Title: Capability of d2 spectrometry for detecting Raman scattering
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Title: Capability of d2 spectrometry for detecting Raman scattering
Physical Description: ix, 88 leaves : ill. ; 28 cm.
Language: English
Creator: Kilpatrick, Wallace Dorman, 1920-
Copyright Date: 1975
 Subjects
Subject: Raman effect   ( lcsh )
Spectrometer   ( lcsh )
Aerospace Engineering thesis Ph. D
Dissertations, Academic -- Aerospace Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Wallace Dorman Kilpatrick.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 86-87.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00098674
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000168808
oclc - 02888104
notis - AAT5208

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CAPABILITY OF d2 SPECTROMETRY FOR DETECTING
RAMAN SCATTERING





By



WALLACE DORMAN KILPATRICK


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



UNIVERSITY OF FLORIDA

1975













ACKNOWLEDGMENTS


Acknowledgments are difficult to make because help has

been offered in many ways, sometimes direct, sometimes unsolic-

ited or casual. I am grateful for contributions from the Uni-

versity Librarians, the Department of Electrical Engineering,

and the Department of Engineering Sciences, where this experi-

mental work was done.

Without Dr. D. T. Williams, who is committee chairman,

the subject investigation would never have been entered upon

nor completed. His optimism, enthusiasm and confidence, and

that of Dr. Knox Millsaps have been essential.

I would like to thank committee members Dr. T. L. Bailey,

Dr. D. R. Keefer, and Dr. J. W. Dufty for several important

discussions and genuine efforts. Specific contributions and

motivations that have originated with Dr. G. D. Ward, Dr. A.

A. Broyles, Dr. E. R. Chenette, Dr. A. H. Wing, and Dr. M.

Zahn are deeply appreciated.













TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS . . . . . . . .. .. ii

LIST OF TABLES . . . . . . .. .. . iv

LIST OF FIGURES . . . . . . . .. .. v

ABSTRACT . . . . . . . . ... . .. vii

CHAPTER

I INTRODUCTION . . . . . . . . . 1

II GENERAL INSTRUMENTATION d2 RAMAN
SPECTROMETER . . . . . . . . .. 12

Optical Input . . . . . . ... 14
Modulator . . . . . . . . . 16
Signal Channel . . . ... . . . 19
Synchronous Channel . . . . . ... 24
Second Detector . . . . . . .. 27

III INSTRUMENT RESPONSE . . . . . ... 30

Signal Intensity Calibrations . . . .. .30
Tuned Amplifier . . . . . . .. 34
Random Noise and Interference . . . .. .46
Interstage Decoupling . . . . . .. 48

IV RESULTS AND DISCUSSION . . . . . ... 50

Carbon Tetrachloride versus Toluene ... .58
Slit Modulation and Stability . . . .. .70
Modified Sync Channel and Second Detector . 72

V SUMMARY AND CONCLUSIONS . . . . ... .75

APPENDIX

A WAVEFORMS OF SELECT POSITIONS IN ELECTRONIC
CIRCUITS OF d2 PRAMAN SPECTROMETER . . ... .79

BIBLIOGRAPHY . ... . . . ... . .. ... . 86

BIOGRAPHICAL SKETCH . . . . . . . . .. 88
iii













LIST OF TABLES


Table Page

I Features Appearing in Figure 14 . . ... .52

II Light Intensity in the Stokes and Anti-
Stokes Regions of Figures 17 and 17 for
Toluene . . . . . . . .... . 64

III Light Intensity in the Stokes and Anti-
Stokes Regions of Figures 18 and 19 for
Carbon Tetrachloride . . . . . ... 66

IV Calculated Wavelengths Using Published
Frequencies . . . . . . . .. 69













LIST OF FIGURES


Page


Transmission function and profile coordinate
scheme . . . . . . . . . .


2 Functional block diagram . . . . . . 13

3 Raman scattering cell . . . . . ... 15

4 Modulator . . . . . . . . . 17

5 Modulator . . . . . . . ... 18

6 Quarter-meter monochromator . . . ... .20

7 Signal channel . . . . . . . . 22

8 Synchronous channel . . . . . . . 25

9 Second detector . . . .... . . . 28

10 Intensity calibration . . . . ... 32

11 Tuned amplifier characteristic . . . . 35

12 Equivalent network for tuned amplifier
analysis . . . . . . . . . . 37

13 Tuned amplifier circuit model . . . ... 42

14 Initial d2 Raman spectrum of carbon tetra-
chloride . .. . . . . . . . . 51

15 Typical d2 line response . . . . . . 53

16 Toluene, Raman anti-Stokes spectrum . . .. .59

17 Toluene, Raman Stokes spectrum . ..... . . 60

18 Carbon tetrachloride, Raman anti-Stokes
spectrum . . . . . . . ... . . . . 61

19 Carbon tetrachloride, Raman Stokes spectrum .. 62


Figure

1








LIST OF FIGURES Continued


Figure Page

20 Amplitude of apparent lines on the Stokes
and anti-Stokes sides of 6328 A excitation
for toluene . . . . . . . .. 65

21 Amplitude of apparent lines onothe Stokes
and anti-Stokes sides of 6328 A excitation
for carbon tetrachloride . . . . ... 67

