an adequate fit is obtained and the information from it is still valid. Therefore, the model was applied to all thalliu m and lead emission profiles. 54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 6.0 mA Experimental Profile Calculated Profile1 = 0.2 2 = 0.25 T = 320 K Theortical Shifts and Intensities54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 10.0 mA Experimental Profile Calculated Profile1 = 0.25 2 = 0.35 T = 350 K Theoretical Shifts and Intensities54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 15.0 mA Experimental Profile Calculated Profile1 = 0.45 2 = 0.58 T = 385 K Theoretical Shifts and Intensities54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 20.0 mA Experimental Profile Calculated Profile1 = 0.70 2 = 0.95 T = 405 K Theoretical Shifts and Intensities

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4746810121416182022242628303234 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 Applied Power (W)Doppler Temperature (K)Applied Current (mA) Galvatron Hollow cathode lamp12.513.013.514.014.515.015.516.016.517.017.518.018.519.0 Electrodeless discharge lamp051015202530354045 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625 650 Doppler Temperature (K)Applied Current (mA) Hollow Cathode Lamp Galvatron Figure 2-12. Doppler temperature values obtain ed from the fit of th e calculated two layer model for A) 535.046 nm transition of thallium and B) 405.7807 nm transition of lead from a galvatron, hollow cat hode lamp, and electrodeless discharge lamp. Doppler temperature values for the thal lium and lead galvatron, hollow cathode lamp, and thallium electrodeless discharge la mp obtained from the fit of the two-layer model can be seen in figure 2-12. These values are in reasonable agreement with previously reported Doppler temperature valu es [15-17] for hollow cathode lamps. The precision of all calculated emission profiles measured was found to be 15 K. 468101214161820222426283032 680000 700000 720000 740000 760000 780000 800000 820000 840000 860000 880000 900000 920000 Galvatron Hollow cathode lampResolving PowerCurrent (mA)051015202530354045 750000 800000 850000 900000 950000 1000000 1050000 1100000 1150000 1200000 Galvatron Hollow cathode lampResolving PowerCurrent (mA) Figure 2-13. Calculated reso lving powers for A) thallium galvatron and hollow cathode lamp and B) lead galvatron and hollow cathode lamp. A) B) A) B)

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48 From the Doppler temperatures obtained, the resolving power for the thallium and lead galvatron and hollow cathode lamp can be calculated by Rpower = / where is the wavelength of the transition (thall ium: 535.046 nm; lead: 405.7807 nm) and is the FWHM of the Doppler broadened absorp tion profile, calculated from Doppler temperatures shown in figure 2-13. The FW HM of an absorption profile from a flame can be approximately 1 to 5 pm, depending on flame type and composition, which results in resolving powers on the order of 100,000 to 500,000. As for commercially available spectrometers, resolving powers of 10,000 to 50,000 are typically obtained. Higher resolving powers can be obtaine d; however, cost and size can be considerably increased and is often accompanied with a loss of throughput. Resolv ing powers for sealed cells can be similar to those found for the galvatr ons and hollow cathode lamps; however, they are dependent on the temperatur e applied as well as the type and pressure of buffer gas used. 2468101214161820222426283032 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 Optical Depth (dimensionless)Applied Current (mA) Galvatron emitting layer Galvatron absorbing layer HCL emitting layer HCL absorbing layer12.513.013.514.014.515.015.516.016.517.017.518.018.519.0 Applied Power (W) EDL emitting layer EDL absorbing layer051015202530354045 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Optical Depth (dimensionless)Applied Current (mA) HCL Emitting Layer HCL Absorbing Layer Galvatron Emitting Layer Galvatron Absorbing Layer Figure 2-14. Optical depth values obtained from the fit of the calculated two layer model for A) 535.046 nm transition of thalli um and B) 405.7807 nm transition of lead for a galvatron, hollow cathode la mp, and electrodeless discharge lamp. B) A)

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49 Figure 2-14 shows that as the current, or power, increases, the optical depth of both layers also increase. This is expected, since the number density, n, increases with increasing current or power. If it is assumed that all atoms in the system can be found in either the emitting layer or absorbing layer, then equation 2-16a can be rearranged to calculate the number density of the thallium and lead metastable state if the absorption cross section and path lengt h of the system are know. l no OD OD T 2 1 Using an absorption cross section [11] of 5.2 x 10-12 cm2 for the thallium 535.046 nm transition, assuming a path length of 2 cm and using optical depth values of 0.32 (emitting layer) and 0.40 (absorbing layer) obtained from the model for the two layers of the thallium galvatron at 10.0 mA, a cal culated a number density of 6.93 x 1010 cm-3 is obtained for the 6 2P3/2 o state. This value is further validated by comparing it to values obtained by saturated fluorescence [32] a nd high resolution absorption measurements [33]. For an applied current of 10.0 mA, number density values of 5.30 x 1010 cm-3 and 4.24 x 1010 cm-3 were obtained from saturated fluorescence and high resolution absorption measurements, respectively, and are in fair agreement with the value obtained from the analysis of the emission profiles. A path length of 2 cm, wh ich is the length of the cathode bore, was used for the number density calculations for all methods. These are reasonable values obtained for this metastable level; however, these are approximate values since the path length of the two layers is not known with a high degree of accuracy. If equation 2-17 is applied to all the emission profiles, the resulting plot of number density for the metastable state of the galvatron for the four currents measured results in figure 2-15 (2-17)

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50 8101214161820222426283032 6.0x10108.0x10101.0x10111.2x10111.4x10111.6x10111.8x10112.0x10112.2x10112.4x10112.6x1011 TlNumber Density (atoms cm-3)Current (mA)246810121416182022 1x10102x10103x10104x10105x10106x10107x10108x10109x10101x1011 PbNumber Density (atoms cm-3)Current (mA) Figure 2-15. Number density values obtained from optical depths obtained from the application of the two laye r model for A) thallium and B) lead using equation 2-17. Similarly, equation 2-17 was applied to the optical depths obtained from analysis of the lead emission profiles in order to calculate the number density for each applied current. Using a calculated absorption cross section of 2.45 x 10-11 cm2 and a path length of 2 cm was used for this calculation a nd results can be seen in figure 2-15. These results are verified by comparison with saturated fluorescence measurements and conventional absorption measurements. Values of 6.90 x 1010 cm-3 and 5.42 x 1010 cm-3 were obtained from saturated fluorescence and conventional absorption measurements, respectively. These values agree we ll with a number density of 5.20 x 1010 cm-3 obtained from emission results for an applied current of 10.0 mA. Values obtained from saturated fluorescence and conventional absorption measurements will be discussed in greater detail in following chapters. Absorption cross section was calculated using an average number density value obtained from saturated fluorescence and conventional absorption measurements, assuming a path length of 2 cm, and using equation 2-17. A) B)

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51Conclusion Measurement of the hyperfine structure of the 535.046 nm transition of thallium and the 405.7807 nm transition of lead in a see-through hollow cathode discharge was accurately measured with a Fabry-Perot spectr ometer to investigate its potential as a narrow band atomic line filter. The data obtained from the two-layer model has shown that the thallium hollow cathode lamp and el ectrodeless discharge la mp both show larger amounts of self-absorption, hi gher Doppler temperatures, and larger optical depths than the thallium galvatron when compared to similar applied currents. However, the opposite was observed from the lead analysis. The twolayer model used to analyze the profiles of the three emission sources was quite successful in view of its simplicity; however, it failed to accurately model the self-rever sed profiles of the hollow cathode lamp and electrodeless discharge lamp. This is expected to be due to the presence of a temperature gradient, therefore, at least two Doppler temperatures should be used in the modeling of the experimentally obtained profiles, one for each layer. The addition of this parameter would make it difficult to obtai n reliable values and should be done with a curving fitting program for best results. The spectral resolution of the thallium galv atron was found to be superior to that of a traditional hollow cathode lamp and el ectrodeless discharge lamp, however, the spectral resolution of the lead galvatron was found to be less than a traditional hollow cathode lamp. Despite these differences, both the galvatron and hollow cathode lamp still yield superior resolving powers when compared to other atom reservoirs and spectrometers. Number densities were al so obtained for both thallium and lead galvatrons by use of the optical depth values obtained from analysis of emission profiles. These number density values were verified by fluorescence and absorption methods and

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52 agree well with values obtained from emission results. These are simple systems capable of producing an acceptable number density that is both stable and reproducible. They are atomic reservoirs that are not plagued by probl ems such as those associated with sealed cells, flames, and ICP torches.

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53 CHAPTER 3 NUMBER DENSITY MEASUREMENTS IN A SEE-TH ROUGH HOLLOW CATHODE DISCHARGES WITH A HIGH RESOLUTION FABRY-PEROT SPECTROMETER Introduction In order to evaluate the resolving power of this atomic line filter, high resolution absorption measurements are needed. Hi gh resolution absorption measurements on atomic vapors are typically done with narro w band diode lasers capable of scanning across the absorption profile. However, most at omic transitions of interest are in the UV region not easily accessible by diode lasers. Another common approach is the use of a continuum source with a high resolution m onochromator; however, typical conventional grating and echelle monochromators [34,35] have been shown to give inadequate resolution and throughput, necessary for these measurements. Fabry-Perot interferometers have also been used in conjunction with continuum sources. In this method, radiation from a c ontinuum source is sent through an absorbing medium and then to a FabryPerot spectrometer. In orde r to better understand how this occurs, it is best to begin with a simp le system containing only two monochromatic wavelengths as shown in figure 3-1. It can be seen that the interferometer produces the characteristic circular fringe pattern for each wavelength with its multiple orders. If this interference pattern is imaged onto the slit of a monochromator, the result will be sections of the dispersed radiation sepa rated vertically. The grati ng of the monochromator then disperses the radiation horizontally according to the wavelength. The final result imaged onto the exit slit of the monochromator is the two wavelengths cross dispersed. If this idea is expanded to a continuum source, the result will be many wavelengths constructively interfered and cr oss dispersed onto the exit slit of the monochromator. As

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54 the Fabry-Perot is tuned, or scanned, the result will be a line source capable of scanning across the absorption profile of interest; however, several problems are associated with this approach. Kirkbright et al. [36] applied this method to the measurement of calcium in a flame using a monochromator with a spectral bandpass of 2 nm. In those measurements, the monochromator had such a poor resolution that absorption measurements were only possible with an extremely high concentration of the salt solution. The weak absorption signal wa s due to a large a nd unknown number of nonabsorbing channels being detected simultaneous ly with the resonant absorbing channels, which resulted in a very weak, or diluted, absorption signal and was only overcome by averaging multiple data along with a very hi gh absorber concentration. Figure 3-2 A clearly demonstrates how the use of a low resolution monochromator results in a very weak, or diluted, absorption signal. Wagenaar et al. [37] also applied this method to the measurement of calcium, but with a high reso lution monochromator capable of resolving one free spectral range. This approach also required a high concentration of calcium in order to obtain absorp tion profiles. The profiles that were obtained yielded a poorly defined baseline due to the monochromator bandpass which resulted in a loss in the wings of the profile as shown in figure 3-2 B. The lack of a well defined baseline makes it difficult for accurate absorption coefficien ts and Doppler widths to be assigned. Another problem encountered was the limited temperature stability of the monochromator, which caused the selected ba ndpass of the monochr omator to slowly drift away from the absorption profile. So me of these problems were alleviated by synchronizing the tuning of the Fabry-Perot with the grating of the monochromator. This allowed the detection of a si ngle order as it scanned acr oss the absorption profile;

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55 however, this approach require d careful synchronization of the two components as well as special grating components capable of achieving the slow scan rate. Figure 3-1. Illustration of a Fabry Perot interferometer and a monochromator used as a cross dispersion system for tw o monochromatic wavelengths. Figure 3-2. Tutorial for the me thod of using a continuum source. A) Represents the use of a monochromator with a large spectral bandpass. B) Represents the use of a monochromator with a small spectral bandpass. In 1970, Bazhov and Zherebenko [38] introduced a method using two electrodeless discharge lamps to create a quasi-continuum source over the absorption order m m+1 m+2 order m m+1 m+2 monochromator bandpass monochromator bandpass absorption profile absorption profile Interference pattern imaged onto the exit slit of the monochromato r m m+1 m+2 m+1 m m+2 1 2 Interference pattern b ehind entrance slit Interference pattern imaged onto the entrance slit of a monochromato r B) A )

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56 profile of interest. This wa s achieved by setting one emissi on source to be self-reversed and another emission source to be self-a bsorbed. These two emission sources superimposed onto one another resulted in a broadened, flat topped emission profile centered over the absorption profile as shown in figure 3-3. Using this approach retains the resolving power of a FabryPerot interferometer and greatly relaxes the restrictions of the monochromator, only needing the resoluti on capable of isolating the broad quasicontinuum from neighboring spectral lines which can be easily achieved with commercially available monochromators. Passing the combined emission profiles through an absorbing medium will result in absorption of the emission and will be characteristic of the absorption profile of the atomic vapor. If the resulting emission profile is obtained by the scanning Fabry-Pero t spectrometer, the result should be the emission profile containing the absorption profil e, as shown in figure 3-3. Since line sources are used, the combined emission pr ofile will be centered directly over the absorption profile and provides excellent wavele ngth stability without the need to worry about wavelength tuning, fluctuations, or dr ift. There was no need for unrealistically high absorber concentrations and the thermal stability of the monochromator was unimportant. The relaxation of the slit width restrictions of the monochromator greatly improved the throughput of the system and allowed for a much higher signal to noise ratio. In addition, the signal to noise ra tio will be further enhanced by the use of an electrodeless discharge lamp and hollow cathode lamp rather than a Xe-arc lamp. Xe-arc lamps have significant low frequency flicker no ise due to arc wander, and since the noise is generated from the source, the use of a lo ck-in will have no effect. The use of the approach proposed by Bazhov and Zherebenko [38], described above, allows both the

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57 determination of the resolving power of the atomic line filter, as well as number density measurements, if the profile can be well resolv ed with an acceptable baseline and signal to noise ratio. Figure 3-3. Illustration of the production of a quasi-continuum s ource from two line sources for the measurement of high resolution absorption measurements. Experimental The 535.046 nm light from a thallium EDL (Perkin Elmer) and thallium hollow cathode lamp (Jarrell Ash) was collimated and combined with a 50/50 beam splitter as shown in figure 3-4. The light is focuse d through the bore of the see-through hollow cathode discharge followed by a lens to re-collim ate the light. Due to the dimensions of the optical table, the light is reflected 90 with a mirror and sent to the interferometer. The interferometer (Coherent Optics Inc. 370) is co mposed of a static mirror and a translating mirror. A high voltage ramp generator (EXFO RG-91) applies a voltage from 0-1000 V in a saw tooth waveform. As the voltage is ramped the piezo-electric crystal linearly translates the mirror and ther efore, scans across the profile. The resulting interference pattern is collect ed and focused onto an apertu re placed in front of the monochromator (Acton 500i). The aperture has a 300 m diameter and allows the passing of only the central portion of the interf erence pattern. Therefore, as the mirror translates, the circular interference pattern co llapses onto the aperture and the transmitted light is filtered by the monoc hromator tuned to the 535.046 nm transition. The scanning + + Self-reversed profile Self-absorbed profile Absorption profile Measured Absorption profile Combined Emission profile

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58 Fabry-Perot was found to have an experiment ally determined finesse of 130. A mirror separation of 6.50 mm resulted in a free spect ral range of 22.0 pm. This arrangement yielded an instrument FWHM of 0.17 pm, which should be more than capable of resolving the absorption profiles. Alignm ent of the interferometer was accomplished with a HeNe laser. Since the see-through hollow cathode di scharge is also a thallium emission source, it will produce 535.0 nm emission. Fo r this reason, a mechanical chopper is used to modulate the combined line sources. Th e resulting signal from the photomultiplier tube (Hamamatsu R928) is then amplified with a current amplifier (Stanford Reseach Systems model SR570) and sent to a lock-i n amplifier (EG&G) for phase sensitive detection. Since the shortest time constant of the lock-in is 1 ms, the scanning of the interferometer must be considerably slower, otherwise a distortion of the true signal will result. For this reason, a function generator is used to control the ramp generator. A Tektronix function generator capable of producing a triangl e waveform with a 2 x 10-4 Hz frequency is used. Scanning the profile at this frequency allowed the use of a 1 s time constant on the lock-in amplifier. This resulted in the best signal to noise ratio without distortion of the recorded profile.

