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Laser excited fluorescence and ionization for flame diagnostics

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Title:
Laser excited fluorescence and ionization for flame diagnostics
Creator:
Rutledge, Michael James, 1960-
Publication Date:
Language:
English
Physical Description:
x, 114 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Atoms ( jstor )
Bandwidth ( jstor )
Box cars ( jstor )
Dye lasers ( jstor )
Flames ( jstor )
Fluorescence ( jstor )
Ionization ( jstor )
Laser beams ( jstor )
Lasers ( jstor )
Signals ( jstor )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Flame spectroscopy ( lcsh )
Fluorescence -- Data processing ( lcsh )
Laser spectroscopy ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1987.
Bibliography:
Bibliography: leaves 110-113.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Michael James Rutledge.

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Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
000947016 ( ALEPH )
16904871 ( OCLC )
AEQ8996 ( NOTIS )
AA00004847_00001 ( sobekcm )

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Full Text


LASER EXCITED FLUORESCENCE AND IONIZATION
FOR FLAME DIAGNOSTICS
BY
MICHAEL JAMES RUTLEDGE
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
1 987


To my parents and family,
whose unending support made all this possible.


ACKNOWLEDGMENTS
I gratefully acknowledge the support of Dr. Benjamin Smith,
Dr. Edward Voigtman, and Dr. Nicolo Omenetto whose knowledge,
enthusiasm, and helpful suggestions were a continuing source of
inspiration.
I thank Dr. James D. Winefordner for the privilege of working
with him for the past four years and with the best spectroscopy group
in the world. His concern and encouragement during my four years
have made my work more pleasurable and an invaluable learning
experience.
My sincerest thanks go to Jeanne Karably and the secretaries of
J.D. Winefordner. They have been my constant friends for the past H
years.
I also thank the members of other research groups in the
analytical department especially Ken Matuszak, Paul McCaslin, and
David Berberich whose help with my golf game may prove invaluable.
iii


TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT ix
CHAPTERS
1 INTRODUCTION 1
2 MEASUREMENT APPROACHES FOR ATOMIC FLUORESCENCE AND
IONIZATION SPECTROSCOPIES 4
Introduction to Laser Atomic Fluorescence Spectroscopy
and Laser Enhanced Ionization Spectroscopy Systems 4
Measurement Approaches and Instrumentation 10
Results and Discussion 17
Conclusions 25
3 ESTIMATION OF ABSOLUTE NUMBER DENSITIES 27
General Curve of Growth Introduction and Evaluation 27
Calculated Curves of Growth 33
Experimental Verification of Curves of Growth 43
Saturation and Collisional Effects 46
Conclusions 62
4 SPATIAL DISTRIBUTIONS OF ATOMS IN INHOMOGENEOUS
FLAMES 63
Concentration Modulated Absorption Spectroscopy 63
Two-Wavelength Laser Enhanced Ionization and
Fluorescence: Spatial Distributions 76
Experimental Setup and Discussion 78
Conclusions 89
5 FINAL COMMENTS AND FURTHER STUDIES 91
IV


APPENDICES
A GLOSSARY OF TERMS AND SYMBOLS 94
B COMPUTER PROGRAM LISTING FOR CALCULATION OF
FLUORESCENCE CURVES OF GROWTH INCLUDING SATURATION,
COLLISIONAL AND PREFILTER AND POSTFILTER EFFECTS 96
REFERENCES 109
BIOGRAPHICAL SKETCH 113
v


LIST OF TABLES
Table Page
2-1 Limits of Detection (ng/mL) 18
3-1 Broadening Effects on the a-Parameter for Self-
Broadening 50
4-1 Ionization Processes, Optical Arrangements, Signals
and Noises for Two-Wavelength Laser Enhanced
Ionization Spectroscopy 85
vi


LIST OF FIGURES
Figure Page
2-1 Lasing Diagram for Copper Vapor Laser 5
2-2 Experimental Setup 8
2-3 Boxcar Plus Lock-In Amplifier Signal Processing
Layout 11
2-4 Boxcar-Active Baseline Subtraction Signal Processing
Layout 14
2-5 Bandwidth Limitation and Conventional Signal
Processing Layout 16
2-6 Bandwidth Limitation Effects 21
2-7 Noise Power Spectrum at 588.9 nm 24
3-1 Diagram for Right Angle Fluorescence 28
3-2 Expression for Right Angle Fluorescence 29
3-3 Curves of Growth for Line Source Excitation 34
3-4 Curves of Growth for Continuum Source Excitation 35
3-5 Curves of Growth for Two Pseudocontinuum Sources 37
3-6 Curves of Growth for Mild, Medium, and Severe
PrefilteringLine Source, Dark = prefilter region 38
3-7 Curves of Growth for Mild, Medium, and Severe
PrefilteringContinuum Source, Dark = prefilter region...39
3-8 Curves of Growth for Mild, Medium, and Severe
PostfilteringLine Source, Dark = prefilter region 41
3-9 Curves of Growth for Mild, Medium, and Severe
PostfilteringContinuum Source, Dark = prefilter
region 42
vii


3~10 Calculated and Experimental Curves of Growth for Na 44
3-11 Calculated and Experimental Curves of Growth for Pb 46
3-12 Expression for Collisional Broadening 48
3-13 Curves of Growth with Added Collisional Broadening 52
3-14 Curves of Growth for Several Intensities for a
Line Source 55
3-15 Curves of Growth for Several Intensities for a
Continuum Source 56
3-16 Curves of Growth for Pb Direct-Line ( ) and
Resonance ( ) Fluorescence for Several Source
Intensities 57
3-17 Equations for Curves of Growth Equalities for
Saturating Irradiances 58
3-18 Prefilter Removal by a Saturating Source, Resonance
( ) and Direct-Line ( ) 60
3-19 Postfilter Effects with Saturation Effects Added,
Resonance ( ) and Direct-Line ( ) 61
4-1 Concentration Modulated Absorption Experimental Setup:
Co-linear Beams 67
4-2 Experimental Setup for Spatial Diagnostics for COMAS 69
4-3 Results for Perpendicular and Parallel Burners
for COMAS 71
4-4 Design of Surface Burner Used 72
4-5 Simple Absorption Results for Perpendicular and
Parallel Burners 75
4-6 Experimental Setup for Two-Wavelength LEIS and LAFS 79
4-7 Spatial Profile Result for LEIS 82
4-8 Spatial Profile Result for LAFS 88
4-9 Three-Dimensional Spatial Profile for LEIS 90
viii


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
LASER EXCITED FLUORESCENCE AND IONIZATION
FOR FLAME DIAGNOSTICS
BY
MICHAEL JAMES RUTLEDGE
May, 1987
Chairman: James D. Winefordner
Major Department: Chemistry
Measurement approaches involving electrical signal manipulation
and signal processing are investigated for a copper vapor laser
pumped dye laser system. Correction methods used involve modulation
of a pulsed laser output and subtraction of noise. Bandwidth
limitation of signals to reduce radio-frequency noise is also
discussed. A general purpose computer program for calculation of the
absolute number density of an atomic species present in an analytical
volume is presented. The program is written in FORTRAN with a high
speed, high-precision approximation of the Voigt profile to
incorporate atomic broadening effects. Comparison to experimentally
measured fluorescence results is included.
A discussion of saturation and collisional broadening effects is
included. Calculated results are found to agree with experimental
results within an order of magnitude in all experimental cases.
Spatial profiling results are presented for two-wavelength excitation
IX


of atomic species with detection via fluorescence and ionization of
the species of interest. A new form of absorption spectroscopy,
termed concentration modulated absorption spectroscopy, is
investigated for spatial profiling applications. These methods are
investigated for detection power, as well as spatial information
obtainable. Comparison to other methods of determining absolute
number densities and spatial information is included.
x


CHAPTER 1
INTRODUCTION
Laser excited atomic fluorescence and laser enhanced ionization
spectroscopies have been used for many different types of
applications. The extreme sensitivity of these techniques has been
shown many times. J Some of the best limits of detection are
obtained using these methods. These sensitive techniques are applied
here to the investigation of absolute number densities and spatial
profiles in inhomogeneous flames.
A copper vapor laser is used for all investigations throughout
these studies. This laser has found limited application in
li 6
chemistry but has found many applications outside this field.
This laser system consists of a pulsed laser plus the dye laser(s)
for tunability to the wavelength(s) of interest. This is a pulsed
laser which operates at a 6 kHz repetition rate with an average power
of 25 W. Measurement approaches for atomic fluorescence and
ionization are presented as preliminary investigations using this
laser system in Chapter 2. These measurement approaches rely on
bandwidth limitation and/or removal of correlated background
noises. A more complete discussion of the use of correlation
functions to increase signal-to-noise ratios is given by Doerffel et
7
al. The extension of these methods to measurement of atomic
1


2
fluorescence for determination of absolute number densities is
discussed in Chapter 3.
Determination of absolute number densities is accomplished using
a computer program to model the expected relationship between
concentration of a species of interest and fluorescence signal
detected. The relationship between fluorescence intensity and
concentration, expressed in a log-log graph, is called a fluorescence
curve of growth (COG). The point of departure from linearity allows
determination of absolute number densities. Many methods have been
presented for determination of absolute number densities in flames,
plasmas and vapor cells. These methods range from the classical
O
approaches of the absolute intensity method and the integral
absorption method^1 ^ to some more recently introduced methods such
as laser induced fluorescence saturation spectroscopy11 and anomalous
dispersion. Several methods have also been presented which allow
absolute number density evaluation from the absolute magnitude of the
signal detected and the experimental detection efficiency.1-^ Several
COG methods have been presented which allow determination of absolute
number densities with a minimal knowledge of the atomic and geometric
1 4
parameters. Other methods include determination of number
densities from vapor pressure measurements of Na and Pb in laser
excited fluorescence experiments.1^1^ Some of the simplest methods
for evaluation of number density rely on the supply of and
atomization efficiency of the analyte of interest. Experimentally,
many of the above mentioned methods are quite difficult or time-
consuming to implement. Many rely on an absolute calibration of the


3
detection optics and photodetector, while some require an additional
calibrated source. Some methods require a detailed knowledge of the
source characteristics including the source intensity and the
spectral profile (Gaussian or otherwise). A general overview of many
of these methods is given in two excellent works by Alkemade and
1 A 17
coworkers. 1
Atomic fluorescence with two-wavelength excitation and a
multichannel image detector has been used for spatial imaging of OH
i O on
and for flow visualization. No research has been presented
which utilizes two-wavelength excitation of atomic species for
spatial resolution with direct detection using laser atomic
fluorescence (LAFS) or laser enhanced ionization (LEIS)
spectrometry. This topic and some related areas are the focus of
Chapter 4. In a recent study by Turk et al., two-wavelength atomic
spectra were measured with detection via ionization. In that study,
only the wavelengths are scanned and the three-dimensional spectra
are presented with axes of one wavelength (X^) and the other
wavelength (\^) versus intensity. Here, the spatial distributions of
atoms using two-wavelength LEIS and LAFS and single-wavelength
absorption are investigated. An initial investigation into
absorption spectroscopy with a modulated pulsed laser is included.
The absorption technique, termed concentration modulated
absorption spectroscopy (COMAS), is investigated for increased
sensitivity and spatial profiling applications. The highly sensitive
techniques of LEIS and LAFS are applied to probing small volumes in
inhomogeneous flames as a final study.


CHAPTER 2
MEASUREMENT APPROACHES FOR
ATOMIC FLUORESCENCE AND IONIZATION SPECTROSCOPIES
Introduction to Laser Atomic Fluorescence Spectroscopy and
Laser Enhanced Ionization Spectroscopy Systems
In these experiments, a 20 W copper vapor laser (Cooper
Lasersonics model 251) and a flowing dye cell were used. This is a
pulsed laser system operating at -6 kHz with moderate peak powers of
-160 kW. Laser action in a cell containing copper vapor was first
pp
reported by Walter et al. in 1966. Lasing action is accomplished
via the thermal production of ground state copper atoms and
electrical pumping of the ground state (2S) to the lowest resonance
p
levels ( P) resulting in spectral output at 510 and 578 nm (see
Figure 2-1). Repetition rates of between 800 and 10,000 pulses per
second have been obtained in our laboratory. This high repetition
rate is accomplished using a thyratron-switched power supply using
-4000 W of electrical power. This high-power, high-frequency
switching produces a large amount of radio-frequency (RF)
interference which was found to be a major noise source in all
analytical experiments. From oscilloscope measurements and gate-
scanned boxcar averager outputs, it was determined that the radio
frequency has a high degree of pulse-to-pulse correlation. Shielding
of the detection electronics was attempted but was inefficient in the
reduction of RF interference.
4


5
LOWEST RESONANCE
LEVELS
Figure 2-1. Lasing Diagram for Copper Vapor Laser


6
Three models were used to correct for and/or reduce background
radio-frequency and other noise sources. Two methods rely on
synchronization of the laser with a high-speed chopper to block
alternate laser pulses. One of these methods involved the use of a
gated integrator and boxcar averager equipped with an active baseline
subtraction circuit. Another used a gated integrator and boxcar
averager plus lock-in amplifier to accomplish the same background
subtraction. The third method used a bandwidth limited amplifier to
reduce high frequency noise components present in the signal. For
comparison purposes, the conventional method of measuring pulsed
laser signals is also included. Analysis for several elements is
included to show consistency of the results.
Chemicals
Stock solutions of all elements were prepared from analytical
grade LiCl, NaCl, Fe wire, and In202 to give 1000 ug/mL solutions.
Standard solutions were prepared by serial dilution of the stock
solutions. Laser dyes (Exciton Corporation) used included oxazine
720 (Li), and mixtures of Rhodamine 6G and Kiton Red 620 (In, Na, and
Fe).
Instrumentation
The frequency-doubled dye laser output (Molectron model DLII
pumped by a Cooper Lasersonics model 251 copper vapor laser with an
Inrad Autotracker II frequency doubler) was used to illuminate a
1 cm^ region of the flame. A flat mirror was mounted 5 cm from the
flame to allow for a second pass of the laser. For frequency-doubled
experiments, the laser had a pulse width of -20 ns, a pulse energy of


7
5-35 uJ, and a spectral bandwidth of 0.02 nm. For experiments
involving the fundamental wavelength of the dye laser, the frequency
doubler was removed from the optical path. The fundamental
wavelength experiments are characterized by a pulse width of 30 ns, a
pulse energy of -100-500 pJ, and a spectral line width of 0.03 nm.
Pulse temporal widths were measured using a gate-scanned boxcar
averager with a 2 ns risetime photomultiplier tube and a 2 ns boxcar
gate. Additionally, line widths were measured by slowly scanning the
dye laser across an atomic transition and measuring the fluorescence
of a 1 pg/mL solution of the element aspirated into the flame. The
flame was produced on a laboratory-constructed, brass capillary
burner^ (1 cm^) mounted on a commercial atomic absorption spray
chamber (Perkin Elmer model 303-0110). An approximately
stoichiometric air-acetylene flame was used for all studies.
Commercial-grade gases were pressure-regulated and flow controlled
using rotometers with needle valves. The experimental setup is shown
in Figure 2-2. Symbols are defined in Appendix A.
The fluorescence was produced in a flame volume of approximately
1 cm^ and detected using a small monochromator (SPEX 1670 Minimate,
f/4.0, 220 mm focal length) and RCA model 1414 photomultiplier
tube. The monochromator optical axis was 90 to the laser beam. No
additional optics were used since the acceptance angle of the
monochromator was filled. With the 1.25 mm slits used, this
monochromator had a 10 nm bandpass. The photocurrent pulse was
stretched slightly by a 1000 ft load resistor and connected directly
to the input of the gated integrator and boxcar averager


8
Figure 2-2. Experimental Setup


9
(Stanford Research Systems model 250). The boxcar was triggered
using a photodiode positioned to receive a portion of the copper
vapor 510 and 578 nm output.
The laser enhanced ionization experiments were performed
similarly with the following exceptions. A 5 om stainless steel slot
burner (Perkin-Elmer model 0040-0277) was used and served as the
detecting electrode. A -1500 V bias potential was applied to a
water-cooled stainless steel electrode placed -1 cm above the burner
surface. The laser beam was positioned to pass parallel to and
-0.3 cm below the bias electrode. The entire assembly was placed
inside a shielded and grounded housing. This experimental
pa
arrangement is a modification of that presented by Travis et al.
Ionization currents were capacitively coupled to reduce flame
background leakage currents and then converted to voltages using a
current-to-voltage converter (Princeton Applied Research model
£
181). Gains of 10 V/A were typically used. This signal was
connected directly into the input of the gated integrator. For the
boxcar plus lock-in amplifier portion of the experiments, the signals
from the boxcar were connected directly into the input of the lock-in
amplifier (Keithley model 840). Signals obtained in all experiments
were integrated using a voltage-to-frequency converter (Analog
Devices model 650) and counted for a 10 s integration period. This
method of signal integration was found to give an unambiguous
result. Limits of detection were determined using the IUPAC
convention, 0 namely, a signal-to-noise ratio equal to three. Noise
levels were determined as the standard deviation of 16 blank


10
measurements. A more complete discussion of this and other methods
for calculating limits of detection is covered by Long and
27
Winefordner. 1
Measurement Approaches and Instrumentation
Gated Integrator and Boxcar Averager Plus
Lock-In Amplifier (BLIA)
This method of background correction is similar to background
correction methods in flame absorption or fluorescence using a
continuous wave (cw) laser or conventional source employing
modulation of the source intensity. For a complete discussion of
background correction methods, the reader is referred to the
p o p q
excellent works of Alkemade et al. and Kirkbright and Sargent. ^
In this experiment, a high speed chopper (Photon Technology) was
used free-running at 3 kHz, and the reference output of the chopper
was used to control the laser repetition rate. The reference from
the chopper was connected to a multiply-by-two circuit constructed
from a monostable multivibrator (74LS123) and an OR gate (7MLS32).
This circuit was set up to give a single pulse output from both the
rising and falling edges of the chopper reference waveform. This
signal was used to trigger the laser externally at a 6 kHz repetition
rate. Initial attempts to control the high speed chopper from the
laser reference output failed due to the momentum and drift of the
chopper blade. Synchronization of the chopper had to be absolute
since any drift resulted in a complete reversal of the signal
polarity for at least a portion of the integration period. The
electrical signal processing system is shown in Figure 2-3.


BOXCAR PLUS LOCK-IN AMPLIFIER METHOD
3 KHz FL. SIGNAL*
3 kHz BKG 180
6kHz
TO LASER
X 2
CIRCUIT
hi
r
BOXCAR
LOCK-IN
+ I0 s

SJ/F COUNTER
3 kHz
FROM CHOPPER
Figure 2~3. Boxcar Plus Lock-In Amplifier Signal Processing Layout


12
Signals obtained from the fluorescence or the photoionization
were fed directly to the input of the gated integrator. The Stanford
boxcar averager has two output signals, a last sample and an average
sample. The average sample is useful for reduction of signal
fluctuation and employs a gated resistor-capacitor low-pass (RC)
filter to average a variable number of samples. The last-sample
output is the most recent signal detected by the boxcar averager.
The last-sample output was used in this instance because the signal
varies between signal plus noise on one pulse and noise only on the
following pulse, and the demodulation of this signal was accomplished
in the lock-in amplifier. The last-sample output was connected
directly to the input of the lock-in amplifier. The reference output
of the high speed chopper was connected to the reference channel of
the lock-in amplifier which was triggered at the 3 kHz repetition
rate. Synchronization of the lock-in reference waveform and the
boxcar signal is obtained using the phase adjustment on the reference
channel of the lock-in amplifier. The output from the boxcar, which
consisted of signal plus noise during one half-period and noise only
during the following half-period, was demodulated and background was
subtracted by the phase-sensitive detector in the lock-in
amplifier. Output signal ripple of the phase-sensitive detector was
smoothed using a 1 s time constant output filter. Signals output
from the lock-in were connected directly to the voltage-to-frequency
converter and then counted for a 10 s integration period.


13
Gated Integrator and Boxcar Averager: Active Baseline
Subtraction (ABS)
This technique was a special method applicable only to the
Stanford Research Systems boxcar used here or similar systems with an
active baseline subtraction method. In this method, the same signals
were connected to the boxcar, but the boxcar was placed in the active
baseline subtraction mode (ABS). This mode caused the electronics in
the boxcar to switch the polarity of alternating samples before
adding each one to a moving average. The moving average circuit was
implemented using a gated RC filter^0 with varying resistors and
capacitors depending on the number of samples to be averaged. This
method of correction is significantly different from the true phase-
sensitive detection methods employed in lock-in amplifiers. The
moving average switch was set at 3000 samples to keep an effective
1 s time constant, consistent with the lock-in amplifier case
(BLIA). Blocking alternating laser pulses resulted in a subtraction
of noise produced during each laser pulse. Signal output from the
boxcar averager was connected directly to a frequency-to-voltage
converter and counted for a 10 s integration period. This is shown
diagrammatically in Figure 2-4.
Bandwidth Limited Signal Processing (BLSP)
Another method of diminishing the effect of high frequency noise
was investigated using a form of low-pass filtering. This "low-pass
filtering" was implemented using a bandwidth-limited amplifier.
Fluorescence photocurrents (-25 ns) were stretched and converted to
voltages using a 1 kft resistor giving a signal of approximately


14
ACTIVE BASELINE SUBTRACTION METHOD
Figure 2-4.
Boxcar Active Baseline Subtraction Signal Processing
Layout


15
100 ns full width at half maximum (FWHM), i.e., a bandwidth of
-10 MHz. Stretching occurred due to the RC time constant of the
photomultipler tube and connecting cables, due to the load resistor
and the stray capacitance in the system. The fluorescence signals
obtained were input to the bandwidth-limited amplifier and then
connected directly to the gated integrator and boxcar averager. The
amplifier used, an Evans model 4131, has a 3 dB bandwidth of 10 MHz
at a gain of 10 times. Signals were stretched to approximately
120 ns (FWHM) by the Evans amplifier. The decreased response of the
amplifier in the high frequency region resulted in a significant
reduction of high frequency noise components. Actual low-pass
filtering would be difficult to implement since a time constant on
the order of 10 ns would be necessary to avoid significant signal
distortion. Stray capacitance and resistance make this low time
constant difficult to obtain. Signals from the Evans amplifier were
connected directly to the gated integrator and boxcar averager.
Signals from the boxcar were connected to a voltage-to-frequency
converter and counted for a 10 s integration period as in all other
cases. The electrical system is shown in Figure 2-5 along with the
conventional method for measuring signals.
Conventional Method (CONV)
Signals obtained from fluorescence and photoionization were
input directly into the gated integrator with no modifications. This
method is included for comparison purposes as a reference.^1 The
signal output from the boxcar averager was connected to the voltage-
to-frequency converter and the signal was counted for a 10 s


BANDWIDTH LIMITED SIGNAL PROCESSING METHOD
CONVENTIONAL METHOD
Figure 2-5. Bandwidth Limitation and Conventional Signal Processing Layout


17
period. In all four measurement methods, the boxcar averager was
operated with a 10 kHz first-order cutoff filter on the input to help
remove unwanted low frequency components.
Results and Discussion
All correction methods used show a significant improvement over
the conventional method (Table 2-1). While no attempt was made to
optimize fully system components or operating conditions, the limits
of detection obtained are very good and demonstrate the improvements
expected. Laser power was found to present a severe problem when
frequency doubling the copper vapor laser (CVL) dye laser output.
The relatively low peak power and squared dependence of frequency
doubling on input power^2 resulted in low power outputs for In and
Fe. The low laser power is partially compensated for (in limits of
detection) by the lack of laser scatter and the associated shot noise
in the direct-line fluorescence of Fe and In. Compromises concerning
excitation wavelengths had to be made since the CVL fundamental
output is in the visible region at 510 and 578 nm. Additionally, RF
interference from this laser was and has been found to limit severely
its analytical applicability for laser enhanced ionization and
qq
florescence. J
The simplicity and nearly equivalent results obtained using the
bandwidth limitation scheme (BW) for signal processing make this the
processing method of choice for most applications. As seen in Table
2-1, results obtained using the bandwidth limited approach for
fluorescence are nearly equivalent to those obtained using


18
Table 2-1. Limits of
Detection
(ng/mL).
CONVa
ABSb
BLIAC
Copper Vapor
Dye Laser
Laser
Enhanced Ionization Detection
Li
2.0
0.3
0.1
Fe
30
5.0
2.0
In
4.0
0.6
0.2
Laser
Excited Fluorescence Detection
Li
14
0.8
0.4
Fe
98
18
5.0
In
43
8.0
5.0
Na
1 4
3.0
1 .0
Excimer Dye Laser
Laser
Enhanced Ionization Detection
Li
0.7
0.3
0.5
Na
4.0
1 .0
2.0
In
0.2
0.2
0.4
BWd
BW+ABSe
BW+3LIAf
Copper Vapor Dye Laser
Bandwidth Limited
Signal ProcessingFluorescence Detection
Li
2.0
0.6
0.3
Na
2.0
1 .1
1.0
In
3.0
Fe
15
a CONV = Conventional method of measuring pulsed laser signals using
a boxcar averager and gated integrator.
b ABS = Active baseline subtraction method using a modulated pulsed
laser. Subtraction of background noise is done by the boxcar
special electronics.


19
Table 2-1 continued.
c BLIA = Boxcar averager plus lock-in amplifier using a modulated
pulsed laser. Subtraction of background noise is accomplished in
the lock-in amplifier.
d BW = Bandwidth limited signal processing in which high frequency
laser noise is not amplified while the signal is amplified to
increase signal-to-noise ratio of fluorescence signals.
e BW+ABS = Bandwidth limitation as discussed above followed by active
baseline subtraction.
f
BW+BLIA = Bandwidth limitation followed by the boxcar averager plus
lock-in amplifier.