22 Raman Spectrometer, proposed option . . .. .73

23 Modulator, sensor amplifier output, U2 .... .80

24 Master oscillator output, Ul . . . ... .80

25 Modulator, driver output to coil, Q4 . . .. .81

26 Signal channel, preamplifier output, US . .81

27 Signal channel, tuned amplifier output, U7 .. 82

28 Sync channel, square wave amplifier output,
U3 . . . . . . ... . . . . 83

29 Sync channel, doubler output, U4 . . ... .83

30 Sync channel, doubler amplifier input, U4 . 84

31 Sync channel, doubler amplifier output, U6 . 85

32 Second detector, rectified tuned amplifier
output, U8 input . . . ... .... . 85







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



CAPABILITY OF d2 SPECTROMETRY FOR DETECTING
RAMAN SCATTERING


by

Wallace Dorman Kilpatrick

June, 1975

Chairman: Dr. D. T. Williams
Major Department: Aerospace Engineering


An outdated model d2 Air Analyzer was used in this exper-

imental investigation as a basis to estimate the capability of

d2 spectroscopy and to develop a d2 Raman Spectrometer. The

first d2 Raman spectra, observed by Darling and Williams

before this study, used a strong 800 milliwatt argon laser

(4880 A), which gave a signal-to-noise ratio, S/N 1 i. With

extensive electronic modifications, the present investigation

has resulted in a reduction of the noise to a level where

Raman spectra using the same scattering cell are observed with

a 3 milliwatt helium-neon laser (6328 A)and S/N 1.

A d2 Spectrometer is an instrument for direct, instantan-

eous recording of the second derivative of the profile of an

optical spectrum line. It derives an especially high sensi-

tivity from intensity modulation of the light transmitted

through the spectrometer followed by amplification of only

the second harmonic component of the photodetector. A phase-

lock technique is then used to determine the cosine component








of this second harmonic, since the leading term of the cosine

coefficient is proportional to the second derivative of the

line profile.

Raman spectra are weak, scattered radiations, about 10-3

in relation to Rayleigh scattered radiations, where the Ray-

leigh radiation is 10-3 of the incident, precollision intensity.

Raman lines appear only because some of the energy of the

photon-molecule collision appears as internal molecular vibra-

tional energy. The importance of the effect is that if the

Raman lines can be measured, internal molecular structure can

be inferred.

The modifications and tests show that the d2 sensitivity

limitation is due to electronic circuitry, and several back-

ground noise sources have been identified. Interstage coup-

ling of operational amplifiers has involved different wave-

forms: square waves, fundamental and harmonic wobble frequen-

cies, power supply ripple, beat frequencies, power line tran-

sients, parasitic oscillations, and the peculiar waveforms of

regenerative and super-regenerative feedback. Because strong

Raman signal levels appeared to be the order of 1 microvolt

at the photodetector, the types of couplings and means to

reduce their contributions below that level essentially out-

line the noise problem.

The means used to reduce noise levels have been: buffer

isolation of each amplification stage from the power supply

through the use of long time constant filters; isolation of

each stage from the other by removing closed inductive loop


viii








circuits and open capacitive circuits; stabilization (thermal,

mechanical, and frequency) to minimize excursions; and reduc-

tion of the amplitude of all waveforms to minimum values con-

sistent with reliable operation. A much quieter d2 circuitry

evolved, and further improvement appears possible.

At the present stage of development, observation of d2

Raman spectra are marginal with a 3 milliwatt helium-neon

laser and cylindrical Raman cell. Acceptable operation with

S/N 100 for strong Raman lines could be obtained with vari-

ous optional conditions: e.g., increase the helium-neon

laser strength to 50 milliwatts with no other changes; or use

at least a 10 milliwatt argon laser (4880 A) because the fre-

quency gives an increase of 2.83 in radiation and an increase

of about 12 for photodetector sensitivity. Changes in Raman

scattering cell efficiency cause linear scaling of any of

these factors.

An optional d2 circuit is presented where the lock-in

feature and second harmonic detection are retained, but the

"chopper" method of detecting the harmonic cosine coefficient

is replaced by a quiet cosine analog system which integrates

over the wobble frequency in a "Fourier coefficient" method.