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59 Figure 3-4. Experimental set up used for high resolution abso rption profile measurements. Results and Discussion The combination of the two line sources results in a quasi-continuum source for the thallium 535.046 nm transition as shown in figure 3-5. The profiles of the EDL and HCL are also measured individually. Figure 3-5. A) Scan of the EDL profile self-re versed. B) Scan of the HCL profile selfabsorbed. C) Resulting profile of the combined profiles yielding a quasicontinuum source over the absorption profile. H.V. H.V. Chopper Monochromator H.V. Piezo Controller Strip chart Recorder 50/50 BS Len Len Len LenLens Iri Mirro Fabry-Perot Thallium Galvatron Thallium EDL Thallium HCL PMT A p erture kl klf I ND filter Current Amplifier Function Generator Lock-in Amplifier Restricting Iris A) B) C)

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60 Figure 3-6. Resulting absorpti on profiles of the thallium 6 2P3/2 o metastable state of thallium due to various currents app lied to the see-through hollow cathode discharge. The blue wing on the quasicontinuum profile is cut off due to a small amount of order overlap from an ad jacent order. This order overlap did not cause distortion of the observed absorption profiles. Figure 3-6 show the results of spectral scans at four currents applied to the galvatron. The results obtained are similar to those obtained by Wagenaar et al. [37], with a poorly defined baseline. An impr oved baseline could be obtained by broadening each profile; however, the width of the prof ile is already slightly too broad for the selected free spectral range of the interferom eter. Increasing the emission profile would result in severe order overla p which would distort the true profile. The free spectral range could be adjusted to accommodate for order overlap but would also result in a broader instrument FWHM, resulting in an unacceptable resolution for these measurements. 10.0 mA 15.0 mA20.0 mA25.0 mA 0.0 mA

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61 The measurements in figure 3-6 are the result of absorption from the F2 F1 transition for the two isotopes, 203Tl and 205Tl, as shown in figure 7. The number density of each isotope can be calculated using the peak absorption coefficient. This method assumes that the spectral line is fully reso lved which is a good a pproximation considering an instrument FWHM of 0.17 pm was used Calculation of the number density by measurement of the peak absorption coe fficient can be done using the following equations [39], where Io is the intensity of incident light and I is the intensity after absorption. The absorption path length, l, is assumed to be 2 cm, the length of the cathode bore. The FWHM of the Doppler broadened absorption profile, D (Hz), can be calculated from equation 3-1b, where o is the central frequency of the transition (5.603 x 1014 Hz), T is the Doppler temperature (K), and M is the atomic mass (204.383 g mol-1). The Doppler temperature values used for this calculat ion were obtained by high resolution emission measurements [40]. Since the hyperfine struct ure was measured, the oscillator strengths (fij) in equation 3-1a must be determined for each hyperfine component. This is accomplished by the following relationship and is calculated as follows [41], l I I k M T f k No o o D D o ln 10 16 7 10 65 2 2 4697 07 12 2 (3-1a) (3-1b) (3-1c)

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62 Figure 3-7. Hyperfine structure fo r the thallium 535.046 nm transition with relative intensities, Iij. ( ) thallium 203 isotope, ( ) thallium 205 isotope. Not drawn to scale. If all calculated values are combined a nd substituted into equation 3-1a, the number densities for each isotope are determined. From equation 3-4, the total number density of the 6 2P3/2 o metastable state can be calculated by high resolution absorption measurements. The results obtained from the F1 F1 I11 = 0.20 F2 F1 I21 = 1 F1 F0 I10 = 0.40 1 2 1 2 m k mn kl mn klF F f f I I 4 5 40 0 1 ] 1 ) 1 2 [( ] 1 ) 2 2 [( 4 4 40 0 20 0 ] 1 ) 1 2 [( ] 1 ) 1 2 [( 4 5 1 20 0] 1 ) 2 2 [( ] 1 ) 1 2 [(10 21 10 21 10 21 10 11 10 11 10 11 21 11 21 11 21 11f f f f I I f f f f I I f f f f I I0331 0 0955 0 0214 010 21 11 f f f (3-2) (3-3) 15 010 21 11 total totalf f f f ftotaln n n 203 205 (3-4) F1 F0 F2 F1 7 2S1/26 2P3/2 o

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63 calculation of the number density are in fair agreement with values obtained by high resolution emission measurements [40] shown in figure 3-8. The discrepancy between the two methods may be attributed to the poor ly defined baseline of the profiles obtained in figure 3-6. As explained previously, th e lack of a well defined baseline makes it difficult to accurately determ ine the Doppler widths, as we ll as calculate the peak absorption coefficient, equation 3-1c, and can yield an inaccurate number density values. 46810121416182022242628303234 101010111012 Number Density (atoms cm-3)Galvatron Current (mA) High resolution emission High resolution absorption Figure 3-8. Number density measurement of the 6 2P3/2 o metastable state of thallium by absorption and emission measurements. Conclusions It has been shown that the combination of two line sources to generate a quasicontinuum source is capable of measuring the absorption profile of a hollow cathode discharge. The results obtained are similar to th ese obtained by Wagenaar et al. [37], who had a poorly defined baseline; however, in these measurements a poor resolution monochromator was used which greatly re laxed the slit width requirement. This increased the throughput of the system resulti ng in a higher signal to noise ratio. Also,

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64 the use of two stable line sources, EDL a nd HCL, greatly reduced the low frequency flicker noise commonly associated with Xe-arc lamps. It should be noted here that the quas i-continuum source co uld potentially be generated by another approach. If the EDL we re subjected to a magnetic field, then the Zeeman effect would split these levels, with a separation dependent on the magnitude of the applied magnetic field. If an appropriate polarizer is used, the combination of this source with a self-absorbed pr ofile should result in a simila r flat-topped quasi-continuum source for high resolution meas urements. To this authors knowledge, the Zeeman approach has never been attempted. In fact, the only paper found that applied the combination of two line sources to create a quasi-continuum source was by Bazhov and Zherebenko [38] in 1970 and no follow up papers or any variation of this method towards the application of absorption measurements could be found. Measurement of the absorption profil e yielded number de nsities that are comparable to those obtained from high re solution emission measurements. The direct measurement of the absorption profile wi dth would not yield an accurate Doppler temperature due to the presence of unresolv ed hyperfine structure components. In addition, it would be difficult to determine the true FWHM due to the poorly defined baseline resulting in inaccurate values. Despite these broadening components, the profile still appears to be Doppler limited and ther efore, has a resolving power superior to a flame and ICP plasma, and comparable to sealed cells.

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65 CHAPTER 4 NUMBER DENSITY OF A SEE-THROU GH HOLLOW CATHODE DISCHARGE BY CONVENTIONAL ABSORPTION SPECTROSCOPY Introduction Conventional absorption spect roscopy can also be applie d to the present system for number density measurements. It is we ll known that as the current applied to a hollow cathode lamp (HCL) is increased, th e width of the emission profile is also increased [15-17,40]. If an HCL is held fixed at a low current relative to that applied to the galvatron, then the emission from the HC L can be roughly approximated as a line source. In the line source approximation, th e source is assumed to have an infinitely narrow width, or delta function, so th e frequency dependence on the absorption coefficient is removed. It is also assume d the line source is centered on the transition, k() = ko. Since both lamps are low pressure discharges, the profiles are limited by Doppler broadening and therefore, there will be no shifting in the peaks of the emission or absorption profiles. Theref ore, it can be assumed that the emission profile from the hollow cathode lamp will be centered on th e absorption profile of the galvatron. If the line source approximation holds true, the absorption measurements can be directly related to the number density of the atomic vapor created, if the path length, absorption profile width, and oscillator st rength are known [33,39] as was shown in equations 3-1a 3-1c. In this work, the 276.787 nm thallium transition will be used to determine the ground state number density of the thallium galvatron and the 405.7807 nm transition will be used to determine the numbe r density of the lead metastable state.

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66 Figure 4-1. Illustration of th e absorption profile (red) of the galvatron and the emission profile (blue) of the HCL. Experimental Absorption measurements are carried out us ing neon filled, thallium (Jarrell Ash) and lead (Fisher) hollow cathode lamps both set at a fixed current of 2.0 mA and modulated with a mechanical chopper (E G&G 5207) at a frequency of 625 Hz. Neon filled thallium and lead galvatrons (Ham amatsu) are used as the see-through hollow cathode discharges. All lenses used are fu sed silica with one inch diameters. A monochromator (Thermo Jarrell Ash) is us ed with a 500 mm focal length, 1200 grooves mm-1 grating, and slit widths of 0.5 mm. Th e detector is a photomultiplier tube (R928 Hamamatsu) with -1000 V applied from a high voltage power supply (Bertan model 342A). The anode current was sent to a low-noise current preamplifier (Stanford Research model SR570) with a gain of 200 nA V-1 and a 6 dB high pass filter at 10 kHz. The amplified signal is sent to a lock-in am plifier (EG&G) for phase sensitive detection with a gain of 50 mV V-1, a time constant of 1 s, and a phase of 153.4. The demodulated signal is monitored on a 100 MHz oscillos cope (Tektronix TDS 3012B) and recorded with a strip chart recorder.

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67 Figure 4-2. Experimental arrangement for ab sorption measurements. Lens 1 and lens 2 are both fused silica with focal lengths of 10 cm. Both irises had a diameter of 2 mm. Not drawn to scale. The experimental design used for the co llection of absorption data is shown in figure 4-2. Since the galvatron is also a spectral line emission source, reduction of background emission is required. This is accomplished by using a lens placed 10 cm from the cathode face of the HCL to collimat e the emission. The emission was spatially filtered with an iris having a diameter of 2 mm. The collection lens used to focus the emission onto the slits of the monochromator is placed approximately one meter from the galvatron. This is done in order to remove as much of the emission from the galvatron as possible, since the galvatron emission is dive rging and the HCL emission was collimated. The galvatron emission is further reduced with a 2 mm iris placed before the collection H.V. Lead/Thallium HCl Lead/Thallium Galvatron H.V. Chopper Current Amplifier Lock-in Amplifier Scope Reference Strip Chart Recorder Thermo Jarrell Ash Monochromator Iris Iris Iris Mirror Mirror Lens 1 Lens 2 H.V.

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68 lens. The monochromator is tuned to the 276. 787 nm emission line of thallium and 405.8 nm emission line of lead. It is important to note that by placing the galvatron with th e anode facing the HCL, rather than facing the detector (see fi gure 4-2) less emission from the galvatron is observed. Orientation in this manner ai ded with the reduction of background emission noise. Number Density Measurements The results obtained from the strip char t recorder were used to calculate the ground state number density for each current us ing equations 3-1a-c. Temperature values used to calculate the Doppler width of the absorption profiles were obtained from results obtained by high resolution emission measurem ents [40]. Figure 4-3 shows that the absorption data obtained for thallium are not in agreement with values obtained from saturated fluorescence measurements [32], whereas the lead data shows excellent agreement with saturated fluorescence values, as well as high resolution emission values. In order to explain this di screpancy, our assumptions mu st be reviewed. Two major assumptions are made; the hollow cathode la mp acts as a line source and that the absorption path length is a constant. Th e method for calculating the number density is based on the assumption that an infinitely na rrow line source is used; however, this is known to not be true since the emission of the hollow cathode lamp will have some inherent width due to Doppler broadening and possibly a sm all amount of broadening due to self-absorption. This will result in number density errors at lower galvatron currents. Therefore, one must know what the relati ve widths of the absorption and emission profiles are in order to accurately apply th e line source approximation. In addition, because the galvatron is also a line source the detector detects the D.C. emission from the

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69 galvatron. At low currents, the background emission noise will be reduced by the lock-in amplifier; however, as the galvatron current is increased the background emission noise will grow to the point where the signal becomes buried in noise. 10-210-11001011071081091010101110121013 Number Density (atoms cm-3)Galvatron Current (mA) Absorption Time-Resolved Laser-Induced Saturated Fluorescence 10-1100101107108109101010111012 Number Density (atoms cm-3)Galvatron Current (mA) Saturated fluorescence Absorption Emission Figure 4-3. Number density measurements by conventional absorption. The results from saturated fluorescence and high resolution emission data are also plotted. For the absorption number density calculati on, temperature values were obtained from high resolution emission measuremen ts [40]. The emission source (HCl) current was fixed at 2.0 mA. Path Length Measurements Throughout the diagnostics of the thallium and lead galv atrons, it was noticed that the discharge extended beyond the ends of the cat hode. Therefore, the optical path length is no longer constant with current or spatially uniform. In equation 3-1c, the path length, l, is assumed to be constant and not to vary with current. In order to validate this assumption, the absorbance was measured acro ss the face of the cathode as a function of distance from the face of the cathode. The experimental arrangement is similar to that shown in figure 4 except the galvatron is rota ted 90 and placed on a translating stage in order to translate the cathode away from the intersecting beam. Thallium Lead

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70242220181614121086420 0.00 0.02 0.04 0.06 0.08 0.10 0.12 AbsorbanceDistance (mm)Galvatron Current 1.0 mA 3.0 mA 5.0 mA 7.0 mA 10.0 mA Figure 4-4. Absorption measurements as the cat hode was translated through the emission beam. The HCl emission source was he ld constant at 10 mA throughout this experiment. A quartz shield surrounds the outer cyli nder of the cathode in order to prevent sputtering process on the cathode. As a result of sputtering on the face of the cathode, a small amount of metal vapor was deposited on th is quartz shield. Therefore, a current of 10 mA was used in order to obtain a measurab le signal. Figure 4-4 clearly shows that absorption occurs beyond the face of the cat hode; however, it is only noticeable at higher currents. Even at higher currents it can be seen that the absorption drops off dramatically past the face of the catho de and only extends out a fe w mm. This validates the assumption of a single value for the absorp tion path length with changing current. Line Source Measurements In order to validate that the HCL can be approximated as a line source, emission profiles of the HCL and galvatron were measur ed at similar currents. This was done by use of a scanning Fabry-Perot in terferometer as described in reference [40]. Because of the spectral range of the in terferometer mirrors, a thallium ground state transition could

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71 not be selected; however, the 535.046 nm tr ansition was accessible a nd allowed relative conclusions to be drawn about the emission and absorption profiles of the ground state. Measurement of the emission profiles from the thallium and lead hollow cathode lamps and galvatrons are shown in figure 4-5. It can be seen that when applying similar currents to the HCL and the galvatron yields profiles of different widths. The thallium galvatron exhibits a slightly narrower profile than the HCL with noticeably less 420246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) Current = 10.0 mA Galvatron Hollow Cathode Lamp420246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm) Current = 15.0 mA Galvatron Hollow Cathode Lamp 54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 10.0 mA Galvatron Hollow Cathode Lamp54321012345 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) (pm)Current = 15.0 mA Galvatron Hollow Cathode Lamp Figure 4-5. High resolution emission meas urements of the lead 405.7807 nm and the thallium 535.046 nm transitions in a galvatron and hollow cathode lamp at similar currents. self-absorption. It is also important to note that the absorption profile is expected to be narrower than the emission profile observed in figure 4-5 due to the absence of the selfabsorption broadening component. From the resu lts in figure 4-5, it cannot be concluded Thallium Thallium Lead Lead

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72 with any degree of certainty the assumption that a line source was used in the measurement of the number density for the th allium galvatron and w ould reflect in an error in the calculation. This explains the discrepancy between the fluorescence measurements and absorption measurements obser ved in figure 4-3. From the results of the lead emission profiles in figure 4-5, it can be seen that the lead galvatron produces a much broader emission profile than the lead hollow cathode lamp at similar currents. Therefore, it can be concluded that the lead hollow cathode lamp can be approximated as a line source relative to the absorption profile of the lead galvatron when operated at a low current, which explains the agreement in number density between the absorption measurements and fluorescence measurements. It assumed that the major reason the two galvatrons behaved so differently is due to the pressure of the buffer gas used in each lamp. Since the galvatrons are manufactured by Hamamatsu, the Pb HCL by Fi sher, and the Tl HCL by Jarrell Ash, it is expected that each lamp will contain a different buffer gas pressure. This can affect the sputtering efficiency, number density, and D oppler temperature of each lamp operated at similar currents. Conclusion Number density measurements of the thallium and lead galvatrons by conventional absorption method yielded conflicti ng results when compared to the results obtained by saturated fluorescence. As shown in figure 4-3, thallium shows a very poor agreement to the saturated fluorescence meas urements, whereas lead showed excellent agreement between the fluorescence and emi ssion methods. It was found that the poor agreement for the thallium galvatron and excel lent agreement of the lead galvatron was due to the relative spectral widths of the emission sour ce and absorbing medium. The

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73 thallium galvatron produced a narrower emi ssion profile relative to the emission profile of the hollow cathode lamp at similar curr ents, whereas the lead galvatron produced broader emission profile relative to the emissi on profile of the lead hollow cathode lamp. From this, it can be concluded that the lead hollow cathode lamp behaved as a line source and in turn resulted in more accurate meas urements. The thallium hollow cathode lamp did not satisfy the line source approximation a nd thus resulted in erroneous results, as was demonstrated. The difference in the obser ved emission profiles is expected to be due to the different construction of each lamp. Each lamp would likely contain a different buffer gas pressure since each HCL came from a different manufacture than the galvatrons. It has been shown that the use of a hollow cathode lamp can be applied to the measurement of number densities by absorp tion; however, the rela tive widths of the emission source and absorption profile should be known in order to correctly apply the line source approximation.