20
more complicated schemes. No correction for the total number of
laser pulses per second has been made. In the BLSP scheme and the
CONV method, 6000 pulses per second pass through the flame and are
detected. In the ABS and BLIA experiments, there are only 3000
pulses passing through and being detected in the flame each second.
The remaining 3000 pulses were blocked by the chopper and the noises
detected in laser enhanced fluorescence and ionization were
subtracted out.
The background subtraction methods (ABS and BLIA) provide an
additional advantage over the BLSP scheme and the CONV method, namely
the removal of low frequency changes in the laser conditions. The
CVL operates in a continuous flow mode with a constant addition of
neon and a constant removal of neon and a small amount of copper
vapor. Conditions within the laser cavity are changing at a very
slow rate (relative to the 6 kHz repetition rate) due to changes in
the neon pressure, partial pressure of the copper vapor, and position
of the electrical arc within the laser tube. These changing
conditions result in small changes in the dye laser power output but,
more importantly, changes in the magnitude of the radio-frequency
signal detected within the boxcar gate. No correction for dye laser
power fluctuations could be obtained, since the fluctuations were in
the source prior to modulation. Correction for flame and analyte
background flicker was accomplished in both the ABS and BLIA methods.
The effect of bandwidth limited signal processing (BLSP) on
fluorescence signals is demonstrated in Figure 2-6. The fluorescence
signals in Figure 2-6 prior to bandwidth limitation demonstrate the


FLUORESCENCE PHOTOCURRENT (nA)
21
Figure 2-6. Bandwidth Limitation Effects


22
high frequency noise which is the limiting noise source for this type
of laser. The temporal effect of bandwidth limitation on
fluorescence signals is also shown in Figure 2-6.
The BLIA results show a marked improvement over CONV results in
all cases. The BLIA results are felt to be slightly better than the
ABS results because a true phase-sensitive detection method was
employed in this scheme. The ABS method used a gated RC filter to
add capacitively signals of alternating polarity to remove background
and was susceptible to capacitor leakage, noise added by the polarity
switching amplifier, and signal fluctuation when a low number of
samples is averaged.
The experiments with active baseline subtraction (ABS and BLIA)
provide some unique opportunities for signal manipulation due to the
extremely high repetition rate of CVL. At the 6 kHz repetition rate
used, signals obtained are well above the low frequency flicker noise
region of the flame (or a plasma) and analyte background flicker.
Additionally based on laser repetition rate, beam diameter, and flame
gas flow rate, it is possible to irradiate each atom present within
the flame with 3 to 10 laser pulses of moderate intensity as the
atoms pass through the flame volume. Indeed, the high repetition
rate of the CVL should make it possible to detect virtually every
atom passing through a flame (or any plasma).
For comparison purposes, results obtained using our excimer
laser (Lumonics model TE-861) are included for laser enhanced
ionization. This laser is capable of providing peak energies of up
to 3 mJ per pulse of fundamental power from the dye laser much higher


23
than the CVL system. Typical energies obtained at 25 Hz repetition
rate were in the range of -80-250 pJ per pulse of frequency doubled
energy in a bandwidth of 0.0015 nm. The inferior performance of the
two methods employing background correction (BLIA and ABS) should be
noted for results obtained using the excimer laser. These results
may be explained in one of two ways: diminished performance of our
lock-in amplifier at the 25 Hz repetition rate (where a larger amount
of flame background flicker and analyte flicker is present); and/or
lower correlation of the interfering noise from the excimer laser
compared to the copper vapor laser. Both effects are felt to
contribute to some extent. At 25 Hz, a much larger flicker component
is present than at the 6 kHz CVL repetition rate. The low frequency
analyte and background flicker component at the sodium wavelength
588.9 nm is shown in Figure 2-7. These signals were measured with
only the flame on and no laser present. Signals were measured using
a cross channel spectrum analyzer (Wavetek, model 5890B) and
represent the total signal present across the frequency range
shown. Several trends are apparent from this figure. Flame
background flicker noises are small and become very small above
approximately 1.0 kHz. Analyte flicker is much higher at low
frequency and decreases at higher frequency. The much higher flicker
noise of the analyte can be attributed to nebulizer noise while the
higher overall signal magnitude is due to analyte emission.
The other contribution to flicker noise is the pulse-to-pulse
fluctuation of the laser. The lower correlation of the pulse-to-
pulse noise from the excimer laser is felt to be a limiting factor in


-o
Figure 2-7. Noise Power Spectra at 588.9 nm
i\)
-tr


25
the improvements obtained with the excimer laser. The excimer
discharge voltage, -32,000 V, is less easily regulated than the
7,000 V used in the copper vapor laser. Oscilloscope comparisons of
the noise from the two lasers confirmed the much higher noise
fluctuations for the excimer laser. No correction for laser noise
could be obtained unless the noise component was present on
successive laser pulses.
The two noise correction methods (BLIA and ABS) were combined
with the noise reduction method, bandwidth limitation (BW) to
determine the individual contributions to noise reduction, and
signal-to-noise enhancement. It was found that the combination of
these techniques results in minimal improvement beyond that obtained
with bandwidth limitation alone. This indicates that the major
improvement is due to bandwidth limitation and thus the major noise
source is RF interference from the laser system.
Conclusions
The methods presented are shown to provide a significant
increase in the detection power for LAFS and LEIS. For active
baseline subtraction, improvements of up to 6 times were obtained
while with the combined bandwidth limitation and boxcar plus lock-in
amplifier (BW+BLIA) improvements of up to 40 times were obtained.
While these improvements may be possible for other laser systems, it
is to be emphasized that many of these methods rely on a certain
stability in the noise levels associated with a given laser system.
Application of these correction methods to a poorly correlated noise


26
source may yield little or no improvement in the detection power (see
excimer laser results). A more highly correlated noise source should
yield correspondingly better results. Additionally, modulation of a
pulsed laser and subsequent loss of one-half of the laser pulses may
be more harmful than the gain in detection power allowed by
subtraction of any noises.


CHAPTER 3
ESTIMATION OF ABSOLUTE NUMBER DENSITIES
General Curve of Growth Introduction and Evaluation
A general overview of methods for determination of the absolute
number density of a species is presented in Chapter 1. In this
chapter, general expressions and a computer program are presented for
evaluation of the fluorescence curve of growth and the absolute
number density determination. The computer program for these
calculations was written in FORTRAN-77 and was approximately 500
lines long. FORTRAN-77 was chosen for the programming language as a
compromise of speed, flexibility, and scientific compatability.
The computer program for evaluation of the absolute number
density calculates the fluorescence intensity vs the concentration of
the species of interest. A log-log plot of these terms is referred
to as a curve of growth (COG). The expression for right angle
fluorescence (diagrammed in Figure 31) is shown in Figure 3-2. The
expression for fluorescence may be divided into several parts: a
primary absorption term, a self-absorption term, and a term for the
optical collection efficiency. (The prefilter and postfilter terms
are considered separately below.) The primary absorption term is
derived from the Beer-Lambert law and can be used for an absorption
curve of growth in conjunction with an optical collection efficiency
terra. The primary absorption term is responsible for some of the
27


28
POSTFILTER
REGION
Figure 3~1. Diagram for Right Angle Fluorescence


= F F JL_ AhA^ALT y (ti ~ ekW Ex +EX L)d\ J_ EX(I -e'MV)LEx^Esx
* P 4n u2 m m P Vffk,L^D ) ) *
L H 0 u -** -#*
)dX
Optical collection term Self-absorption term
Primary absorption term
4<* Q 5
F = /' EXP[-k(X)L "W ( 1^ )] dX- /1 EXP[- k(X) X lkr] d X
fT A -#o A *
/'-EXPf-WM^s L]dX
40* +<*>
F = /|-EXP[-k(X)5l( |.£-)]dx-j"l- EXp[-k(X)5l^]dX
PO -oo
-4 oo
/1- Exp[-k(X)e]dx
Figure 3-2. Expression for Right Angle Fluorescence
l\)
VO


30
curvature in a curve of growth at higher number density. The source
irradiance becomes increasingly absorbed at high number densities
until the entire source irradiance is absorbed at extremely high
number densities. The self-absorption term is a dimensionless factor
accounting for reabsorption of fluorescence photons, within the
excitation volume, as they traverse the atom reservoir. The self
absorption term also contributes to the curvature of the curve of
growth and continues to increase with increasing number density.
This term may or may not be important depending on whether resonance
or direct-line fluorescence is measured. The remaining term to
account for the optical collection efficiency includes Tg, the
transmittance of the collection optics; m^ and m^, magnifications of
the length and height dimensions of the source on the atom cell; and
n, the refractive index of the medium (to account for the change of
solid angle of collection due to medium to air transfer of
radiation). The term AhAJtAL is used to give the observed radiant
fluorescence flux, A<)>.
Shown in Figure 3-1 (with expressions in Figure 3~2) are regions
for prefiltering of the excitation source and postfiltering of the
fluorescence radiation. A prefilter region is one in which the
analyte of interest is present and is illuminated by the excitation
beam but the resulting fluorescence is not viewed by the detector. A
postfilter region is one in which the analyte of interest is present
but the region is not illuminated by the excitation source. These
terms become important in some analytical situations where it may not
be possible to avoid prefiltering and/or postfiltering.


31
Some simplifying considerations used in the development and
evaluation of the expressions are as follows:
(i)a single atomic transition is considered for the atomic
emission and absorption methods while results are
included for both direct-line and resonance fluorescence;
(ii)for the absorption and fluorescence cases, the excitation
beam is of rectangular cross section (i, x H) and is
spatially, as well as temporally, homogeneous;
(iii)the atom reservoir consists of a uniform ground state
number density distribution at a uniform temperature in
the absence of the excitation beam;
(iv)the absorption and fluorescence spectral line profiles
may be described by a Voigt function;
(v)no restrictions are made as to source intensity, but it
should be noted that saturation of a transition by an
apparent line source may result in saturation broadening
of the spectral excitation profile until the source no
longer may be considered effectively a line source. The
validity and applicability of many of these
-314
considerations are discussed by Zeegers et al.
Definitions of all terms used in the fluorescence expression
(and other equations used in this text) are included in Appendix A.
The computer program used for evaluation of the fluorescence
expressions is included in Appendix B.
In this research, no simplifying assumptions were made other
than those noted above. Assumptions of line or continuum source


32
excitation would greatly simplify the equations and calculations
involved, but the much more difficult case of an intermediate source
is considered here. The shapes of curves for line or continuum
excitation have been studied thoroughly.J Jl A more complete
development of the curve of growth equation is given in these
sources.
The program for curve of growth calculation uses some
approximations to enable the calculation to be performed. The first
of these approximations is the substitution of a large polynomial
approximation for the Voigt profile. The Voigt profile is the
spectral convolution of a Doppler profile with added collisional
broadening and is used in calculating the atomic absorption
profile k(v) where
k(v) = kQV(a,v)
and
V(a,v) = j
7T J
exp(~y )dy
2 2
a +(v-y)
The Voigt integral cannot be solved in closed form and a substitution
proposed by Hui et al.^ is used. This approximation is extremely
accurate (one part in 10^) and evaluation is fast with no loss in
overall accuracy of the COG. The limiting accuracy of the COG is
determined by the accuracy of the integration limits used in the
evaluation of the other integrals of the fluorescence expression and
the accuracy of the experimental parameters used. The other major
approximation involved in the COG calculation is in the evaluation of
the primary, self-absorption, prefilter, and postfilter integrals.


33
The integrals should be evaluated from minus infinity to infinity.
Obviously, this integration is not possible and a tolerance for the
convergence of the integral must be chosen. In most cases, a
convergence tolerance of a maximum of 0.001 percent of the value of
interest was used. In some cases where a tighter convergence was
desired, an even smaller tolerance was used, although a greater
accuracy was not generally available.
Calculated Curves of Growth
The general COG in atomic spectroscopy is described by a linear
low concentration (or low number density) region and a noticeable
curvature at higher number densities. The degree of curvature and
the final slope of the COG at high number densities depends on the
source spectral width and the atomic parameters used in evaluation of
the fluorescence intensity expression. The curves of growth for line
and continuum sources are presented in Figures 3-3 and 3-i+,
respectively. These curves are shown for several a values. The a
value or a-parameter is a measure of the ratios of the collisional
width to the Doppler width:
AX,
a = /In 2(-)
axd
The collisional width, AX is largely dependent upon the mass and
number of collisional species present and the temperature of the
atoms. The Doppler width, AX^, depends upon the mass and temperature


LOG REL. FLUORESCENCE
Figure 3-3
Curves of Growth for Line Source Excitation


LOG REL. FLUORESCENCE
LOG NUMBER DENSITY
Figure 3-4. Curves of Growth for Continuum Source Excitation
LO


36
of the atom. The expression for is presented below with
expressions for collisional broadening widths presented later.
AAd = 4-irX/C /2 RT In 2/M .
The curves presented for line and continuum sources agree well
with the other literature and experimental results presented
previously. The abscissa in all curves is shown in relative units
since we are not concerned with the absolute signal magnitude but
rather the shape of the COG. Here, we are more concerned with the
intermediate case of a pseudocontinuum source, i.e., a laser.
The spatial line widths of dye lasers (measured as the full
width at one-half maximum (FWHM)) typically are on the order of -0.01
to 0.05 nm when only a grating is used as a tuning element. Atomic
spectroscopy line widths in analytical flames vary from about
0.0005 nm to 0.02 nm.^ Thus, the laser will vary from approximately
equal to, to approximately 100 times the line width of the atom of
interest. This can be considered a pseudocontinuum source for most
applications. The curves of growth for pseudocontinuum sources of
equal laser and atom line atomic width and a laser which is 10 times
the atomic absorption profile (FWHM) are shown in Figure 3~5.
Curves of growth are shown for prefilter and postfilter effects
in the next series of figures. These curves are presented for an a-
parameter value of 1.0, which is used as an average value of
40-41
approximately 40 elements in an air-acetylene flame. Shown in
Figures 3_6 and 37 are prefilter effects for mild, medium, and


LOG REL. FLUORESCENCE
LOG NUMBER DENSITY
Curves of Growth for Two Pseudocontinuum Sources
Figure 3~5.


0.0
Figure 3-
O.OI 0.1 I 10 100
LOG ( k0L )
Curves of Growth for Mild, Medium, and Severe Prefiltering--Line Source, Dark = prefilter
region


LOG REL FLUORESCENCE
Curves of Growth for Mild, Medium, and Severe Prefiltering--Continuum Source, Dark
prefilter region


40
severe prefiltering for line and continuum sources, respectively.
The equivalent curves of growth for line and continuum sources are
shown for postfiltering in Figures 3-8 and 3-9, respectively.
The COGs for all prefilter and postfilter calculations are shown
with log (kQL) as the abscissa. This is used, instead of the log
number density, to partially compensate for the reduced absorption
pathlength involved. The relationship between the peak absorption
coefficient (for pure Doppler broadening), k and the number
density, n, is presented below.
/4irln2 e2X2nf
*o 5^-
me AXD
This relationship is developed in Mitchell and Zemansky1 and is
based on the absorption oscillator strength, f, and the central
wavelength, Xq, and Doppler width, AAp, (FWHM) of the atom of
interest (other terras are defined in Appendix A).
General trends which may be noted for these curves are
relatively simple. Prefiltering of the source results in an increase
in the rate of curvature for line and continuum sources. This
increase in curvature is accompanied by a general decrease in the
signal strength. This is due primarily to the decreased fluorescence
volume observed. The postfilter effect results in a general decrease
in the overall fluorescence intensity. A more complete discussion of
the prefilter and postfilter effects is included in a later section
on collision broadening and saturation effects. From the figures and


LOG REL FLUORESCENCE
Curves of Growth for Mild, Medium, and Severe Postfiltering Line Source, Dark
postfilter region


gure 3~
Curves of Growth for Mild, Medium, and Severe Postfiltering Continuum Source, Dark
postfilter region
-Cr
rv>


43
discussion presented above, it can be seen that it is important to
minimize prefilter and postfilter effects (to achieve higher signal-
to-noise ratios and maximum linear dynamic range). It is generally
possible to do so by simple modification of the optical design.
Experimental Verification of Curves of Growth
Figure 310 shows the calculated curve of growth for sodium
resonance fluorescence in an air-acetylene flame. The experimental
data points are included on this curve also. The curve of growth was
calculated for a flame of 2500 K using a Gaussian source of 0.03 nm
(FWHM) and a damping parameter of 1.0. These represent the line
width of the copper vapor pumped dye laser and resonable parameters
for Na in an air-acetylene flame.^ The fit of the curve of growth
to the experimental points is obtained by transposition of the COG
until this curve overlaps the experimental points. The overlap of
these curves gives a direct relationship between the concentration of
the species introduced and the absolute number density present in the
flame.
The experimental curve of growth was obtained using the same
experimental arrangement as described and diagrammed earlier in
Chapter 2 (Figure 2-2). Aqueous solutions of sodium were prepared by
dissolving sodium chloride in deionized water. Solutions below
1000 mg/L were prepared by dilution, while solutions above 1000 mg/L
were prepared directly by weighing.
The fluorescence results are in good agreement with a calculated
estimate of the absolute number density. This estimate is based on


log rel. fluorescence
No RESONANCE FLUORESCENCE
PPM, FLUORESCENCE
I I 10 100 1000 10000 100 000
Figure 3"10.
Calculated and Experimental Curves of Growth for Na


45
the solution concentration, the solution uptake rate, the
nebulization and atomization efficiencies, and the flow rate and
thermal expansion of flame gases. These terms are grouped to form a
single term, 0, which should be within the range shown in Figure
3-10.
To confirm these experimental results and to extend the curve of
growth calculations to direct-line fluorescence, the same experiments
were performed using another laser system. Poor doubling
efficiencies with the copper vapor laser system (see Chapter 2) make
the wavelength used for Pb fluorescence difficult to obtain, at least
at a laser intensity level which will provide enough sensitivity for
these studies. The COG for lead with 283-3 nm excitation and
resonance (283-3 nm) and direct-line (405-7 nm) fluorescence were
calculated and measured experimentally. The curves were calculated
for a 0.019 nm source spectral line width (FWHM) with a-parameters of
1.0 (283-3 nm) and 1.5 (405.7 nm). These are estimates based on
calculations given by Parsons et al. since no known measured values
are available. The 0.019 nm source line width is obtained from our
Nd:YAG laser pumped frequency doubled dye laser (Quantel, model
YG580). The Pb experimental results were measured by Dr. Benjamin
Smith. His measurements were performed using an experimental setup
similar to that previously described (Figure 2-2). In this
experiment, two curves must be transposed to match with two sets of
experimental curves. The two experimental curves, shown in Figure
3-11, were found to give reasonable agreement between themselves and
are within one order of magnitude agreement with the estimated number


LOG NUMBER DENSITY (cm3)
Figure 311. Calculated and Experimental Curves of Growth for Pb
-fcr
cr*


47
density (from the nebulization and atomization efficiencies, etc.).
The agreement of these curves with the experimental values
demonstrates the accuracy and applicability of these methods.
Saturation and Collisional Effects
A further extension of the curve of growth calculations involves
the inclusion of some of the lesser noted effects in atomic
fluorescence spectroscopy. The expression for fluorescence presented
previously (Figure 3-2) and merely be extended here. The expressions
for saturation effects are included in Figure 3-2 but were not
previously discussed. The collisional broadening terms have not been
discussed yet and will be presented here.
Collisional broadening effects may be considered from two
separate aspects: collisional broadening due to analyte collisions
with analyte termed self-broadening or resonance broadening and
collisional broadening due to collisions with other species. The
first will be referred to as self-broadening and the second will be
termed collisional broadening. The general expression for
hp
collisional broadening is presented in Figure 3-12. The theory of
collisional broadening was originally developed by Lorentz and later
extended by Lenz and Weisskopf. A complete development is presented
42 10
by Breene and Mitchell and Zemansky. The general expression for
collisional broadening simplifies when only resonance broadening is
considered. The summation of all atomic and molecular concentrations
simplifies to involve only the analyte concentration. The mass


48
COLLISIONAL BROADENING
aAc =
22 r
2IN X TTC
-1 '2.
27TkT nT7 + TT )
A Mn Mn
RESONANCE BROADENING
2 2
v 2NX (T
A ar ttc
[4trkTNAC-ff)]
Figure 3-12. Expression for Collisional Broadening


49
terra, 1/m^ + 1/m simplifies to involve only the mass of the analyte
(see Figure 3-12). Worst case collisional broadening effects will be
seen for situations of small atomic mass, long wavelength
transitions, and large collisional cross sections.
The self-broadening effects for two elemental cases have been
included in Table 3~1. The elements evaluated represent the two
extremes encountered in atomic spectroscopy: a high mass, low
wavelength case and a low mass, high wavelength case. The
collisional cross sections used here represent the range of values
40
measured. From curve of growth calculations and the results in
Table 3~1 it can be seen that no significant differences due to
self-broadening are expected for experimentally realizable
situations. No appreciable changes are seen in the a-parameter until
number densities of greater than 101^ atoms/cra^ are approached.
Based on previous measurements in Chapter 2, this corresponds to an
initial atomic concentration of greater than 100 M and an unrealistic
Q
aspirated concentration of 10 parts-per-million. Additionally, at
high number densities where self-broadening effects should become
apparent, the primary absorption term will typically have reached
absorption saturation and any change in the a-parameter and line
shape will not affect the absorption of radiation. Very weak
transitions (kQ/n < 10-1') may show some small self-broadening
effects at high number densities since the absorption terms are very
small and allow considerable transmittance at high number densities.


50
Table 3~1 Broadening Effects on the a-Parameter for Self-Broadening
Best Case
(Low Collisional Broadening)
Worst Case
(High Collisional Broadening)
Pb
Li
X = 283.3 nra
X = 670.8 nm
T = 2500 K
T = 2500 K
mA = 207.2 g/Mol
mA = 6.9A g/Mol
n(cm 3)
a2
a-Param
(A2)
eters
n(em-3)
a2
(A2)
30
100
30
100
1 O16
1 .0007
1 .0023
1 01 6
1 .0035
1 .0097
101?
1.0068
1.0227
101?
1.0350
1.0970
1018
1 .0680
1 .2270
1 01 8
1 .350
1 .9700


51
Collisional broadening effects due to an added matrix species,
termed simply collisional broadening effects, are included also. The
collisional broadening effects are somewhat different than the self
broadening effect in that these effects are seen over the entire
range of analyte concentrations and are due to some constant
concentration of an added species. The effect of collisional
broadening may or may not be noticeable depending on the spectral
width of the source used and the spectral width of the atomic
profile. For line sources, the wings of the absorption profile
(described by the a-parameter) will not matter since absorption
occurs only at the line center. As the source width increases, the
wings of the absorption profile may affect the curve of growth. At
low atomic concentrations, however, the a-parameter does not affect
the curve of growth (see Figures 3-3 to 3-9).
One of the few situations where collisional broadening may need
to be considered is the technique of graphite furnace atomic
spectroscopy. In many instances, a high concentration of species is
added to serve as a matrix modifier. The added species will be
vaporized in a small volume of the graphite furnace and result in a
high atomic concentration.4^
ii
In a recent publication, Schleramer and Welz used an aliquot of
Pd and Mg for matrix modification, resulting in an atomic
1 C 1 <7
concentration of 10 0 to 10 in a typical tube furnace atomizer.
Collisional broadening effects become barely noticeable at this
level. The curves of growth for Li with added Mg matrix modifier are
shown in Figure 3-13- These curves are calculated in the same manner


LOG REL. FLUORESCENCE
Figure 3-13. Curves of Growth with Added Collisional Broadening
U1
ro


53
as before (Figures 3-3 to 3-5) but with the added term for
collisional broadening. Each of the relationships discussed
previously, a-parameter dependence and source width dependence, are
shown in this figure. The expected source dependence is seen in the
curves of this figure. The differences calculated for the
pseudocontinuum (AX = 0.19 A) and the line source
s
(AXq = 0.005 A) are too small to be seen here but occur in a region
somewhat smaller than that seen in the other pseudocontinuum
sources. These results represent an extreme case, not likely to be
seen in conventional flame spectroscopy and only infrequently seen in
nonflame spectroscopies. Generally, collisional and self-broadening
effects will have a very small influence, and in fact may not be
apparent at all.
Saturation (optical) effects are dependent on the source
spectral irradiance and do not depend upon the analyte of interest,
at least not in the same manner as the collisional broadening does.
As seen in the expression for right-angle fluorescence (Figure 3~2),
an increase of the source spectral irradiance E(A), above the
saturation spectral irradiance E (A), will result in an effective
decrease in the absorption coefficient. This decrease will occur at
all wavelengths at which the source irradiance is above the
saturation spectral irradiance. Prefilter terms are affected in the
same manner as the primary absorption term. The self-absorption term
may or may not be affected by saturation, depending upon whether the
fluorescence wavelength is within the saturating source spectral
profile. A postfilter region will not be affected by a saturating


54
irradiance since the source does not pass through the postfilter
region. A complete discussion of saturation effects and practical
4 5
measurement of saturation curves is given by Alkemade.
Curves of growth for several source intensities are presented in
Figures 3~1 4 and 3~1 5 for line and continuum sources, respectively.
The general trend seen is an increase in the linear regions of these
curves. No change of shape in the COG is seen. Curves of growth
were also calculated for the same Pb transitions previously measured
(283-3 nm resonance fluorescence and 405.7 nm direct-line
fluorescence). These curves are shown in Figure 3~16 and are
calculated for the same 0.019 nm source spectral width (FWHM) used
previously. As seen in this figure, it is possible to extend the
resonance fluorescence COG using a saturating source to equal linear
dynamic range and even beyond that of the direct-line fluorescence
case.
The source intensity at which equality occurs for the direct-
line and resonance fluorescence curves can be shown to be related to
the fractional populations of the two lower levels used. The
equations relating the source intensity necessary for equality of the
direct-line and resonance curves are shown in Figure 3"17- These are
derived from the initial curve of growth equation. As seen in Figure
3-16, the equality for the resonance and direct-line curves occurs at
a source irradiance approximately 100 times greater than the
saturation irradiance for the lead transitions. This agrees with the
ratios of the populations of the two levels 98.6% to 1.05?, a ratio
of approximately 100 to 1. This is calculated using the continuum


LOG REL. FLUORESCENCE
Figure 314. Curves of Growth for Several Intensities for a Line Source


LOG REL. FLUORESCENCE
gure 3-15. Curves of Growth for Several Intensities for a Continuum Source
CT\


Figure 3-16. Curves of Growth for Pb Direct-Line ( ) and Resonance Fluorescence (
Source Intensities
) for Several


58
GENERAL CASE
- fv ,
f\ e k(v) e^e^1- dv J y*| e _k(,/ d V k0
LINE SOURCE CASE
k0V (a,v) -g-l-gs p(
k'0V(a' vO ^2
CONTINUUM SOURCE CASE
Ev
^
S u' k(i/) F2
Figure 3-17. Equations for Curves of Growth Equalities for
Saturating Irradiances


59
source approximation since the source spectral width (FWHM) is
roughly 25 times larger than atom profile and as such closely
approximates a continuum.
The prefilter and postfilter effects with a saturating laser
source (0.019 nm) are shown in Figures 3_18 and 3-19. A 0.5 cm
prefilter length and a 0.5 cm postfilter length were used in the
corresponding curves. A 0.5 cm absorption path and a 0.5 cm
fluorescence path length are used in all curves here. In both cases,
it is possible to extend the calculated curve of growth to some
extent. Curves with prefiltering show the greatest extension. This
is due to removal of prefilter effects by the saturating laser and an
extension of the primary absorption linear region. The constant
difference between the curves of growth with and without prefilter is
due to the decreased source irradiance passing through the detected
volume. This corresponds to an additional primary absorption term
with no additional fluorescence. For the postfilter curves of growth
in Figure 3~19, the difference between the curves with and without
postfilter is seen to increase with increasing source irradiance.
The increasing difference between curves is due to the increase in
linearity of the curve which does not have postfiltering while the
curve with postfilter does not have the same increase in linearity.
If the source intensity is increased drastically, the overall curve
of growth will become limited by the curvature due to the postfilter
region. In no manner is it possible to remove postfilter effects by
using a more intense source.