An innovative, quiet, all-electric modulator is also proposed

which could be versatile in frequency adjustment, programmable

for synchronous operation, and workable at a lower power level.












CHAPTER I

INTRODUCTION



This is an experimental investigation into the capability

of d2 instrumentation for detecting weak laser light scattered

by the Raman effect. The d2 principle of detecting optical

signals was devised by D. T. Williams [1], developed by R. N.

Hager, Jr. [2], and commercialized by the firms of Spectro-

metrics, Inc., Tampa, Florida [3], and Lear Siegler, Inc.,

Englewood, Colorado [4]. An outdated commercial Model III d2

Air Analyzer, designed for monitoring the optical absorption

of air pollutants, was modified and used as a basis for the

high sensitivity instrumentation required for Raman spec-

troscopy.

Prior to this study, J. i. Darling [5] reported a laser

Raman spectrum with the same Air Analyzer used here. Although

he used a strong argon laser, 0.8 watts at 4880 A, the result-

ing signal-to-noise ratio in the Raman spectrum was S/N 1.

Reasons for the poor performance of the d2 instrumentation

were presumably a "high noise level" of the instrumentation

during operation. The observed "noise" was basically an

erratic wandering of the base line (i.e., zero signal level)

at a rate which was comparable to that oF the scanned line

signal. The Raman spectra were major lines of carbon tetra-

chloride and toluene, and appeared at known locations.
1







The instrumentation problem of sensitivity and noise can

be appreciated from a relative scale of scattered light inten-

sities, where the light may be scattered by small particles

(Tyndall effect), whole molecules (Rayleigh effect), solids

(Brillouin effect), or by individual atoms in molecules (Raman
-3
effect). Apparently the Rayleigh intensity, IC, is about 10

that of the incident radiation [6]. Brillouin intensities,
-I
IB, are less than Rayleigh intensities, IB/IC is about 10

for carbon tetrachloride and 10-2 for water; and Brillouin

wavelength shifts are small. Raman intensities, IR, are

smaller yet, IR/IC is 10-3 or less [6] depending on the vibra-

tion levels of the energy absorbed. Raman frequency shifts,

however, are greater than Brillouin shifts because modulation

from atom-atom rotation, bending, and elongation frequencies

are greater than for sound frequencies.

From simple theory of classical spectral emission, the

amount of radiation depends on the frequency. Consider a

steady, one-dimensional motion of a harmonically bound elec-

tron of charge e and mass m forced to vibrate by an external

electromagnetic wave of amplitude Eo and frequency v [7],


[d2y/dt2] + 2y = [eE/m] exp(jvt),


which has the solution


y = [eFo/m][l/(v'2 2)] xp(jvt)

In genera], for v' = 0 the electron forms part of a

dipole, p which produces a radiation field E(r) at large r








and at angle 6 from the dipole axis


E(r) = n p v2 sin 2/eg r c2) exp(jvt)


The radiated intensity varies as E(r)2, so that after inte-

gration over all 6, the total intensity per unit time, I,

has a classical fourth power frequency dependence


I = 4 r3 po v/3 c3
p0

where E is the permittivity of free space, and c is the

velocity of light. If the electrons are strongly bound,

their motion is modified by the molecular motion of frequency

v' and the Raman intensity IR is related to the incident

intensity


IR/IC (V,2 2)2 ~ v4 V' v

Comparing the argon laser (4880 A) data of Darling and

Williams with that for a helium-neon laser (6328 A), the

Raman intensities would be less by at least a factor of

(4880/6328) = 1/2.83. Furthermore, scaling the power which

they used (800 milliwatts) as well as the photomultiplier

response, comparable results should be obtained with the 3

milliwatt helium-neon laser if the d2 instrument sensitivity

were improved by the factor (800/3)(2.83)(12.5) = 9430. The

value 12.5 is the relative sensitivity of the particular

photodetector used, obtained by the ratio of quantum efficient

cies at 4880 and 6328 A (10% and 0.8, respectively).