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74 CHAPTER 5 TIME-RESOLVED LASER-INDUCED SATURATED FLUORESCENCE MEASUREMENTS: EVALUATION OF NUMBER DENSITY AND QUANTUM EFFICIENCY Introduction As previously mentioned, the luminosity-r esolving power produc t is an important figure of merit when comparing different spectroscopic systems; however, other parameters must also be evaluated in order to properly assess the effectiveness of an atomic filter. One of these parameters is the number density of the metal vapor. An effective filter should be able to easily pr oduce, and reproduce, a desired number density for extended periods of time with little to no fluc tuations or drift. An ideal system would be simple, compact, and portable if possible. If the system is not able to generate an acceptable number density, the result will be much of the signal radiation transmitted through the filter, thus, will not be detected. The quantum efficiency of the system is another important parameter. Under a high collision, high quenching e nvironment, the atoms that re sonantly absorb the signal photons must compete with non-radiative pathwa ys. Atoms that collisionally de-excited prior to fluorescing or ionizing result in a loss of the signal. Quantum efficiencies as low as 0.03 0.001 have been reported for flames [1 3,14], and values as low as 0.1 have been found for sealed cells [39]. Therefore, the qua ntum efficiency of the atomic system is directly related to the overall detection efficiency of the filter and is very important for sensitive fluorescence and i onization detection [42-44]. The advantages that a galvatron offers over conventional atomic reservoirs makes it an attractive candidate for the applicati on as an atomic line filter, however, little spectroscopic data has been f ound in the literature. Ther efore, time-resolved laser-

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75 induced saturated fluorescence was used to determine number density and quantum efficiency of the metal vapor produced in a thallium and lead galvatron. Thallium and lead were chosen as the atomic vapor for th eir three level schemes shown in figure 5-1. The relatively strong transition probabilitie s make these transitions promising for fluorescence and ionization detection. Figure 5-1. Partial energy le vel diagrams for thallium and lead displaying the possible transitions involved with wavelengths and oscillator strengths labeled. Collision constants between levels 1 and 2 are neglected. 1 3 2 405.7807 nm (0.13) 1.32 eV 63P06 3P27 3P1 oB23 B32 A21 A23 k23k32 k31k13283.3053 nm (0.21) 4.373 eV P b 1 3 2 535.046 nm (0.15) 0.966 eV 62P1/2 o6 2P3/2 o7 2S1/2 B21 B12 A21A23 k23k32 k31k13377.572 nm (0.13) 3.283 eV Tl

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76Theory Rate Equation Approach Versus Density Matrix Approach In general, there are three approaches to treat the interaction of light with an atomic (molecular) system; the classical, semi -classical, and the fu ll quantum mechanical approach. The rate equation (RE) approach is a classical approach which treats both the incident light and the atomic system in a cl assical way. The populations of the various levels involved are described by use of the Ei nstein coefficients for stimulated emission and absorption (Bjk and Bkj, respectively), Einstein coefficients for spontaneous emission (Ajk), and collisional excitation and de-excitation rate constants (kkj and kjk, respectively). The RE approach considers the source to be incoherent with a smooth featureless structure over the absorption profile of the at omic vapor. Therefore, in order for the RE formalism to be valid, the bandwidth of the in cident laser must be much broader than the absorption profile of the atomic vapor, ev en under very high laser intensities where power broadening could dominate the width of the absorpti on profile [45,46]. There must also be several closely spaced l ongitudinal modes present under the absorption profile in order for the source to be consider ed smooth and featureless. In addition, the rate of dephasing collisions in the atomic vapor must be hi gh in order to destroy any coherence created by the monochr omatic laser field [47]. A convenient way to check if the use of the RE approach is valid is if the following condition is fulfilled; laser >> B12 [45,47]. The RE approach is a commonl y used method by laser spectroscopists due to its simplicity, versatility, and accuracy when the aforementioned condition is met. Laser spectroscopists may often find themse lves with a laser spectral profile that does not meet the condition validating the RE approach. Under these high resolution conditions, coherence phenomena, such as the well known Rabi osci llation frequency and

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77 Stark splitting effects can be observed. Thes e effects can not be e xplained quantitatively, or even qualitatively, by use of the RE appr oach and are only realized by use of the density matrix (DM) formalism. The DM a pproach is a semi-classical approach, which treats the incident light classically and the atomic system quantum mechanically [45-48]. Even though it provides a more accurate desc ription of the light/atom interaction under intense monochromatic radiation, it is, however, mathematically a great deal more complicated compared to the RE approach. The RE approach only produces m differential equations; one for each energy level considered. The DM approach, however, produces m2 coupled differential equations sinc e the phase of the wave function must also be considered. In addition, each de generate energy level is also treated as an individual state; therefore, the mathema tics becomes increasingly cumbersome with every energy level that is considered. If the DM approach were applied to the limiting case were a broad-band pulsed laser is used, with a pulse duration much longer than the inverse of the laser bandwidth ( laser -1), then the Rabi oscilla tions quickly damp out, resulting in the DM approach mathematica lly reducing to the RE approach [46-48]. Therefore, in this broad-band limit, it woul d be unreasonable to use the DM approach when the much simpler RE approach could be used with equal accuracy. Taking into consideration values used for the thallium measurements, the FWHM of the laser profile, laser, was found to be 14.0 GHz and from the maximum laser output, a stimulated absorption rate, B12 max, was found to be 2.3 GHz. Therefore, with the present laser system and atomic reser voir, the use of the rate equation for the description of this atomic vapor is validated by fulfilling the condition laser >> B12 and therefore, the RE approach will be the only approach considered.

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78 Of course, the most complete theoretical description of the light/atom interaction would necessitate a full quantum mechanical tr eatment. This would require the quantum mechanical nature of light to be included, where creation and annihi lation operators are used to describe the interaction between light and matter. This is known as the quantumelectrodynamical (QED) approach and has been applied to two and three level systems [49-51]; however, this approach lies beyond the scope of this research and will not be discussed further. Ideal Two-Level Saturation Curve Under Steady State Conditions Figure 5-1 shows a partial energy level diagram of thallium and lead with the transitions labeled. It should be noted here that the theoretical section of this paper will make use of the laser spectral energy density, o (J cm-3 Hz-1), however, the laser spectral irradiance, E (J s-1 cm-2 nm-1) will be used throughout the rest of the paper. They are related to one another th rough the speed of light constant, c (2.9979 x 1010 cm s-1) by c Eo One should be aware of the units used here. Equation 5-1 is in the form of frequency, Hz; however, results in this paper are reported in units of wavelength, nm. To begin with the simplest case, the th allium and lead atom will be assumed to behave as a two-level atom. If these atomic systems are excited with a broad band, spatially uniform, step-like laser pulse ha ving duration much longer than the effective lifetime of the excited state, a steady st ate fluorescence waveform will result. The intensity of the resulting fluorescence signal is dependent on the population of the excited state, n2, and is a function of the laser spectral energy density. Using the RE approach (5-1)

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79 and neglecting collisional excitation ( k12 = k32 = 0), we have the ge neral rate equation for n2( t ) [45-47], Tn n n n k A t B n t B dt dno o 2 1 2 21 21 21 1 12 2) ( ) ( where A21 (s-1) is the Einstein coefficient of spontaneous emission, B21 (J-1 cm3 s-1 Hz) is the Einstein coefficient for stimulated emission, B12 (J-1 cm3 s-1 Hz) is the Einstein coefficient for stimulated absorption, k21 (s-1) is the collisional de-excitation rate constant, and nj (cm-3) represents the number density of th e level indicated by the subscript. Combining equations 5-2a, and 5-2b, and assuming steady state conditions, dn2/ dt = 0, yields the following equation [47], where o (J cm-3 Hz-1) is the spectral energy density, So (J cm-3 Hz-1) is the saturation spectral energy density, or sa turation parameter, and S(o ) is defined as the ideal saturation function [47]. The plateau value for o is given by max 2 1 1 max 2S g g g n nT where gj are the statistical weights of the state indicated by the subscript. The saturation parameter,So is give by 21 3 3 2 1 11 8 Y c h g g go So o o oS n n n nS T T 1 1max 2 2 (5-2a) (5-2b) (5-3) (5-4) (5-5a)

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80 21 21 21 21k A A Y where h (6.626 x 10-34 J s) is Plancks constant, o (Hz) is the central frequency of the transition, and Y21 is the defined as the quantum effici ency of the transition. Evaluation of equation 5-3 can be carried out by considering three limits. First, if o >>So, then the equation reduces to (n2/nT) max which is the plateau value of the saturation curve. In this region, the number density of the excited state, n2, becomes independent of the laser energy density and has a value equal to half of the total population of the system (if g1 = g2). The second limit is the point at which o =So. When this condition is met, the population of the excited state has reached half of its plateau value and a quarter of the total population of the system (if g1 = g2). At this point, the combined stimulated emission and absorption rate constants (B12 + B21)o are equivalent to the combined spontaneous emission and collisiona l de-excitation ra te constants (A21 + k21). The last limit is the region when o <
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81 r SSt t n t n exp 1 ) (2 2 where n2 SS is the steady state populati on of the exc ited level and tr is defined as the response time of the system [53]. It can be seen that in the limit t equation 5-6 reduces to the steady state condi tion, as would be expected. 21 21 12 2 11 1 k A B g g tr r T SSt B n n2 Equation 5-7a clearly demonstrates that th e response time of the atomic system is dependent on the laser energy density. Th erefore, under complete saturation, the response time of the system will be very fast and dominated by stimulated processes. This implies that levels 1 and 2 become l ock together by the laser, with the atoms rapidly circulating between the two levels ; each level having population determined by their statistical weights. Therefore, under complete saturation the peak of the fluorescence waveform can be described as a two level system under steady state conditions despite the presence of a third inte rmediate level. Thus, a two level steady state fluorescence waveform can be achieved with a short laser pulse if the transition is completely saturated. If o is attenuated to where B12o becomes negligible, then the response time simply reduces to the effective lifetime of the atomic system. This also implies that the two levels are no longer loc ked together by the laser and therefore, can no longer be considered a two level system due to the branching of the fluorescence into the laser locked level and into the third interm ediate level. In addition, if a short laser pulse is used at these lower energy densities, the response time of the atomic system will (5-6) (5-7a) (5-7b)

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82 not be sufficient to achieve a steady state resulting in a distortion of the measured saturation curve. This distortion also produ ces an apparent saturation parameter whose value will be higher than the true saturati on parameter and is dependent on the pulse duration. This type of non-steady state response has been previously described and modeled by Omenetto et al. [52]. Three-Level Saturation Curve in the Presence of a Trap The previous two sections approximated th allium and lead as a two-level system, however, the atomic systems shown in figure one is a three-level system. Here, the laser is coupled to levels one and two, with level two radiativly connected to a third metastable level. This metastable state is l ong lived in a low collision environment (k31 ~ 0), as is the present case. If this metastable level acts as a true trap, or loss-less sink, then all atoms fluorescing into this level will be take n out of circulation, or trapped, during the pulse duration and will not further contribute to the fluorescence signal. The presence of this third level is important in both the linea r portion of the saturation curve as well as in the saturation region. In the linear region, the fluorescence quantum efficiency for both radiative pathways, A21 and A23, will affect the overall detect ed saturation curve. Thus, the resulting signal will be aff ected by the spontaneous decay, A23, into this third level and must be taken into account. This th ird level becomes esp ecially important under saturation conditions. As mentioned prev iously, under saturati on conditions, the response time of the system (equation 5-7a ) is dominated by stimulated processes between the two laser locked levels [52,53]. Therefore, if complete saturation has been achieved, then the system can initially be c onsidered a two-level system. However, as the pulse increases in duration, a significan t number of atoms will accumulate in this third level trap, resulting in fewer atoms circul ating in the two laser coupled levels. This

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83 is observed as a loss in the popul ation of level 2 and results in a decrease in the observed fluorescence signal. In order to properly apply this metastable trap level to the thallium and lead atomic systems, the time dependent ra te equations must be used to determine the temporal behavior of atoms in each of the thr ee states. Therefore, the time dependent rate equations for the three levels can be written as [47,54] 3 2 1 23 23 2 3 23 23 21 21 21 2 12 1 2 21 21 21 2 12 1 1) ( ) ( ) ( n n n n k A n dt dn k A k B A n B n dt dn k B A n B n dt dnT where all variables have been previously de fined and all transitions correspond to those for thallium in figure 5-1. These equations can easily be rearranged to take into account the excitation of lead from the metastable level. Equation 5-8d implies that the system is closed and no losses occur. To simplify the mathematics, let 23 23 23 21 21 21 12k A A k A B Bo It is assumed that at t = 0 all atoms can be found in the gr ound state resulti ng in the initial condition n1 = nT and n2 = n3 = 0. Solving equations 5-8a-c yields [54], 2 1 2 1 2 2 1 1 2 1 3 2 1 1 2 2 2 2 1 2 1 1 1 2 1exp ) ( exp ) ( ) ( exp exp ) ( exp 1 exp 1 ) ( o T o T o T T o T o Tn t n t n t n t t n t n t n t n t n (5-8a) (5-8b) (5-8c) (5-8d) (5-9c) (5-9b) (5-9a)

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84 with t being the instantaneous point at whic h the fluorescence value is measured. 1 and 2 are defined as [54] o o o o o o 2 2 2 12 2 2 2 If a time-integrated, or time averaged, method of detection is used i.e. a boxcar, then the total number of photons emitted with a frequency 23 within a pulse duration, laser (s), can be given as [54] 1 2 2 1 1 2 0 2 23exp exp 1 ) ( laser laser o T fl fln I dt t n A Ilaser Another potential trap ofte n considered is the ionization continuum, where the recombination of ions and electrons can be a long process [55] compared to a pulse duration of a few nanoseconds. As can be seen for thallium in figure 5-1, level 2 is 3.283 eV above the ground state. If this excited atom were to ab sorb another photon at 377.572 nm, it would promote the atom 6.566 eV above the ground state. This would put the atom into the ionization continuum since the i onization potential for th allium is 6.11 eV. As for lead, the 405.7807 nm laser promotes an atom to an energy level 4.373 eV above the ground state. A second photon at 405.7807 nm would only promote the atom to an energy level 6.106 eV above the ground state, and since lead has an ionization energy of 7.42 eV, this second photon would not have su fficient energy for ionization of the lead system and could only be achieved by a multi-photon process or by some collisional process. Therefore, the poten tial of the ionization conti nuum acting as a possible trap (5-10a) (5-10b) (5-11a) (5-11b)