LOG REL. FLUORESCENCE
LOG NUMBER DENSITY
Figure 3-18.
Prefilter Removal by a Saturating Source,
Resonance ( ) and Direct Line ( )
O'
o


LOG NUMBER DENSITY
Figure 3-19. Postfilter Effects with Saturation Effects Added, Resonance (
) and Direct-Line ( )


62
Conclusions
A general purpose computer program has been presented and is
investigated for applications to determine the absolute number
density of an atomic species. Various aspects of this curve of
growth program have been investigated including prefilter and
postfilter effects, saturation using various sources and collisional
broadening due to resonance broadening and broadening due to
quenchers.
It was found that collisional broadening, in all forms, should
present very minimal effects if they are seen at all. Prefilter and
postfilter regions are shown to cause a premature curvature of the
curve of growth. Prefilter and postfilter effects may be accounted
for and an absolute number density obtained if the exact geometry is
known. The prefilter effect may be removed to a large degree by a
saturating excitation source. The use of a saturating source may not
be desirable, as it adds another complication to the curve of growth
measurement and calculation of the absolute number density. Much of
the work of this chapter has been theoretical in nature and some
would be difficult to verify experimentally. Nevertheless, the
experimental results obtained for two of the simpler cases discussed
in this chapter show extremely good agreement between the
calculations and the experimentally measured results.


CHAPTER 4
SPATIAL DISTRIBUTIONS OF ATOMS
IN INHOMOGENEOUS FLAMES
Concentration Modulated Absorption Spectroscopy
A technique for increased sensitivity in atomic absorption
spectroscopy with pulsed lasers was recently introduced by Langley et
al.^ The technique was employed by the authors to yield absolute
number densities for atoms in flames and for molecules in
solutions. This experiment is based on a pump-probe arrangement of
optical beams and relies on a linear relationship between source
intensity and fraction absorbed. This technique, along with two
other related techniques using pulsed lasers in atomic spectroscopy,
are applied for the determination of spatial distributions of atoms
in inhomogeneous flames and are described in this chapter.
Many of the techniques presented in Chapter 1 are not applicable
to spatial profiling. This is due to the moderate to low sensitivity
of those techniques and the small region, and thus the small atomic
concentration, probed by these methods. The combination of these two
limitations and the limitations presented by pulse-to-pulse
instabilities and the spectral bandwidth of some pulsed dye lasers
make many techniques unsuitable for spatial diagnostics.
Concentration modulated absorption spectroscopy (COMAS) was
1 fa
initially applied by Langley et al. for absolute number density
determination. The development of the COMAS expression follows from
63


64
the interaction of two focused Gaussian beams and is based to a large
47
degree on the Beer-Lambert absorption expressions. 1 The beams are
assumed to be derived from the same pulsed laser source with a
spatially Gaussian electric field amplitude. From the Beer-Lambert
absorption expression, the change in the number of laser photons in
an incremental length dz will be
di = anAi dz
P P
where ip is the number of laser photons, A is the equilibrium
fractional population between levels 1 and 2, and o is the absorption
cross section. This fractional population is equal to the difference
of levels 1 and 2 divided by the total analyte concentration
A = (N1 N^/n. Based upon expressions for focused Gaussian beams
and the interaction volume for these beams, an expression for the
modulation of the probe signal is obtained:
2
di = (2iro nA/A)i i
pr p pr
Obtaining the fractional change in the number of probe photons or
gain gives
di /i
pr pr
= G = (2iro nA/A)i
Substituting the original Beer-Lambert law ln(1/T) = anA and


65
2
substituting for o gives G = (2iri / (nAA)) (ln( 1/T)) A plot of gain
2
times concentration vs In 1/T will give straight-line plot, the
slope of which is the proportionality factor in the relationship
between concentration and analyte number density C = xNA where C is
the analyte concentration. Thus, this experiment was viewed as a way
of obtaining an absolute number density which required only measuring
readily available analytical signals in a relatively simple optical
arrangement. Some optical restrictions were applied in the
development of the expressions which limit the applicability of these
equations.
The development of the COMAS expressions is not questioned here,
a £
and in fact extremely good results are obtained by Langley et al.
for molecular solution-phase analyses, but the assumption of a true
Beer-Lambert relationship for excitation of atoms in flames with a
relatively broad spectral width dye laser is not valid. The Beer-
Lambert relationship works well for molecular analyses since the
molecular absorption band is typically much wider spectrally than the
line width of the dye laser excitation source used. The results for
molecular analyses by Langley et al.2^ were easily checked assuming
1 5
no solution phase decomposition and were found to be 7.4x10
molecules/cm^ experimentally for a solution concentration of 6.0x101'*
molecules/cm^. When considering the atomic experiments, the dye
laser spectral bandwidth is much wider than the atomic line width.
Using the expression in Figure 3~2 for the primary absorption term of
the fluorescence curve of growth, a difference in signals of 5 times
(for the low-density linear region) is calculated for the signals


66
expected with a narrow line source and the signal obtained with a
source width 10 times greater than the Doppler width of the atom.
This will result in a direct error of the absolute number density
determined by this factor. A correction for this error may be
obtained by evaluating the overlap of the two profiles expected and a
correction factor obtained.
The concentration modulated method involves a pump-probe
arrangement of optical beams as shown in Figure 4-1. In this
arrangement the probe is approximately 5% of total dye laser
output. This method was originally investigated for Na in an air-
acetylene flame. The same copper vapor laser and dye laser system
presented in Chapter 2 were used for this application. The bandwidth
limitation approach was used for the absorption measurements.
An initial investigation of the method presented by Langley et
46
al. was carried out. This arrangement of counterpropagating co-
linear beams involves modulation of one of the two beams. The COMAS
signal is obtained by subtraction of the absorption signal with and
without the pump beam present. Subtraction of the two signals is
obtained using the active baseline subtraction method employed in
Chapter 2. The absorption signals were detected by a fast photodiode
(United Detector Technology, model PIN-1ODP) and connected to a
current-to-voltage converter (Thorn EMI Gencom Inc., model A1).
These signals were connected directly to the gated integrator and
46
boxcar averager. The COMAS experiment conducted by Langley et al.
was confirmed and a limit of detection of 1 part-per-million (ppm)


67
Figure 4-1. Concentration Modulated Absorption Experimental Setup:
Co-linear Beams


68
was found for an interaction volume of approximately 1 cm^. This
46
agrees closely with previous results found. The COMAS technique
relies on the linear interaction of the two beams and allows direct
determination of absolute number densities. Better limits of
detection are obtainable with simple experiments using hollow cathode
48
lamps.
An extension of COMAS was attempted to determine spatial
concentration profiles. The arrangement of optical beams was
modified to form a pair of crossing beams (Figure 4-2). A scanning
motor (General Scanning Inc., model G3) with a mirror attached and a
pair of lenses was added to scan a focused probe beam through the
flame. The scanner in conjunction with the first lens serves to
position the probe beam within the flame. With the first lens
positioned at a distance of one focal length from the scanning
mirror, beams from the scanning mirror pass through the flame
perpendicular to the pump beam. The second lens served to turn the
probe beam and redirect the beams to the photodiode detector. The
scanning is controlled by the computer interface (Stanford Research
Systems, model 24S) and allowed rapid collection of the entire
spatial profile of the flame. For these experiments the computer
controlled the scanning of optical beams and collection of all
data. For increased spatial resolution several optical elements were
added. A small pinhole, diameter 0.5 mm, was used in the optical
path of the probe beam to limit the beam size. Additionally, a lens
was used in the optical path of the pump beam to produce a smaller
beam. Relatively long focal length lenses (200 mm, 2" dia.) were


69
Figure 4-2. Experimental Setup for Spatial Diagnostics for COMAS


70
used in all cases. These lenses provide a relatively uniform beam
iiq
waist over the width of the flame. 7 The volume probed by the
interaction of these two beams is approximately 0.1 mm^ (0.4 mm
diameter probe by 0.5 mm diameter pump). This interaction volume is
50
calculated using the method of Jackson et al. and relies on the
overlap of two spatially Gaussian beams. The beams were measured and
closely approximate a Gaussian spatial profile. Additionally, the
spectral line profile of a dye laser has been measured here by
scanning the dye laser across an atomic transition and elsewhere by
this and other-' methods and closely approximates a Gaussian
spectral profile. The optical arrangement used allows scanning while
maintaining the same optical axes and beam size. Horizontal beam
placement was found to be extremely important for a uniform
interaction region. The results obtained for scanning the flame
produced by an inhomogeneous surface burner*^ are shown in Figure
4-3. The surface burner used in these experiments was provided
courtesy of Dr. R.J. Krupa and the construction is shown in Figure
4-4. The COMAS results are shown for an initial solution
concentration of approximately 5000 ppm Na. The COMAS results are
shown for a single region located above one row of analyte
capillaries in both the parallel and diagonal burner orientations.
The measurements were taken in a region approximately 6 mm above the
surface of the burner head. This corresponded to the top of the
flame cones-^ for gas flow rates of 1.6 1/m acetylene, 2.2 1/m
oxygen, and 8.3 1/m nitrogen with this type of surface burner. Based
on a measured nebulization efficiency of 0.14 and an estimated


71
5000 ug/mL Na
PERPENDICULAR
BURNER
:::::
.....
~_0_O'0_
5000 ug/mL Na
DIAGONAL
BURNER
CONCENTRATION MODULATED
ABSORPTION
Figure 4-3. Results for Perpendicular and Parallel Burners for COMAS


i0.0.00.0
:!!!:
rWVW
[oZoZoZojx
OXIDANT HOLES (0.03l" da.)
O FUEL CAPILLARIES (0. 042" l.d., 0.058"o.d.)
Figure 4-4. Design of Surface Burner Used


73
atomization efficiency^11 of 0.6, the analytical region of 0.1 mm^
calculated for the COMAS crossed beam experiments should have -10 J
atoms present during each laser pulse. The relative insensitivity of
this technique is seen in the high concentration of analyte necessary
to obtain any analytical signal. This low sensitivity is due to
several experimental problems. The relatively large spectral
bandwidth of the dye laser (0.3 A) is approximately 6 times greater
than the Doppler-width (FWHM) of Na in an air-acetylene flame with an
estimated temperature of 2500C. This large bandwidth results in
unabsorbed source irradiation reaching the detector and increased
background shot noise. The peak-to-peak fluctuation of the dye laser
intensity also limits the minimum absorption measurable.Radio
frequency noise is also thought to contribute to some degree (see
Chapter 2). At any rate, COMAS has been found to be too insensitive
for applications in spatial profiling.
The minimum detectable signal may also be calculated based upon
the spectral bandwidth of the laser, the parameters for Na in an air-
acetylene flame, the region probed in the interaction volume and the
S6
minimum detectable absorbance which may be typically measured. The
same curve of growth program used in Chapter 3 is used for this
calculation with only the primary absorption term calculated (see
Figure 32). The minimal concentration detectable based on this
calculation and a minimum detectable absorbance was found to be
approximately 1000 ppm Na. This does not consider the effect of
pulse-to-pulse fluctuations of the laser or any shot noise or radio
frequency (RF) noise added by the laser.


74
Results were also obtained for a simple atomic absorption
experiment with only the relatively weak probe beam and optical
scanning system (no pump beam). Results for the parallel and
diagonal burner configuration are shown in Figure 4-5. Again a
solution concentration of 10 ppm Na was used for these experiments.
The increased sensitivity of this technique is seen immediately since
these results are for an initial atomic concentration 50 times lower
than the COMAS results. This increase in sensitivity is accomplished
at a loss in spatial information since the analytical signal is
obtained for the entire absorption path length (1 cm or greater for
the burner used) and are not obtained for a much smaller interaction
region. The interaction volume is approximately 1.3 mm^ (0.4 mm
diameter by 10 mm (or greater in the diagonal burner case)),
approximately 13 times greater than in the COMAS case. This accounts
for a significant portion of the increased sensitivity. The spatial
information obtainable with this system is still somewhat
remarkable. Since the laser beam is coherent and has an extremely
low degree of divergence, good spatial resolution may be obtained.
An attempt was made to perform the same series of experiments with a
hollow cathode lamp. The hollow cathode lamp, with its much narrower
spectral bandwidth (compared to the dye laser), should have had a
higher sensitivity. No suitable optical arrangement could be found
to give a tightly focused beam within the flame volume. With the
high repetition rate of this laser and the fast optical beam scanning
method employed, entire spatial profiles of the atom cell may be
obtained in a very short period of time.


75
1 O ug/mL Na
PERPENDICULAR
BURNER
::::::
:

10 ug/tnL Na
DIAGONAL
BURNER
o*
c*o
c*o*o*
oooc
c*ooo*o*
o*ooo#
cc#o
co
o*
SIMPLE ABSORPTION
Figure 4-5. Simple Absorption Results for Perpendicular and Parallel
Burners


76
In an attempt to decrease the spectral bandwidth of the dye
laser, an etalon was added within the oscillator cavity of the dye
S7
laser. The decreased spectral bandwidth would have resulted in an
increased sensitivity in all absorption results. The etalon was
found to reduce the oscillator cavity gains to such an extent that
lasing would not occur. The dye laser was then switched to an
oscillator-only configuration with 100% of the copper vapor laser
output used to pump a single dye laser cell. The etalon was found to
S 8
increase cavity losses and decrease the stability of the dye laser
(in terms of pulse-to-pulse fluctuations) and gave only a slight
reduction in the spectral bandwidth (0.3 A to 0.18 A). The only
slight reduction in the spectral bandwidth of the dye laser is due to
the relatively poor quality of the etalon used.
Concentration modulated absorption spectroscopy was initially
investigated by us as a means of performing spatial profiling and
determining absolute number densities. The low sensitivity of the
technique prevented this application; in addition, complications far
beyond those expected were present. As a result of these
complications, other methods were investigated for increased
sensitivity in spatial profiling applications.
Two-Wavelength Laser Enhanced Ionization
and Fluorescence: Spatial Distributions
In several recent articles,1^^0 the use iaser excited
fluorescence for spatial distribution measurement has been studied


77
using a planar laser beam and a 2-dimensional image detector. The
spatial resolution element for this technique was found to be =1 mm
with concentrations between 1 and 20 ppm being used for spatial
profiling results. In other studies, spatial profiles have been
k q 60
measured in inductively coupled plasmas and in flames with a lens
and image detector or lenses and monochromators used to obtain the
spatial profiles. One advantage of image detection has been pointed
out in a recent publication where spatial information was obtained in
' -i
an entire plane within the flame volume on a single laser pulse.
Other studies have included probing of local electrical fields in
flames using LEIS which involved measurement of the atomic line
£ p
widths. The electrically-broadened atomic line width is a measure
of the strength of the local electrical field. Several of these
methods are applied later in this chapter for similar applications
with some modifications.
Two of the most sensitive methods for atomic species
determinations in flames are laser excited atomic fluorescence
spectrometry (LEAFS) and laser enhanced ionization spectrometry
(LEIS). The sensitivity of these techniques has been discussed
previously in Chapters 2 and 3 and the discussion is extended here.
Recent results presented by Magnusson et al.^^ anc¡ Axrier et al.^
in graphite furnaces and flames, respectively, show limits of
detection which approach 1 part-per-trillion (ppt) for single
wavelength excitation. For two-wavelength excitation in a graphite
furnace, results approaching 1 pg absolute limits of detection have
been obtained. Two-wavelength excitation was found to give an


78
ionization signal enhancement of up to 6000 times over single
Ail
wavelength excitation. With the high temperatures present in an
inductively coupled plasma (ICP) and the hazards of arcing of the
high power radio-frequency field, an optical method of detection of
laser induced ionization was presented by Turk et al. This is
instead of an electrode placed within the atom cell. As yet, no one
has applied two-wavelength LEIS and LEAFS for spatial measurements.
Experimental Setup and Discussion
The experimental arrangement of optical beams for two-wavelength
LEIS and LEAFS for spatial diagnostics is shown in Figure 4-6. This
is an extension of the technique presented previously for COMAS with
an additional wavelength of excitation and fluorescence and
ionization detection instead of an absorption detection method. The
same copper vapor laser used earlier was also used here. The beam
from this laser was used to pump two dye lasers. The dye lasers used
C O
(Hansch-design) were pumped in the oscillator-only configuration.
That is, only one flowing dye cell in each dye laser was excited by
the copper vapor beam. This was found to be a more efficient method
for pumping the dye lasers since the power per pulse of the copper
vapor laser is relatively low. Approximately 40? of the copper vapor
beam was used to pump the first dye laser with the remainder used in
the second. A fast photodiode placed at the end of the second dye
laser received the small fraction of the copper vapor beam which was
not reflected by the 99? reflector in the second dye laser. The
signal from this photodiode was used to trigger the boxcar detection


Figure 4-6
Experimental Setup for Two-Wavelength LEIS and LAFS


80
electronics and the oscilloscope. The same signal, used to trigger
the boxcars, was divided by multiples of 10 to trigger the computer
interface. This division was necessary in many instances since the
computer interface was only capable of transferring data to the
computer at a rate of 960 samples per second. The necessity of
division was dependent on the number of data points taken since the
computer interface contained a buffer memory which accumulated
untransferred data points. Scans across the burner in one direction
were obtained using the rotating mirror. To obtain the total profile
across the burner, the burner itself was translated using a
micrometer stage, with profiles obtained at several positions using
the rotating mirror. An initial attempt to obtain profiles by
positioning the X-| beam at different places within the flame volume
was investigated. Voltage field variances and voltage field
collection effects were found which complicated all spatial results
obtained. With a water-cooled bias electrode (-1500 V) placed
directly in the flame, spatial profiles were obtained. When the
laser beam was positioned directly under and parallel to the
electrode, signals were found to reach a maximum. Translation of the
laser beam, while maintaining the same burner and electrode position,
to a horizontal distance of approximately 0.5 cm from directly under
the electrode, but still at approximately the same atomic
concentration (see COMAS and absorption results), the analyte signal
was found to drop by more than one order of magnitude. This is due
to field collection effects and voltage field differences. Other
field collection effects have been investigated by other


31
authors.^ To minimize voltage field effects, the burner head was
translated and was found to give no appreciable voltage field effects
when measured by the method of Axner and Berglind. The placement
of a large electrode within the flame volume does disturb the
laminarity and shape of the flame and may result in somewhat
distorted profiles. For these reasons, fluorescence was investigated
as an alternate means of detection.
In the course of these investigations, several important factors
were discovered. To obtain a uniform interaction volume and an equal
sensitivity over the entire optical path probed, the two optical
beams had to be horizontal and intersect or remain a fixed distance
apart, over the entire distance probed. Additionally, the burner and
electrode also had to be horizontal to maintain a constant distance
between the laser beam and the electrode and to reduce voltage field
effects.
A typical profile obtained in a single scan is shown in Figure
4-7. This profile was obtained approximately 7 mm above the surface
of the burner at the tips of the flame cones. This profile was
obtained for an initial atomic concentration of 1 ppm Na with
excitation at 588.9 nm and 568.8 nm. From the signal-to-noise ratio
apparent in this figure, the atomic concentration produced by 1 ppm
Na is well above the limit of detection. These results were obtained
for a 1000 point scan, each point representing an average of 10 laser
shots (for reasons discussed earlier). With the high repetition rate
of the laser and the data acquisition system, these results required
only 1.67 s to obtain. Thus, the speed, ease, and high capacity for


83
information gathering is shown. The slightly irregular profile
obtained for this case is due to a slight flow constriction in one of
the analyte capillaries. This only served to illustrate the
analytical usefulness of this technique, as it was possible to
correct this flow restriction in later studies. Two arrangements of
optical beams were investigated for these studies. These
arrangements involved swapping the positions of the two laser
beams. Each arrangement had its own advantages. When the first
wavelength laser (X^) was positioned directly under the electrode, a
large pulsed ionization current was created by X1. The ionization
current created by X2 occurs only in the interaction region. Thus
the current produced by X-| had to be subtracted from that due to
X2+X-| to obtain the interaction volume. The current due to X-¡
produced a background shot noise which could not be corrected for.
An additional consideration was the thermal population of the lowest
excited state. Thermally excited atoms are excited by X2 and
collected.
In the first configuration with X-| directly under the electrode,
the collection of thermally excited and optically excited (X2) atoms
was limited by the electric field decrease with distance away from
the electrode. In the second configuration with X2 directly under
the electrode, there was a lower background current produced due to
X-| but a higher current which could not be corrected for due to
thermal excitation of atoms. The best analytical scheme would be
that one which gives the lowest background signals. It would seem


REL, IONIZATION SIGNAL
82
(mm)
Figure 4-7. Spatial Profile Result for LEIS


84
that as long as A-| is of higher energy than kT, the first scheme
would be best but this is complicated by the electric field effects
and the intensities of the lasers employed. For these experiments,
the first configuration was found to give better signal-to-noise
ratio. The contributions of the thermal, electric field, and optical
arrangement effects to signals obtained, corrections obtainable and
noises for each ionization process are summarized in Table 4-1.
The best arrangement for subtraction of signals due to
ionization out3ide the interaction region would involve modulation of
both A1 and A2. A modulation scheme which would give equivalent
results for both optical arrangements would be to sequentially excite
the analyte with then A2, and then the combined beams, A-|+A2.
The analytical signal would be obtained by subtracting the single
wavelength signals from the combined signals A-j+A2. Such a
modulation scheme would involve custom design of the optical choppers
or the use of acousto-optic deflectors and electronic circuits to
form the modulation pulses. Demodulation of the signals obtained
would be complicated also and would require a custom design lock-in
amplifier. Considering the complications expected from the
discussion above and the minimal improvement expected, this method of
correction was not attempted. This method of modulation would also
use three pump laser pulses for each data point and shift the
effective data taking rate to 2 kHz for this laser system. For any
pulsed laser system other than copper vapor (or mode-locked cavity-
dumped lasers), this modulation scheme would result in a shift in the
data taking rate back into a flicker noise dominated region (i.e.,


85
Table 4-1. Ionization Processes, Optical Arrangements, Signals and
Noises for Two-Wavelength Laser Enhanced Ionization
Spectroscopy
PROCESSES
1
2
3
4
SIGNALS
Nonspecific thermal ionization of atoms and molecules
Ionization due to X-| and thermal processes
Ionization due to thermal processes and X2
Ionization due to X-|+X2 in interaction region
OPTICAL ARRANGEMENTS
1
X-] directly beneath electrode, X2 perpendicular
2
X2 directly beneath electrode, X-j perpendicular
PROCESSES
1
2
3
4
CORRECTION
D.C. signals
Modulation
Modulation
Analytical
METHODS
blocked by
of X2
of X1
signal. No
boxcar input
correction
capacitor.
necessary.
NOISES
Shot noise
Signal magni
Signal magni
Noises and
due to D.C.
tude and
tude and
signal are
signal. Equi
noise greater
noise greater
the same
valent noises
for arrange
for arrange
for both
for both
ment 1. Shot
ment 2 but
optical
optical
noise uncor
smaller than
arrangements.
arrangements.
rectable .
that due to
Magnitude
process 2 in
will vary for
arrangement
different
1 (due to
elements.
lower popu
Analyte &
lation of
background
fluctuations
excited state)

corrected for
by modulating
on A2.