Although complicated interpretations are'necessary, the

usefulness of Raman spectra are their value in inferring

details of molecular structure. This usefulness, however, is

tempered by the smallness of the effect. Modern Raman spec-

troscopy [8,9] employs, simultaneously, laser excitation to

increase observable signal strengths, and a "double monochro-

mator" to reduce background. Even for carefully designed

monochromators, where careful attention is paid to internal

baffling and minimal scattering, large amounts of stray radi-

ation are always present. This radiation, as well as the

desired Raman radiation, escapes through the exit slit. In

double monochromators, the undesirable radiation is redis-

persed, reducing the interference. A good double monochroma-
_g
tor presumably has a ratio of 10 between laser radiation

transmitted at 10 cm- and the line center [10]. In d

instrumentation, the stray radiation which escapes through

the exit slit is identical, but modulated in time, and this

modulation is in synchronism with the Raman line.
2 1 0
However, in the d system, d and d are excluded from

measurement. This means that the stray light is a non-

contributor, unless it results from a virtual source corre-

lated with the grating position in the manner of an optical

"ghost." If such false lines should appear, then calibration

of their location (i.e., laser transmission without Raman

scattering present) identifies them, and the d2 sensitivity

to Raman spectroscopy is unimpaired. Therefore, the d







Spectrometer eliminates the need for a second monochromator

function, rejecting background interference by electrical

means.

A first requirement of the second derivative spectrometer

is the equivalent of a "wobbler" in the form of an oscillating

entrance slit to a single monochromator. The purpose of the

wobble is to produce a time varying signal in the detector

following the exit slit. The wobbler does this by moving

periodically across the path of light emitted from the laser,

and so causes the optical image at the output slit to move

periodically across the output slit. When the optical line

is centered at the exit slit, the wobble produces a second

harmonic of the wobble frequency. When the line is not

centered, a second harmonic still exists, its amplitude is

less, and recurrent waveforms occur twice over each wobble

period in a succession of even parity.

A second requirement for the d2 spectroscopy is proper

phase selection of the cosine component of the second har-

monic. This is accomplished by rectification in phase-lock

with the wobble frequency. In general, the phase of the

detector signal varies with respect to the wobbler (modulat-

ing slit), and depends on the position of the spectrum lines

at the detector. Accordingly, for a narrow slit which covers

only a fraction of a line, only a phase increment is trans-

mitted, and this has a particular phase relative to the steady

state wobbler. In effect, a narrow slit scanning a line pro-

file with the wobbler under fixed conditions produces an ac








signal with a phase proportional to the displacement. A for-

ward wobble produces a signal which is followed by a similar

(but reversed) pattern when the wobble reverses, thus giving

a double frequency response. In general, phase-lock rectifi-

cation (i.e., "chopping") produces positive or negative sig-

nals corresponding to positive or negative second derivatives

of the spectrum line profile as the line is scanned.

To establish the relative importance between the phase

and amplitude of the signal due to transmitted light, consider

a mathematical convolution of a spectrum line profile with the

exit slit width of 2b at x Let the transmission function

of the slit be rectangular, T(x) = 1, when xl < x < x2, other-

wise T(x) = 0. x2 = x + b, and xl = xo b. See Figure 1

for the relation between these variables.

For a line with its maximum at xo, not located at the

center of the slit, x the signal S(xo) which is transmitted

through the slit to the photomultiplier is


S(x ) = / I(x) T(x) dx
-o0
x2
= f I(x) dx
Xl

A Taylor expansion of I(x) around x is convenient,


I(x, x ) = I(0)(x ) + I(l)(xo)(X x0)

+ 1(2)(x )(x x ) 2/2! + .
















Transmission
Through Exit Slit

x=O xl= x







Spectrum
Line Profile









x -x = a sin wt -
0 0


_ T(x) = 1; xl < x < x2
= 0; otherwise









I (x)

















Modulation
(Wobble around xo)


Figure 1. Transmission function and profile coordinate
schelime.







where I(n)(x ) is the nth derivative of I(x) evaluated at xo

Integration over the limits gives

S(x) = I(O)(x)[(x2 xo) (xl x )]

+ I(1)( )[(2 x ) 2 (x x ) /2!

+ I(2) )[(x2 x )3 (x x )3]/3! +


If the point I(x ) is periodically displaced by an amount

a sin ut, then the limits of integration, xl and x2, are
effectively

x2 = x + a sin wt + b

x = x + a sin at b

The light signal transmitted is then

S(xo = Ao I(0)(x) + A1 I(1)(x)/2!

+ A2 I(2)(x )/3! + . .