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85 does exist for thallium and lead, however, this type of photo-ionization typically have low photo-ionization cross sections and would onl y become a factor if very intense laser energies were used, well in excess of th e saturation parameter and above what was achievable with the current experimental setup. In addition, since the system is a low pressure environment, ionization due to collisio nal processes is expected to be negligible. Thus, the ionization continuum will not be considered here. Number Density Under Steady-State Saturation Conditions One advantage of saturated fluores cence spectroscopy over traditional fluorescence is the independence of the signal on the source intensity. In other words, fluctuations that occur in the source will not translate to the observed fluorescence signal under saturation conditions. This results in a higher signal to noise ratio, especially if direct-line fluorescence measurements are ma de. Also, in special situations where absolute measurements are required, the achie vement of saturation allows one to obtain the number density of a species without th e tedious need to measure accurately the spectral energy density of the source. As mentioned previously, under complete saturation the system initially can be consider ed a quasi-two level system after which the presence of a trap influences the fluorescen ce intensity. If the fluorescence is measured in absolute units at this p eak value, then quasi-two le vel steady state conditions are achieved, and the number densit y can be calculated from a si mple two level approach if the transition probabilities, statistical wei ghts, and the path length are known. The fluorescence radiance equation for a basic two level system can be written as [45,56]

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86 2 1 21 211 1 1 4 g g n A h l BT F where l (cm) is the path length and o is the modified saturation spectral energy density which is given by [56] 21 21 21 *Y B A with Y21 is the quantum efficiency of the system (equation 5-5b). The saturation spectral energy density is defined as the energy dens ity required to produce half of the maximum fluorescence radiance, BF, which occurs at complete saturation and is related to o by 2 1 2 g g gS As can be seen, if complete saturation has occurred, (o >> o *), then equation 5-12 reduces to [45,56] 2 1 2 21 21 max4 g g g n A h l BT F Equation 5-15 shows the simplification of the number density calculation in the saturation region due to the removal of the source dependence. Therefore, if BFmax is measured in absolute units and the fundame ntal parameters are known, then the number density of the ground state can easily be determined. In the introduction, it was mentioned that the atomic reservoir needs to be able to produce an appropriate number density to be an effective atomic line filter. Of course (5-12) (5-13) (5-14) (5-15)

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87 this raises the question as to what is an appropriate number density. This is a question not easily answered si nce little information is known a bout the spectral profile of the signal and how it compares to the absorption prof ile of the atomic vapor. However, if we take the limit of the signal to be a line s ource, then a curve of growth calculation will provide information as to the number density ne eded to absorb a desired fraction of light. For this calculation, the absorption profile for thallium and lead was assumed to be purely Doppler broadened, i.e. a damping parameter equal to zero, with a path length of 2 cm and a Doppler temperature of 500 K. These ar e typical values commonly associated with hollow cathode discharges [1517]. A more detail descriptio n of the calculation for this curve of growth can be seen in Appendix A. Based on this calcula tion, with appropriate parameters used, a number density of 8.90 x 1011 cm-3, 5.44 x 1011 cm-3, and 8.10 x 1011 cm-3 would be needed for 99.9 % of the signal radiation to be absorbed by the thallium ground state transition, thallium metastable state transition, and lead metastable state transition, respectively. Therefore, it needs to be determined what current applied to the galvatron will produce this number density. Experimental Laser System The experimental system for the measurements in this paper can be found in figure 5-2. The laser system consisted of a Lambda Physik LPX 200 XeCl excimer laser used to pump a Lambda Physik Scanmate 1 dye laser with a 20 mm cuvette. The excimer operated at 10 Hz with an output energy of a pproximately 75 mJ/pulse. The dye used to achieve the 377.572 nm thallium resonance line was BBQ (Exciton) at a concentration of 5 x 10-3 M in ACS grade cyclohexane. The dye used to achieve the 535.046 nm thallium transition was Coumarine 540A (Excit on) at a concentration of 8 x 10-3 M in ACS grade

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88 methanol. The dye used to achieve the 405.7807 nm lead transition was DPS (Exciton) at a concentration of 1 x 10-3 M in ACS grade p-dioxane. Two irises were used to isolate the central portion of the laser beam. This helped to reduce laser scatter, as well as make the beam more homogenous. The diameters were set to 2 mm so that the beam just filled the bore of the cathode. The see-through ho llow cathode discharge used was a thallium galvatron (Hamamatsu) with neon filler gas at a pressure of 14 torr [57] and a lead galvatron (Hamamatsu) with neon filler ga s with an unknown pressure. The applied current was accurately measured with a home made pick-off circuit and monitored on a Fluke 29 series II multimeter. L P X 2 0 0 S c a n m a t e Bertan Monochromator PMTH.V. SupplyPhotodiode Trigger Beam Trap Pierced Mirror +300 V 0.175 V H.V. Supply Vacuum Photodiode Lens Lens Interference filter Glass slide Glass slide 50 50 Neutral density filter IrisMirrorThallium Galvatron Figure 5-2. Experimental set-up used for all saturation curve and number density measurements.

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89Detection System The monochromator was a McPherson m odel 218 with criss-cross Czerny-Turner geometry, a grating of 1200 grooves mm-1, blazed at 300 nm, reciprocal linear dispersion of 2.6 nm mm-1, ruled grating area of 50 x 50 mm, focal length of 300 mm, and an fnumber of 5.3. The entrance and exit slits were set to 1 mm. Glass color filters were placed directly in front of the entrance slit to allow the fluorescence radiation to pass and to block any stray laser light. Fluorescen ce was detected with a photomultiplier tube (Hamamatsu R1414) with -1000 V applied a nd a measured rise time of 1.0 ns. Triggering was accomplished with a photodiode from a small portion of the excimer radiation. Laser irradiance was determined using a Fisherbrand plain microscope slide and reflecting a small portion of the laser beam to a Hamamatsu R1328U-03 vacuum photodiode. The vacuum photodiode was supplie d with +300 V from a Bertan series 105, 1 kW high voltage power supply. The si gnal was detected on a 400 MHz Tektronix oscilloscope. Vacuum Photodiode Calibration Calibration of the vacuum photodiode was accomplished by removing the lamp and inserting a Melles Griot broad band power/energy meter type 13PEM001 with an AOSK0032 sampling head. The photodiode was ch ecked for linearity over a wide range of energies with calibrated neutral density filters and was found to be linear over the entire energy range reported in this paper. Equation 5-16 shows the calculation used to obtain the conversion factor, P (J s-1 cm-2 nm-1 mV-1),

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90 ) ( ) ( ) ( ) ( ) (2mV S nm s t cm A J Q PmV laser laser laser laser where Qlaser (J) is the energy/pulse measured on the energy meter, Alaser (cm2) is the cross sectional area of the laser beam filtered by the two irises, tlaser (s) is the FWHM of the laser temporal profile, laser (nm) is the FWHM of the spectral profile, and SmV (mV) is the voltage signal obtained on the oscill oscope for a given energy. Multiplying P by the signal obtained on the oscillosc ope yields the spectral irradian ce of the laser at any given attenuation. Values for the laser parameters used in this calculation will be discussed later. Spectrometer Calibration Calibration of the spectrometer was acco mplished by use of a calibrated Oriel instruments 1000 W quartz tungsten halogen irradiance standard (serial # 7-1121). Linearity of the detector was checked to en sure the proper conversi on factor. Equation 517a shows the conversion of the measured fluorescence voltage into a fluorescence radiance. The spectrometer was calibrated with the same optics, filters, and settings as the fluorescence measurements. 6 110 g mV FS F I B 2f A Apiercing lens Here ImV (mV) is the peak voltage measured, sg (nm) is the geometric spectral bandpass of the monochromator determined by a slit width of 1 mm, and (sr) is the collection solid angle of the lens. Since a pierced mirror was used to collect the fluorescence, a small portion of the fluorescence is loss due to this piercing. This loss can be corrected (5-16) (5-17b)

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91 for by subtracting the resulting solid angle that is lost and is ill ustrated in figure 5-3. The parameter F (J s-1 cm-2 nm-1 mV-1) is the conversion factor for measured voltage to irradiance at 535.046, 377.572, and 283.3 nm. This was obtained by relating the measured signal from the spectral irradiance la mp to the calibrated spectral irradiance value supplied by the manufacture. Table 5-1 di splays all values used in the calculation of the fluorescence radiance of thallium. All va lues are the same for lead as well with the exception of the fluorescence radiance conversion factor. Figure 5-3. Representation of the losses th at would be encounte red in the collection optics. Not drawn to scale. Table 5-1. Values used for fluorescence radiance calculation with symbols and descriptions provided. Symbol Description Value BF fluorescence radiance (W cm-2 sr-1) ImV measured signal intensity (mV) E reported value for the irradiance standard @ 535.0 nm 9.4986 W cm-2 nm-1 Rd reciprocal linear dispersion 2.6 nm mm-1 W entrance and exit slit widths 1 mm sg geometric spectral bandpass 2.6 nm Alens fluorescence collection lens area (d = 2.54 cm) 5.07 cm2 Apiercing piercing area (d = 0.40 cm) 0.1257 cm2 f focal length of the fluorescence collection lens 12 cm F calibration factor 5.8282 W cm-2 nm-1 mV-1 collection solid angle (corrected) 0.0312 sr 10-6 conversion from W to W 0.4 cm 2.54 cm Pierced mirror Lens (f = 12 cm)

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92Evaluation of Dye Laser Parameters Spectral Profile An assumption made in the theoretical section assumed that the laser source is broadband. This is to validated the use of th e RE approach and to ensure that each atom is subjected to the same spectral irradiance rega rdless of its velocity. For this assumption to be valid, the spectral profile of the laser needs to be determined. The laser beam was diverged with a concave lens and passed th rough an air-spaced Fabr y-Perot etalon with a spacer of 3.011 mm and a finesse greater than 30 (instrumental FWHM = 0.79 pm). The fringe pattern created was projected onto the vacuum photodiode. In front of the photodiode was a 100 m pinhole which was used to isolate a small portion of the central fringe. The laser was scanned from 377.60 nm to 377.70 nm at a rate of 1 pm/s and a repetition rate of 30 Hz. The signal was dete cted with a boxcar and recorded on a strip chart recorder (Picoscope). 1412108642024681012140.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Longitudinal mode structureIntensity (a.u.) (pm) Calculated absorption profile, T = 500 K a ~ 0 Measured laser spectral profile Figure 5-4. Experimentally measured dye la ser spectral profile with FWHM of 6.63 pm. Also shown is the calculated mode stru cture obtained from a cavity length of 35 cm. Intensities shown are arbitr ary and do not represent any physical quantity. F1 F1 I11 = 0.577 F0 F1 I01 = 0.173 F1 F0 I10 = 0.250 = 6.63 pm

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93 Determination of the spectral profile m easured can be achieved by making use of the free spectral range of the etalon from equation 5-18, pm dFSR6 23 22 with = 377.572 nm, being the refractive index of the medium between the etalon plates (= 1.001 for air), and d = 3.011 mm being the separation between the mirrors. This free spectral range value is equal to the p eak separation of two adjacent orders on the strip chart recorder, therefor e, providing a spectral ruler and allowing the calibration of the x-axis. From figure 5-4, it can be seen that the FWHM of the dye laser output was determined to be 6.63 pm. The mode spaci ng calculated from e quation 5-19 shows that the FWHM output of the dye laser contains approximately 32 longitudinal modes. Here c is the speed of light (2.9979 x 1010 cm s-1), L is the length of the cavity ( 35 cm), and the factor 2 represents one round trip in the cav ity. It should be noted that this equation represents the spacing between two adjacent mo des in Hz and that figure 5-4 displays it in terms of wavelength. L c 2 In order to verify that the laser sour ce behaves as a quasi-continuum, the number of longitudinal modes present within the abso rption profile of the tr ansition needs to be determined. In order to verify this, the absorption profile for the 377.572 nm transition was calculated. A value of 500 K was used fo r the Doppler temperat ure and a value of 3 x 10-3 was used for the damping parameter, which are values commonly associated with hollow cathode discharges [15-17]. It wa s found from figure 5-4 that the central transitions contain approximately 10 modes which justifies the assumption of a quasi(5-18) (5-19)

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94 continuum source. It can also be seen that the laser intens ity does not change significantly across the absorption profile. This results in a fairly smooth spectral irradiance over the absorption profile; therefor e, every velocity class will be subjected to approximately the same spectral irradiance. Similar results were obtained for the thallium 535.046 nm and 405.7807 nm laser profiles. It can be seen from figure 5-4 that the red wing of the laser profile, when tuned to the central transition, slightly overlaps the F0 F1 hyperfine component resulting in a slight excitation of this transition. Thus, as the spectral irradiance increases, the central transition will become saturated, however, the hyperfine component under the red wing of the laser will not experience the irradiance necessary for satu ration. This will result in a distortion of the saturation curve in whic h a high irradiance plateau will never be practically achieved. However, by inspecti on of figure 5-4, it can be seen that the spectral irradiance observed by the F0 F1 hyperfine component is about an order of magnitude less than that experienced by the central transition and should not significantly contribute to the signal. It is important to note here that the la ser profile only encomp asses the central two transitions. These two transitions are a result of the F1 F1 hyperfine transition of the two thallium isotopes, thallium 205 (70.5 % natural abundance) and thallium 203 (29.5 % natural abundance). Therefore, for an accu rate calculation of the number density, the transition probability, AF1 F1, for this transition needs to be determined. A more detailed description of this calculati on can be found in appendix B. Spatial Profile In order to avoid unnecessary distortion in the saturation curve, the spatial beam profile must be homogenous. This ensures th at every atom in the analytical volume is

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95 subjected to the same spectral irradiance. A distortion in the measured saturation curve will result if this requirement is not met [47,58,59]. For this reason, a spatial beam profile measurement was done. x x Figure 5-5. A) A three dimensional spatia l profile obtained by translating photodiode with a 100 m pinhole through the Scanmate 1 dye laser beam. B) A two dimensional view of the same profile demonstrating the fairly homogenous profile. A certified 100 m pinhole (Melles Griot) was inserted onto the face of a photodiode and was secured to an x-z transla tional stage. The laser beam was sent through the two irises for spatial filtering and then to the face of th e photodiode with the pinhole so that only a small portion of the beam was detected. The output from the photodiode was detected with a boxcar averag er and the resulting averaged output was measured with a Keithley 182 sensitive digital voltmeter. The result from translating the photodiode through the spatially filtered laser b eam can be seen in the three dimensional plot in figure 5-5. The laser beam was measured to have an area, Alaser, of 0.0314 cm2 which is the area of the two ir ises and cathode bore. It can be seen then that the beam quality after spatial filtering is satisfactory and can be c onsidered fairly homogenous. A) B)

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96 Therefore, no distortions of the saturation curv e are to be expected as a result of spatial heterogeneity. Temporal profile Determination of the dye laser temporal profile is of great importance for several reasons. A time-resolved measurement of th e laser pulse can determine the temporal mode structure of the dye laser, the puls e duration necessary for the laser spectral irradiance calculations, and help to veri fy if steady-state conditions apply. The profile was obtained with an ET 2000 photodiode (Electro-Optics Technology, Inc.) with a 200 ps rise ti me and was measured with a 500 MHz oscilloscope (Tektronix TDS 520D). Neutral density filters were inserted into the path of the beam to assure the profile remained the same regardless of intensity and that the photodiode was not saturated. The photodiode was also placed at different positions of the beam to verify that the temporal response did not vary within the beam. The temporal profile of the dye laser output can be seen in figure 5-6. It was found that the dye laser used for thallium had a pulse FWHM of 7.0 ns and lead was found to have a FWHM of 4.0 ns. 3025201510505101520253035 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.) Time(ns) tlaser = 7.0 ns Figure 5-6. A) Scanmate 1 dye laser te mporal profile for the thallium 377.572 nm transition. Recorded with a photodi ode (rise time of 200 ps) and 500 MHz oscilloscope.