86
<100 Hz). The only laser system which comes close to the high-
repetition rate needed is a 500 Hz excimer system, with an effective
data taking rate of approximately 160 Hz. This is still within the
flicker noise region for a typical analytical flame.
Similar results were obtained for two-wavelength laser excited
atomic fluorescence spectrometry (LEAFS). A lower sensitivity is
obtained for this technique compared to LEIS due to several
reasons. The detector in this instance is placed a significant
distance from the region excited by the two beams. Since the
fluorescence is isotropic, this detector will only receive a small
fraction of the fluorescence emitted. Using two-wavelength
excitation, atoms are excited to levels within several kT of the
ionization continuum. Losses of these atoms to the ionization
continuum are likely and make the fluorescence from the second
excited level to the first excited level less sensitive. Monitoring
the fluorescence from the first excited level to the ground state is
possible and the change in this fluorescence, when ^2 i3 added> is
6Q
referred to as fluorescence dip spectroscopy. Monitoring
fluorescence from the first excited state to the ground state is
somewhat complicated by shot noise from analyte emission and noise
due to analyte and laser flicker. Fluorescence from the second
excited state to the first excited state is limited by shot noise of
the scatter of ^ and losses to the ionization continuum. For
monitoring fluorescence, the best method would primarily depend upon
the proximity of the second excited level to the ionization
continuum. For these results, the fluorescence from the second level


87
70
to the first was found to yield the best results. Oraenetto et al.'
have investigated two-wavelength fluorescence of ions produced in an
inductively coupled plasma. The results approach low part-per-
trillion levels and benefit from the lower losses to the ionization
continuum (the doubly ionized species is especially difficult to form
in most instances) compared to the two-wavelength atomic fluorescence
case.
A typical result for two-wavelength excitation and fluorescence
detection is shown in Figure 4-8 for 10 ppm Na at a height of
approximately 4 mm in the same burner used previously. The increased
separation of the spatial distribution for each capillary within the
burner are evident in this figure. Approximately the same
representation was obtained at a height of 7 mm as shown for
ionization results in Figure 4-7. These two figures demonstrate that
this burner has very good laminarity low in the flame which
deteriorates rapidly. The fluorescence was monitored at X2 The
presence of fluorescence was confirmed (versus scatter) by detuning
One major advantage of the fluorescence method is that it is not
necessary to place an electrode within the flame volume, which makes
it possible to detect signals without disturbing the flame. This
also makes the fluorescence method more applicable, especially in
situations where it is not possible to place an electrode within the
cell volume.
As a direct result of these techniques, it was possible to
spatially map the entire combustion zone. By translating the burner
and obtaining successive profiles across the burner, it was possible


REL. FLUORESCENCE INTENSITY
88
Figure 4-8. Spatial Profile Result for LAFS


89
to map a horizontal plane within the flame volume. If multiple
horizontal planes are obtained a four-dimensional structure may be
developed, three spatial dimensions and a concentration dimension. A
single horizontal plane located at approximately the top of the flame
cones is shown in Figure 4-9 using ionization detection for a 1 ppm
solution of Na.
Conclusions
Single-wavelength and two-wavelength methods for obtaining
spatial information within inhomogeneous flames have been
presented. While the single wavelength concentration-modulated
absorption results were not particularly sensitive or useful, the
two-wavelength LEIS and LEAFS results demonstrated exceptional
spatial resolution and very good sensitivity. The spatial results
shown here represent the first application of two-wavelength LEIS and
LAFS to this area. The high-repetitive rate laser used and an
optical method of scanning the beams through the flame were shown to
allow rapid determination of spatial profiles of analyte
concentrations. While the applications here are limited in scope, it
is felt that these techniques will find many applications.


Full Text

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LASER EXCITED FLUORESCENCE AND IONIZATION
FOR FLAME DIAGNOSTICS
BY
MICHAEL JAMES RUTLEDGE
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
1 987

To my parents and family,
whose unending support made all this possible.

ACKNOWLEDGMENTS
I gratefully acknowledge the support of Dr. Benjamin Smith,
Dr. Edward Voigtman, and Dr. Nicolo Omenetto whose knowledge,
enthusiasm, and helpful suggestions were a continuing source of
inspiration.
I thank Dr. James D. Winefordner for the privilege of working
with him for the past four years and with the best spectroscopy group
in the world. His concern and encouragement during my four years
have made my work more pleasurable and an invaluable learning
experience.
My sincerest thanks go to Jeanne Karably and the secretaries of
J.D. Winefordner. They have been my constant friends for the past H
years.
I also thank the members of other research groups in the
analytical department especially Ken Matuszak, Paul McCaslin, and
David Berberich whose help with my golf game may prove invaluable.
iii

TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT ix
CHAPTERS
1 INTRODUCTION 1
2 MEASUREMENT APPROACHES FOR ATOMIC FLUORESCENCE AND
IONIZATION SPECTROSCOPIES 4
Introduction to Laser Atomic Fluorescence Spectroscopy
and Laser Enhanced Ionization Spectroscopy Systems 4
Measurement Approaches and Instrumentation 10
Results and Discussion 17
Conclusions 25
3 ESTIMATION OF ABSOLUTE NUMBER DENSITIES 27
General Curve of Growth Introduction and Evaluation 27
Calculated Curves of Growth 33
Experimental Verification of Curves of Growth 43
Saturation and Collisional Effects 46
Conclusions 62
4 SPATIAL DISTRIBUTIONS OF ATOMS IN INHOMOGENEOUS
FLAMES 63
Concentration Modulated Absorption Spectroscopy 63
Two-Wavelength Laser Enhanced Ionization and
Fluorescence: Spatial Distributions 76
Experimental Setup and Discussion 78
Conclusions 89
5 FINAL COMMENTS AND FURTHER STUDIES 91
IV

APPENDICES
A GLOSSARY OF TERMS AND SYMBOLS 94
B COMPUTER PROGRAM LISTING FOR CALCULATION OF
FLUORESCENCE CURVES OF GROWTH INCLUDING SATURATION,
COLLISIONAL AND PREFILTER AND POSTFILTER EFFECTS 96
REFERENCES 109
BIOGRAPHICAL SKETCH 113
v

LIST OF TABLES
Table Page
2-1 Limits of Detection (ng/mL) 18
3-1 Broadening Effects on the a-Parameter for Self-
Broadening 50
4-1 Ionization Processes, Optical Arrangements, Signals
and Noises for Two-Wavelength Laser Enhanced
Ionization Spectroscopy 85
vi

LIST OF FIGURES
Figure Page
2-1 Lasing Diagram for Copper Vapor Laser 5
2-2 Experimental Setup 8
2-3 Boxcar Plus Lock-In Amplifier Signal Processing
Layout 11
2-4 Boxcar-Active Baseline Subtraction Signal Processing
Layout 14
2-5 Bandwidth Limitation and Conventional Signal
Processing Layout 16
2-6 Bandwidth Limitation Effects 21
2-7 Noise Power Spectrum at 588.9 nm 24
3-1 Diagram for Right Angle Fluorescence 28
3-2 Expression for Right Angle Fluorescence 29
3-3 Curves of Growth for Line Source Excitation 34
3-4 Curves of Growth for Continuum Source Excitation 35
3-5 Curves of Growth for Two Pseudocontinuum Sources 37
3-6 Curves of Growth for Mild, Medium, and Severe
Prefiltering—Line Source, Dark = prefilter region 38
3-7 Curves of Growth for Mild, Medium, and Severe
Prefiltering—Continuum Source, Dark = prefilter region...39
3-8 Curves of Growth for Mild, Medium, and Severe
Postfiltering—Line Source, Dark = prefilter region 41
3-9 Curves of Growth for Mild, Medium, and Severe
Postfiltering—Continuum Source, Dark = prefilter
region 42
vii

3~10 Calculated and Experimental Curves of Growth for Na 44
3-11 Calculated and Experimental Curves of Growth for Pb 46
3-12 Expression for Collisional Broadening 48
3-13 Curves of Growth with Added Collisional Broadening 52
3-14 Curves of Growth for Several Intensities for a
Line Source 55
3-15 Curves of Growth for Several Intensities for a
Continuum Source 56
3-16 Curves of Growth for Pb Direct-Line ( ) and
Resonance ( ) Fluorescence for Several Source
Intensities 57
3-17 Equations for Curves of Growth Equalities for
Saturating Irradiances 58
3-18 Prefilter Removal by a Saturating Source, Resonance
( ) and Direct-Line ( ) 60
3-19 Postfilter Effects with Saturation Effects Added,
Resonance ( ) and Direct-Line ( ) 61
4-1 Concentration Modulated Absorption Experimental Setup:
Co-linear Beams 67
4-2 Experimental Setup for Spatial Diagnostics for COMAS 69
4-3 Results for Perpendicular and Parallel Burners
for COMAS 71
4-4 Design of Surface Burner Used 72
4-5 Simple Absorption Results for Perpendicular and
Parallel Burners 75
4-6 Experimental Setup for Two-Wavelength LEIS and LAFS 79
4-7 Spatial Profile Result for LEIS 82
4-8 Spatial Profile Result for LAFS 88
4-9 Three-Dimensional Spatial Profile for LEIS 90
viii

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
LASER EXCITED FLUORESCENCE AND IONIZATION
FOR FLAME DIAGNOSTICS
BY
MICHAEL JAMES RUTLEDGE
May, 1987
Chairman: James D. Winefordner
Major Department: Chemistry
Measurement approaches involving electrical signal manipulation
and signal processing are investigated for a copper vapor laser
pumped dye laser system. Correction methods used involve modulation
of a pulsed laser output and subtraction of noise. Bandwidth
limitation of signals to reduce radio-frequency noise is also
discussed. A general purpose computer program for calculation of the
absolute number density of an atomic species present in an analytical
volume is presented. The program is written in FORTRAN with a high¬
speed, high-precision approximation of the Voigt profile to
incorporate atomic broadening effects. Comparison to experimentally
measured fluorescence results is included.
A discussion of saturation and collisional broadening effects is
included. Calculated results are found to agree with experimental
results within an order of magnitude in all experimental cases.
Spatial profiling results are presented for two-wavelength excitation
IX

of atomic species with detection via fluorescence and ionization of
the species of interest. A new form of absorption spectroscopy,
termed concentration modulated absorption spectroscopy, is
investigated for spatial profiling applications. These methods are
investigated for detection power, as well as spatial information
obtainable. Comparison to other methods of determining absolute
number densities and spatial information is included.
x

CHAPTER 1
INTRODUCTION
Laser excited atomic fluorescence and laser enhanced ionization
spectroscopies have been used for many different types of
applications. The extreme sensitivity of these techniques has been
shown many times. J Some of the best limits of detection are
obtained using these methods. These sensitive techniques are applied
here to the investigation of absolute number densities and spatial
profiles in inhomogeneous flames.
A copper vapor laser is used for all investigations throughout
these studies. This laser has found limited application in
li í 6
chemistry but has found many applications outside this field.
This laser system consists of a pulsed laser plus the dye laser(s)
for tunability to the wavelength(s) of interest. This is a pulsed
laser which operates at a 6 kHz repetition rate with an average power
of 25 W. Measurement approaches for atomic fluorescence and
ionization are presented as preliminary investigations using this
laser system in Chapter 2. These measurement approaches rely on
bandwidth limitation and/or removal of correlated background
noises. A more complete discussion of the use of correlation
functions to increase signal-to-noise ratios is given by Doerffel et
7
al. The extension of these methods to measurement of atomic
1

2
fluorescence for determination of absolute number densities is
discussed in Chapter 3.
Determination of absolute number densities is accomplished using
a computer program to model the expected relationship between
concentration of a species of interest and fluorescence signal
detected. The relationship between fluorescence intensity and
concentration, expressed in a log-log graph, is called a fluorescence
curve of growth (COG). The point of departure from linearity allows
determination of absolute number densities. Many methods have been
presented for determination of absolute number densities in flames,
plasmas and vapor cells. These methods range from the classical
O
approaches of the absolute intensity method and the integral
absorption method^’1 ^ to some more recently introduced methods such
as laser induced fluorescence saturation spectroscopy11 and anomalous
dispersion. Several methods have also been presented which allow
absolute number density evaluation from the absolute magnitude of the
signal detected and the experimental detection efficiency.1-^ Several
COG methods have been presented which allow determination of absolute
number densities with a minimal knowledge of the atomic and geometric
1 4
parameters. Other methods include determination of number
densities from vapor pressure measurements of Na and Pb in laser
excited fluorescence experiments.1^’1^ Some of the simplest methods
for evaluation of number density rely on the supply of and
atomization efficiency of the analyte of interest. Experimentally,
many of the above mentioned methods are quite difficult or time-
consuming to implement. Many rely on an absolute calibration of the

3
detection optics and photodetector, while some require an additional
calibrated source. Some methods require a detailed knowledge of the
source characteristics including the source intensity and the
spectral profile (Gaussian or otherwise). A general overview of many
of these methods is given in two excellent works by Alkemade and
1 A 17
coworkers. 1
Atomic fluorescence with two-wavelength excitation and a
multichannel image detector has been used for spatial imaging of OH
•i O on
and for flow visualization. ¿ No research has been presented
which utilizes two-wavelength excitation of atomic species for
spatial resolution with direct detection using laser atomic
fluorescence (LAFS) or laser enhanced ionization (LEIS)
spectrometry. This topic and some related areas are the focus of
Chapter 4. In a recent study by Turk et al., two-wavelength atomic
spectra were measured with detection via ionization. In that study,
only the wavelengths are scanned and the three-dimensional spectra
are presented with axes of one wavelength (X^) and the other
wavelength (A^) versus intensity. Here, the spatial distributions of
atoms using two-wavelength LEIS and LAFS and single-wavelength
absorption are investigated. An initial investigation into
absorption spectroscopy with a modulated pulsed laser is included.
The absorption technique, termed concentration modulated
absorption spectroscopy (COMAS), is investigated for increased
sensitivity and spatial profiling applications. The highly sensitive
techniques of LEIS and LAFS are applied to probing small volumes in
inhomogeneous flames as a final study.

CHAPTER 2
MEASUREMENT APPROACHES FOR
ATOMIC FLUORESCENCE AND IONIZATION SPECTROSCOPIES
Introduction to Laser Atomic Fluorescence Spectroscopy and
Laser Enhanced Ionization Spectroscopy Systems
In these experiments, a 20 W copper vapor laser (Cooper
Lasersonics model 251) and a flowing dye cell were used. This is a
pulsed laser system operating at -6 kHz with moderate peak powers of
-160 kW. Laser action in a cell containing copper vapor was first
pp
reported by Walter et al. in 1966. Lasing action is accomplished
via the thermal production of ground state copper atoms and
electrical pumping of the ground state (2S) to the lowest resonance
p
levels ( P) resulting in spectral output at 510 and 578 nm (see
Figure 2-1). Repetition rates of between 800 and 10,000 pulses per
second have been obtained in our laboratory. This high repetition
rate is accomplished using a thyratron-switched power supply using
-4000 W of electrical power. This high-power, high-frequency
switching produces a large amount of radio-frequency (RF)
interference which was found to be a major noise source in all
analytical experiments. From oscilloscope measurements and gate-
scanned boxcar averager outputs, it was determined that the radio¬
frequency has a high degree of pulse-to-pulse correlation. Shielding
of the detection electronics was attempted but was inefficient in the
reduction of RF interference.
4

5
LOWEST RESONANCE
LEVELS
Figure 2-1. Lasing Diagram for Copper Vapor Laser

6
Three models were used to correct for and/or reduce background
radio-frequency and other noise sources. Two methods rely on
synchronization of the laser with a high-speed chopper to block
alternate laser pulses. One of these methods involved the use of a
gated integrator and boxcar averager equipped with an active baseline
subtraction circuit. Another used a gated integrator and boxcar
averager plus lock-in amplifier to accomplish the same background
subtraction. The third method used a bandwidth limited amplifier to
reduce high frequency noise components present in the signal. For
comparison purposes, the conventional method of measuring pulsed
laser signals is also included. Analysis for several elements is
included to show consistency of the results.
Chemicals
Stock solutions of all elements were prepared from analytical
grade LiCl, NaCl, Fe wire, and In202 to give 1000 ug/mL solutions.
Standard solutions were prepared by serial dilution of the stock
solutions. Laser dyes (Exciton Corporation) used included oxazine
720 (Li), and mixtures of Rhodamine 6G and Kiton Red 620 (In, Na, and
Fe).
Instrumentation
The frequency-doubled dye laser output (Molectron model DLII
pumped by a Cooper Lasersonics model 251 copper vapor laser with an
Inrad Autotracker II frequency doubler) was used to illuminate a
1 cm^ region of the flame. A flat mirror was mounted 5 cm from the
flame to allow for a second pass of the laser. For frequency-doubled
experiments, the laser had a pulse width of -20 ns, a pulse energy of

7
5-35 uJ, and a spectral bandwidth of 0.02 nm. For experiments
involving the fundamental wavelength of the dye laser, the frequency
doubler was removed from the optical path. The fundamental
wavelength experiments are characterized by a pulse width of 30 ns, a
pulse energy of -100-500 pJ, and a spectral line width of 0.03 nm.
Pulse temporal widths were measured using a gate-scanned boxcar
averager with a 2 ns risetime photomultiplier tube and a 2 ns boxcar
gate. Additionally, line widths were measured by slowly scanning the
dye laser across an atomic transition and measuring the fluorescence
of a 1 pg/mL solution of the element aspirated into the flame. The
flame was produced on a laboratory-constructed, brass capillary
burner^ (1 cm^) mounted on a commercial atomic absorption spray
chamber (Perkin Elmer model 303-0110). An approximately
stoichiometric air-acetylene flame was used for all studies.
Commercial-grade gases were pressure-regulated and flow controlled
using rotometers with needle valves. The experimental setup is shown
in Figure 2-2. Symbols are defined in Appendix A.
The fluorescence was produced in a flame volume of approximately
1 cm^ and detected using a small monochromator (SPEX 1670 Minimate,
f/4.0, 220 mm focal length) and RCA model 1414 photomultiplier
tube. The monochromator optical axis was 90° to the laser beam. No
additional optics were used since the acceptance angle of the
monochromator was filled. With the 1.25 mm slits used, this
monochromator had a 10 nm bandpass. The photocurrent pulse was
stretched slightly by a 1000 ft load resistor and connected directly
to the input of the gated integrator and boxcar averager

8
Figure 2-2. Experimental Setup

9
(Stanford Research Systems model 250). The boxcar was triggered
using a photodiode positioned to receive a portion of the copper
vapor 510 and 578 nm output.
The laser enhanced ionization experiments were performed
similarly with the following exceptions. A 5 om stainless steel slot
burner (Perkin-Elmer model 0040-0277) was used and served as the
detecting electrode. A -1500 V bias potential was applied to a
water-cooled stainless steel electrode placed -1 cm above the burner
surface. The laser beam was positioned to pass parallel to and
-0.3 cm below the bias electrode. The entire assembly was placed
inside a shielded and grounded housing. This experimental
pa
arrangement is a modification of that presented by Travis et al.
Ionization currents were capacitively coupled to reduce flame
background leakage currents and then converted to voltages using a
current-to-voltage converter (Princeton Applied Research model
£
181). Gains of 10° V/A were typically used. This signal was
connected directly into the input of the gated integrator. For the
boxcar plus lock-in amplifier portion of the experiments, the signals
from the boxcar were connected directly into the input of the lock-in
amplifier (Keithley model 840). Signals obtained in all experiments
were integrated using a voltage-to-frequency converter (Analog
Devices model 650) and counted for a 10 s integration period. This
method of signal integration was found to give an unambiguous
result. Limits of detection were determined using the IUPAC
convention, 0 namely, a signal-to-noise ratio equal to three. Noise
levels were determined as the standard deviation of 16 blank

10
measurements. A more complete discussion of this and other methods
for calculating limits of detection is covered by Long and
27
Winefordner. 1
Measurement Approaches and Instrumentation
Gated Integrator and Boxcar Averager Plus
Lock-In Amplifier (BLIA)
This method of background correction is similar to background
correction methods in flame absorption or fluorescence using a
continuous wave (cw) laser or conventional source employing
modulation of the source intensity. For a complete discussion of
background correction methods, the reader is referred to the
p o p q
excellent works of Alkemade et al. ° and Kirkbright and Sargent. ^
In this experiment, a high speed chopper (Photon Technology) was
used free-running at 3 kHz, and the reference output of the chopper
was used to control the laser repetition rate. The reference from
the chopper was connected to a multiply-by-two circuit constructed
from a monostable multivibrator (74LS123) and an OR gate (7MLS32).
This circuit was set up to give a single pulse output from both the
rising and falling edges of the chopper reference waveform. This
signal was used to trigger the laser externally at a 6 kHz repetition
rate. Initial attempts to control the high speed chopper from the
laser reference output failed due to the momentum and drift of the
chopper blade. Synchronization of the chopper had to be absolute
since any drift resulted in a complete reversal of the signal
polarity for at least a portion of the integration period. The
electrical signal processing system is shown in Figure 2-3.

BOXCAR PLUS LOCK-IN AMPLIFIER METHOD
3 KHz FL. SIGNAL*
3 kHz BKG - 180°
6kHz
TO LASER
X 2
CIRCUIT
hi—
r
BOXCAR
LOCK-IN
+ I0 s
»
SJ/F COUNTER
3 kHz
FROM CHOPPER
Figure 2~3. Boxcar Plus Lock-In Amplifier Signal Processing Layout

12
Signals obtained from the fluorescence or the photoionization
were fed directly to the input of the gated integrator. The Stanford
boxcar averager has two output signals, a last sample and an average
sample. The average sample is useful for reduction of signal
fluctuation and employs a gated resistor-capacitor low-pass (RC)
filter to average a variable number of samples. The last-sample
output is the most recent signal detected by the boxcar averager.
The last-sample output was used in this instance because the signal
varies between signal plus noise on one pulse and noise only on the
following pulse, and the demodulation of this signal was accomplished
in the lock-in amplifier. The last-sample output was connected
directly to the input of the lock-in amplifier. The reference output
of the high speed chopper was connected to the reference channel of
the lock-in amplifier which was triggered at the 3 kHz repetition
rate. Synchronization of the lock-in reference waveform and the
boxcar signal is obtained using the phase adjustment on the reference
channel of the lock-in amplifier. The output from the boxcar, which
consisted of signal plus noise during one half-period and noise only
during the following half-period, was demodulated and background was
subtracted by the phase-sensitive detector in the lock-in
amplifier. Output signal ripple of the phase-sensitive detector was
smoothed using a 1 s time constant output filter. Signals output
from the lock-in were connected directly to the voltage-to-frequency
converter and then counted for a 10 s integration period.