A = (a sin wt + b) (a sin at b)

Al = (a sin at + b) (a sin at b)






Terms of the form sinnct can be expressed as multiple fre-

quencies of the wobble frequency with the use of the







relation


sin2n t = (1/2n)(1 cos 2wt)n

To minimize the mathematical manipulations, and before

substituting for sinnut, recall that the d2 instrument has a

capacitor following the photomultiplier so that no dc signal

levels are admitted, and it also has a tuned amplifier which

responds to the second harmonic of the wobble frequency. If

the mathematical operation Eh is defined as the selection of

only the even second harmonics terms, i.e., excluding constant

terms (dc), excluding odd harmonics (sines), and excluding all

other frequencies, then the following terms appear for S(x):


Eh Ao = Eh (2b) = 0

Eh'A1 = Eh (4ab sinut) = 0


Eh.A2 = Eh (6a2b sin2mt + 2b3) = [-3a2b] cos 2wt

Eh A3 = Eh (8a3b sin3 t + 8ab3 sinwt) = 0

Eh.A4 = Eh (10a4b sin4mt + 20 a2b3 sin2t + 2b5

= [-5a4b 10a2b3] cos 2wt


Eh A5 = Eh (12a5b sinat + 40a3b3 sin 3t + 12ab5 sint)
= 0


E -A6 = Eh (14a6b sin 5t + 70a4b sin4 t + 42a2b5 sin2t

+ 2b7) = [-7a6b 35a4b3 21a2b5] cos 2(t








The first d2 instrument terms of the photomultiplier signal

are then


Eh.S(wt) = -a2b[I(2)(x )/2! + I(4)(x )/4! (a2 + 2b2)

+ I(6)(x )/6! (a4 + Sa2b2 + 3b4)


+ .] cos 2wt .


This result does not agree precisely with that of Hager

[9], because the development and analysis are different. Here

the intensity distribution is integrated over the slit width

before the time variation is introduced. However, for a

specific profile (i.e., sin x/x), Hager finds that the lead-

ing term of I(2)x () for the second harmonic is proportional

to a which is an order of agreement. Otherwise, there is

no statement for comparison.

In general, extracting the second harmonic with a filter

mechanism, and selecting only the cosine component with a

phase-lock mechanism, results in an effective approximation

to the second derivative of the arbitrary profile function,

I(x). The mathematics indicates that only even order deriva-

tives are observed. Amplitudes decrease with order, and an

oversimplified measure of importance of terms is indicated by

the ratio of d2 to d4 which, for an assumed Gaussian profile,

would be 6:1 at the center of the line.

To complete a description of second derivative instru-

mentation, it is necessary to provide for the line to be

scanned in order to correlate the observed intensity with








d2(I(x)) whenever the line crosses the exit slit. A simple

technique of recording in synchronism with the moving grating

provides such a d2 profile of a line.

It is important to note that Fresnel diffraction patterns

are not considered here because the image of the first slit

is produced by optical focusing at the second slit while the

Fresnel patterns incident on the grating, for example, are

subsequently focused into a "line." Also, Fresnel patterns

after the second slit occur over the detector surface where

all of the light from the second slit is collected, and there-

fore the electrical output is not altered.

Because noise (i.e., erratic zero-signal level) seemed

at the time to be the major limitation in laser d2 Raman spec-

troscopy, the present investigation was designed to examine

practical noise sources and to eliminate unstable electronic

performance. The Model III Air Analyzer was used as a start-

ing point, and extensive modifications which evolved are

described below. The cataloging of Raman lines, derivations

of molecular structures from Raman line information, and

research into laser properties -- all of which have bearing

on d2 performance -- have been essentially avoided because

they are extensive subject areas in their own right.












CHAPTER II

GENERAL INSTRUMENTATION d2 RAMAN SPECTROMETER



Raman d2 instrumentation consists of the functional

parts: optical input, modulator (wobble generator), signal

channel, synchronous (sync) channel, second detector and

recorder output, as shown in Figure 2. Except for the Raman

scattering cell and laser, d2 instrumentation is the founda-

tion of the system.

Extensive modification of a d2 Air Analyzer resulted in

such improved d2 sensitivity that Raman spectra of carbon

tetrachloride were detected with a He-Ne laser of 3 milliwatts.

The main limitation for Raman d2 spectroscopy has turned out

to be not the d2 principle, or light scattered in the spectrom-

eter, but various electronic couplings in the form of cross-

talk between components. In particular, printed circuits

were used, a construction which offered means (but not the

only means) for undesirable interstate coupling. Accordingly,

observation of Raman spectra, after accomplishing some degree

of isolation between electronic components and their functions,

indicates that even greater sensitivity using the d2 principle

is possible. Redesign with hard wiring and with special atten-

tion to electrical decoupling techniques should produce

either or both an advance in the state-of-the-art for Raman








LASER
Optical SCATTERING CELL
Input
RAMAN SCATTERING


Signal
Channel












Second
Detector


SLIT
MONOCHROMATOR
PHOTO DETECTOR
PRE AMPLIFIER
TUNED AMPLIFIER




,1


FEEDBACK CONTROL
OSCILLATOR
DRIVER
DRIVE COIL
SENSOR COIL
SENSOR AMP







SQUARE WAVE AMP
DOUBLER
DOUBLER AMP


Figure 2. Functional block diagram.