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97 It should be noted, however, that the idea of pulse duration may be confusing when applying it to real situations. The value used for calculation of theoretical saturation curves comes from time zero to the point where the fluorescence measurements are recorded, in this case the peak of the fluorescence pulse. If a theoretical square pulse is considered, then this would correspond to the pulse width. However, in real optical systems, pulses take on more of a Gaussian profile at best. Therefore, time zero is the instant the lase r pulse begins and the pulse duration as described in the theoretical section is th e time at which the fluorescence signal is measured. For the measurements thallium 377.572 nm transition, fluorescence values were taken at a time of 10 ns and for the lead 405.7807 nm transition, fluorescence values were taken at a time of 4 ns. Therefore, the correct pulse duration for theoretical calculations is a value of 10 ns for thallium and 4 ns for lead. Results and Discussion Saturation Curve Measurement: Evalua tion of the Quantum Efficiency Having measured the optical parameters of the laser system and calibrated the laser spectral irradiance and fluorescence radi ance detectors, a saturation curve for the thallium see-through hollow cathode lamp can be generated for the excitation with the 377.572 nm line and observing the direct line fluorescence at 535.046 nm. Similarly, the lead galvatron can be generated for the excitation with the 405.7807 nm line and observing the direct line fluor escence at 283.3 nm. Measurement of the saturation curve was done by inserting neutral density filte rs into the path of the beam. The photomultiplier tube linearity was checked peri odically by inserting a 0.3 neutral density filter. Considering that thallium fluorescence va lues were recorded at 10 ns and that the effective lifetime of the 7 2S1/2 state has been measured to be 7.7 ns [60], it would not be

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98 expected that steady state conditi ons apply. Similarly, the 7 3P1 o lead state has a calculated lifetime of 5.50 ns; therefore, a pulse duration of 4 ns would not be expected to produce a steady state. Theref ore, modeling the data obtain ed was done with a two-level time dependent model as well as a three-level time dependent model in the presence of a trap. A collisional de-excitation rate constant between the 6 2P3/2 o metastable state and the 6 2P1/2 o ground state of thallium has been found by Taylor et al. [60] to be on the order of 105 s-1. This value is quite reasonable for a low pressure discharge and is expected to be on the same order of magnitude, or less, between the 6 2P1/2 o and 7 2S1/2 state of thallium and is expected to be simila r for the lead galvatron. This suggests that all collisional rate constants can be considered negligible (kij ~ 0). Initially, a time dependent two-level model was used and the satu ration curves can be seen in figure 5-7. It should also be noted that the 100 ns theore tical curve in figure 57 also represents a two-level steady state theoretica l curve since this time is mu ch longer than the response time of the system (see equation 5-7a). As mentioned previously, due to the presence of an intermediate level, a time dependent two-level model does not accurately represent the thallium atomic system in the linear region of the saturati on curve. This has been demonstrated in figure 5-7 where the 10 ns curve, which should give the most accurate results due to the experimental parameters used, somewhat lacks agr eement with the experimental data.

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9910110210310410510610-410-310-210-1100 Fluorescence Intensity (a.u.)Spectral Irradiance (J s-1 cm-2 nm-1) Experimental Data 1.0 ns 10.0 ns 100.0 ns Figure 5-7. Experimentally measured satu ration curve from a thallium galvatron with 10.0 mA applied. This data was mo deled with time dependent two-level saturation curves for laser pulse durations of 1, 10, and 100 ns. Y21 = 1 was used for all three theoretical curves. For a more accurate analysis of the data a three-level time dependent saturation curve in the presence of a trap need s to be considered. The thallium 6 2P3/2 o metastable state has a radiative lifetime of 250 ms [11] and a measured effective lifetime of a few microseconds [60]. Since these lifetimes ar e much longer than the pulse duration, the metastable state will act as a trap, or loss-less sink. It can be seen in figure 5-8 that the 10 ns theoretical curve shows excellent agreement with the experimentally measured saturation curve. From the intersection of the linear and plateau asymptotes of the experimentally measured saturation curv e, a saturation parameter of 2.06 x 104 J s-1 cm-2 nm is obtained. This is in good agreemen t with the theoretical value of 1.84 x 104 J s-1 cm-2 nm-1. It should be mentioned that th e saturation parame ter calculated and experimentally determined for time-depende nt theory under non-steady state conditions are apparent values due to distortion of the saturation curve. The theoretical value for a two-level system under steady state cond itions is calculated to be 9.75 x 103 J s-1 cm-2

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100 nm-1, which is lower than the experimental va lue as expected. A table of saturation parameter values obtained by previous authors is listed in table 5-2. 10110210310410510610-410-310-210-1100 Fluorescence Intensity (a.u.)Spectral Irradiance (J s-1 cm-2 nm-1) experimental data 1.0 ns 10.0 ns 100.0 ns Figure 5-8. Experimentally measured satu ration curve from a thallium galvatron with 10.0 mA applied. This data was mode led to a time dependent three-level saturation curves in the presence of a tr ap for pulse durations of 1, 10, and 100 ns. For all three plots, the collisio nal de-excitation rate constants were assumed to be zero. The theoretical saturation cu rve in figure 5-8 was calculated with collisional rate constants equal to zero. Since this curve shows excellent agreement with the experimentally measured saturation curve, it can be concluded that the quantum efficiency of this atomic system is limited only to the transition probabilities and that any collisional rate constants are to be considered negligible (kij << Aij). This conclusion is quit reasonable based on the f it of the model and is furthe r supported by the collisional rate constant value of 105 s-1 [60] reported by Taylor et al. [60], when compared to the spontaneous transition probability of 6.08 x 107 s-1 for the 7 2S1/2 6 2P1/2 o transition.

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101 Table 5-2. Previously reported saturation pa rameter values for various elements under various experimental conditions. Source Element Transition (nm) E s (J s-1 cm-2 nm-1) Method Bolshov et. al. [54]1 Pb 283.3053 3.33 x 105 -done in a low pressure system (assumed ks ~0) with a Nd:YAG pumped dye laser (doubled with KDP crystal) Olivares and Hieftje [58] Tl 377.572 5.90 x 104 -done in an air-hydr ogen flame with a N2 pumped dye laser Olivares and Hieftje [58] Tl 535.046 6.33 x 104 -same as previous (both used 377 nm excitation and observed the fl of each wavelength) Smith et al. [61]2 Na 589.5924 8.0 x 105 -done in an air-acetylene flame w/ an argon shield with a cw Ar+ pumped dye laser Calcar and Alkemade [60] Na 589.5924 2.3 x 104 -done in an Hydrogen-oxygen-argon flame with a flash lamp pumped dye laser Taylor et al. [32] Tl 377.572 2.06 x 104 -done in a low pressure system with Excimer pumped dye laser Taylor [present work] Pb 405.7807 8.91 x 103 -done in a low pressure system with Excimer pumped dye laser 1Measurements in this work were time-integrated ra ther than time-resolved wh ich accounts for the high value despite the low pressure system. 2The high value obtained in this wo rk is due to the use of an air-acet ylene flame which results in a high quenching environment. Similar measurements are also applied to th e lead metastable state. In this case, the 405.7807 nm transition is excited and di rect line fluorescence is measured at 283.3053 nm. The reason this transition was chos en was due to the fact that sufficient energy was not available to achieve saturation of the gr ound state transition of 283.3053 nm. This is due to the great loss in ener gy from the frequency doubling crystal used to achieve the 283.3053 nm transition. Even though the metastable state is excited, rather than the ground state, the same concept can be applied. In this par ticular case, the ground state behaves as the trap, were collisional excita tion from the ground state is considered negligible, thus, atoms fluorescing into this stat e are taken out of circulation. Therefore, the same theory that was applied to the th allium ground state can be appropriately applied to the lead metastable state. An expe rimentally obtained saturation curve for the

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102 405.7807 nm transition of a lead galvatron at an applied current of 10.0 mA can be seen in figure 5-9. This curve is shown in figur e 5-9 with a theoretical time dependent three level saturation curve in the pres ence of a trap. This curve is calculated with appropriate parameters, a pulse duration of 4 ns, and coll isional rate constants equal to zero. The saturation parameter measured by experiment was found to be 8.91 x 103 J s-1 cm-2 nm-1, which is in good agreement with a theoretical value of 8.50 x 103 J s-1 cm-2 nm-1. From the excellent fit of the theoretical curve to th e experimental data, it can be concluded that the quantum efficiency of the lead galvat ron is limited only by spontaneous emission rates, as was found from the thallium results. 10210310410510610-310-210-1100 Fluorescence Intensity (a.u.)Spectral Irradiance (J s-1 cm-2 nm-1) Experimental Data Theoretical Curve Figure 5-9. Experimentally measured satura tion curve from a lead galvatron with 10.0 mA applied. This data was modeled to a time dependent three-level saturation curve in the presence of a trap for a pu lse duration of 4 ns. All collisional deexcitation rate constants were set to zero.

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103Number Density Measurement Based on the measurement of the saturati on curves obtained for thallium and lead, the maximum laser spectral irradiance produc es nearly complete saturation of the selected transition. Theref ore, operating in this region results in fluorescence values equivalent to the maximum fluorescence achievable, BF max, which are directly related to the ground state number density. Converting this fluorescence signal into absolute units allows calculation of the number dens ity for each current applied. Smith et. al. [62] preformed a similar measurement on a lead hollow cathode lamp and their results agree well with the results found in the present work A direct comparison can not be made due to differences in the lamp design and cathode geometry, the cathode element, sputtering efficiency, as well as the pressure of the filler gas; however, the relative relationship between the current applied and number densit y agrees well with the results found here. 10-210-11001011071081091010101110121013 Number Density (atoms cm-3)Galvatron Current (mA) Figure 5-10. Plot of the ground state number density as a function of current. 16.0 mA

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104 Based on the curve of grow th calculation in appendix A, a number density of 8.90 x 1011 cm-3 is needed for 99.9 % absorption of a line source signal. From the results in figure 5-10, an applied current of 16.0 mA produces a number density of 9.52 x 1011 cm3, therefore, a current of 16. 0 mA or higher provides an appropriate number density to absorb nearly all signal photons incident on the detector. It wa s also observed that number densities measured at applied curre nts higher than 16.0 mA began to deviate from linearity. This is assumed to be due to post-filter effects, which is a result of the metal vapor becoming optically thick. Ther efore, fluorescent photons created from the metal vapor will be reabsorbed by atoms betw een the emitting atom and the detector and translates into a distortion of the true numb er density present. This observation is in agreement with the curve of growth calculati on, in which the bend in the calculated curve is a result of the metal vapor moving from the optically thin region into the optically thick region. Applying this method for the measurement of the thallium metastable state can also be accomplished. The same procedur es and calculations are applied, the only difference being the laser wavelength t uned to the 535.046 nm transition and the spectrometer must be recalibrated for the direct line fluorescence at 377.572 nm. A complete saturation curve does not necessarily need to be generated in order to evaluate if complete saturation is achieved. If the peak fluorescence signal does not change after the laser beam has been sufficiently attenuat ed, then saturation ha s been achieved and BFmax can be measured for various currents. Sin ce the thallium metastable state has been measured previously by high resolution emission and high resolution absorption measurement, it can be compared to values obtained with the saturated fluorescence

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105 method. The results of this analysis combin ed with previous measurements can be seen in figure 5-11. 10-1100101106107108109101010111012 Number Density (atoms cm-3)Galvatron Current (mA) Laser-Induced Saturated Fluorescence Emission Absorption Figure 5-11. Plot of the metastable state number density of thallium as a function of current. From the values obtained for the thallium metastable state, a maximum number density of 2.29 x 1011 cm-3 is found for an applied current of 30.0 mA. From a curve of growth calculation, this number density is capable of absorbing only 95 % of the signal radiation. In order to obta in a number density of 5.44 x 1011 cm-3 pumping of this metastable state would be needed in order to absorb 99.9 % of the signal radiation. For a final analysis, the number density of the lead metastable state was also measured by excitation of the 405.7807 nm transition and observing the direct line fluorescence at 283.3053 nm. The same parameters were used as in table 5-1, with the exception of the calibration factor, F = 5.0723 W cm-2 nm-1 mV-1, which was measured for 283.3053 nm. From measured values and using equation 5-15, number densities are

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106 obtained for this metastable state and are show n in figure 5-12. These values are also in agreement from conventional absorption and high resolution emission values. 10-1100101107108109101010111012 Saturated Fluorescence Conventional Absorption High Resolution EmissionNumber Density (atoms cm-3)Galvatron Current (mA) Figure 5-12. Plot of the metastable state numbe r density of lead as a function of current. Saturated fluorescence values are comp ared to results obtained from conventional absorption and high re solution emission measurements. Conclusion A thallium see-through hollow cathode discharge, or galvatron, has been investigated as a potential atomic line filter. Number density values for the thallium galvatron have been obtained at various a pplied currents by time-resolved laser-induced saturated fluorescence and are reasonable comp ared to previous studies [62]. Results obtained show that the galvatron is easily able to produce number densities capable of 99.9 % absorption of a line source when a curr ent of 16.0 mA or higher is applied. However, applied currents greater than 16.0 mA begin to demonstrate post-filter affects as seen by the deviation from linearity in th e measured number density values in figure 5-

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107 10. This is a result of the metal vapor becoming optically thick which is reasonable based on the curve-of-growth calculation (see appendix A). The quantum efficiency of the system was also evaluated. A theoretical saturation curve calculated for a three-leve l atom in the presence of a trap showed excellent agreement with the experimental satu ration curve. All theoretical curves were calculated with all collisional de-excitation rate constants equal to zero (kij = 0) and, therefore, only the spontane ous transition probabilities, Aij, need to be considered in calculating the quantum efficiency of any a llowed transition. This is a perfectly reasonable conclusion since the ga lvatron is relatively low pressure system with virtually no molecular species present. In conclusion, it has been demonstrated that a galvatron is an attractive atomic reservoir for applications as an atomic lin e filter. A desired number density can be rapidly produced by applying the appropriate current and can be reproduced from one experiment to the next. In addition, the quant um efficiency of this system is limited only by the competing radiative pathways of the particular energy leve l arrangement which allows it to be a very efficient detector. This system has the potential to be simple, compact, and portable which makes it an ideal atomic line filter.

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108 CHAPTER 6 LIFETIME MEASUREMENTS OF SEVERAL S, P, AND DJ STATES IN A THALLIUM SEE-THROUGH HO LLOW CATHODE DISCHARGE Introduction Several elements have been studied for the use as atomic line filters, such as the alkali metals [63,64], alka line earths [65,66], and thalliu m [67]. As previously recognized by Liu et al. [67], thallium is especially attractive since the 535.046 nm metastable transition overlaps with the second harmonic output of a Nd:La2Be2O5 (BEL) laser (1070 nm). This makes the 535.046 nm thal lium metastable state transition ideal for certain applications as an atomic line filter. Oehry et al. [68] have also reported use of the thallium metastable state as an atomic line filter. In this report, a hollow cathode lamp was used to pump the metastable state of a thallium atomic vapor in a heated sealed cell. With appropriate cell dimensions and buffer gas pressure, the lifetime of the metastable state could last for several ms. Th is allows the detection of a weak signal well after the state has been initially pumped. The idea proposed by Oehry et al. [68] is expanded upon with the use of a seethrough hollow cathode discharge, or galvatron (Hamamatsu), as an alternative atomic reservoir. The advantage of a galvatron is that they may be used continuously over long periods of time without need to remove any molecular impurities such as oxygen, a major contributor to the quenching of the thallium metastable state [11,69]. This is a simple system, capable of easily producing an accepta ble and stable number density of both ground state and metastable state number densities. If the si gnal were to be enhanced by pumping the metastable state, the effective lifetime of this state would need to be determined. The lifetimes of all st ates radiatively coupled to the 6 2P3/2 o metastable state are also determined.