13
Gated Integrator and Boxcar Averager: Active Baseline
Subtraction (ABS)
This technique was a special method applicable only to the
Stanford Research Systems boxcar used here or similar systems with an
active baseline subtraction method. In this method, the same signals
were connected to the boxcar, but the boxcar was placed in the active
baseline subtraction mode (ABS). This mode caused the electronics in
the boxcar to switch the polarity of alternating samples before
adding each one to a moving average. The moving average circuit was
implemented using a gated RC filter^0 with varying resistors and
capacitors depending on the number of samples to be averaged. This
method of correction is significantly different from the true phase-
sensitive detection methods employed in lock-in amplifiers. The
moving average switch was set at 3000 samples to keep an effective
1 s time constant, consistent with the lock-in amplifier case
(BLIA). Blocking alternating laser pulses resulted in a subtraction
of noise produced during each laser pulse. Signal output from the
boxcar averager was connected directly to a frequency-to-voltage
converter and counted for a 10 s integration period. This is shown
diagrammatically in Figure 2-4.
Bandwidth Limited Signal Processing (BLSP)
Another method of diminishing the effect of high frequency noise
was investigated using a form of low-pass filtering. This "low-pass
filtering" was implemented using a bandwidth-limited amplifier.
Fluorescence photocurrents (-25 ns) were stretched and converted to
voltages using a 1 kft resistor giving a signal of approximately

14
ACTIVE BASELINE SUBTRACTION METHOD
Figure 2-4.
Boxcar Active Baseline Subtraction Signal Processing
Layout

15
100 ns full width at half maximum (FWHM), i.e., a bandwidth of
-10 MHz. Stretching occurred due to the RC time constant of the
photomultipler tube and connecting cables, due to the load resistor
and the stray capacitance in the system. The fluorescence signals
obtained were input to the bandwidth-limited amplifier and then
connected directly to the gated integrator and boxcar averager. The
amplifier used, an Evans model 4131, has a 3 dB bandwidth of 10 MHz
at a gain of 10 times. Signals were stretched to approximately
120 ns (FWHM) by the Evans amplifier. The decreased response of the
amplifier in the high frequency region resulted in a significant
reduction of high frequency noise components. Actual low-pass
filtering would be difficult to implement since a time constant on
the order of 10 ns would be necessary to avoid significant signal
distortion. Stray capacitance and resistance make this low time
constant difficult to obtain. Signals from the Evans amplifier were
connected directly to the gated integrator and boxcar averager.
Signals from the boxcar were connected to a voltage-to-frequency
converter and counted for a 10 s integration period as in all other
cases. The electrical system is shown in Figure 2-5 along with the
conventional method for measuring signals.
Conventional Method (CONV)
Signals obtained from fluorescence and photoionization were
input directly into the gated integrator with no modifications. This
method is included for comparison purposes as a reference.^1 The
signal output from the boxcar averager was connected to the voltage-
to-frequency converter and the signal was counted for a 10 s

BANDWIDTH LIMITED SIGNAL PROCESSING METHOD
CONVENTIONAL METHOD
Figure 2-5. Bandwidth Limitation and Conventional Signal Processing Layout

17
period. In all four measurement methods, the boxcar averager was
operated with a 10 kHz first-order cutoff filter on the input to help
remove unwanted low frequency components.
Results and Discussion
All correction methods used show a significant improvement over
the conventional method (Table 2-1). While no attempt was made to
optimize fully system components or operating conditions, the limits
of detection obtained are very good and demonstrate the improvements
expected. Laser power was found to present a severe problem when
frequency doubling the copper vapor laser (CVL) dye laser output.
The relatively low peak power and squared dependence of frequency
doubling on input power^2 resulted in low power outputs for In and
Fe. The low laser power is partially compensated for (in limits of
detection) by the lack of laser scatter and the associated shot noise
in the direct-line fluorescence of Fe and In. Compromises concerning
excitation wavelengths had to be made since the CVL fundamental
output is in the visible region at 510 and 578 nm. Additionally, RF
interference from this laser was and has been found to limit severely
its analytical applicability for laser enhanced ionization and
qq
flúorescence. J
The simplicity and nearly equivalent results obtained using the
bandwidth limitation scheme (BW) for signal processing make this the
processing method of choice for most applications. As seen in Table
2-1, results obtained using the bandwidth limited approach for
fluorescence are nearly equivalent to those obtained using

18
Table 2-1. Limits of
Detection
(ng/mL).
CONVa
ABSb
BLIAC
Copper Vapor
Dye Laser
Laser
Enhanced Ionization Detection
Li
2.0
0.3
0.1
Fe
30
5.0
2.0
In
4.0
0.6
0.2
Laser
Excited Fluorescence Detection
Li
14
0.8
0.4
Fe
98
18
5.0
In
43
8.0
5.0
Na
1 4
3.0
1 .0
Excimer Dye Laser
Laser
Enhanced Ionization Detection
Li
0.7
0.3
0.5
Na
4.0
1 .0
2.0
In
0.2
0.2
0.4
BWd
BW+ABSe
BW+3LIAf
Copper Vapor Dye Laser
Bandwidth Limited
Signal Processing—Fluorescence Detection
Li
2.0
0.6
0.3
Na
2.0
1 .1
1.0
In
3.0
Fe
15
a CONV = Conventional method of measuring pulsed laser signals using
a boxcar averager and gated integrator.
b ABS = Active baseline subtraction method using a modulated pulsed
laser. Subtraction of background noise is done by the boxcar
special electronics.

19
Table 2-1 — continued.
c BLIA = Boxcar averager plus lock-in amplifier using a modulated
pulsed laser. Subtraction of background noise is accomplished in
the lock-in amplifier.
d BW = Bandwidth limited signal processing in which high frequency
laser noise is not amplified while the signal is amplified to
increase signal-to-noise ratio of fluorescence signals.
e BW+ABS = Bandwidth limitation as discussed above followed by active
baseline subtraction.
f
BW+BLIA = Bandwidth limitation followed by the boxcar averager plus
lock-in amplifier.

20
more complicated schemes. No correction for the total number of
laser pulses per second has been made. In the BLSP scheme and the
CONV method, 6000 pulses per second pass through the flame and are
detected. In the ABS and BLIA experiments, there are only 3000
pulses passing through and being detected in the flame each second.
The remaining 3000 pulses were blocked by the chopper and the noises
detected in laser enhanced fluorescence and ionization were
subtracted out.
The background subtraction methods (ABS and BLIA) provide an
additional advantage over the BLSP scheme and the CONV method, namely
the removal of low frequency changes in the laser conditions. The
CVL operates in a continuous flow mode with a constant addition of
neon and a constant removal of neon and a small amount of copper
vapor. Conditions within the laser cavity are changing at a very
slow rate (relative to the 6 kHz repetition rate) due to changes in
the neon pressure, partial pressure of the copper vapor, and position
of the electrical arc within the laser tube. These changing
conditions result in small changes in the dye laser power output but,
more importantly, changes in the magnitude of the radio-frequency
signal detected within the boxcar gate. No correction for dye laser
power fluctuations could be obtained, since the fluctuations were in
the source prior to modulation. Correction for flame and analyte
background flicker was accomplished in both the ABS and BLIA methods.
The effect of bandwidth limited signal processing (BLSP) on
fluorescence signals is demonstrated in Figure 2-6. The fluorescence
signals in Figure 2-6 prior to bandwidth limitation demonstrate the

FLUORESCENCE PHOTOCURRENT (nA)
21
Figure 2-6. Bandwidth Limitation Effects

22
high frequency noise which is the limiting noise source for this type
of laser. The temporal effect of bandwidth limitation on
fluorescence signals is also shown in Figure 2-6.
The BLIA results show a marked improvement over CONV results in
all cases. The BLIA results are felt to be slightly better than the
ABS results because a true phase-sensitive detection method was
employed in this scheme. The ABS method used a gated RC filter to
add capacitively signals of alternating polarity to remove background
and was susceptible to capacitor leakage, noise added by the polarity
switching amplifier, and signal fluctuation when a low number of
samples is averaged.
The experiments with active baseline subtraction (ABS and BLIA)
provide some unique opportunities for signal manipulation due to the
extremely high repetition rate of CVL. At the 6 kHz repetition rate
used, signals obtained are well above the low frequency flicker noise
region of the flame (or a plasma) and analyte background flicker.
Additionally based on laser repetition rate, beam diameter, and flame
gas flow rate, it is possible to irradiate each atom present within
the flame with 3 to 10 laser pulses of moderate intensity as the
atoms pass through the flame volume. Indeed, the high repetition
rate of the CVL should make it possible to detect virtually every
atom passing through a flame (or any plasma).
For comparison purposes, results obtained using our excimer
laser (Lumonics model TE-861) are included for laser enhanced
ionization. This laser is capable of providing peak energies of up
to 3 mJ per pulse of fundamental power from the dye laser much higher

23
than the CVL system. Typical energies obtained at 25 Hz repetition
rate were in the range of -80-250 pJ per pulse of frequency doubled
energy in a bandwidth of 0.0015 nm. The inferior performance of the
two methods employing background correction (BLIA and ABS) should be
noted for results obtained using the excimer laser. These results
may be explained in one of two ways: diminished performance of our
lock-in amplifier at the 25 Hz repetition rate (where a larger amount
of flame background flicker and analyte flicker is present); and/or
lower correlation of the interfering noise from the excimer laser
compared to the copper vapor laser. Both effects are felt to
contribute to some extent. At 25 Hz, a much larger flicker component
is present than at the 6 kHz CVL repetition rate. The low frequency
analyte and background flicker component at the sodium wavelength
588.9 nm is shown in Figure 2-7. These signals were measured with
only the flame on and no laser present. Signals were measured using
a cross channel spectrum analyzer (Wavetek, model 5890B) and
represent the total signal present across the frequency range
shown. Several trends are apparent from this figure. Flame
background flicker noises are small and become very small above
approximately 1.0 kHz. Analyte flicker is much higher at low
frequency and decreases at higher frequency. The much higher flicker
noise of the analyte can be attributed to nebulizer noise while the
higher overall signal magnitude is due to analyte emission.
The other contribution to flicker noise is the pulse-to-pulse
fluctuation of the laser. The lower correlation of the pulse-to-
pulse noise from the excimer laser is felt to be a limiting factor in

I'-»
-o
Figure 2-7. Noise Power Spectra at 588.9 nm
i\)
-tr

25
the improvements obtained with the excimer laser. The excimer
discharge voltage, -32,000 V, is less easily regulated than the
7,000 V used in the copper vapor laser. Oscilloscope comparisons of
the noise from the two lasers confirmed the much higher noise
fluctuations for the excimer laser. No correction for laser noise
could be obtained unless the noise component was present on
successive laser pulses.
The two noise correction methods (BLIA and ABS) were combined
with the noise reduction method, bandwidth limitation (BW) to
determine the individual contributions to noise reduction, and
signal-to-noise enhancement. It was found that the combination of
these techniques results in minimal improvement beyond that obtained
with bandwidth limitation alone. This indicates that the major
improvement is due to bandwidth limitation and thus the major noise
source is RF interference from the laser system.
Conclusions
The methods presented are shown to provide a significant
increase in the detection power for LAFS and LEIS. For active
baseline subtraction, improvements of up to 6 times were obtained
while with the combined bandwidth limitation and boxcar plus lock-in
amplifier (BW+BLIA) improvements of up to 40 times were obtained.
While these improvements may be possible for other laser systems, it
is to be emphasized that many of these methods rely on a certain
stability in the noise levels associated with a given laser system.
Application of these correction methods to a poorly correlated noise

26
source may yield little or no improvement in the detection power (see
excimer laser results). A more highly correlated noise source should
yield correspondingly better results. Additionally, modulation of a
pulsed laser and subsequent loss of one-half of the laser pulses may
be more harmful than the gain in detection power allowed by
subtraction of any noises.

CHAPTER 3
ESTIMATION OF ABSOLUTE NUMBER DENSITIES
General Curve of Growth Introduction and Evaluation
A general overview of methods for determination of the absolute
number density of a species is presented in Chapter 1. In this
chapter, general expressions and a computer program are presented for
evaluation of the fluorescence curve of growth and the absolute
number density determination. The computer program for these
calculations was written in FORTRAN-77 and was approximately 500
lines long. FORTRAN-77 was chosen for the programming language as a
compromise of speed, flexibility, and scientific compatability.
The computer program for evaluation of the absolute number
density calculates the fluorescence intensity vs the concentration of
the species of interest. A log-log plot of these terms is referred
to as a curve of growth (COG). The expression for right angle
fluorescence (diagrammed in Figure 3“1) is shown in Figure 3-2. The
expression for fluorescence may be divided into several parts: a
primary absorption term, a self-absorption term, and a term for the
optical collection efficiency. (The prefilter and postfilter terms
are considered separately below.) The primary absorption term is
derived from the Beer-Lambert law and can be used for an absorption
curve of growth in conjunction with an optical collection efficiency
terra. The primary absorption term is responsible for some of the
27

28
POSTFILTER
REGION
Figure 3“1• Diagram for Right Angle Fluorescence

= F Foa-ü- AhAj?ALT« Y fo - e kW ir%xs L)dk
4tt u2m m pVnkl_A*D J
Optical collection term Self-absorption term
aX.
Jex(I -e'k(v)LEx*XEsx )dX
Primary absorption term
C 5
F = /' -EXP [-k(X)L e-^s ( 14* )] / ' - EXP[~ k(X)ET^lLH d X
[T A A lif A A
T
J I- EXP[â– 
k(X)
Et s
JdX
P = /l-EXP[-kiXU(h|£-°)]dX-J^I- EXp[-k(X)5l|^]dX
P° -» -CO
♦ oo
/I- EXp[-k(X)i]dX
— oo
Figure 3-2. Expression for Right Angle Fluorescence
l\)
vO

30
curvature in a curve of growth at higher number density. The source
irradiance becomes increasingly absorbed at high number densities
until the entire source irradiance is absorbed at extremely high
number densities. The self-absorption term is a dimensionless factor
accounting for reabsorption of fluorescence photons, within the
excitation volume, as they traverse the atom reservoir. The self¬
absorption term also contributes to the curvature of the curve of
growth and continues to increase with increasing number density.
This term may or may not be important depending on whether resonance
or direct-line fluorescence is measured. The remaining term to
account for the optical collection efficiency includes Tg, the
transmittance of the collection optics; m^ and m^, magnifications of
the length and height dimensions of the source on the atom cell; and
n, the refractive index of the medium (to account for the change of
solid angle of collection due to medium to air transfer of
radiation). The term AhAJtAL is used to give the observed radiant
fluorescence flux, A<)>.
Shown in Figure 3-1 (with expressions in Figure 3~2) are regions
for prefiltering of the excitation source and postfiltering of the
fluorescence radiation. A prefilter region is one in which the
analyte of interest is present and is illuminated by the excitation
beam but the resulting fluorescence is not viewed by the detector. A
postfilter region is one in which the analyte of interest is present
but the region is not illuminated by the excitation source. These
terms become important in some analytical situations where it may not
be possible to avoid prefiltering and/or postfiltering.

31
Some simplifying considerations used in the development and
evaluation of the expressions are as follows:
(i)a single atomic transition is considered for the atomic
emission and absorption methods while results are
included for both direct-line and resonance fluorescence;
(ii)for the absorption and fluorescence cases, the excitation
beam is of rectangular cross section (i, x H) and is
spatially, as well as temporally, homogeneous;
(iii)the atom reservoir consists of a uniform ground state
number density distribution at a uniform temperature in
the absence of the excitation beam;
(iv)the absorption and fluorescence spectral line profiles
may be described by a Voigt function;
(v)no restrictions are made as to source intensity, but it
should be noted that saturation of a transition by an
apparent line source may result in saturation broadening
of the spectral excitation profile until the source no
longer may be considered effectively a line source. The
validity and applicability of many of these
3 ii
considerations are discussed by Zeegers et al.
Definitions of all terms used in the fluorescence expression
(and other equations used in this text) are included in Appendix A.
The computer program used for evaluation of the fluorescence
expressions is included in Appendix B.
In this research, no simplifying assumptions were made other
than those noted above. Assumptions of line or continuum source

32
excitation would greatly simplify the equations and calculations
involved, but the much more difficult case of an intermediate source
is considered here. The shapes of curves for line or continuum
excitation have been studied thoroughly.-^ Jl A more complete
development of the curve of growth equation is given in these
sources.
The program for curve of growth calculation uses some
approximations to enable the calculation to be performed. The first
of these approximations is the substitution of a large polynomial
approximation for the Voigt profile. The Voigt profile is the
spectral convolution of a Doppler profile with added collisional
broadening and is used in calculating the atomic absorption
profile k(v) where
k(v) = kQV(a,v)
and
V(a,v) = - j
7T J
exp(~y )dy
2 2
a +(v-y)
The Voigt integral cannot be solved in closed form and a substitution
proposed by Hui et al.^® is used. This approximation is extremely
accurate (one part in 10^) and evaluation is fast with no loss in
overall accuracy of the COG. The limiting accuracy of the COG is
determined by the accuracy of the integration limits used in the
evaluation of the other integrals of the fluorescence expression and
the accuracy of the experimental parameters used. The other major
approximation involved in the COG calculation is in the evaluation of
the primary, self-absorption, prefilter, and postfilter integrals.

33
The integrals should be evaluated from minus infinity to infinity.
Obviously, this integration is not possible and a tolerance for the
convergence of the integral must be chosen. In most cases, a
convergence tolerance of a maximum of 0.001 percent of the value of
interest was used. In some cases where a tighter convergence was
desired, an even smaller tolerance was used, although a greater
accuracy was not generally available.
Calculated Curves of Growth
The general COG in atomic spectroscopy is described by a linear
low concentration (or low number density) region and a noticeable
curvature at higher number densities. The degree of curvature and
the final slope of the COG at high number densities depends on the
source spectral width and the atomic parameters used in evaluation of
the fluorescence intensity expression. The curves of growth for line
and continuum sources are presented in Figures 3-3 and 3-i+,
respectively. These curves are shown for several a values. The a
value or a-parameter is a measure of the ratios of the collisional
width to the Doppler width:
AX,
a = /In 2{—r—)
axd
The collisional width, AX , is largely dependent upon the mass and
number of collisional species present and the temperature of the
atoms. The Doppler width, AX^, depends upon the mass and temperature

LOG REL. FLUORESCENCE
Figure 3-3
Curves of Growth for Line Source Excitation

LOG REL. FLUORESCENCE
LOG NUMBER DENSITY
Figure 3-4. Curves of Growth for Continuum Source Excitation
LO
U1

36
of the atom. The expression for AAD is presented below with
expressions for collisional broadening widths presented later.
AAd = 4-irX/C /2 RT In 2/M .
The curves presented for line and continuum sources agree well
with the other literature and experimental results presented
previously. The abscissa in all curves is shown in relative units
since we are not concerned with the absolute signal magnitude but
rather the shape of the COG. Here, we are more concerned with the
intermediate case of a pseudocontinuum source, i.e., a laser.
The spatial line widths of dye lasers (measured as the full
width at one-half maximum (FWHM)) typically are on the order of -0.01
to 0.05 nm when only a grating is used as a tuning element. Atomic
spectroscopy line widths in analytical flames vary from about
0.0005 nm to 0.02 nm.^ Thus, the laser will vary from approximately
equal to, to approximately 100 times the line width of the atom of
interest. This can be considered a pseudocontinuum source for most
applications. The curves of growth for pseudocontinuum sources of
equal laser and atom line atomic width and a laser which is 10 times
the atomic absorption profile (FWHM) are shown in Figure 3~5.
Curves of growth are shown for prefilter and postfilter effects
in the next series of figures. These curves are presented for an a-
parameter value of 1.0, which is used as an average value of
40-41
approximately 40 elements in an air-acetylene flame. Shown in
Figures 3_6 and 3“7 are prefilter effects for mild, medium, and

LOG REL. FLUORESCENCE
LOG NUMBER DENSITY
Curves of Growth for Two Pseudocontinuum Sources
Figure 3~5.

0.0
Figure 3-
O.OI 0.1 I 10 100
LOG ( k0L )
Curves of Growth for Mild, Medium, and Severe Prefiltering--Line Source, Dark = prefilter
region

LOG REL FLUORESCENCE
Curves of Growth for Mild, Medium, and Severe Prefiltering--Continuum Source, Dark
prefilter region

40
severe prefiltering for line and continuum sources, respectively.
The equivalent curves of growth for line and continuum sources are
shown for postfiltering in Figures 3-8 and 3-9, respectively.
The COGs for all prefilter and postfilter calculations are shown
with log (kQL) as the abscissa. This is used, instead of the log
number density, to partially compensate for the reduced absorption
pathlength involved. The relationship between the peak absorption
coefficient (for pure Doppler broadening), k , and the number
density, n, is presented below.
/4irln2 e2X2nf
*o 5^-
me AXD
This relationship is developed in Mitchell and Zemansky1 ® and is
based on the absorption oscillator strength, f, and the central
wavelength, Xq, and Doppler width, AAp, (FWHM) of the atom of
interest (other terras are defined in Appendix A).
General trends which may be noted for these curves are
relatively simple. Prefiltering of the source results in an increase
in the rate of curvature for line and continuum sources. This
increase in curvature is accompanied by a general decrease in the
signal strength. This is due primarily to the decreased fluorescence
volume observed. The postfilter effect results in a general decrease
in the overall fluorescence intensity. A more complete discussion of
the prefilter and postfilter effects is included in a later section
on collision broadening and saturation effects. From the figures and

LOG REL FLUORESCENCE
Curves of Growth for Mild, Medium, and Severe Postfiltering Line Source, Dark
postfilter region

gure 3~
Curves of Growth for Mild, Medium, and Severe Postfiltering Continuum Source, Dark
postfilter region
-Cr
ro

43
discussion presented above, it can be seen that it is important to
minimize prefilter and postfilter effects (to achieve higher signal-
to-noise ratios and maximum linear dynamic range). It is generally
possible to do so by simple modification of the optical design.
Experimental Verification of Curves of Growth
Figure 3—10 shows the calculated curve of growth for sodium
resonance fluorescence in an air-acetylene flame. The experimental
data points are included on this curve also. The curve of growth was
calculated for a flame of 2500 K using a Gaussian source of 0.03 nm
(FWHM) and a damping parameter of 1.0. These represent the line
width of the copper vapor pumped dye laser and resonable parameters
for Na in an air-acetylene flame.^ The fit of the curve of growth
to the experimental points is obtained by transposition of the COG
until this curve overlaps the experimental points. The overlap of
these curves gives a direct relationship between the concentration of
the species introduced and the absolute number density present in the
flame.
The experimental curve of growth was obtained using the same
experimental arrangement as described and diagrammed earlier in
Chapter 2 (Figure 2-2). Aqueous solutions of sodium were prepared by
dissolving sodium chloride in deionized water. Solutions below
1000 mg/L were prepared by dilution, while solutions above 1000 mg/L
were prepared directly by weighing.
The fluorescence results are in good agreement with a calculated
estimate of the absolute number density. This estimate is based on

log rel. fluorescence
No RESONANCE FLUORESCENCE
PPM, FLUORESCENCE
I I 10 100 1000 10000 100000
Figure 3“1 0.
Calculated and Experimental Curves of Growth for Na

45
the solution concentration, the solution uptake rate, the
nebulization and atomization efficiencies, and the flow rate and
thermal expansion of flame gases. These terms are grouped to form a
single term, 0, which should be within the range shown in Figure
3-10.
To confirm these experimental results and to extend the curve of
growth calculations to direct-line fluorescence, the same experiments
were performed using another laser system. Poor doubling
efficiencies with the copper vapor laser system (see Chapter 2) make
the wavelength used for Pb fluorescence difficult to obtain, at least
at a laser intensity level which will provide enough sensitivity for
these studies. The COG for lead with 283-3 nm excitation and
resonance (283-3 nm) and direct-line (405-7 nm) fluorescence were
calculated and measured experimentally. The curves were calculated
for a 0.019 nm source spectral line width (FWHM) with a-parameters of
1.0 (283-3 nm) and 1.5 (405.7 nm). These are estimates based on
calculations given by Parsons et al. since no known measured values
are available. The 0.019 nm source line width is obtained from our
Nd:YAG laser pumped frequency doubled dye laser (Quantel, model
YG580). The Pb experimental results were measured by Dr. Benjamin
Smith. His measurements were performed using an experimental setup
similar to that previously described (Figure 2-2). In this
experiment, two curves must be transposed to match with two sets of
experimental curves. The two experimental curves, shown in Figure
3-11, were found to give reasonable agreement between themselves and
are within one order of magnitude agreement with the estimated number

LOG NUMBER DENSITY (cm3)
Figure 3—11. Calculated and Experimental Curves of Growth for Pb
-fcr
cr*

47
density (from the nebulization and atomization efficiencies, etc.).
The agreement of these curves with the experimental values
demonstrates the accuracy and applicability of these methods.
Saturation and Collisional Effects
A further extension of the curve of growth calculations involves
the inclusion of some of the lesser noted effects in atomic
fluorescence spectroscopy. The expression for fluorescence presented
previously (Figure 3-2) and merely be extended here. The expressions
for saturation effects are included in Figure 3-2 but were not
previously discussed. The collisional broadening terms have not been
discussed yet and will be presented here.
Collisional broadening effects may be considered from two
separate aspects: collisional broadening due to analyte collisions
with analyte termed self-broadening or resonance broadening and
collisional broadening due to collisions with other species. The
first will be referred to as self-broadening and the second will be
termed collisional broadening. The general expression for
lip
collisional broadening is presented in Figure 3-12. The theory of
collisional broadening was originally developed by Lorentz and later
extended by Lenz and Weisskopf. A complete development is presented
42 10
by Breene and Mitchell and Zemansky. The general expression for
collisional broadening simplifies when only resonance broadening is
considered. The summation of all atomic and molecular concentrations
simplifies to involve only the analyte concentration. The mass

48
COLLISIONAL BROADENING
aAc =
?2 r
2IN X TTC
-1 '2.
27TkT nÍT7 + TT )
A Mn Mn •
RESONANCE BROADENING
2 2
v . 2NX (T
A ar ttc
[4 TT k T N AC-¿r)]
Figure 3-12. Expression for Collisional Broadening

49
terra, 1/m^ + 1/m , simplifies to involve only the mass of the analyte
(see Figure 3-12). Worst case collisional broadening effects will be
seen for situations of small atomic mass, long wavelength
transitions, and large collisional cross sections.
The self-broadening effects for two elemental cases have been
included in Table 3~1. The elements evaluated represent the two
extremes encountered in atomic spectroscopy: a high mass, low
wavelength case and a low mass, high wavelength case. The
collisional cross sections used here represent the range of values
40
measured. From curve of growth calculations and the results in
Table 3~1 , it can be seen that no significant differences due to
self-broadening are expected for experimentally realizable
situations. No appreciable changes are seen in the a-parameter until
number densities of greater than 101^ atoms/cra^ are approached.
Based on previous measurements in Chapter 2, this corresponds to an
initial atomic concentration of greater than 100 M and an unrealistic
Q
aspirated concentration of 10° parts-per-million. Additionally, at
high number densities where self-broadening effects should become
apparent, the primary absorption term will typically have reached
absorption saturation and any change in the a-parameter and line
shape will not affect the absorption of radiation. Very weak
transitions (kQ/n < 10-1'’) may show some small self-broadening
effects at high number densities since the absorption terms are very
small and allow considerable transmittance at high number densities.