Modulator
















Sync
Channel








spectroscopy (sensitivity), or a considerable reduction in

cost for performance comparable to that of a double mono-

chromator.

The arrangement and circuitry described below is not an

ultimate, but rather the specific system in use when the 3

milliwatt He-Ne Raman d2 spectrum of carbon tetrachloride was

observed. Additional specific changes have been made, but the

principles are the most important to record, because redesign

alone is insufficient to avoid relocating some of the sources

of undesirable noise, instability or crosstalk.



Optical Input


Optical input is derived from a 3 milliwatt He-Ne laser,

Model 132, made by Spectra Physics [11]. The laser emission

enters a cell, as shown in Figure 3, which was used by Darling

and Williams for detecting Raman scattering from liquids.

The glass cell has aluminum vacuum-evaporated on the exterior

surfaces and acts as a multiple-reflecting surface to increase

the effective path length of the laser radiation through the

sample liquid. A void of 1 mm by 5 mm in the vacuum coating

allows the laser energy into the cell. Although this is

neither a sophisticated nor efficient Raman scattering cell,

it serves the purpose of evaluating d2 Raman spectroscopy.










51 mm 40 mm



rI1WF'-


To d2 Raman
Spectrometer


j- Slit (0.1 mm)


Laser
(Vertical polarization)


Figure 3. Raan.ai scattering cell.


r
19 mm
diameter

L








Modulator


The starting point of the modulator is the vibrating

entrance slit of the monochromator. The slit moves physically

on the order of a slit width, 0.1 mm, across the optical path

of light emitted from the Raman scattering cell. This causes

an intensity modulated signal to pass through the monochro-

mater to the photodetector. Accurate control of the slit

vibration is critical.

A driver coil and a sensor coil are attached to the slit,

and both of these coils are electrically included in a feed-

back loop with a free-running oscillator. The object of the

feedback loop (collectively this is the modulator shown in

Figures 4 and 5, and wobbles the slit) is to maintain constant

slit oscillatory amplitudes by varying the oscillator drive

power. The oscillator frequency is about the same as the

natural mechanical frequency of the slit assembly, nominally

45 Hz.

Both frequency and amplitude stability are essential for

d2 Raman spectroscopy because of the necessary averaging of

the rectified second harmonic component of the optical signal.

For example, each line scan occurs over a finite time inter-

val so that variation in the integration limits of the recti-

fied signal equates with amplitude variation. Measured vari-

ation in the modulation frequency was less than one period in

10 min, i.e., one part in 2.7 x 104








The sensor coil output is a sinusoidal voltage, derived

from sinusoidal slit motion carrying the sensor coil through

a local magnetic field. The sensor amplifier, U2, inverts

the signal which is then rectified to obtain a negative bias

with a long decay time of several seconds (5 pf x 1 M = 5 sec).

This negative bias regulates the input of a field effect tran-

sistor whose output in turn adjusts the bias of the electronic

oscillator Ul. The power output of Ul is thus reduced if the

sensor voltage is excessive (large oscillation amplitude).

A 10 K potentiometer in the common leg adjusts the frequency

of U1 by changing the time constant of its feedback.



Signal Channel


Raman scattered light which is transmitted through the

entrance slit goes through a quarter-meter Ebert monochroma-

tor, Model 82-410, manufactured by Jarrel-Ash [12]. Details

of the monochromator arrangement are shown in Figure 6. Opti-

cal transmission through the monochromator occurs if a diffuse

light source is placed before the slit but within an angle

defined by the mirror diameter to focal length, 38/250, or

about +5 degrees around the optical axis. Omnidirectional

Raman scattering originating in this region is accepted for

transmission, so that for a given laser excitation, normal to

the slit and to the optical axis, the amount of Raman radia-

tion reaching the slit is constant provided the sample and

the excitation fill the acceptance region. Since the entrance









Photomultiplier


Entrance Slit


Speed: f6.5.

Grating: Dispersion = 33 A/mm, 11,000 lines/mm,
Blaze at 5000 A, Plane and 64 mm x 64 mm.


Modifications:


Baffling at B,J; Felt at A,K;
Opaque paint at A,C,D,E,F,G,H.


Figure 6. Quarter-meter monochromator.








slit causes a Fresnel pattern to appear across the mirror and

grating surfaces, more intense lasers cause more intense pat-

terns, which in turn cause more stray radiation backgrounds.

Attenuation of the stray radiation is accomplished by addi-

tion of baffles and absorption materials.