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109 Figure 6-1. Partial energy level diagram for thallium. In this chapter, the lifetimes of the 7 2S1/2, 6 2D3/2, and 6 2D5/2 states are determined by time-resolved single-step fl uorescence shown by the partial energy level diagram in figure 6-1. However, the 6 2P3/2 o metastable state coul d not be analyzed by a single-step fluorescence approach. The di rect magnetic-dipole transition at 1.28 m is extremely weak and observing the resulting fl uorescence would be very difficult. In order to determine the lifetime of such a l ong lived state, a two-step fluorescence method is used [69,70]. This two-step method invol ves the use of pump and probe laser pulses. The pump laser pulse transfers ground state atom s into the state of interest directly or indirectly by fluorescence or collisional processes. The te mporally delayed probe pulse interrogates the population of the pumped state by either observing the resulting fluorescence or opto-galvanic signa l. A plot of the resulting signal as a function of time delay results in the decay waveform for the metastable state. From the lifetime values obtained, collisional deexcitation rate constant s for each current applied are also derived. 6 2 D3/2 6 2 D5/2 7 2 S1/2 6 2 P3/2 o 6 2 P1/2 o = 351.924 nm = 352.943 nm ex = 276.787 nm = 377.572 nm probe = 535.046 nm 7 2 P1/2 o 7 2 P3/2 o 0.119 eV = 1301.32 nm = 1151.28 nm = 1.28 m

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110Experimental Lasers and Optics The experimental setup used for this work was the same for both the single step and two-step fluorescence measurements (figure 6-2). For single step excitation of the 6 2D3/2 and 6 2D5/2 states, a XeCl excimer (Lambda Physiks LPX 200) pumped dye laser (Lambda Physiks Scanmate 1) was used. Coumarin 540A (Exciton) dissolved in methanol was used at a concentration of 8 x 10-3 M. The dye laser output was sent to a second harmonic generation unit (Lambda Phys iks) for frequency doubling to obtain the 276.787 nm ground state thallium transition. To obtain the 535.046 nm transition, a nitrogen (Laser Science Inc. model VS L-337ND) pumped dye laser (Photochemical Research Associates Inc. m odel LN102) was used. The dye for this transition was the same as that for the generation of the funda mental of the 276.787 nm transition. Mirrors 1-4 are UV enhanced aluminum coated and ar e used in order to obtain the appropriate beam height and orientation. A pierce d mirror directed the collected fluorescence towards the monochromator and allows both the 276.787 nm and 535.046 nm laser beams to pass. Fused silica lenses collected the fluorescence and imaged it onto the slit of the monochromator. In orde r to filter stray laser scatter, a glass slide was placed in front of the entrance slit of the monochromator when the 276.787 nm laser was used and a color glass filter when the 535.046 nm laser was used.

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111 Figure 6-2. Experimental se tup used for both single-step and two-step laser excited fluorescence measurements. IF is an interference filter used to remove laser scatter. Mirrors 1-4 are used for laser beam height and orientation alignment. PD-1 and PD-2 are photodiodes used to monitor the time delay between the two pulses for two step fluorescence measurements. PD-3 is a photodiode used to trigger the signal acquisition. For the two-step fluorescence measurements, the two laser systems had to operate in temporal synchrony. This was done by adopting a method used by Omenetto et al. [69]. In this scheme, pulse generator-1 (W avetek model 802) is used to trigger the excimer laser while the synchronous output is us ed to trigger a boxcar (Stanford Research Systems model SR250). The temporally adjustab le gate output of the boxcar is used to trigger pulse generator-2 (S ystron Donner model 101). The output of pulse generator-2 triggers the nitrogen laser system, which is used to generate the 535.046 nm laser beam. Monochromator Pulse Generator-2 Nitrogen Laser Dye Laser Dye Excimer Laser Frequency doubling unit PM Mirror-4 Mirror-3 Mirror-2 Mirror-1 Pierced Mirror Lens H.V Thallium Galvatron Scope p robe = 535.046 nm ex = 276.787 nm Boxcar (Delay generator) Pulse Generator-1 Fast Scope Glass PD-3 PD-1 PD-2 Lens IF

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112 The boxcar in this arrangement acts as a conve nient delay generator. The jitter between the two laser pulses was approximately 10 ns acceptable for the present measurement. Detection The monochromator used was a McPherson model 218 with crossed CzernyTurner geometry, a grating of 1200 grooves mm-1, blazed at 300 nm, reciprocal linear dispersion of 2.6 nm mm-1, ruled grating area of 50 x 50 mm, focal length of 300 mm, and an f-number of 5.3. The entr ance and exit slits were set at 200 m giving a geometric spectral bandpass of 0.52 nm. This was more than sufficient to resolve the 351.924 nm fluorescence from the 352.943 nm fluorescence. Detection was accomplished with a high speed photomultiplier tube (Hamamatsu R3091) having a rise time of 400 ps, a spectral res ponse 300 to 850 nm, and -2500 V applied. The resulting fluorescence waveform was observed on a 500 MHz oscilloscope (Tektronix TDS 520D). Results and Discussion 6 2D3/2 and 6 2D5/2 Lifetime Measurements Lifetime measurements on the 6 2D3/2 and 6 2D5/2 thallium states were done by single-step laser-induced fluorescen ce. The population of the 6 2D3/2 state was pumped by the 276.787 nm ground state transition. The 6 2D3/2 state was measured by tuning the monochromator to the 352.943 nm transition and observing th e resulting direct line fluorescence waveform. Calculated values were also obtained from equation 1, jkA 1 where Ajk (s-1) are the transition probabilities for a ll radiative de-excitation pathways of the state of interest. Values for all transi tion probabilities covered in this work were (1)

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113 obtained from the National Institute of Standards and Technology website (http://physics.nist.gov/PhysRefData/ASD/lines_form. html) and are shown in table 6-1. Table 6-1. Transition probabilities obtained from the National Institute of Standards and Technology Transition Transition Probability, Ajk (s-1) 7 2S1/2 6 2P1/2 o 6.25 x 107 s-1 7 2S1/2 6 2P3/2 o 7.05 x 107 s-1 6 2D3/2 6 2P3/2 o 2.20 x 107 s-1 6 2D3/2 6 2P1/2 o 1.26 x 108 s-1 6 2D5/2 6 2P3/2 o 1.24 x 108 s-1 The resulting waveform for the 6 2D3/2 state can be seen in figure 6-3. The experimental data was fitted with a nonlinear least squares fit in order to obtain the lifetime for the fluorescence waveform. From figure 6-3, a value of 6.4 0.1 ns was found and agrees fairly well with the calculated value, as well as values obtained from previous works shown in table 6-2. The lifetime for this stat e was independent of the applied current, as expected, since this is a low pressure in ert gas system where quenching effects are expected to be negligible. 0246810121416182022 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 Intensity (V)Time (ns) Experimental Data (14.0 mA) Non-linear least squares fit y = co + c1e-t/ = 6.4 0.1 ns Figure 6-3. Measured fluorescence curve for the thallium 6 2D3/2 state.

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114 Table 6-2. Comparison of previously reported values on the spontaneous lifetime of the 6 2D3/2 state Source Reported value Gough and Series [71] 5.2 0.8 ns Gallagher and Lurio [72] 6.2 1 ns Anderson and Sorensen [73] 6.8 0.5 ns Cunningham and Link [74] 6.9 0.4 ns Shimon and Erdevdi [75] 6.9 0.5 ns Lindgrd et al. [76] 6.1 0.7 ns Bimont et al. [77] 8.5 0.5 ns Calculated 6.76 ns Present work 6.4 0.1 ns The same approach was applie d to the measurement of the 6 2D5/2 state, the only difference being that the monochromator was tu ned to the 351.924 nm transition. This is not a direct excitation, howe ver, and involves the transfer of atoms through collisional coupling into this higher lying energy level. Figure 6-4 clearly shows that the resulting signal was much weaker, with a greatly reduced signal-to-noise ratio. Omenetto and Matveev [78] observed comparable fluorescence waveforms using a similar energy level scheme for gold with comparable signal-to-noi se ratio. Despite the poor signal-to-noise ratio obtained with the presen t results, a lifetime of 7.5 1.1 ns is obtained for the 6 2D5/2 state. Despite an uncertainty of 14.7 %, th e value obtained agrees fairly well with the calculated value, as well as values obtained fr om previous authors show n in table 6-3. As in the case of the 2D3/2 state, the 6 2D5/2 state showed no dependence on the applied current. For a more precise lifetime measurement of the 6 2D5/2 state, a more direct excitation transition should be used.

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1150246810121416 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 Experimental Data (Current = 14.0 mA Non-linear least squares fit y = co + c1e-t/ = 7.5 1.1 nsIntensity (V)Time (ns) Figure 6-4. Measured fluorescence curve for the thallium 6 2D5/2 state. Table 6-3. Comparison of previously reported values on the spontaneous lifetime of the 6 2D5/2 state Source Reported value Shimon and Erdevdi [75] 7.2 0.6 ns Lindgrd et al. [76] 6.5 0.7 ns Gough and Griffiths [79] 6.8 0.4 ns Anderson and Sorensen [73] 7.6 0.5 ns Calculated 8.06 ns Present Work 7.5 1.1 ns 7 2S1/2 Lifetime Measurement The lifetime of the 7 2S1/2 state was also measured by single-step laser-induced fluorescence. The 535.046 nm output of the nitrogen pumped dye laser was used to populate the 7 2S1/2 state. The fluorescence was collected by tuning the monochromator to the 377.572 nm transition. As can be seen in figure 6-5, an experimental lifetime for this state, 7.7 0.2 ns, is in good agreement with the calculated va lue of 7.52 ns, as well as previously reported values show n in table 6-4. As with the 2DJ states, since the lifetime of this transition is only 7.7 ns, th e excited atoms do not have sufficient time to

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116 interact with their environment; therefore, no current dependence was observed. This suggest that the collis ional rate constants, kij, for the S and 2DJ states are much less than that of the spontaneous transition probabiliti es, yielding a high quantum efficiency and low quenching environment. 05101520253035 0.000 0.005 0.010 0.015 0.020 0.025 Intensity (V)Time (ns) Experimental Data (Current = 18.0 mA) Non-linear least squares fit y = co + c1e-t/ = 7.7 0.2 ns Figure 6-5. Measured fluorescence curve for the thallium 7 2S1/2 state. Table 6-4. Comparison of previously reported values on the spontaneous lifetime of the 7 2S1/2 state Source Reported value Demtrder [80] 8.7 0.3 ns Gallagher and Lurio [72] 7.6 0.2 and 7.4 0.3 ns Penkin and Shabanova [81] 8.25 0.6 ns Lawrence et al. [82] 8.1 0.8 ns Norton and Gallagher [83] 7.45 0.2 ns Cunningham and Link [74] 7.65 0.2 Anderson and Sorensen [73] 7.7 0.5 ns Shimon and Erdevdi [75] 7.4 0.5 ns Harvey et al. [84] 7.8 0.3 ns Lindgrd et al. [76] 6.9 1.0 and 6.3 0.7 ns

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117 Table 6-4. Continued Hsieh and Baird [85] 7.55 0.08 ns Rebolledo et al. [86] 7.61 0.16 ns Bimont et al. [77] 7.3 0.4 ns Calculated 7.52 ns Present work 7.7 0.2 ns 6 2P3/2 o Lifetime Measurement The thallium 6 2P3/2 o state is a metastable state 0.996 eV above the ground state. Since the 6 2P3/2 o 6 2P1/2 o transition is forbidden, it wi ll be very weak and long lived, having a reported spontaneous lifetime of 250 ms [11]. Since this is a weak transition observation of the 1.28 m fluorescence from the 6 2P3/2 o 6 2P1/2 o transition would be difficult. A diode laser at 535.046 nm could be used to monitor the lifetime of the metastable state by relating the observed abso rption to the population of the metastable state as a function of time; however, such a diode laser was not available. For this reason, a two-step laser-induced fluorescen ce measurement was used to determine the effective lifetime of the 6 2P3/2 o metastable state. This was done by pumping the metastable state with a 276.787 nm laser pulse Pumping of the metastable state could also have been accomplished using a 377.572 nm laser pulse, but since a 276.787 nm laser was already available from the previous measurements, it was used as the excitation source. To avoid losses due to photo-ionization from the pump laser beam, the pulse energy was held to approximately 1 J per pulse. In a low pressure system, this pulse energy approaches the saturation spectral i rradiance for this transition; therefore, maximum population enhancement is nearly achie ved. The direct line fluorescence into the 6 2P3/2 o metastable state allowed indirect pumpi ng of this state, a nd since the lifetime of the 6 2D3/2 state was found to be only 6.4 0.1 ns, there should be no distortion of the

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118 measured lifetime. The 276.787 nm laser pulse is followed by the 535.046 nm laser pulsed, which is temporally controlled by the boxcar. The 535.046 nm laser pulse probes the population of this metastable state and the resulting fluorescence is observed at 377.572 nm. The intensity of the resulting fl uorescence is directly related to the population of the probed state; therefore, measuring the fluorescence intensities at different time delays with respect to the pump pulse allowed the determination of the effective lifetime of the 6 2P3/2 o state. 0246810121416 0.01 0.1 1 Intensity (Normalized)Time Delay (s) Experimental Data 6.0 mA 8.0 mA 10.0 mA 12.0 mA 14.0 mA Figure 6-6. Measured lifetime curves for the thallium 6 2P3/2 o metastable state. The resulting lifetime curves were fitted with a nonlinear le ast squares method to obtain the lifetimes of the metastable state fo r the different currents applied. The values of the experimental and fitted curves were normalized shown in figure 6-6. Values from 0 to 100 ns time delays could not be taken due to the collisional transfer of atoms into the 7 2P1/2 o and the 7 2P3/2 o states, which also result in 377.572 nm fluorescence as shown in

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119 figure 6-7. The long rise time and decay is du e to the spontaneous lif etimes [87] of 61.9 1.7 ns and 48.4 1.3 ns for the 7 2P1/2 o and 7 2P3/2 o states, respectively. Since the atoms must decay through many states, their fina l observed fluorescence waveform becomes stretched, thus resulting in the observed fluorescence waveform. Therefore, in order to avoid distortion to the measured lifetime curves for the metast able level, values prior to 100 ns time delay were not recorded. This is acceptable for th e present two-step fluorescence approach since the measured lifetimes are on the order of a few s. If a highly quenching atomic reservoir were to be used, such as an air-acetylene flame, where the effective lifetime of the 6 2P3/2 o state has been reported to be only 81 ns [69], this fluorescence approach could not be used. -20020406080100120140160 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Intensity (a.u.)Time (ns) Current = 14.0 mA Figure 6-7. Measured fluorescence wa veform at 377.572 nm due to 276.787 nm excitation. To explain the observed lifetimes for this metastable state, the different deexcitation factors need to be c onsidered. As described by Magerl et al.[11], effective lifetimes are dependent on four factors, the natural lifetime, natural, the lifetime due to collisions with the buffer gas, buffer, the lifetime due to col lisions with ground state thallium atoms, self, and the lifetime due to collisions with the walls of the container, wall, as shown in equation 6-1.