50
Table 3~1• Broadening Effects on the a-Parameter for Self-Broadening
Best Case
(Low Collisional Broadening)
Worst Case
(High Collisional Broadening)
Pb
Li
X = 283.3 nra
X = 670.8 nm
T = 2500 K
T = 2500 K
mA = 207.2 g/Mol
mA = 6.9A g/Mol
n(cm 3)
a2
a-Param
(A2)
eters
n(em-3)
a2
(A2)
30
100
30
100
1 01 6
1 .0007
1 .0023
1 01 6
1 .0035
1 .0097
101?
1.0068
1.0227
101?
1.0350
1 .0970
1018
1 .0680
1 .2270
1 01 8
1 .350
1 .9700

51
Collisional broadening effects due to an added matrix species,
termed simply collisional broadening effects, are included also. The
collisional broadening effects are somewhat different than the self¬
broadening effect in that these effects are seen over the entire
range of analyte concentrations and are due to some constant
concentration of an added species. The effect of collisional
broadening may or may not be noticeable depending on the spectral
width of the source used and the spectral width of the atomic
profile. For line sources, the wings of the absorption profile
(described by the a-parameter) will not matter since absorption
occurs only at the line center. As the source width increases, the
wings of the absorption profile may affect the curve of growth. At
low atomic concentrations, however, the a-parameter does not affect
the curve of growth (see Figures 3-3 to 3-9).
One of the few situations where collisional broadening may need
to be considered is the technique of graphite furnace atomic
spectroscopy. In many instances, a high concentration of species is
added to serve as a matrix modifier. The added species will be
vaporized in a small volume of the graphite furnace and result in a
high atomic concentration.4^
üii
In a recent publication, Schleramer and Welz used an aliquot of
Pd and Mg for matrix modification, resulting in an atomic
1 C 1 <7
concentration of 10 0 to 10 in a typical tube furnace atomizer.
Collisional broadening effects become barely noticeable at this
level. The curves of growth for Li with added Mg matrix modifier are
shown in Figure 3-13- These curves are calculated in the same manner

LOG REL. FLUORESCENCE
Figure 3-13. Curves of Growth with Added Collisional Broadening
U1
r\j

53
as before (Figures 3-3 to 3-5) but with the added term for
collisional broadening. Each of the relationships discussed
previously, a-parameter dependence and source width dependence, are
shown in this figure. The expected source dependence is seen in the
curves of this figure. The differences calculated for the
pseudocontinuum (AX = 0.19 A) and the line source
s
(AXq = 0.005 A) are too small to be seen here but occur in a region
somewhat smaller than that seen in the other pseudocontinuum
sources. These results represent an extreme case, not likely to be
seen in conventional flame spectroscopy and only infrequently seen in
nonflame spectroscopies. Generally, collisional and self-broadening
effects will have a very small influence, and in fact may not be
apparent at all.
Saturation (optical) effects are dependent on the source
spectral irradiance and do not depend upon the analyte of interest,
at least not in the same manner as the collisional broadening does.
As seen in the expression for right-angle fluorescence (Figure 3~2),
an increase of the source spectral irradiance E(A), above the
saturation spectral irradiance E (A), will result in an effective
decrease in the absorption coefficient. This decrease will occur at
all wavelengths at which the source irradiance is above the
saturation spectral irradiance. Prefilter terms are affected in the
same manner as the primary absorption term. The self-absorption term
may or may not be affected by saturation, depending upon whether the
fluorescence wavelength is within the saturating source spectral
profile. A postfilter region will not be affected by a saturating

54
irradiance since the source does not pass through the postfilter
region. A complete discussion of saturation effects and practical
4 5
measurement of saturation curves is given by Alkemade.
Curves of growth for several source intensities are presented in
Figures 3~14 and 3—15 for line and continuum sources, respectively.
The general trend seen is an increase in the linear regions of these
curves. No change of shape in the COG is seen. Curves of growth
were also calculated for the same Pb transitions previously measured
(283-3 nm resonance fluorescence and 405.7 nm direct-line
fluorescence). These curves are shown in Figure 3~16 and are
calculated for the same 0.019 nm source spectral width (FWHM) used
previously. As seen in this figure, it is possible to extend the
resonance fluorescence COG using a saturating source to equal linear
dynamic range and even beyond that of the direct-line fluorescence
case.
The source intensity at which equality occurs for the direct-
line and resonance fluorescence curves can be shown to be related to
the fractional populations of the two lower levels used. The
equations relating the source intensity necessary for equality of the
direct-line and resonance curves are shown in Figure 3"17• These are
derived from the initial curve of growth equation. As seen in Figure
3-16, the equality for the resonance and direct-line curves occurs at
a source irradiance approximately 100 times greater than the
saturation irradiance for the lead transitions. This agrees with the
ratios of the populations of the two levels 98.6% to 1.05?, a ratio
of approximately 100 to 1. This is calculated using the continuum

LOG REL. FLUORESCENCE
Figure 3-14. Curves of Growth for Several Intensities for a Line Source

LOG REL. FLUORESCENCE
gure 3-15. Curves of Growth for Several Intensities for a Continuum Source
cr>

Figure 3-16. Curves of Growth for Pb Direct-Line ( ) and Resonance Fluorescence (
Source Intensities
) for Several

58
GENERAL CASE
- , fv ,
f\ - e k(v) e^e^1- dv _ J y"| - e _k(,/ d \/ k0
LINE SOURCE CASE
^VÍa^J-pf-gs F,
k'0V(a' vO ^2
CONTINUUM SOURCE CASE
Ev
^
S u' k(i/) F2
Figure 3-17. Equations for Curves of Growth Equalities for
Saturating Irradiances

59
source approximation since the source spectral width (FWHM) is
roughly 25 times larger than atom profile and as such closely
approximates a continuum.
The prefilter and postfilter effects with a saturating laser
source (0.019 nm) are shown in Figures 3_18 and 3-19. A 0.5 cm
prefilter length and a 0.5 cm postfilter length were used in the
corresponding curves. A 0.5 cm absorption path and a 0.5 cm
fluorescence path length are used in all curves here. In both cases,
it is possible to extend the calculated curve of growth to some
extent. Curves with prefiltering show the greatest extension. This
is due to removal of prefilter effects by the saturating laser and an
extension of the primary absorption linear region. The constant
difference between the curves of growth with and without prefilter is
due to the decreased source irradiance passing through the detected
volume. This corresponds to an additional primary absorption term
with no additional fluorescence. For the postfilter curves of growth
in Figure 3~19, the difference between the curves with and without
postfilter is seen to increase with increasing source irradiance.
The increasing difference between curves is due to the increase in
linearity of the curve which does not have postfiltering while the
curve with postfilter does not have the same increase in linearity.
If the source intensity is increased drastically, the overall curve
of growth will become limited by the curvature due to the postfilter
region. In no manner is it possible to remove postfilter effects by
using a more intense source.

LOG REL. FLUORESCENCE
LOG NUMBER DENSITY
Figure 3-1
) and Direct-Line ( )
8. Prefilter Removal by a Saturating Source
Resonance (
CT>
O

LOG NUMBER DENSITY
Figure 3-19. Postfilter Effects with Saturation Effects Added, Resonance (
) and Direct-Line ( )

62
Conclusions
A general purpose computer program has been presented and is
investigated for applications to determine the absolute number
density of an atomic species. Various aspects of this curve of
growth program have been investigated including prefilter and
postfilter effects, saturation using various sources and collisional
broadening due to resonance broadening and broadening due to
quenchers.
It was found that collisional broadening, in all forms, should
present very minimal effects if they are seen at all. Prefilter and
postfilter regions are shown to cause a premature curvature of the
curve of growth. Prefilter and postfilter effects may be accounted
for and an absolute number density obtained if the exact geometry is
known. The prefilter effect may be removed to a large degree by a
saturating excitation source. The use of a saturating source may not
be desirable, as it adds another complication to the curve of growth
measurement and calculation of the absolute number density. Much of
the work of this chapter has been theoretical in nature and some
would be difficult to verify experimentally. Nevertheless, the
experimental results obtained for two of the simpler cases discussed
in this chapter show extremely good agreement between the
calculations and the experimentally measured results.

CHAPTER 4
SPATIAL DISTRIBUTIONS OF ATOMS
IN INHOMOGENEOUS FLAMES
Concentration Modulated Absorption Spectroscopy
A technique for increased sensitivity in atomic absorption
spectroscopy with pulsed lasers was recently introduced by Langley et
al.^ The technique was employed by the authors to yield absolute
number densities for atoms in flames and for molecules in
solutions. This experiment is based on a pump-probe arrangement of
optical beams and relies on a linear relationship between source
intensity and fraction absorbed. This technique, along with two
other related techniques using pulsed lasers in atomic spectroscopy,
are applied for the determination of spatial distributions of atoms
in inhomogeneous flames and are described in this chapter.
Many of the techniques presented in Chapter 1 are not applicable
to spatial profiling. This is due to the moderate to low sensitivity
of those techniques and the small region, and thus the small atomic
concentration, probed by these methods. The combination of these two
limitations and the limitations presented by pulse-to-pulse
instabilities and the spectral bandwidth of some pulsed dye lasers
make many techniques unsuitable for spatial diagnostics.
Concentration modulated absorption spectroscopy (COMAS) was
¿I
initially applied by Langley et al. for absolute number density
determination. The development of the COMAS expression follows from
63

64
the interaction of two focused Gaussian beams and is based to a large
47
degree on the Beer-Lambert absorption expressions. 1 The beams are
assumed to be derived from the same pulsed laser source with a
spatially Gaussian electric field amplitude. From the Beer-Lambert
absorption expression, the change in the number of laser photons in
an incremental length dz will be
di = anAi dz
P P
where ip is the number of laser photons, A is the equilibrium
fractional population between levels 1 and 2, and o is the absorption
cross section. This fractional population is equal to the difference
of levels 1 and 2 divided by the total analyte concentration
A = (N1 - N^/n. Based upon expressions for focused Gaussian beams
and the interaction volume for these beams, an expression for the
modulation of the probe signal is obtained:
2
di = (2iro nA/A)i i
pr p pr
Obtaining the fractional change in the number of probe photons or
gain gives
di /i
pr pr
= G = (2iro nA/A)i
Substituting the original Beer-Lambert law ln(1/T) = anA and

65
2
substituting for o gives G = (2iri / (nAA)) (ln( 1/T)) . A plot of gain
2
times concentration vs In 1/T will give straight-line plot, the
slope of which is the proportionality factor in the relationship
between concentration and analyte number density C = xNA where C is
the analyte concentration. Thus, this experiment was viewed as a way
of obtaining an absolute number density which required only measuring
readily available analytical signals in a relatively simple optical
arrangement. Some optical restrictions were applied in the
development of the expressions which limit the applicability of these
equations.
The development of the COMAS expressions is not questioned here,
li £
and in fact extremely good results are obtained by Langley et al.
for molecular solution-phase analyses, but the assumption of a true
Beer-Lambert relationship for excitation of atoms in flames with a
relatively broad spectral width dye laser is not valid. The Beer-
Lambert relationship works well for molecular analyses since the
molecular absorption band is typically much wider spectrally than the
line width of the dye laser excitation source used. The results for
molecular analyses by Langley et al.2^ were easily checked assuming
1 5
no solution phase decomposition and were found to be 7.4x10
molecules/cm^ experimentally for a solution concentration of 6.0x101'*
molecules/cm^. When considering the atomic experiments, the dye
laser spectral bandwidth is much wider than the atomic line width.
Using the expression in Figure 3~2 for the primary absorption term of
the fluorescence curve of growth, a difference in signals of 5 times
(for the low-density linear region) is calculated for the signals

66
expected with a narrow line source and the signal obtained with a
source width 10 times greater than the Doppler width of the atom.
This will result in a direct error of the absolute number density
determined by this factor. A correction for this error may be
obtained by evaluating the overlap of the two profiles expected and a
correction factor obtained.
The concentration modulated method involves a pump-probe
arrangement of optical beams as shown in Figure 4-1. In this
arrangement the probe is approximately 5% of total dye laser
output. This method was originally investigated for Na in an air-
acetylene flame. The same copper vapor laser and dye laser system
presented in Chapter 2 were used for this application. The bandwidth
limitation approach was used for the absorption measurements.
An initial investigation of the method presented by Langley et
46
al. was carried out. This arrangement of counterpropagating co-
linear beams involves modulation of one of the two beams. The COMAS
signal is obtained by subtraction of the absorption signal with and
without the pump beam present. Subtraction of the two signals is
obtained using the active baseline subtraction method employed in
Chapter 2. The absorption signals were detected by a fast photodiode
(United Detector Technology, model PIN-1ODP) and connected to a
current-to-voltage converter (Thorn EMI Gencom Inc., model A1).
These signals were connected directly to the gated integrator and
46
boxcar averager. The COMAS experiment conducted by Langley et al.
was confirmed and a limit of detection of 1 part-per-million (ppm)

67
Figure 4-1. Concentration Modulated Absorption Experimental Setup:
Co-linear Beams

68
was found for an interaction volume of approximately 1 cm^. This
agrees closely with previous results found. The COMAS technique
relies on the linear interaction of the two beams and allows direct
determination of absolute number densities. Better limits of
detection are obtainable with simple experiments using hollow cathode
48
lamps.
An extension of COMAS was attempted to determine spatial
concentration profiles. The arrangement of optical beams was
modified to form a pair of crossing beams (Figure 4-2). A scanning
motor (General Scanning Inc., model G3) with a mirror attached and a
pair of lenses was added to scan a focused probe beam through the
flame. The scanner in conjunction with the first lens serves to
position the probe beam within the flame. With the first lens
positioned at a distance of one focal length from the scanning
mirror, beams from the scanning mirror pass through the flame
perpendicular to the pump beam. The second lens served to turn the
probe beam and redirect the beams to the photodiode detector. The
scanning is controlled by the computer interface (Stanford Research
Systems, model 24S) and allowed rapid collection of the entire
spatial profile of the flame. For these experiments the computer
controlled the scanning of optical beams and collection of all
data. For increased spatial resolution several optical elements were
added. A small pinhole, diameter 0.5 mm, was used in the optical
path of the probe beam to limit the beam size. Additionally, a lens
was used in the optical path of the pump beam to produce a smaller
beam. Relatively long focal length lenses (200 mm, 2" dia.) were

69
Figure 4-2. Experimental Setup for Spatial Diagnostics for COMAS

70
used in all cases. These lenses provide a relatively uniform beam
¿10
waist over the width of the flame. 7 The volume probed by the
interaction of these two beams is approximately 0.1 mm^ (0.4 mm
diameter probe by 0.5 mm diameter pump). This interaction volume is
50
calculated using the method of Jackson et al. and relies on the
overlap of two spatially Gaussian beams. The beams were measured and
closely approximate a Gaussian spatial profile. Additionally, the
spectral line profile of a dye laser has been measured here by
scanning the dye laser across an atomic transition and elsewhere by
this and other-' methods and closely approximates a Gaussian
spectral profile. The optical arrangement used allows scanning while
maintaining the same optical axes and beam size. Horizontal beam
placement was found to be extremely important for a uniform
interaction region. The results obtained for scanning the flame
produced by an inhomogeneous surface burner*^ are shown in Figure
4-3. The surface burner used in these experiments was provided
courtesy of Dr. R.J. Krupa and the construction is shown in Figure
4-4. The COMAS results are shown for an initial solution
concentration of approximately 5000 ppm Na. The COMAS results are
shown for a single region located above one row of analyte
capillaries in both the parallel and diagonal burner orientations.
The measurements were taken in a region approximately 6 mm above the
surface of the burner head. This corresponded to the top of the
flame cones-^ for gas flow rates of 1.6 1/m acetylene, 2.2 1/m
oxygen, and 8.3 1/m nitrogen with this type of surface burner. Based
on a measured nebulization efficiency of 0.14 and an estimated

71
5000 ug/mL Na
PERPENDICULAR
BURNER
:::::
“ : o_
5000 ug/mL Na
DIAGONAL
BURNER
CONCENTRATION MODULATED
ABSORPTION
Figure 4-3. Results for Perpendicular and Parallel Burners for COMAS

i0.0.0.0.0
•:!!!:
rWVW
[oZoZoZojx
• OXIDANT HOLES (0.03l" día.)
O FUEL CAPILLARIES (0. 042" l.d., 0.058"o.d.)
Figure 4-4. Design of Surface Burner Used

73
atomization efficiency^11 of 0.6, the analytical region of 0.1 mm^
calculated for the COMAS crossed beam experiments should have -10 J
atoms present during each laser pulse. The relative insensitivity of
this technique is seen in the high concentration of analyte necessary
to obtain any analytical signal. This low sensitivity is due to
several experimental problems. The relatively large spectral
bandwidth of the dye laser (0.3 A) is approximately 6 times greater
than the Doppler-width (FWHM) of Na in an air-acetylene flame with an
estimated temperature of 2500°C. This large bandwidth results in
unabsorbed source irradiation reaching the detector and increased
background shot noise. The peak-to-peak fluctuation of the dye laser
intensity also limits the minimum absorption measurable.Radio¬
frequency noise is also thought to contribute to some degree (see
Chapter 2). At any rate, COMAS has been found to be too insensitive
for applications in spatial profiling.
The minimum detectable signal may also be calculated based upon
the spectral bandwidth of the laser, the parameters for Na in an air-
acetylene flame, the region probed in the interaction volume and the
S6
minimum detectable absorbance which may be typically measured. The
same curve of growth program used in Chapter 3 is used for this
calculation with only the primary absorption term calculated (see
Figure 3”2). The minimal concentration detectable based on this
calculation and a minimum detectable absorbance was found to be
approximately 1000 ppm Na. This does not consider the effect of
pulse-to-pulse fluctuations of the laser or any shot noise or radio¬
frequency (RF) noise added by the laser.

74
Results were also obtained for a simple atomic absorption
experiment with only the relatively weak probe beam and optical
scanning system (no pump beam). Results for the parallel and
diagonal burner configuration are shown in Figure 4-5. Again a
solution concentration of 10 ppm Na was used for these experiments.
The increased sensitivity of this technique is seen immediately since
these results are for an initial atomic concentration 50 times lower
than the COMAS results. This increase in sensitivity is accomplished
at a loss in spatial information since the analytical signal is
obtained for the entire absorption path length (1 cm or greater for
the burner used) and are not obtained for a much smaller interaction
region. The interaction volume is approximately 1.3 mm^ (0.4 mm
diameter by 10 mm (or greater in the diagonal burner case)),
approximately 13 times greater than in the COMAS case. This accounts
for a significant portion of the increased sensitivity. The spatial
information obtainable with this system is still somewhat
remarkable. Since the laser beam is coherent and has an extremely
low degree of divergence, good spatial resolution may be obtained.
An attempt was made to perform the same series of experiments with a
hollow cathode lamp. The hollow cathode lamp, with its much narrower
spectral bandwidth (compared to the dye laser), should have had a
higher sensitivity. No suitable optical arrangement could be found
to give a tightly focused beam within the flame volume. With the
high repetition rate of this laser and the fast optical beam scanning
method employed, entire spatial profiles of the atom cell may be
obtained in a very short period of time.

75
1 O ug/mL Na
PERPENDICULAR
BURNER
••••••
::::::
10 ug/tnL Na
DIAGONAL
BURNER
•c#
•c*o«
•c*o*o*
•o«o«o«c«
»c*c«o»o*o«
•o*o«o«o»
•c«c«o«
•o«o«
•o*
SIMPLE ABSORPTION
Figure 4-5. Simple Absorption Results for Perpendicular and Parallel
Burners

76
In an attempt to decrease the spectral bandwidth of the dye
laser, an etalon was added within the oscillator cavity of the dye
S7
laser. The decreased spectral bandwidth would have resulted in an
increased sensitivity in all absorption results. The etalon was
found to reduce the oscillator cavity gains to such an extent that
lasing would not occur. The dye laser was then switched to an
oscillator-only configuration with 100% of the copper vapor laser
output used to pump a single dye laser cell. The etalon was found to
S 8
increase cavity losses and decrease the stability of the dye laser
(in terms of pulse-to-pulse fluctuations) and gave only a slight
reduction in the spectral bandwidth (0.3 A to 0.18 A). The only
slight reduction in the spectral bandwidth of the dye laser is due to
the relatively poor quality of the etalon used.
Concentration modulated absorption spectroscopy was initially
investigated by us as a means of performing spatial profiling and
determining absolute number densities. The low sensitivity of the
technique prevented this application; in addition, complications far
beyond those expected were present. As a result of these
complications, other methods were investigated for increased
sensitivity in spatial profiling applications.
Two-Wavelength Laser Enhanced Ionization
and Fluorescence: Spatial Distributions
In several recent articles,1^“^0 the use iaser excited
fluorescence for spatial distribution measurement has been studied

77
using a planar laser beam and a 2-dimensional image detector. The
spatial resolution element for this technique was found to be =1 mm
with concentrations between 1 and 20 ppm being used for spatial
profiling results. In other studies, spatial profiles have been
k q 60
measured in inductively coupled plasmas and in flames with a lens
and image detector or lenses and monochromators used to obtain the
spatial profiles. One advantage of image detection has been pointed
out in a recent publication where spatial information was obtained in
¿' -i
an entire plane within the flame volume on a single laser pulse.
Other studies have included probing of local electrical fields in
flames using LEIS which involved measurement of the atomic line
£ p
widths. The electrically-broadened atomic line width is a measure
of the strength of the local electrical field. Several of these
methods are applied later in this chapter for similar applications
with some modifications.
Two of the most sensitive methods for atomic species
determinations in flames are laser excited atomic fluorescence
spectrometry (LEAFS) and laser enhanced ionization spectrometry
(LEIS). The sensitivity of these techniques has been discussed
previously in Chapters 2 and 3 and the discussion is extended here.
Recent results presented by Magnusson et al.^’^ anc¡ Axrier et al.^
in graphite furnaces and flames, respectively, show limits of
detection which approach 1 part-per-trillion (ppt) for single
wavelength excitation. For two-wavelength excitation in a graphite
furnace, results approaching 1 pg absolute limits of detection have
been obtained. Two-wavelength excitation was found to give an

78
ionization signal enhancement of up to 6000 times over single
All
wavelength excitation. With the high temperatures present in an
inductively coupled plasma (ICP) and the hazards of arcing of the
high power radio-frequency field, an optical method of detection of
laser induced ionization was presented by Turk et al. This is
instead of an electrode placed within the atom cell. As yet, no one
has applied two-wavelength LEIS and LEAFS for spatial measurements.
Experimental Setup and Discussion
The experimental arrangement of optical beams for two-wavelength
LEIS and LEAFS for spatial diagnostics is shown in Figure 4-6. This
is an extension of the technique presented previously for COMAS with
an additional wavelength of excitation and fluorescence and
ionization detection instead of an absorption detection method. The
same copper vapor laser used earlier was also used here. The beam
from this laser was used to pump two dye lasers. The dye lasers used
C O
(Hansch-design) were pumped in the oscillator-only configuration.
That is, only one flowing dye cell in each dye laser was excited by
the copper vapor beam. This was found to be a more efficient method
for pumping the dye lasers since the power per pulse of the copper
vapor laser is relatively low. Approximately 40? of the copper vapor
beam was used to pump the first dye laser with the remainder used in
the second. A fast photodiode placed at the end of the second dye
laser received the small fraction of the copper vapor beam which was
not reflected by the 99? reflector in the second dye laser. The
signal from this photodiode was used to trigger the boxcar detection

Figure 4-6
Experimental Setup for Two-Wavelength LEIS and LAFS

80
electronics and the oscilloscope. The same signal, used to trigger
the boxcars, was divided by multiples of 10 to trigger the computer
interface. This division was necessary in many instances since the
computer interface was only capable of transferring data to the
computer at a rate of 960 samples per second. The necessity of
division was dependent on the number of data points taken since the
computer interface contained a buffer memory which accumulated
untransferred data points. Scans across the burner in one direction
were obtained using the rotating mirror. To obtain the total profile
across the burner, the burner itself was translated using a
micrometer stage, with profiles obtained at several positions using
the rotating mirror. An initial attempt to obtain profiles by
positioning the beam at different places within the flame volume
was investigated. Voltage field variances and voltage field
collection effects were found which complicated all spatial results
obtained. With a water-cooled bias electrode (-1500 V) placed
directly in the flame, spatial profiles were obtained. When the
laser beam was positioned directly under and parallel to the
electrode, signals were found to reach a maximum. Translation of the
laser beam, while maintaining the same burner and electrode position,
to a horizontal distance of approximately 0.5 cm from directly under
the electrode, but still at approximately the same atomic
concentration (see COMAS and absorption results), the analyte signal
was found to drop by more than one order of magnitude. This is due
to field collection effects and voltage field differences. Other
field collection effects have been investigated by other

31
authors.^ To minimize voltage field effects, the burner head was
translated and was found to give no appreciable voltage field effects
C O
when measured by the method of Axner and Berglind. The placement
of a large electrode within the flame volume does disturb the
laminarity and shape of the flame and may result in somewhat
distorted profiles. For these reasons, fluorescence was investigated
as an alternate means of detection.
In the course of these investigations, several important factors
were discovered. To obtain a uniform interaction volume and an equal
sensitivity over the entire optical path probed, the two optical
beams had to be horizontal and intersect or remain a fixed distance
apart, over the entire distance probed. Additionally, the burner and
electrode also had to be horizontal to maintain a constant distance
between the laser beam and the electrode and to reduce voltage field
effects.
A typical profile obtained in a single scan is shown in Figure
4-7. This profile was obtained approximately 7 mm above the surface
of the burner at the tips of the flame cones. This profile was
obtained for an initial atomic concentration of 1 ppm Na with
excitation at 588.9 nm and 568.8 nm. From the signal-to-noise ratio
apparent in this figure, the atomic concentration produced by 1 ppm
Na is well above the limit of detection. These results were obtained
for a 1000 point scan, each point representing an average of 10 laser
shots (for reasons discussed earlier). With the high repetition rate
of the laser and the data acquisition system, these results required
only 1.67 s to obtain. Thus, the speed, ease, and high capacity for