The grating is a replica, made from the "sandwich type"

construction where the master (typically ruled Au or Al) is

coated with separation oil, then aluminum is vacuum-deposited

on it, and a sandwich is formed when the entire assemblage is

epoxy-glued to a glass base. The replica surface is then

formed when the master and oil are removed. It is not uncom-

mon to find spurious light penetration into the thinner parts

of the groove structure, but it has been observed here only

under direct illumination with the 3 milliwatt helium-neon

laser and did not jeopardize its use for Raman spectroscopy.

The electrical part of the signal channel consists of a

photomultiplier, a preamplifier and an amplifier tuned to

double the wobble frequency, as shown in Figure 7. The photo-

multiplier output is negative, showing short negative noise

pulses of about 10 seconds' duration and 1 volt amplitude.

Groups of pulses form into a negative waveshape in synchronism

with the motion of a spectrum line as it crosses the exit slit.

Two waveshapes are generated for each wobble, and these wave-

shapes "fuse" together when the center of the spectrum line

appears at one end or the other of the slit. Thus a "phase

effect" appears in the photomultiplier waveshape, and con-

tinues into the following tuned amplifier.












Page 22 missing from original








The photodetector is a seven-stage photomultiplier,

Model 9783B, made by EMI [13], and operated from an 800-volt

battery which is by-passed with 0.125 pf. This photomulti-

plier has a characteristic quantum efficiency of 15, 17, 10,

and 2% at 2000, 3500, 4880, and 6000 A, respectively. At

6800 A the efficiency is 0.1%, essentially zero. The noise

level according to the manufacturer is about 0.1 na of aver-

age dark current. The observed peaks of 1 pv across 100 K are

0.01 na, which generally agrees because of 10% on-time. The

d2 instrumentation handles the noise output easily, but not

the low signal response at 6328 A (1% quantum efficiency).

A quantum efficiency of 15%, factor of 15 increase in sensi-

tivity at 6328 A, can be obtained with a more expensive end-on

linear photomultiplier, Model 9658B, from the same manufac-

turer.

The preamplifier input is also the photomultiplier load,

but the circuit frequency response can be low, 45 Hz. An

important point in the preamplifier design is to discourage

high frequency amplifications and also regenerative feedbacks,

because they are both sources of unstable operation. To accom-

plish this, a 0.01 pf capacitor is placed between the output

and input terminals of the amplifier U5, and a 14 K resistor

is put in series with the input to decouple feedback through

the printed circuit from the following tuned amplifier stage.

In fact, without these decoupling means, a "super-regenera-

tive" action of the preamplifier occurs when a signal results

from any convenient transient and quenches itself in such a









way as to contribute false signals which are completely

unacceptable for Raman spectroscopy. The frequency response

of the preamplifier prior to degenerative feedback was

broadly peaked at about 10 KHz, which became the character-

istic frequency of the "super-regenerative" action. Super-

regenerative action is not necessarily undesirable, since it

exploits the high gain which appears near resonance, but

practically it is unstable and a source of considerable noise.

The tuned amplifier is a double-tee filter connected as

an active amplifier. It has a gain of about 500 at twice

the wobble frequency, a bandwidth of about 12 Hz, and an excep-

tional stability. It seems to respond to harmonics, but it

works well in the signal channel. It is a very interesting

device and its performance will be pursued further.


Synchronous Channel


The purpose of the synchronous channel (sync channel),

which is represented in Figure 8, is to provide the proper

phase for rectifying (chopping) the tuned amplifier signal.

Phasing is referred to the sensor coil, actually the sensor

amplifier, so that changes in wobble frequency do not influ-

ence the phase relation between the signal channel and the

chopper. The sync channel consists of a square wave ampli-

fier, doubler, and doubler amplifier. It is important that

the sync channel introduce no jitter or unstable operations,

because changes in the chopper limits influence the time
















































































OO(

o < U 0 N
0 1~ W1 )
r( / i=; 2-__ )|
-\ m I








constant integrator as effectively as variations in optical

signal strength.

The square wave amplifier, U3, converts a sinusoidal

input into a square wave by driving the input in excess of its

linear limits. Two zener diodes in the output increase the

rate of rise of the leading and trailing edges of the square

wave, but shunting capacitors are provided to reduce jitter

as the waveform crosses the zero potential level. Small

phase adjustments are possible with the 100 K potentiometer

input.

The doubler consists of two speaker RC elements which

effectively differentiate each edge of the square wave, thus

doubling the basic frequency. Adjustment of the resistive

elements is provided for balancing on and off conduction

times, so that equal duration pulses can be set. The trail-

ing edge of each "peak" has inherently less rate of change in

its decay, and can be a source of jitter in the operation of

the integrated circuit amplifier, U4. Practically, the vari-

ations are typically 5 microseconds which, over a half period
4
of 11 milliseconds, represents a variation of 5 parts in 104

Output from the doubler can cause ringing, a parasitic

behavior, in the following doubler amplifier stage, U6. The

ringing is reduced by changing the waveform to a softer,

sinusoidal shape by introducing 1 pf shunts across the zener

diodes in the U4 output. Further suppression of ringing is

accomplished by adding an 0.0005 pf capacitor across the feed-

back resistor of the doubler amplifier, as well as 0.001 uf








across its output resistor. A sharp switching of the chopper

function is less important than consistent stable operation.