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120 The contribution due to the natural, or spontaneous, lif etime is the result of an isolated atom, unperturbed by its environment, naturally decaying. In the present system, the natural lifetime of the 6 2P3/2 o metastable state has been re ported to be 0.250 ms [11]. The expected lifetime of the thallium meta stable state due to collisions with the buffer gas, buffer, can be calculated by th e following equation [11], relative Ne Ne Tl buffern 1 where Tl-Ne (3 x 10-24 cm2) is the collision cross section [88] between metastable state thallium atoms and neon atoms, and nNe (4.51 x 1017 cm-3) is the number density of neon atoms at a pressure of 14 torr. The parameter relative is the relative velocity between the thallium metastable state and the neon buffer gas and is calculated [70] by equation 6-3, T kb relative8 where kb (1.38 x 10-20 mJ K-1) is the Boltzmann constant, T (495 K) is the Doppler temperature [40] of the system at an applied current of 10.0 mA, and is the reduced mass of the system, 2 1 2 1m m m m where m1 and m2 are the masses of neon (3.531 x 10-23 g) and thallium (3.394 x 10-22 g), respectively, and is calculated to be 3.198 x 10-23 g. When these values are substituted into equation 6-2, a calculated lifetime value of 10.02 s is obtained for the 6 2P3/2 o state due to collisions with the neon buffer gas. This long calculated lif etime is due to the wall self buffer natural 1 1 1 1 1 (6-1) (6-2) (6-3) (6-4)

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121 extremely small collisional cross section between the thallium metastable state and neon atoms. The expected lifetime of the thallium me tastable state due to collisions with ground state thallium atoms, self, is calculated [11] in a similar fashion to that in equation 6-2, and is shown in equation 6-5, relative Tl Tl Tl selfn 1 where Tl-Tl (5 x 10-16 cm2) is the collisional cross section [11] between the metastable state thallium atoms and ground state thallium atoms. The parameter nTl (3.4 x 1011 cm-3) is the number density [32] of ground state thallium atoms and relative (3.20 x 104 cm s-1) is the relative velocity between the two thalliu m atoms calculated from equation 6-3 for an applied current of 10.0 mA. If these values are substituted in to equation 6-5, a value of 0.180 s is obtained for the que nching lifetime of the thalliu m metastable state due to collisions with ground state thallium atoms. Despite the higher col lisional cross section, the lifetime is relatively long due to the sma ll ground state number density for an applied current of 10.0 mA. It is generally accepted that the presence of oxygen, O2, is the main contributor for the quenching of the thallium metastable st ate in oxygen rich environments such as a flame [11,69] due to its high quenc hing cross section [89] of 2.8 x 10-15 cm2. If this were the case here, the resulting lifetime at a cu rrent of 10.0 mA would correspond to an oxygen partial pressure of approximately 10-2 torr. It is known, however, that the concentration of oxygen in the present atom ic reservoir does not exceed 1 ppm (6 x 10-4 torr) [30]. In the present work, the lifetim e measurements were carried out in a low (6-5)

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122 pressure, very pure neon buffer gas with neg ligible molecular species present so the quenching contribution due to oxygen, nitroge n, hydrocarbons, water, or any other molecular species is expected to be negligible This would also negate any losses due to chemical reactions. The lifetime due to collisions with the walls of the cell [11] is given by equation 6-6a and 6-6b, 2 2405 2 1 l r F p p D Fgeometry buffer o o geometry wall where Fgeometry is the geometry factor of the first diffusion mode, r is the radius (0.1 cm) and l is the length (2 cm) of the cylinder, Do is the diffusion constant (0.7 cm2 s-1) [11] of thallium metastables in neon at a reference gas pressure po (75 torr) [11], and pbuffer is the pressure of the neon buffer gas (14 torr) [57] in the discharge. From these values, an effective lifetime value of 4.59 x 10-4 s is calculated. Therefore, based on equation 6-1, the lifetime for this system is expected to be dominated by deexcitation with the walls of the cathode. However, the calculated valu e does not agree with the lifetime values experimentally observed. Since the present study was done in a lo w pressure steady state glow discharge rather than in the afterglow of a pulsed di scharge or a static sealed cell, certain considerations need to be made. Magerl et al. [11] explain that by increasing the buffer gas pressure, the lifetime of the metastable state also increases. This is due to collisions with the buffer gas reducing the mean free path of the thallium metastable and therefore, diffusion of thallium atoms to the walls of th e container is reduce d. However, in the (6-6a) (6-6b)

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123 present atomic reservoir, thallium atoms ar e generated at the walls of the cathode and diffusion into the negative glow region is re duced with increasing buffer gas pressure due to a shorter mean free path. Bruhn and Harriso n [90] reported that as high as 90 % of the metal atoms that are sputtered redepos it back on the cathode surface through backdiffusion. Taking this into account, most of the sputtered thallium atoms would reside between the cathode surface and the mean free pa th of the sputtered atom. It is also known that the Doppler temperature of the spu ttered atoms is higher close to the surface of the cathode and decreases as the dist ance is increased [ 91,92]. High resolution emission measurements [40] have found a Doppler temperature of 495 15 K for an applied current of 10.0 mA; how ever, this is predominately a Doppler temperature measurement of the negative glow region wh ere most of the emission occurs. If a Doppler temperature of 1000 K were used with a pressure of 14 torr of neon for this region, a mean free path of 82.6 m is calculated. If this mean free path is used as the radius in equation 6-6b, then a calculated li fetime, due to collisions with the cathode surface, of 3.2 s is obtained, in good agreement with the experimental value of 3.1 0.3 s for an applied current of 10.0 mA. For a more accurate calculation, the Doppler temperature of this region would need to be determined for various applied currents. Since the lifetimes were measured in a D.C. discharge, other factors need to be considered as well, such as the presence of ions and electrons. It has been observed by Turk and Omenetto [55] that increasing the co ncentration of electrons in an air acetylene flame, by the addition of cesium, affected the slow decay rate of ion-electron recombination of strontium at oms with lifetimes on the orde r of a few microseconds. It was also observed by Axner et al. [70] that the addition of cesium resulted in a slightly

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124 shorter effective lifetime of a lead metastable state in an air acetylene flame. Taking into account these observations along with the re sults found in the pr esent study would suggest a lifetime contribution due to electronthallium collisions. It is also known that the highest concentration of electrons in a glow discharge is found in the region between the cathode dark space and ne gative glow region, due to electron multiplication from fast high energy electrons and the pr oduction of slow thermal elec trons. The contribution of electrons along with wall quenching collisions would explain the observed lifetime dependence on the applied current; however, furt her analysis would be needed before any direct conclusions can be made. Such studi es would include determination of quenching cross sections, number densities, and relative velocities. A comparison of the effective lifetime values obtained in the present study to those obtained from previous work is shown in table 6-5. Table 6-5. Comparison of previously reported values on the effective lifetime of the 6 2P3/2 o metastable state Source Reported ValueAtomic Reservoir Omenetto et al. [69] 81 ns Air-Acetylene flame (~2500 K, ~760 torr) Axner et al. [70] 2 s Graphite furnace (in pure N2 buffer gas, ~2500 K, ~760 torr) Magerl et al. [11] 48 ms Sealed cell (5 cm long and 3 cm diameter, 723 K, 75 torr Ar) Aleksandrov et al .[88] 20 ms Sealed cell (18 cm long and 5.8 cm diameter, 668 K, 10 torr Ne) Pickett and Anderson [93] 12.7 s Sealed cell (15 cm long and 5 cm diameter, 1089 K, no buffer gas) Lurio and Gallagher [94] 30 s Sealed cell (In vacuum) Lurio and Gallagher [94] 1 ms Sealed cell (low pressure Ar) 4.8 0.6 s Galvatron (6.0 mA, 467 K, 14 torr Ne) 3.8 0.4 s Galvatron (8.0 mA, 481 K, 14 torr Ne) 3.1 0.3 s Galvatron (10.0 mA, 495 K, 14 torr Ne) 2.8 0.1 s Galvatron (12.0 mA, 509 K, 14 torr Ne) Present Work 2.1 0.2 s Galvatron (14.0 mA, 523 K, 14 torr Ne)

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125Collisional Deexcitation Rate Constant Since the lifetime of the metastable st ate has been measured, the collisional deexcitation rate constant be tween this level and the ground state can also be calculated by the following relationship, where A21 is the spontaneous emission transition probability (s-1) and k21 is the collisional deexcitation rate constant (s-1). If k21 is assumed to be much greater than A21 ( k21 >> A21), then equation 6-7 reduces to, 121 k which is a safe assumption since A21 is calculated to be 4 s-1 due to a spontaneous lifetime of 250 ms. Results from these calculations can be seen in figure 6-8. The lifetime and collisional deexcitation rate c onstant both show a linear relati onship with current, further suggesting a contribution of electron-thallium collisions to the obser ved effective lifetime of the thallium metastable state. 56789101112131415 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Lifetime (s)Galvatron Current (mA) Lifetime2.0x1052.5x1053.0x1053.5x1054.0x1054.5x1055.0x105 Collision deexcition rate constant (s-1) Collision Deexcitation Constant Figure 6-8. Plot of the lifetimes, and calculated deexcitation rate constant, k21, at various currents for the thallium 6 2P3/2 o metastable state. 21 211 k A (6-7) (6-8)

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126Conclusion The lifetimes of several S, P, and D states of a thallium see-through hollow cathode discharge have been determined by tim e-resolved single-step and two-step laser excited fluorescence. The lifetime values obtai ned for the S and D states agree well with calculated values, as well as values obtained from previous work. It can therefore be concluded that these are high qua ntum efficiency transitions and collisional de-excitation is considered negligible for these transitions. The lifetime of the 6 2P3/2 o metastable state was found to be in the low microsecond region and is expected to be due to collisions with wall of the cathode. In order to more accurately explain the results obtained, temperature measurements in the dark cathode region of the discharge are n eeded. In addition, before any direct conclusion is made, diagnostic measurements ar e needed in order to better understand the contribution that electrons have on the lifetime of the thallium metastable. In conclusion, the use of this atomic reservoir as an atomic line filter for the detection of input radiation at 535.046 nm from sources such as the second harmonic of a Nd:BEL laser would not be as efficient as a se aled cell due to the relatively low effective lifetime of the metastable state. This reservoi r does have the advantage in that it is a D.C. discharge and so the metastable state will be thermally populated without the need for an external pumping source. If pumping is desi red for signal enhancement, it would be best if the metastable state were continuously pumped by use of a cw diode laser. Future studies should also involve effective lifetime measurements with the galvatron operating in pulsed mode. Working in pulsed mode would effectively populate the metastable state, remove any resonant background radia tion generated by the ga lvatron, and increase the signal-to-background ratio. The use of th is atomic line filter in combination with a

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127 frequency doubled Nd:BEL laser could prove to be a superior detection system for applications involving a high optical background.

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128 CHAPTER 7 FINAL CONCLUSIONS AND FUTURE WORK Concluding Remarks Several parameters of a see-through hollow cathode discharge, or galvatron, were measured in order to evaluate its potentia l as an atomic line filter. Among these parameters was the resolving power that such an atomic reservoir would yield for various applied currents. Resolving power measur ements were accomplished by obtaining high resolution emission profiles for thallium and l ead at various applied currents. The profiles obtained were analyzed with a two-layer m odel from which Doppler temperatures were determined. Based on these results, resolving powers were found to be similar to sealed cells and hollow cathode lamps, and superi or to flames, ICP, and conventional spectrometers. Number densities were also determined for both thallium and lead from the optical depths acquired from the two-laye r model, and values are in fair agreement with measurements from other methods. Hyperfine Structure Considerations To achieve a high resolving power in an atomic line filter, a narrow absorption profile must be obtained. However, one mu st also consider the width of the hyperfine structure. If the thallium and lead systems are considered, both of which have a mildly broad hyperfine structure, then the width of the hyperfine structure must be taken into account when considering the resolving power of the entire atomic system. These atomic systems have relatively wide hyperfine struct ure, which results in a lower effective resolving power. This problem may be alleviated by use of a mono-isotopic cathode of the element. If lead is consider ed, then a cathode compose purely of 208Pb would result in a single line, with no hyperfine splitting of the state. A single absorption line dominated

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129 purely by Doppler broadening will result in resolving powers re ported in this work. As for thallium, the two naturally occurring isotopes both have hype rfine components and can not be narrowed by a mono-isotopic cat hode. However, thallium was specifically chosen for its 535.046 nm metastable transi tion which conveniently overlaps with the second harmonic of a Nd:BEL laser. The spectra l output of this laser may be as broad as 30 pm, assuming the laser is not operated in si ngle mode. In this particular case, the signal is much broader than the absorption pr ofile of the atomic reservoir; therefore, much of the signal will be transmitted without detection. Therefore, it would be beneficial if the absorption profile of the atomic vapor were broader, with a broad hyperfine structure, in order to absorb as mu ch of the signal as possible. This could enhance the sensitivity and possibly increase the signal-to-noise ratio of the filter and still retain a high background rejection. Absorption Measurements High resolution absorption measurements were made on the thallium discharge by combining a self-reversed profile from a thalli um electrodeless discharge lamp and a selfabsorbed profile from a thallium hollow cathode lamp. The combination of these two line sources produces a quasi-continuum source over the absorption of the atomic vapor. This quasi-continuum source, after passed thr ough the atomic vapor, can be reconstructed using a scanning Fabry-Perot interferomet er, with the resulting emission profile containing the absorption profile of the atomic vapor. Unfortunately, due to the complicated hyperfine structure of thallium, and the resolutio n of the interferometer, a poorly defined baseline was obt ained for all currents measured. The poor baseline makes it difficult to assign the 100 % transmission va lue, therefore, inaccurate Doppler widths and inaccurate peak absorption coefficients w ould be obtained. This would result in

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130 slightly inaccurate number densities; however, the results obtained are in fair agreement with number densities obtained from high resolution emission profile analysis. For improvement of the baseline, a broader quasi -continuum would be needed in order to improve the baseline, however, the profile used already fills the free spectral range and an increase would result in the emission prof ile spilling into adjacent orders and would result in distortion of the measured absorp tion profiles despite the gain in baseline improvement. The free spectral range could be increased in order to compensate for this profile broadening; unfortunately this also decreases the reso lution of the interferometer and results in an unacceptable instrumental FWHM. Despite these difficulties, it has been shown that high resolution absorption prof iles can be obtained by use of a scanning Fabry-Perot interferometer and can be used as an alternative to diode lasers if such a laser at the transition of interest does not exist. The mirrors of the inte rferometer can cover a larger spectral range than a diode laser, and therefore, can be applied to several transitions of various elements. The enhan ced spectral scanning ability allows one to measure absorption profiles that may be t oo broad for the scanning capabilities of a narrow band diode laser. Conventional absorption measurements we re also done on the thallium and lead galvatrons by use of a hollow cathode lamp with a fixed low current. Results obtained for thallium were not in agreement w ith results from saturated fluorescence measurements. This discrepancy was attribut ed to the relative width of the emission profile from the hollow cathode lamp to the abso rption profile of the thallium galvatron. As for the lead metastable state, good ag reement was found from conventional absorption measurements compared to results obtained from saturated fluorescence and high

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131 resolution emission measurements. This agreement was due to the relative widths of the emission from a hollow cathode lamp and the abso rption profile of the galvatron. It has been shown that a hollow cathode lamp can be used for accurate absorption measurements in a low pressure glow discha rge; however, the relative widths of the absorption profile of the disc harge and the emission profile of the hollow cathode lamp need to be known in order for accurate measurements to be made. Saturated Fluorescence Measurements Analysis of the quantum efficiency and number density of the atomic system was evaluated by use of time-resolved laser-indu ced saturated fluorescence spectroscopy. Saturation curves were obtained for thallium and lead by measuring the peak of the fluorescence waveform at various attenuated laser spectral irra diances. These saturation curves were fitted with a time dependent threelevel theoretical curve in the presence of a trap, or loss less sink. From known parameters and setting collisional rate constants to zero, an excellent fit was obtained for both thallium and lead. This translates into quantum efficiencies that were limited onl y by spontaneous emission rates. This is advantageous over high quenching reservoirs such as flames, ICP plasma, or sealed cells, depending on buffer gas and pressure. Number density values were also obtain ed and are compared to values obtained from other spectroscopic methods. It was f ound that the thallium and lead galvatrons produce an acceptable number density based on curve-of-growth calculations; however, pumping of the thallium and lead metastable states may be needed in order to enhance the population of these levels and therefore, enha nce the fraction of signa l radiation that is absorbed by the atomic vapor. The present di scharge has an advantage over other atomic

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132 reservoirs, since the atomic vapor is eas ily produced, and reproduced, by simply applying a stable current and can be sustai ned for extended periods of time. Lifetime Measurements The lifetimes of several S, P, and D st ates were measured by single step and two step laser excited fluorescence. The single st ep measurements of the S and D states were found to be in good agreement with values ob tained from previous works as well as calculated values. Since the th allium metastable state is a very weak and long lived, with a spontaneous lifetime of 250 ms, a pump and probe me thod was used for this measurement. Lifetimes on the order of a few microseconds was found for the discharge when operated at various currents in D.C. m ode. If the thallium metastable state were pumped, a window of a few microseconds exists before the state needs to be re-pumped. The metastable state could be directly pumped by a cw diode laser at 1.28 m in order to achieve an increased number density for signa l enhancement. The lifetimes reported here are superior compared to high quenching envi ronments such as flames, where a lifetime of 81 ns has been reported; however, sealed cells do offer an advantage in this case, where lifetimes of several milliseconds can be obtained with the appropriate cell dimensions and buffer gas pressure. In the sealed cell reservoir, however, the population of the metastable state is extremely low, and therefore, pumping of this metastable state is required for this reservoir. For hollow cat hode discharges, the me tastables state is already thermally populated due to collisions with thermal electrons, ions, metastables, and buffer gas atoms. Therefore, this metastable state will only need mild pumping from the ground state.