83
information gathering is shown. The slightly irregular profile
obtained for this case is due to a slight flow constriction in one of
the analyte capillaries. This only served to illustrate the
analytical usefulness of this technique, as it was possible to
correct this flow restriction in later studies. Two arrangements of
optical beams were investigated for these studies. These
arrangements involved swapping the positions of the two laser
beams. Each arrangement had its own advantages. When the first
wavelength laser (X^) was positioned directly under the electrode, a
large pulsed ionization current was created by X1. The ionization
current created by X2 occurs only in the interaction region. Thus
the current produced by X-| had to be subtracted from that due to
X2+X-| to obtain the interaction volume. The current due to X-¡
produced a background shot noise which could not be corrected for.
An additional consideration was the thermal population of the lowest
excited state. Thermally excited atoms are excited by X2 and
collected.
In the first configuration with X-| directly under the electrode,
the collection of thermally excited and optically excited (X2) atoms
was limited by the electric field decrease with distance away from
the electrode. In the second configuration with X2 directly under
the electrode, there was a lower background current produced due to
X-| but a higher current which could not be corrected for due to
thermal excitation of atoms. The best analytical scheme would be
that one which gives the lowest background signals. It would seem

REL, IONIZATION SIGNAL
82
(mm)
Figure 4-7.
Spatial Profile Result for LEIS

84
that as long as A-| is of higher energy than kT, the first scheme
would be best but this is complicated by the electric field effects
and the intensities of the lasers employed. For these experiments,
the first configuration was found to give better signal-to-noise
ratio. The contributions of the thermal, electric field, and optical
arrangement effects to signals obtained, corrections obtainable and
noises for each ionization process are summarized in Table 4-1.
The best arrangement for subtraction of signals due to
ionization out3ide the interaction region would involve modulation of
both A1 and A2. A modulation scheme which would give equivalent
results for both optical arrangements would be to sequentially excite
the analyte with , then A2, and then the combined beams, A-|+A2.
The analytical signal would be obtained by subtracting the single
wavelength signals from the combined signals A-j + A2. Such a
modulation scheme would involve custom design of the optical choppers
or the use of acousto-optic deflectors and electronic circuits to
form the modulation pulses. Demodulation of the signals obtained
would be complicated also and would require a custom design lock-in
amplifier. Considering the complications expected from the
discussion above and the minimal improvement expected, this method of
correction was not attempted. This method of modulation would also
use three pump laser pulses for each data point and shift the
effective data taking rate to 2 kHz for this laser system. For any
pulsed laser system other than copper vapor (or mode-locked cavity-
dumped lasers), this modulation scheme would result in a shift in the
data taking rate back into a flicker noise dominated region (i.e.,

85
Table 4-1. Ionization Processes, Optical Arrangements, Signals and
Noises for Two-Wavelength Laser Enhanced Ionization
Spectroscopy
PROCESSES
1
2
3
4
SIGNALS
Nonspecific thermal ionization of atoms and molecules
Ionization due to X-| and thermal processes
Ionization due to thermal processes and X2
Ionization due to X-|+X2 in interaction region
OPTICAL ARRANGEMENTS
1
X1 directly beneath electrode, X2 perpendicular
2
X2 directly beneath electrode, X-j perpendicular
PROCESSES
1
2
3
4
CORRECTION
D.C. signals
Modulation
Modulation
Analytical
METHODS
blocked by
of X2
of X1
signal. No
boxcar input
correction
capacitor.
necessary.
NOISES
Shot noise
Signal magni¬
Signal magni¬
Noises and
due to D.C.
tude and
tude and
signal are
signal. Equi¬
noise greater
noise greater
the same
valent noises
for arrange¬
for arrange¬
for both
for both
ment 1. Shot
ment 2 but
optical
optical
noise uncor¬
smaller than
arrangements.
arrangements.
rectable .
that due to
Magnitude
process 2 in
will vary for
arrangement
different
1 (due to
elements.
lower popu¬
Analyte &
lation of
background
fluctuations
excited state)
•
corrected for
by modulating
*1 on A2.

86
<100 Hz). The only laser system which comes close to the high-
repetition rate needed is a 500 Hz excimer system, with an effective
data taking rate of approximately 160 Hz. This is still within the
flicker noise region for a typical analytical flame.
Similar results were obtained for two-wavelength laser excited
atomic fluorescence spectrometry (LEAFS). A lower sensitivity is
obtained for this technique compared to LEIS due to several
reasons. The detector in this instance is placed a significant
distance from the region excited by the two beams. Since the
fluorescence is isotropic, this detector will only receive a small
fraction of the fluorescence emitted. Using two-wavelength
excitation, atoms are excited to levels within several kT of the
ionization continuum. Losses of these atoms to the ionization
continuum are likely and make the fluorescence from the second
excited level to the first excited level less sensitive. Monitoring
the fluorescence from the first excited level to the ground state is
possible and the change in this fluorescence, when ^2 i3 added> is
6Q
referred to as fluorescence dip spectroscopy. Monitoring
fluorescence from the first excited state to the ground state is
somewhat complicated by shot noise from analyte emission and noise
due to analyte and laser flicker. Fluorescence from the second
excited state to the first excited state is limited by shot noise of
the scatter of ^ and losses to the ionization continuum. For
monitoring fluorescence, the best method would primarily depend upon
the proximity of the second excited level to the ionization
continuum. For these results, the fluorescence from the second level

87
70
to the first was found to yield the best results. Oraenetto et al.'
have investigated two-wavelength fluorescence of ions produced in an
inductively coupled plasma. The results approach low part-per-
trillion levels and benefit from the lower losses to the ionization
continuum (the doubly ionized species is especially difficult to form
in most instances) compared to the two-wavelength atomic fluorescence
case.
A typical result for two-wavelength excitation and fluorescence
detection is shown in Figure 4-8 for 10 ppm Na at a height of
approximately 4 mm in the same burner used previously. The increased
separation of the spatial distribution for each capillary within the
burner are evident in this figure. Approximately the same
representation was obtained at a height of 7 mm as shown for
ionization results in Figure 4-7. These two figures demonstrate that
this burner has very good laminarity low in the flame which
deteriorates rapidly. The fluorescence was monitored at The
presence of fluorescence was confirmed (versus scatter) by detuning
^2• One major advantage of the fluorescence method is that it is not
necessary to place an electrode within the flame volume, which makes
it possible to detect signals without disturbing the flame. This
also makes the fluorescence method more applicable, especially in
situations where it is not possible to place an electrode within the
cell volume.
As a direct result of these techniques, it was possible to
spatially map the entire combustion zone. By translating the burner
and obtaining successive profiles across the burner, it was possible

REL. FLUORESCENCE INTENSITY
88
Figure 4-8. Spatial Profile Result for LAFS

89
to map a horizontal plane within the flame volume. If multiple
horizontal planes are obtained a four-dimensional structure may be
developed, three spatial dimensions and a concentration dimension. A
single horizontal plane located at approximately the top of the flame
cones is shown in Figure 4-9 using ionization detection for a 1 ppm
solution of Na.
Conclusions
Single-wavelength and two-wavelength methods for obtaining
spatial information within inhomogeneous flames have been
presented. While the single wavelength concentration-modulated
absorption results were not particularly sensitive or useful, the
two-wavelength LEIS and LEAFS results demonstrated exceptional
spatial resolution and very good sensitivity. The spatial results
shown here represent the first application of two-wavelength LEIS and
LAFS to this area. The high-repetitive rate laser used and an
optical method of scanning the beams through the flame were shown to
allow rapid determination of spatial profiles of analyte
concentrations. While the applications here are limited in scope, it
is felt that these techniques will find many applications.

90
Figure 4-9. Three-Dimensional Spatial Profile for LEIS

CHAPTER 5
FINAL COMMENTS AND FURTHER STUDIES
Several new applications for laser atomic fluorescence and laser
enhanced ionization spectroscopies have been presented. Several
electrical signal processing methods which were especially applicable
to a copper vapor laser system were presented. These results show
that it is possible to obtain a significant improvement in detection
power by electrical bandwidth limitation and subtraction of slowly
varying noises. Further studies which could provide some degree of
detection power improvement include more bandwidth limitation to
extend the preliminary results obtained here and optimization of the
photomultiplier tube voltage to increases with the sensitivity. The
noise of the photomultipler also increased voltage but since this
noise from the photomultiplier tube was not the limiting noise
source, improvement of the detection power should be possible. This
work is currently being studied at the National Bureau of Standards
by Epstein et al.^3
A general-purpose computer program was written and evaluated for
determination of absolute number densities of atomic species in
flames via fluorescence. This method was found to agree well with
other previously developed methods within one order of magnitude for
both resonance and direct-line fluorescence. Computer-based
91

92
investigations were conducted into the effects of collisions with
other atoms or molecules and the effect of saturation by a high
intensity laser source. Studies into the development of a general
purpose program for similar investigations using LEIS should be one
of the first methods available for absolute number densities.
Several new and novel methods were developed and evaluated for
obtaining spatial information within flames. A recently introduced
technique for absolute number density termed concentration modulated
absorption spectroscopy, COMAS, was investigated for spatial
profiling applications. Absorption measurements obtained with a
pulsed fluctuating relatively broadband dye laser were found to be
too insensitive for any analytical applicability even at high analyte
concentrations (5000 ppm). Other studies involving ionization and
fluorescence were shown to be quite sensitive with high resolution
spatial profiles being obtained for both methods. Other studies by
the J.D. Winefordner research group and others using these spatial
profiling results with two-wavelength excitation are varied. Two-
wavelength excitation has been applied in many instances to measure
ionization processes and wavelength dependencies, but only in a gross
spatial manner with no consideration given to inhomogeneous
profiles. These two-wavelength spatial results may be used to
measure lifetimes of species in very localized regions, to measure
concentrations of analyte and flame radicals in small zones, and to
determine mixing rates of close lying excited states in small regions
by the use of a delayed second laser. Many other results which have
only been obtained for an average value within the entire atom cell

93
can now be determined accurately and rapidly with extremely good
sensitivity. Further studies which should be well-suited to these
techniques include investigation of different types of flames and
burners, especially measuring the laminarity of flow within various
flame types.

APPENDIX A
DEFINITION OF TERMS AND SYMBOLS
ABS
BLIA
BW or BLSQ
COMAS
FWHM
f'
HV
Ah
k
Active Baseline Subtraction Method
Boxcar Plus Lock-In Amplifier Method
Bandwidth Limited Signal Processing
Concentration Modulated Absorption Spectroscopy-
full width of an analytical signal measured at the half
maximum
a-parameter for absorption transition, dimensionless
a-parameter for fluorescence transition, dimensionless
beam dump
speed of light ms 1
charge of an electron, esu
-2 -1 -1
source spectral irradiance, Jm s Hz
-2 -1 -1
saturation spectral irradiance, Jm s Hz
fast photodiode
oscillator strength of absorption transition,
dimensionless
oscillator strength of fluorescence transition,
dimensionless
high voltage
height of volume element detected, cm
Boltzmann constant, J°K 1
94

95
k(X)
1
Al
L
AL
lpo
Lpr
AX,
AX,
AX.
m
ma
mb
mH’mL
N
A
n
$
a
PM
PR
R
REF
T
2 2 -1
/4ln2 e XNf/(mc AXp) = peak absorption coefficient, cm
k V(a,v)
o
fluorescence path length, cm
width of volume element detected, cm
absorption path length, cm
depth of volume element detected, cm
fluorescence postfilter length, cm
absorption prefilter length, cm
collisional halfwidth, cm
Doppler halfwidth, cm
source spectral halfwidth, cm
mirror
mass of an electron, g
mass of the analyte, g
mass of the majority quenching species present, g
magnification in the height and length dimensions induced
by the source collection optics
Avagadro's number, mol-1
analyte number density, atoms/cm^
-1 -2
fluorescence radiance detected, Js cm
solid angle of fluorescence collected, sr
photomultiplier tube
partial reflector
universal gas constant, J°K 1mol 1
reference pulse
temperature of flame cell, °K

96
v
V(a,v)
v
transmission of optics used for fluorescence detection,
dimensionless
index of refraction of flame, dimensionless
Voigt profile factor, dimensionless
41n2(A-Aq)/AXd, dimensionless
central frequency of absorption transition, s-1
central frequency of fluorescence transition, s 1
spectral luminescence power efficiency, dimensionless

APPENDIX B
COMPUTER PROGRAM LISTING FOR CALCULATION OF
FLUORESCENCE CURVES OF GROWTH INCLUDING SATURATION,
COLLISIONAL AND PREFILTER AND POSTFILTER EFFECTS
$STORAGE:2
$NOFLOATCALLS
C CALCULATION OF FLUORESCENCE CURVE OF GROWTH
C USES HUIS APPROXIMATION OF VOIGT FUNCTION
C IN COMPLEX NUMBER ROUTINE FOR PREFILTER AND POSTFILTER IN
C DIRECT OR RESONANCE FLUORESCENCE COG
C PROGRAM WAS ORIGINALLY WRITTEN TO CALCULATE ONLY RESONANCE CASES
C THEN LATER EXPANDED TO INCLUDE DIRECT-LINE FLUORESCENCE
C
C FOR DEFINITION OF TERMS AND GEOMETRIES SEE SMITH, B.W., RUTLEDGE, M.J.
C AND WINEFORDNER, J.D. APPLIED SPECTROSCOPY 1987
IMPLICIT REAL*8 (Q-R)
COMMON /VOIGT/ DOPPLR,APARAM,SOURCE,ABSP,CONC1,FPATH,APATH
COMMON /DUMMY/ FRAC1,ABS2,FRAC2,APARM2,D0PPL2,APOST,APRE
COMMON Q(7),R(8)
C OPEN DATA STORATE ARRAYS
REAL ALPHA(70), BETA(70), GAMMA(70), NPDEC
REAL DELTA(70),ZETA(70),THETA(70),LAMBDA(70)
REAL C0NC1,LOW,SIZ,ITMAX,KS1,K1.LIMIT
REAL KLINE,K02
C OPEN FILES FOR DATA STORAGE "2" IS FOR ALL DATA, "3" IS FOR ONLY
C FLUORESCENCE VALUES AND CAN BE USED FOR PLOTTING PURPOSES
OPEN (2,FILE»1 ',STATUS»'NEW')
OPEN (3,FILE»' '.STATUS»'NEW')
DATA LOW,ITMAX/O.0,40.0/
WRITE(*,3)
3 FORMAT( ' CALC OF COG FOR A SINGLE LINE N PTS/DEC)
WRITE(*,10)
10 FORMAT(' INPUT A PARAMETER FOR EXC (REAL)')
READ(*,150)APARAM
WRITE(*,20)
20 FORMAT(' INPUT DOPPLER LINE WIDTH FOR EXC. (A,REAL)')
READ(*,150)DOPPLR
WRITE(*,30)
30 FORMAT(' INPUT SOURCE PROFILE (A,REAL)')
READ(*,150)SOURCE
97

98
C SET INTEGRATION LIMIT
LIMIT=5.0*S0URCE
WRITE(*,40)
TO 5 x SOURCE WIDTH
40
45
50
55
FORMAT(
READ(*,200)KLINE
WRITE(*
FORMAT(
READ(*,1
WRITE(*
FORMAT(
WRITE(*
58 FORMAT(
READ(*,
WRITE(*
60 FORMAT(
READ(*,1
WRITE(*
62 FORMAT(
READ(*,
WRITE(*
65 FORMATC
READ(*,150)LO
WRITE(*,70)
C INTEGRATION LIMIT
C 10**-6 IS USUALLY
INPUT ABS Ko/N FIRST LEVEL (EXPONENTIAL)')
45)
INPUT ABS PATH LENGTH (CM,REAL)')
50)APATH
50)
INPUT SOURCE IRRADIANCE W/CM/CM/NM/NM/S (EXP)')
READ(*,200)ESRC
WRITE(*,55)
FORMATC INPUT SATURATION SPECTRAL IRRADIANCE (EXPONENTIAL)')
READ(*,200)ESAT
KLINE=KLINE*ESAT/(ESRC+ESAT)
58)
TEMPERATURE OF ATOM CELL K (REAL)')
INPUT
50)TEM
60)
INPUT MASS OF ATOM G/MOLE (REAL)')
50) AM
62)
INPUT C0LLI3I0MAL CROSS SECTION ANGSTROMS (REAL)')
50)SIG
65)
INPUT ABSORPTION WAVELENGTH ANGSTROMS (REAL)')
IS A CONVERGENCE TOLERANCE LIMIT FOR INTEGRATION
A GOOD START. THIS VALUE IS INCREMENTED LATER TO
C PRODUCE
C
70
CONVERGENCE WITHIN 0.1(5-0.001?
LIMIT (EXPONENTIAL)
FORMATC INPUT TOLERANCE
READ(*,200)TOL1
WRITE(*,80)
80 FORMAT(' INPUT NUMBER OF
READ(*,150)NPDEC
150 FORMAT( F1 0.4)
200 F0RMAT(E12.4)
WRITE(*,210)
POINTS PER DECADE (REAL)
210 FORMAT(
READ(*,900)K02
220
230
240
WRITE(*
FORMAT(
WRITE(*
FORMAT(
WRITE(*
FORMAT(
INPUT Ko/N SECOND LEVEL (REAL)’)
220)
INPUT
FRACTIONAL POP.OF FIRST LEVEL (REAL)')
READ(*,900)FRAC 1
230)
INPUT
FRACTIONAL POP OF LAST LEVEL (REAL)')
READ(*,900)FRAC2
240)
INPUT
a-PARAMETER OF SECOND TRANSITION (REAL)')
READ(*,900)APARM2

99
WRITE(*,250)
250 FORMAT(' INPUT ABS. PREFILTER LENGTH (CM,REAL)')
READ(*,900)APRE
WRITE(*,260)
260 FORMAT(' INPUT POST FILTER LENGTH (CM,REAL)')
READ(*,900)APOST
WRITER, 350)
350 FORMAT(' INPUT DOPPLER LINE WIDTH OF SECOND TRANSITION (A,REAL)')
READ(*,900)D0PPL2
DLC=APARM2*D0PPL2*1.20112
900 F0RMAT(F10.4)
ABSP=KLINE*APATH
ABS2=K02* APATH
WRITE(*,1902)
C CALCULATION IS DONE OVER THE RANGE FROM LOWER TO HIGHER ABSOLUTE NUMBER
C DENSITY WITH N POINTS SPACED EVENTLY ON A LOGARITHMIC SCALE
C
1902 FORMAT(' INPUT UPPER NUMBER DENSITY (EXPONENTIAL)')
READ(*,1906)CHIGH
WRITE(*,1905)
1905 FORMAT(' INPUT LOWER NUMBER DENSITY (EXPONENTIAL)')
READ(*,190 6)CONG1
1906 FORMAT(El 2.4)
V=L0G10(C0NC1)
C WRITE PARAMETERS TO FILE
WRITE(2,1910)APARAM,APARM2
WRITE(2,1920)D0PPLR,D0PPL2
WRITE(2,1925)APATH,FPATH
WRITE(2,1930)SOURCE
WRITE(2,1940)ABSP,ABS2
WRITE(2,1950)LIMIT,T0L1
WRITE(2,1960)FRAC1,FRAC2
WRITE(2,1970)APRE,APOST
1910 FORMAT(1 APARAMETER FOR EXC AND FLUOR =',F10.4,F10.4)
1920 FORMAT('DOPPLER LINEWIDTH FOR EXC AND FLUOR=',F12.6,F12.6)
1925 FORMAT(' ABS AND FLUOR PATH LENGTH^',F10.4,F10.4)
1930 FORMATC SOURCE HALFWIDTH= ', FI 0.4)
1940 FORMATC ABS FACTOR KoL/N FOR EXC AND FLUOR ' , E1 2. 4, E1 2. 4)
1950 FORMATC INTEGR LIMIT',F12.4, 'INTEGRATION TOLERANCE',E12.4)
1960 FORMATC FRAC. POP OF LEVELS 1 AND 2 ' , F1 2. 6, F1 2.6)
1970 FORMATC PRE AND POSTFILTER LENGTHS' ,F1 2.6,F1 2.6)
WRITE(2,2000)
2000 FORMAT(5X,'ALPHA',5X,'SLF ABS',2X,'PRFLTR',4X,'PSTFLTR',5X,
'LOG 1 PHI',5X,'NUM DENS')
C CALCULATION OF FRACTION ABSORBED USING REAL FUNCTION FAB AND
C HUI’S APPROXIMATION FOR VOIGT PROFILE
UP=LIMIT
DLUP=50.0*D0PPLR
C DIRECT LINE INTEGRATION OCCURS OVER 50 TIMES THE DOPPLER WIDTH NOT
C ASSOCIATED WITH RESONANCE INTEGRATION LIMITS. THIS WORKS WELL IF
C APARAMETER DOES NOT GET TOO LARGE OTHERWISE THE INTEGRATION LIMIT

C MUST BE INCREASED.
K1=0.797884561
N=1
PI=3.1415926
C=2.997E10
2060 DNT=0.0
ALPHA(0)=0.0
VAR1=(1.0449E9*TEM/AM)**0.5
VAR2=L0*L0*SIG/PI/C*VAR1*2*1.0E-16
DLCP=DLC+CONC1*VAR2*1.0E-8
APARAM=0.83255*DLCP/D0PPLR
APARM2=(DLC2+CONC1*VAR2*1.OE-8)*0.83255/D0PPL2
WRITE(*,2065)APHARM,APARM2
2065 FORMAT(' '),f10.4)
1=0
C NORMALIZE FOR GAUSSIAN SOURCE
KS1=2.35482/SOURCE
C IF PREVIOUS RESULT CA. 1.0 SKIP CALCULATION:CHECK FOR OPTICAL
C SATURATION
IF (ALPHA(N-1).GT.0.9995) THEN
ALPHA(N)=1.0
GOTO 2510
ENDIF
1=0
FRST=1
X=LOW
Y=FAB(X)
DNT=DNT+Y
X=UP
Y=FAB(X)
TEMP=DNT+Y
C SIMPSONS RULE INTEGRATION
2080 1=1+1
2160 Z=2**(real(i))
SIZ=(UP-LOW)/Z
X=SIZ+LOW
Y=FAB(X)
DNT=DNT+4*Y
DARG=LOW
2190 DARG=DARG+2*SIZ
IF (DARG.LT.UP) GOTO 2340
DNT=SIZ*DNT/3
IF (FRST.EQ.O) GOTO 2290
FRST=0
GOTO 2310
2290 IF (I.LE.3) GOTO 2310
IF (ABS(DNTOLD-DNT).GE.T0L1) GOTO 2310
GOTO 2500
2310 DNTOLD=DNT
DNT=TEMP
GOTO 2080

1 01
2340 X=DARG
Y=FAB(X)
DNT=DNT+2*Y
X=DARG+SIZ
Y=FAB(X)
DNT=DNT+4*Y
GOTO 2190
2500 ALPHA(N)=1-DNT*K1*KS1
C CALCULATION OF SELF ABSORPTION FACTOR IN THIS AND NEXT PART
C FACTOR = BETA/GAMMA
2510 DNT=0.0
1=0
FRST=1.0
X=LOW
Y=BPART(X)
DNT=DNT+Y
X=DLUP
Y=BPART(X)
TEMP=DNT+Y
DNT=DNT+Y
2580 1=1+1
2660 Z=2**(REAL(I))
SIZ=(DLUP-LOW)/Z
X=SIZ+LOW
Y=BPART(X)
DNT=DNT+4*Y
DARG=LOW
2690 DARG=DARG+2*SIZ
IF (DARG.LT.DLUP) GOTO 2840
DNT=SIZ*DNT/3
IF (FRST.EQ.O) GOTO 2790
FRST=0
GOTO 2810
2790 IF (I.LE.3) GOTO 2810
T=DNTOLD-DNT
IF (ABS(T).GE.T0L1) GOTO 2810
GOTO 3000
2810 DNTOLD=DNT
DNT=TEMP
GOTO 2580
2840 X=DARG
Y=BPART(X)
DNT=DNT+2*Y
X=DARG+SIZ
Y=BPART(X)
DNT=DNT+4*Y
GOTO 2690
3000 BETA(N)=DNT
3510 DNT=0.0
1=0
FRST=1.0

1 02
X=L0W
Y=CPART(X)
DNT=DNT+Y
X=DLUP
Y=CPART(X)
TEMP=DNT+Y
DNT=DNT+Y
3580 1=1+1
3660 Z=2**(REAL(I))
SIZ=(DLUP-L0W)/Z
X=SIZ+L0W
Y=CPART(X)
DNT=DNT+4*Y
DARG=LOW
3690 DARG=DARG+2*SIZ
IF (DARG.LT.DLUP) GOTO 3840
DNT=SIZ*DNT/3
IF (FRST.EQ.O) GOTO 3790
FRST=0
GOTO 2810
3790 IF (I.LE.3) GOTO 3810
T=DNTOLD-DNT
IF (ABS(T).GE.T0L1) GOTO 3810
GOTO 3990
3810 DNTOLD=DNT
DNT=TEMP
GOTO 3580
3840 X=DARG
Y=CPART(X)
DNT=DNT+2*Y
X=DARG+SIZ
Y=CPART(X)
DNT=DNT+4*Y
GOTO 3690
3990 GREEK=DNT
4000 GAMMA(N)=1.7527576*1.064467*DOPPL2*K02*CONC1*FRAC2*FPATH
4060 DNT=0.0
C PREFILTER TERM CALCULATION
1=0
FRST=1
X=LOW
Y=FPART(X)
DNT=DNT+Y
X=UP
Y=FPART(X)
TEMP=DNT+Y
DNT=DNT+Y
4080 1=1+1
4160 Z=2**(REAL(I))
SIZ=(UP-LOW)/Z
X=SIZ+LOW