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133 Collisional rate constants are obtaine d from the lifetimes of the thallium metastable state. These values we re found to be on the order of ~ 105 s-1. These values are several orders of magnitude less th an spontaneous transition rates, ~ 107 s-1, making collisional quenching negligible for this atomic system at various currents. These results are further supported by the resu lts obtained from analysis of the saturation curves obtained for both thallium and lead, which conc luded that the collisional rate constants are considered negligible. A see-through hollow cathode discharge ha s been extensively studied by several spectroscopic methods as a poten tial atomic reservoir for use as an atomic line filter. Each method used provided valuable data on the characterization of this discharge and was evaluated in terms of its a pplication as an atomic line filter. It has been found that this reservoir is a high quantum efficiency system and is capable of producing an acceptable number density for use as an atomic line filter. Resolving powers have been found to be superior to flames, plasmas, and conventional spectrometers, and are comparable to sealed cells. The see-th rough hollow cathode is a simple, compact, and portable system which can be appl ied to a number of applications. Future Work Signal-to-Noise Ratio Considerations Future work on the characterization of a see through hollow cathode discharge would involve analysis of the signal to noise ratio of the discharg e as an atomic line filter. Many of the parameters evaluated in this work were in an attempt to find optimal operating currents for this reservoir. As prev iously discussed, there are trade-offs that must be considered in choosing an optimal operating current, such as number density and resolving power. The signal-to-noise ratio mu st also be considered. For example, it has

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134 been reported by Pertucci [95] that the optim al signal-to-noise ratio was found to be at low currents applied to a hollow cathode lamp when opto-galvanic detection was employed. If opto-galvanic detection is us ed, then an optimal resolving power would also be found at these lower currents; howev er, the trade-off is a drastic reduction in number density of the atomic vapor. As it is known from curve-of-growth theory, a low number density would result in a large porti on of the signal radiation to pass through the atomic vapor, resulting in a lo ss of the signal. This could reduce the sensitivity of the filter and limit its applications. Therefore, optimal signal-to-noise ratios for detection by fluorescence, ionization, and opt o-galvanic detection would n eed to be determined in order to evaluate its effectiv eness in certain applications. Atomic Reservoir Element In the present study, thallium and lead we re chosen as the two elements for the atomic vapor. The reasons these two elements were chosen is due to their three energy level system, the relatively st rong oscillator strengths at th ese transitions, the overlap of an atomic transition with the output of an effi cient solid state laser (thallium), and for the mass of the two elements. The mass is a fact or since the absorption profiles are Doppler broadened, therefore, heavier elements will ha ve a slower relative velocity compared to lighter elements in a similar thermal envir onment. The result is a narrower absorption profile and higher resolving power. In additi on, it has already been mentioned that the hyperfine structure of the transition is importa nt in the resolving power of the atomic vapor. If a very high resolving power is re quired, then an atomic system that is composed of a single line would be desired, such as calcium or a cathode composed of a mono-isotopic element. In contrast, me rcury has a complicated hyperfine structure approximately 45 pm wide [28]; therefore, much of the resolving power is lost with this

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135 element; however, this broad hyperfine struct ure will increase the fr action of absorbed signal and could possibly enhan ce the sensitivity. In terms of oscillator strength for ground state transitions, cesium, barium, a nd magnesium have very high values of 0.7131, 1.64, and 1.80, respectively (obtaine d from NIST). In addition, these ground state transitions occur at 852.113 nm, 553.5481 nm, and 283.2127 nm for Cs, Ba, and Mg, respectively, so transitions in the UV, Visible, and near-IR can be achieved depending on the specific application. High os cillator strengths are also important in the number density required for the desired frac tion of signal absorbed. Therefore, high oscillator strengths relax the number density re quirements for the atomic reservoir. If ionization is the method of de tection, then an atom with a relatively low ionization potential may be desired. For example, ces ium has an ionization potential of only 3.8939 eV compared to mercury, which has an ionization potentials of 10.4375 eV. Since virtually any metal can be chosen, many elem ents possess attractive features. Clearly, there are many factors that must be considered before selecting an element for the atomic reservoir, and the detection method and specifi c application must be taken into account. Consequently, it would benefit if the meas urements taken in the present work are repeated for other cathode elements of see-through hollow cathode discharges for potential application as atomic line filters. Pulsed Discharge Measurements Presently, all the work that was perf ormed on the thallium and lead see-through hollow cathode discharge had been done by operating the discharge in D.C. mode. However, the discharge can also be operated in pulsed mode. Operation in pulsed mode would be beneficial in term s of signal-to-background ratio if fluorescence detection is performed. The reason for this is due to the fa ct that the lamp also emits at the detection

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136 wavelength. By delaying the signal input until the emission has been removed could enhance the sensitivity of det ection. However, this would really only be applicable for measurements that include the ground state, si nce excited states will radiatively de-excite to the ground state, leaving an unacceptable num ber density. In addi tion, there would be an optimal window in which the number density of the ground state is acceptable for measurements, since the atomic vapor will diffu se out of the analytical volume or redeposit back onto the cathode su rface. There are many paramete rs that would need to be considered such as pulse amplitude, duration, and frequency. Operation in pulsed mode could provide a valuable method of detection; however, work on this is needed in order to confirm or refute this approach. The main intent and scope of this rese arch is based on the evaluation of a seethrough hollow cathode discharge as a potential atomic line f ilter. Based on the results obtained in this work, this discharge does offer several advantages over other atomic reservoirs, however, applications of this discharge is not limited solely to atomic line filters. This discharge has demonstrated quantum efficiencies, number densities, and lifetimes that could be attractive for other types of research, pure and applied that may necessitate a simple and cont rollable atomic reservoir.

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137 APPENDIX A CURVE-OF-GROWTH CALCULATIONLINE SOURCE APPROXIMATION In atomic absorption, the fraction of light absorbed can be described by [95], o o where o is the incident radiant power and is the transmitted radiant power. The transmitted spectral radiant power at a given wavelength is given by Beers law as [95], l ko ) ( exp The total radiant power transmitted is given by [95], do o Thus, can be expressed as [95], d d l ko oexp 1 where k( ) is the wavelength dependent absorption coefficient (m-1) and l is the path length (m). The integral in equation A-3 extends over the enti re wavelength interval for which the incident spectral radiant power is measured. If a line source approximation is used, then the wavelength dependent absorp tion coefficient becomes constant over the source profile. This means that the waveleng th dependence is removed and is equal to the maximum, or peak absorption coefficient, ko. Therefore, for the limit of a line source, equation A-4 now becomes [95, 96], l ko L exp 1 where ko is defined as, D e o ij o oc m f n e k 2 2 24 (A-1) (A-2) (A-3) (A-4) (A-5) (A-6)

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138 Here e is the charge of an electron (1.602 x 10-19 C), o is the wavelength at the peak of the transition (377.572 x 10-9 m), n is the number density of the absorber (m-3), fij is the oscillator strength of the transition (0.13 unitless), o is the permittivity of a vacuum (8.854 x 10-12 C2 J-1 m-1), me is the electron rest mass (9.109 x 10-31 kg), c is the speed of light (2.9979 x 108 m s-1), and D is the FWHM of a Doppler broadened absorption profile (4.228 x 10-13 m for a temperature of 500 K). Substitution of equation A-6 into equation A-5 yields the expres sion for the fraction of light absorbed as function of number density, D e o ij o Lc m f n e 2 2 24 exp 1 Therefore, a plot of fraction of light absorbed as a function of number density results in figure A-1. By rearrangement of equation A7, the number density can be calculated for any desired fraction of light absorption fo r this atomic system and is given by, l f e c m nij o L D e o 2 2 21 ln 4 Therefore, if 99.9 % of incident radia tion is to be absorbed, then setting L to 0.999 yields a number density of 8.90 x 1011 cm-3. (A-7) (A-8)

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139107108109101010111012101310140.01 0.1 1 10 100 Percent Absorbed (Lx100)Number Density (atoms cm-3) Figure A-1. Theoretical curve of growth pl ot for a purely Doppler broadened absorption profile assuming a line source. The number density in this plot was converted to atoms cm-3, where as the calculation above defined the number density as atoms m-3.

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140 APPENDIX B SPONTANEOUS TRANSITION PROBABIL ITY CALCULATION FOR THE 377.572 NM HYPERFINE STRUCTURE As can be seen in figure 5-4, the lase r spectral profile only probed thallium atoms residing in the F1 ground level. The two transitions excited are from the two naturally occurring isotopes of th e same transition, F1 F1; therefore the transition probability will be the same for each isotope. In order to calculate the total number density of the system, the transition probability needs to be calculated in order to properly evaluate equation 5-15. The relative intensities of the three hyperfine components of each isotope allows the oscillator strength for each tr ansition to be calculated by the following relationship [41], 1 2 1 2 m k mn kl mn klF F f f I I 13 001 10 11 total totalf f f f f where ftotal is the oscillator strength for the enti re hyperfine struct ure. By applying equation B-1 and intensities found in figure 54, the oscillator strength ratios can be determined and is calculated as follows, 3 1 173 0 25 0 1 0 2 1 1 2 3 3 25 0 577 0 1 1 2 1 1 2 3 1 173 0 577 0 1 0 2 1 1201 10 01 10 01 10 10 11 10 11 10 11 01 11 01 11 01 11f f f f I I f f f f I I f f f f I I By substituting these ratios into equation B-2, the oscillator strength for each hyperfine component is obtained. For the thallium 377. 572 nm transition, the oscillator strengths were found to be, (B-1) (B-2)

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141 0242 0 0501 0 0557 010 01 11 f f f and from the relationship between the osci llator strength and spontaneous emission transition probability [95], 2 510 67 6o i ij j ijg f g A the transition probability for each hyperfine component can be calculated and were found to be, 1 7 01 1 6 10 1 7 1110 35 2 10 77 3 10 61 2 s A s A s A Therefore, in this work a value of 2.61 x 107 s-1 was used to calculate the number density of the thallium galvatron for each current applied. An important point should be made here. In equation 5-15, the number density is also dependent of the statis tical weights of the lower and upper levels. In general, statistical weights are found by the relationship, 1 2 i iJ g however, using the J value from the spectroscopic terms in figure 5-1 yields an average statistical weight of the stat e. Since this work involved the excitation of a selected hyperfine component, and not the entire hyperfine structure, th e statistical weights of the lower and upper level of the hyperfine transition, shown in figure B-1, need to be applied in equation 5-15. In this particular work the average statistical weights of the lower and upper level are the same ( g1 = 2 and g2 = 2), as are the statistical weights of the selected hyperfine transition that was excited ( g1 = 3 and g2 = 3); therefore, in this particular case (B-3) Eq. 31

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142 the statistical weight factor, g2/(g1+g2), still yields a value of 0.5. If a different hyperfine transition were excited, then the statistical weights of that transition would need to be applied along with the appropr iate transition probability. Figure B-1. Energy level diagram for the hyperfine structure of the thallium 377.572 nm transition [11]. Units in this figure are given in frequency; however, wavelength units are used in the text. 21.11 GHz 12.17 GHz 7 2S1/2 6 2P1/2 o g = 3 g = 3 g = 1 g = 1 g = 1 g = 1 g = 3 g = 3 13.32 GHz 1 3 0.45 GHz 1.21 GHz 3 1 1 3 1 3 21.31 GHz F = 1 F = 0 F = 1 F = 0 F = 1 F = 0 F = 0 F = 1 377.572 nm 81Tl 205 (70.5 %) 81Tl 203 (29.5 %)

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143 APPENDIX C LIST OF SYMBOLS USED THROUGHOUT THIS WORK WITH DESCRIPTIONS AND UNITS GIVEN Symbol Description Units Wavelength nm wavenumber cm-1 resolution nm o peak wavelength nm o peak frequency Hz L collisional broadening FWHM Hz H Holtzmark broadening FWHM Hz IF Instrumental FWHM Hz D Doppler broadening FWHM Hz S Stark broadening FWHM Hz MQ molecular quenching broadening FWHM Hz laser laser spectral FWHM Hz FSR, FSR, FSR free spectral range nm, Hz, cm-1 Fu ultimate finesse unit less FR reflection finesse unit less FF flatness and parallelism finesse unit less FA aperture finesse unit less L collisional broadening cross section cm2 H Holtzmark broadening cross section cm2 ( ) frequency dependent absorption cross section cm2 o peak absorption cross section cm2 T transmission coefficient unit less Tmax maximum transmission unit less Ro reflection coefficient unit less refractive index unit less d mirror separation distance mm angle of incidence degrees M degree of flatness unit less f lens focal length cm B diameter of the aperture cm E energy difference between two states J

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144Symbol Description Units T temperature K M atomic molar mass g mol-1 Vo ground voltage V Vb breakdown voltage V ni number density of the respective state cm-3 Ii( ) frequency dependent intensity unit less l path length cm OD optical depth unit less Rpower resolving power unit less k ( ) frequency dependent absorption coefficient cm-1 ko peak absorption coefficient cm-1 fjk absorption oscillator strength unit less Io incident intensity unit less F total angular momentum quantum number unit less J total electronic angular momentum quantum number unit less Bkj stimulated absorption coefficient J-1 cm3 s-1 Hz Bjk stimulated emission coefficient J-1 cm3 s-1 Hz Ajk spontaneous emission transition probability s-1 kjk collisional de-excitation rate constant s-1 g j degeneracy unit less Yjk quantum efficiency unit less t time s tr response time s nj ss steady state population cm-3 E spectral irradiance J s-1 cm-2 nm-1 E s saturation spectral irradiance J s-1 cm-2 nm-1 o spectral energy density J cm-3 Hz-1 modified spectral energy density J cm-3 Hz-1 o s saturation spectral energy density J cm-3 Hz-1 BF fluorescence radiance J s-1 cm-2 sr-1 BF max fluorescence radiance under saturation J s-1 cm-2 sr-1 Qlaser laser energy per pulse J Alaser cross section laser beam area cm2 tlaser temporal FWHM of the laser pulse s

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145Symbol Description Units laser spectral FWHM of the laser nm SmV peak voltage signal produced from laser pulse mV P laser spectral irradiance conversion factor J s-1 cm-2 nm-1 mV-1 F conversion factor for i rradiance to radiance J s-1 cm-2 sr-1 mV-1 Sg geometric spectral bandpass nm collection solid angle sr ImV peak voltage from fluorescence signal mV Alens area of collection lens cm2 Apiercing area of piercing on collection mirror cm2 W slit widths mm Rd reciprocal linear dispersion nm mm-1 L cavity length cm effective (spontaneous) lifetime of an excited state ns natural natural (or spontaneous) lifetime of an excited state ns buffer effective lifetime due to collisions with buffer gas ns self effective lifetime due to collisions with atoms of the same kind ns wall effective lifetime due to collisions with the walls of the container ns relative relative velocity between two species cm s-1 mi atomic mass g reduced mass g Do diffusion constant cm2 s-1 po reference gas pressure torr pbuffer buffer gas pressure torr r radius cm Fgeometry geometry factor cm-2 fraction of light absorbed unit less transmitted radiant power unit less o incident radiant power unit less ( )o total radiant power at a given wavelength unit less radiant power at a given wavelength unit less e charge of an electron 1.602 x 10-19 C o permittivity of a vacuum 8.854 x 10-12 C2 F-1 m-1 me electron rest mass 9.109 x 10-31 kg c speed of light constant 2.99.7 x 1010 cm s-1

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146Symbol Description Units kb Boltzmann constant 1.38 x 10-23 J K-1 R gas constant 8314.51 mJ mol-1 K-1 h Plancks constant 6.626 x 10-34 J s

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153 BIOGRAPHICAL SKETCH Nicholas Roger Taylor was bor n in the small town of Bloo mington, Wisconsin, on July 7, 1979. Upon graduating from River Ridge hi gh school in 1998, he attended Winona State University in Winona, Minnesota. In May of 2003, Nick graduated with a Bachelor of Science in chemistry and a minor in biochemistry. In August 2003, Nick began his graduate studies in analytical chemistry at the University of Flor ida. Under the superv ision of Dr. James D. Winefordner, he completed his doctoral research in October 2007. In July 2007, he accepted a post-doctoral position with Dr. Pa ul Farnsworth at Brigham Young University, located in Provo, Utah.