Y=FPART(X)
DNT=DNT+4*Y
DARG=LOW
4190 DARG=DARG+2*SIZ
IF (DARG.LT.UP) GOTO 4340
DNT=SIZ*DNT/3
IF (FRST.EQ.O) GOTO 4290
FRST=0
GOTO 4310
4290 IF (I.LE.3) GOTO 4310
IF (ABS(DNTOLD-DNT).GE.T0L1) GOTO 4310
GOTO 4500
4310 DNTOLD=DNT
DNT=TEMP
GOTO 4080
4340 X=DARG
Y=FPART(X)
DNT=DNT+2*Y
X=DARG+SIZ
Y=FPART(X)
DNT=DNT+4*Y
GOTO 4190
4500 LAMBDA(N)=1-DNT*K1*KS1
4510 DNT=0.0
C POSTFILTER TERM CALCULATION
1=0
FRST=1
X=LOW
Y=DPART(X)
DNT=DNT+Y
X=DLUP
Y=DPART(X)
TEMP=DNT+Y
DNT=DNT+Y
4580 1=1+1
4660 Z=2**(real(i))
SIZ=(DLUP-LOW)/Z
X=SIZ+LOW
Y=DPART(X)
DNT=DNT+4*Y
DARG=LOW
4690 DARG=DARG+2*SIZ
IF (DARG.LT.DLUP) GOTO 4840
DNT=SIZ*DNT/3
IF (FRST.EQ.O) GOTO 4790
FRST=0
GOTO 4810
4790 IF (I.LE.3) GOTO 4810
IF (ABS(DNTOLD-DNT).GE.T0L1) GOTO 4810
GOTO 5000
4810 DNTOLD=DNT

DNT=TEMP
GOTO 4580
4840 X=DARG
Y=DPART(X)
DNT=DNT+2*Y
X=DARG+SIZ
Y=DPART(X)
DNT=DNT+4*Y
GOTO 4690
5000 DELTA(N)=DNT
5060 DNT=0.0
FRST=1
C PREFILTER TERM CALCULATION
X=LOW
Y=GPART(X)
DNT=DNT+Y
X=UP
Y=GPART(X)
TEMP=DNT+Y
DNT=DNT+Y
5080 1=1+1
5160 Z=2**(REAL(I))
SIZ=(UP-LOW)/Z
X=SIZ+LOW
Y=GPART(X)
DNT=DNT+4*Y
DARG=LOW
5190 DARG=DARG+2*SIZ
IF (DARG.LT.UP) GOTO 5340
DNT=SIZ*DNT/3
IF (FRST.EQ.O) GOTO 5290
FRST=0
GOTO 5310
5290 IF (I.LE.3) GOTO 5310
IF (ABS(DNTOLD-DNT).GE.T0L1) GOTO 5310
GOTO 5500
5310 DNTOLD=DNT
DNT=TEMP
GOTO 5080
5340 X=DARG
Y=GPART(X)
DNT=DNT+2*Y
X=DARG+SIZ
Y=GPART(X)
DNT=DNT+4*Y
GOTO 5190
5500 THETA(N)=1-DNT*K1*KS1
5510 DNT=0.0
C POSTFILTER TERM CALCULATION
1=0
FRST=1

X=LOW
Y=EPART(X)
DNT=DNT+Y
X=DLUP
Y=EPART(X)
TEMP=DNT+Y
DNT=DNT+Y
5580 1=1+1
5660 Z=2**(REAL(I))
SIZ=(DLUP-L0W)/Z
X=SIZ+L0W
Y=EPART(X)
DNT=DNT+4*Y
DARG=LOW
5690 DARG=DARG+2*SIZ
IF (DARG.LT.DLUP) GOTO 5840
DNT=SIZ*DNT/3
IF (FRST.EQ.O) GOTO 5790
FRST=0
GOTO 5810
5790 IF (I.LE.3) GOTO 5810
IF (ABS(DNTOLD-DNT).GE.T0L1) GOTO 5810
GOTO 6000
5810 DNTOLD=DNT
DNT=TEMP
GOTO 5580
5840 X=DARG
Y=EPART(X)
DNT=DNT+2*Y
X=DARG+SIZ
Y=EPART(X)
DNT=DNT+4*Y
GOTO 5690
6000 ZETA(N)=DNT
FP0=2.0*(DELTA(N)-ZETA(N))/GREEK
FPRE=(LAMBDA(N)-THETA(N))/ALPHA(N)
SLFABS=B ETA(N)/GAMMA(N)
6010 PHI=L0G10(ALPHA(N)*SLFABS*FPATH*APATH*FPRE*FPO)
C ALPHA=FRACTION ABSORBED, SLFABS=SELF ABSORPTION TERM, FPRE=PREFILTER
C TERM, FPOST=POSTFILTER TERM
WRITE(2,6100).ALPHA(N),SLFABS,FPRE,FPO,PHI,C0NC1
WRITE(3,6101)PHI
WRITE(*,6100)ALPHA(N).SLFABS,FPRE,FPO,PHI,C0NC1
6100 FORMAT(' ',F10.6,F10.6,FI 0.6,F10.6,E12.4,E12.4)
6101 F0RMAT(F12.4)
V=V+1.O/NPDEC
T0L=10.0**ANINT(L0G10(ALPHA(N))=3-0)
C TEST FOR INCREMENTATION OF TOLERANCE
IF (T0L.GT.T0L1) THEN
T0L1=TOL
ENDIF

o o
N=N + 1
C0NC1=10**(V)
C INCREMENT CONCENTRATION TO BE CALCULATED ON NEXT DATA PT.
IF (CONC1,GT.CHIGH) GOTO 6110
GOTO 2060
611 0 STOP
END
BLOCK DATA FOR HUI'S APPROXIMATION
BLOCK DATA
C COEFFICIENTS FOR EVALUATION OF VOIGT FUNCTION USING HUI'S APPROX.
IMPLICIT REAL*8 (Q-R)
COMMON Q(7),R(8)
DATA Q(1),R(1 )/122.6079317771 04326, 122.60793177387535/
DATA Q(2),R(2)/21 4.382388694706425, 352.730625110963558/
DATA Q(3),R(3)/181.928533092181549, 457.334478783897737/
DATA Q(4),R(4)/93.155580458138441, 348.703917719495792/
DATA Q(5),R(5)/30.1801421 96210589, 170.354001821 091472/
DATA Q(6),R(6)/5.912626209773153, 53-992906912940207/
DATA Q(7),R(7)/0.564189583562615, 10.479857114260399/
DATA R(8)/1.0/
END
REAL FUNCTION FAB(X)
IMPLICIT REAL*8 (Q-R)
C EVALUATION OF VOIGT FUNCTION FOR PRIMARY ABSORPTION
REAL*8 C,D
REAL KS2,KK,RESR
COMMON /VOIGT/DOPPLR,APARAM,SOURCE,ABSP,C0NC1,FPATH,APATH
COMMON /DUMMY/ FRAC1,ABS2,FRAC2,APARM2,D0PPL2,APOST,APRE
COMMON Q(7),R(8)
COMPLEX*16 F.BTM,TOP,RATIO
D=1.66511/D0PPLR*X
C=APARAM
F=DCMPLX(C,D)
TOP=(((((Q(7)*F+Q(6))*F+Q(5))*F+Q(4))*F+Q(3))*F+Q(2))*F+Q(1)
BTM=((((((F+R(7))*F+R(6))*F+R(5))*F+R(4))*F+R(3))*F+R(2))*F+R(1)
RATIO=TOM/BTM
RESR=REAL(RATIO)
KK=ABSP*C0NC1*FRAC1
KS2=5.5451 8/SOURCE/SOURCE
FACT0R=REAL(-1.0*(X*X*KS2/2)-KK*RESR)
IF (FACTOR.LT.-50.) THEN
FAB=0
ELSE
FAB=EXP(FACTOR)
ENDIF
RETURN
END
C
REAL FUNCTION BPART(X)
IMPLICIT REAL*8 (Q-R)

REAL*8 C,D
C EVALUATION OF VOIGT FUNCTION FOR SELF ABSORPTION TERM
REAL RESR
COMMON /VOIGT/DOPPLR, APARAM, SOURCE, ABSP,CONC1,FPATH,APATH
COMMON /DUMMY/ FRAC1,ABS2,FRAC2,APARM2,DOPPL2,APOST,APRE
COMMON Q(7),R(8)
COMPLEX*16 F,BTM,TOP,RATIO
D=1.66511/DOPPL2*X
C=APARM2
F=DCMPLX(C,D)
TOP=(((((Q(7)*F+Q(6))*F+Q(5))*F+Q(4))*F+Q(3))*F+Q(2))*F+Q(1)
BTM=((((((F+R(7))*F+R(6))*F+R(5))*F+R(4))*F+R(3))*F+R(2))*F+R(1)
RATIO=TOP/BTM
RESR=REAL(RATIO)
TEMPI=(CONC1*ABS2*M .772454)*RESR*FPATH/APATH*FRAC2)
IF (TEMPI.LT.-50.) THEN
BPART=2.0
ELSE
BPART=2*(1-EXP(TEMPI ))
ENDIF
RETURN
END
C
REAL FUNCTION CPART(X)
IMPLICIT REAL*8 (Q-R)
REAL*8 C,D
REAL RESR
COMMON /VOIGT/DOPPLR,APARAM,SOURCE,ABSP,CONC1,FPATH,APATH
COMMON Q(7),R(8)
COMPLEX*16 F,8TM,TOP,RATIO
D=2.0*SQRT(L0G(2.0))/DOPPLR*X
C=APARAM
F=DCMPLX(C,D)
TOP=(((((Q(7)*F+Q(6))*F+Q(5))*F+Q(4))*F+Q(3))*F+Q(2))*F+Q(1)
BTM=((((((F+R(7))*F+R(6))*F+R(5))*F+R(4))*F+R(3))*F+R(2))*F+R(1)
RATIO=TOP/BTM
RESR=REAL(RATIO)
IF (RESR.LT.1.OE-12) THEN
CPART=2.0
ELSE
CPART=2.0*(1.0-EXP(1.7724*CONC1*ABSP*RESR*FPATH/APATH*FRAC2))
ENDIF
RETURN
END
C
REAL FUNCTION DPART(X)
IMPLICIT REAL*8 (Q-R)
REAL*8 C,D
REAL KS2,KK,RESR
COMMON /VOIGT/DOPPLR,APARAM,SOURCE,ABSP,CONC1,FPATH,APATH
COMMON /DUMMY/ FRAC1,ABS2,FRAC2,APARM2,D0PPL2,APOST,APRE

108
COMMON Q(7),R(8)
COMPLEX*18 F,BTM,TOP,RATIO
D=1.66511/D0PPL2*X
C=APARM2
F=DCMPLX(C,D)
TOP=(((((Q(7)*F+Q(6))*F+Q(5))*F+Q(4))*F+Q(3))*F+Q(2))*F+Q(1)
BTM=((((((F+R(7))*F+R(6))*F+R(5))*F+R(4))*F+R(3))*F+R(2))*F+R(1)
RATIO=TOP/BTM
RESR=REAL(RATIO)
TEMPI=(CONC1*ABS2*(-1.772454)*RESR*FPATH/APATH)
TEMPI=TEMP1*FRAC2*(1+APOST/FPATH)
IF (TEMPI.LT.-50.) THEN
DPART=1.0
ELSE
DPART=(1-EXP(TEMPI))
ENDIF
RETURN
END
REAL FUNCTION EPART(X)
IMPLICIT REAL*8 (Q-R)
REAL*8 C,D
REAL KS2,KK,RESR
COMMON /VOIGT/DOPPLR,APARAM,SOURCE,ABSP,C0NC1,FPATH,APATH
COMMON /DUMMY/ FRAC1,ABS2,FRAC2,APARM2,D0PPL2,APOST,APRE
COMMON Q(7),R(8)
C0MPLEX*16 F.BTM,TOP.RATIO
D=1.66511/D0PPL2*X
C=APARM2
F=DCMPLX(C,D)
TOP=(((((Q(7)*F+Q(6))*F+Q(5))*F+Q(4))*F+Q(3))*F+Q(2))*F+Q(1)
BTM=((((((F+R(7))*F+R(6))*F+R(5))*F+R(4))*F+R(3))*F+R(2))*F+R(1)
RATIO=TOP/BTM
RESR=REAL(RATIO)
TEMPI=(-1.77245*C0NC1*ABS2*RESR*FPATH/APATH*FRAC2*AP0ST/FPATH)
IF (TEMPI.LT.-50.) THEN
EPART=1.0
ELSE
EPART=(1-EXP(TEMP1))
ENDIF
RETURN
END
REAL FUNCTION FPART(X)
IMPLICIT REAL*8 (Q-R)
REAL*8 C,D
REAL KS2,KK,RESR
COMMON /VOIGT/DOPPLR,APARAM,SOURCE,ABSP,C0NC1,FPATH,APATH
COMMON /DUMMY/ FRAC2,ABS2,FRAC2,APARM2,D0PPL2,APOST,APRE
COMMON Q(7),R(8)
COMPLEX*!6 F.BTM,TOP,RATIO

109
D=1.66511/D0PPLR*X
C=APARAM
F=DCMPLX(C,D)
TOP=(((((Q(7)*F+Q(6))*F+Q(5))*F+Q(4))*F+Q(3))*F+Q(2))*F+Q(1)
BTM=((((((F+R(7))*F+R(6))*F+R(5))*F+R(4))*F+R(3))*F+R(2))*F+R(1)
RATI0=T0P/BTM
RESR=REAL(RATIO)
KK=ABSP*C0NC1*FRAC1*( 1+APRE/APATH)
KS2=5.5451 8/SOURCE/SOURCE
FACTOR=REAL(-1.0*(X*X*KS2/2)-KK*RESR)
IF (FATOR.LT.-50.) THEN
FPART=0.0
ELSE
FPART=EXP(FACTOR)
ENDIF
RETURN
END
REAL FUNCTION GPART(X)
IMPLICIT REAL*8 (Q-R)
REAL*8 C,D
REAL KS2,KK,RESR
COMMON /VOIGT/COPPLR,APARAM,SOURCE,ABSP,C0NC1,FPATH,APATH
COMMON /DUMMY/ FRAC1,ABS2,FRAC2,APARM2,D0PPL2,APOST,APRE
COMMON Q(7),R(8)
C0MPLEX*16 F.BTM,TOP,RATIO
D=1.66511/DOPPLR*X
C=APARAM
F=DCMPLX(C,D)
TOP=(((((Q(7)*F+Q(6))*F+Q(5))*F+Q(4))*F+Q(3))*F+Q(2))*F+Q(1)
BTM=((((((F+R(7))*F+R(6))*F+R(5))*F+R(4))*F+R(3))*F+R(2))*F+R(1)
RATIO=TOP/BTM
RESR=REAL(RATIO)
KK=ABSP*C0NC1*FRAC2*APRE/APATH
KS2 = 5.54518/SOURCE/SOURCE
FACT0R=REAL(-1.0*(X*X*KS2/2)-KK*RESR)
IF (FACTOR.LT.-50.) THEN
GPART=0.0
ELSE
GPART=EXP(FACTOR)
ENDIF
RETURN
END

REFERENCES
1. J.C. Travis, J. Chera. Ed. 59, 909 (1982).
2. G.S. Hurst, M.G. Payne, S.D. Kramer, and J.P. Young, Rev. Mod. Phys.
51_, 767 (1979).
3. J.D. Winefordner and N. Omenetto in "Analytical Applications of
Lasers," E.H. Piepmeier, Ed., Wiley Interscience, New York (1986),
Chapter 2.
4. M. Broyer, J. Chevalyre, G. Delacretaz, and L. Woste, Appl. Phys.
B35, 31 (1984).
5. D.B. McDonald and C.D. Jonah, Rev. Sci. Instrum. 55_, 1 1 66 ( 1 984).
6. R.E. Grove, Laser Focus Magazine, July (1982).
7. K. Doerffel, A. Wundrack, and S. Tarigopula, Fresenius Z. Anal. Chem.
324, 507 (1986).
8. C.Th.J. Alkemade, Ph.D. Thesis, Utrecht, Netherlands (1954).
9. H.C. Meng, and H.J. Kunze, Phys. Fluids 22, 1082 (1979).
10. A.C.G. Mitchell and M.W. Zemansky, "Resonance Radiation and Excited
Atoms," Cambridge University Press, New York (1971).
11. L. Pasternack, A.P. Baronavski, and J.R. McDonald, J. Chera. Phys. 69_,
4830 (1979).
12. P.W.J.M. Boumans, "Theory of Spectrochemical Excitation," Plenum
Press, New York (1966).
13. C.Th.J. Alkemade, T. Hollander, W. Snelleman, and P.J.Th. Zeegers,
"Metal Vapors in Flames," Pergamon Press, New York (1982), Chapter 5.
14. W.W. McGee and J.D. Winefordner, J. Quant. Spectrosc. Radiat.
Transfer. ]_, 261 (1967).
15. C.L. Pan, J.V. Prodan, W.M. Fairbank, Jr., and C.Y. She, Opt. Lett.
5, 459 (1980).
16. M.A. Bolshov, A.V. Zybin, V.G. Koloshnikov, and M.V. Vasnetsov,
Spectrochim. Acta 36B, 345 (1981).
110

111
17. C.Th.J. Alkemade in "Analytical Applications of Lasers," E.H.
Piepmeier, Ed., Wiley-Interscience, New York (1986), Chapter 4.
18. J.E.M. Goldsmith and R.J.M. Anderson, Appl. Opt. 2_4, 607 (1985).
19. M.J. Dyer and D.R. Crosley, Optics Lett. 381 (1982).
20. G. Kychakoff, R.D. Howe, and R.K. Hanson, Appl. Opt. 2_3, 704 (1984).
21. G.C. Turk, F.C. Ruegg, J.C. Travis, and J.R. Devoe, Appl. Spectrosc.
40, 1146 (1986).
22. W.T. Walter, M. Piltch, N. Solimene, and G. Gould, Bull. Am. Phys.
Soc. U_, 11 3 (1966).
23- R.J. Krupa, T.F. Culbreth, B.W. Smith, and J.D. Winefordner, Appl.
Spectrosc. 4jD, 729 (1986).
24. J.C. Travis, G.C. Turk, and R.B. Green, Anal. Chem. j>4_, 1007A (1982).
25. C.Th.J. Alkemade, W. Snelleman, G.D. Boutilier, B.D. Pollard, J.D.
Winefordner, T.L. Chester, and N. Omenetto, Spectrochim. Acta 33B,
383 (1978).
26. "IUPAC, Nomenclature, Symbols, Units and Their Usage in
Spectrochemical Analysis," Revision 1975 Part II Spectrochim. Acta
33B, 248 (1978).
27. G.L. Long and J.D. Winefordner, Anal. Chem. 55_, 712A (1983).
28. C.Th.J. Alkemade, Tj. Hollander, W. Snelleman, and P.J.Th. Zeegers,
"Metal Vapors in Flames," Pergamon Press, Elmsford, New York (1982),
Chapter 3.
29. G.F. Kirkbright and M. Sargent, "Atomic Absorption and Fluorescence
Spectrometry," Academic Press, New York (1974), Chapter 10.
30. E. Voigtman and J.D. Winefordner, Prog. Analyt. Atom. Spectrosc. 9_, 7
(1986).
31. S. Cova and A. Longini in "Analytical Laser Spectroscopy," N.
Omenetto, Ed., J. Wiley and Sons, New York (1979), Chapter 7.
32. A. Yariv, "Quantum Electronics," John Wiley and Sons, New York
(1975), Chapter 16.
33. M.S. Epstein and J.C. Travis, Appl. Spectrosc. (in press).
34. P.J.Th. Zeegers, R. Smith, and J.D. Winefordner, Anal. Chem. 40, 26A
(1968).

112
35. H.P. Hoomayers, Spectrochim. Acta 23B, 567 (1968).
36. P.J.Th. Zeegers and J.D. Winefordner, Spectrochim. Acta 26B, 161
(1971).
37. V. Svoboda, R.F. Browner, and J.D. Winefordner, Appl. Spectrosc. 26_,
505 (1972).
38. A.K. Hui, B.H. Armstrong, and A.A. Wray, J. Quant. Spectrosc. Radiat.
Transfer JJ9, 509 (1978).
39. M.L. Parsons, W.J. McCarthy, and J.D. Winefordner, Appl. Spectrosc.
20, 223 (1966).
40. M.L. Parsons, B.W. Smith, and G.W. Bentley, "Handbook of Flame
Spectroscopy," Plenum Press, New York (1975).
41. H.C. Wagenaar and L. DeGalen, Spectrochim. Acta 28B, 157 (1973).
42. R.G. Breene, Jr., "The Shift and Shape of Spectral Lines," Pergamon
Press, New York (1961).
43. B.V. L'vov, V.G. Nikolaev, E.A. Norman, L.K. Polzik and M. Mojica,
Spectrochim. Acta 41B, 1043 (1986).
44. G. Schlemmer and B. Welz, Spectrochim. Acta 41B, 1157 (1986).
45. C.Th.J. Alkemade, Spectrochim. Acta 40B, 1331 (1985).
46. A.J. Langley, R.A. Beamon, A.N. Davies, W.J. Jones, and J. Baran,
Chemical Physics 101, 117 (1986).
47. C.Th.J. Alkemade and R. Hermann, "Fundamentals of Analytical Flame
Spectroscopy," Adam Hilger Ltd., Bristol, England (1979), Chapter 2.
48. J.D. Messraan, M.S. Epstein, T.C. Rains, and T.C. O'Haver, Anal. Chem.
55, 1055 (1983).
49. W. Demtroder, "Laser Spectroscopy," Springer Verlag, New York (1982),
Chapter 5.
50. W.B. Jackson, N.M. Amer, A.C. Boccarra, and D. Fournier, Appl. Opt.
20, 1333 (1981).
51. A. Rose, Y.X. Nie, and R. Gupta, Appl. Opt. 25_, 1733 (1986).
52. T.W. Hansch, Appl. Opt. 11, 895 (1972).

113
53. A.G. Gaydon and H.G. Wolfhard, "Flames: Their Structure, Radiation,
and Temperature," John Wiley and Sons, New York (1960), Chapter 2.
54. L. deGalan and J.D. Winefordner, Spectrochim. Acta 25B, 245 (1970).
55. M.S. Epstein and J.D. Winefordner, Prog. Analyt. Atom Spectrosc.
67 (1984).
56. T.C. O'Haver in "Trace Analysis: Spectroscopic Methods for
Elements," J.D. Winefordner, Ed., Wiley-Interscience, New York
(1976), Chapter 2.
57. E.H. Piepmeier in "Analytical Laser Spectroscopy," E.H. Piepmeier,
Ed., Wiley Interscience, New York (1986), Chapter 1.
58. F.P. Schafer in "Dye Lasers," F.P. Schafer, Ed., Springer Verlag, New
York (1973), Chapter 1.
59. G. Gilson and G. Horlick, Spectrochim. Acta 41B, 1299 (1986).
60. N. Omenetto and H. Human, Spectrochim. Acta 39B, 1333 (1984).
61. M. Alden, H. Edner, G. Holrastedt, S.S. Vanberg, and T. Hogberg, Appl.
Opt. 21_, 1236 (1982).
62. 0. Axner and T. Berglind, Appl. Spectrosc. _40_, 1 224 (1986).
63. I. Magnusson, 0. Axner, I. Lindgren, and H. Rubinsztein-Dunlop, Appl.
Spectrosc. 40, 968 (1986).
64. I. Magnusson, S. Sjostrom, M. Lejon, and H. Rubinsztein-Dunlop,
Spectrochim. Acta B (in press).
65. 0. Axner, I. Magnusson, J. Petersson, and S. Sjostrom, Appl.
Spectrosc. 4J_, 19 (1987).
66. G.C. Turk, 0. Axner, and N. Omenetto, Spectrochim. Acta B (in press).
67. G.C. Turk and N. Omenetto, Appl. Spectrosc. _40, 1085 (1 986).
68. G.J. Havrilla and R.B. Green, Anal. Chem. 52_, 2376 (1 980).
69. N. Omenetto, G.C. Turk, M.J. Rutledge, and J.D. Winefordner,
Spectrochim. Acta B (in press).
70. N. Omenetto, B.W. Smith, L.P. Hart, P. Cavelli, and G. Rossi,
Spectrochim. Acta 40B, 1411 (1985).

BIOGRAPHICAL SKETCH
Michael James Rutledge was born in Auburn, Alabama, on June 27,
1960. He attended Woodham High School in Pensacola, Florida, where he
learned the value of a good tan and the beach scenery. He graduated with
a B.S. in chemistry from Auburn University in 1983. Since that time he
has attended the University of Florida where he received his Ph.D. in
chemistry in 1987 under the direction of Dr. James D. Winefordner.
114

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the
degree of Doctor of Philosophy.
Jaíhes D. Winefordpér, Chairman
Graduate Research Professor of
Chemistry
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the
degree of Doctor of Philosophy.
Dorsey
te Professor of Chemistr
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the
degree of Doctor of Philosophy.
/.
r
Robert Gould /
Professor of Materials Science
This dissertation was submitted to the Graduate Faculty of the
Department of Chemistry in the College of Liberal Arts and Sciences
and to the Graduate School and was accepted as partial fulfillment of
the requirements for the degree of Doctor of Philosophy.
May, 1987
Dean, Graduate School

UNIVERSITY OF FLORIDA
3 1262 08554 1679

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