Second Detector


The second detector is a group of functions, as shown in

Figure 9, which starts with a second harmonic of the wobble

frequency of amplitude proportional to the optical signal,

and ends up with a dc signal proportional to the same optical

signal. Inputs from both the signal channel and the sync

channel are required for a dc output to the recorder.

The second harmonic output from the tuned amplifier is

rectified by proper timing (i.e., proper phase with respect

to the wobble) of the conductance of a field effect transis-

tor, Q5. This rectified signal, which may be either positive

or negative depending on the optical signal phase, is then

integrated (demodulated) to essentially a dc level by a time

constant circuit of 100 seconds (500 -f x 200 K) before enter-

ing the buffer amplifier, U8. At this point, dc signals are

relatively small.

The analog device AD/426 is a transconductance type

divider, in a mathematical sense. Two input voltages, Z and

X, when properly connected, result in an output Y, where Y =

Z/X. In the present description of a d2 Raman Spectrometer,

the AD/426 device is used as a variable dc amplifier, con-

trolled for convenience by the dc level, X, derived from a

1.5-volt, size AA battery. The divider was originally used













U

00


0
r-1
30
3 0.
002








in the Air Analyzer absorption spectrometer as a normalizing

device, in the mathematical sense, to compensate for changes

in light source intensity -- a dO function. This feature is

not useful for Raman d2 spectroscopy where maximum sensitivity

is always desired.*

The final stage of the second detector is a buffer for

isolating the AD/426 device and the recorder. A long time

constant of 25 seconds is introduced into the output to aid

in the integration of noise which may have appeared after the

rectifier time constant of 10 seconds. The total time response

of the dc section is the result of these two time constants,

practically about 30 seconds.




















*A good description of a transconductance multiplier/
divider can be found in reference 14. It is basically a
thermally well-balanced operational amplifier which contains
an additional control terminal to the usual operational am-
plifier. The output current is proportional to the voltage
at its input terminals; output current, I is the product
of mutual conductance, g1, and applied voltage, X, 10 = gm X.
Mien g, = Y, then I, ~ X-Y, an analog multiplication function.













CHAPTER III

INSTRUMENT RESPONSE



The d2 Raman Spectrometer has optical, electronic and

mechanical features to consider, but the chief innovative

advantage for Raman spectroscopy comes through the electronics

treatment of the light signal and background noise. Since the
-6
Raman scattering intensity is about 10 that of the incident

light, a known optical sensitivity of the system should indi-

cate the laser excitation intensity, I, required to produce

usable signals. If the electronic noise level could also be

established at the same time, then the d2 performance should

be predictable.



Signal Intensity Calibrations


If the helium-neon laser (6328 A) of 3 milliwatts is

aimed directly into the acceptance cone of the modulating

slit, there will be a major one-line contribution to the

photomultiplier. Attenuation of the radiation by absorbers

or scatterers will then allow extrapolation to laser inten-

sity (upper limit) and noise levels (lower limit). Between

these extremes is the dynamical range of the system where the

Rayleigh and Raman spectra should fall to be useful.







Three- by five-inch index cards turned out to be very

uniform in quality, and when clipped together to form a mini-

mal spacing between the cards, made a convenient reproducible

variable strength scatterer. The scattering stack apparently

followed Lambert's law where the ratio of intensity leaving

the stack to that which enters is a constant per card. Assum-

ing that intensity, I, is diminished to a value Ik after

passing through k cards, and that the decrease is proportional

to the number of cards,


dlk/dk -ak a = constant


I Ie -ak
Ik = oI e

Thus, the intensity recorded by the d2 system should be semi-

logarithmic versus the number of cards. This relationship

was consistent with signals which were electrically attenuated,

and for each of the intensity levels over the measured range.

Measurements of intensity are displayed in Figure 10 as

logloF 1 number of attenuating cards, k, in the scattering

deck. F is an intensity index, the product of recorder ampli-

tude, electrical attenuation, and divider voltage (analog

device AD/426 [15]) -- all in arbitrary units -- taken when

the stack was located 60 nun from the slit between the slit

and the laser.

The slope of a line through experimental points gives an

absorption constant of a = 0.95, and represents an average

output to input factor of c09 = 2.58 per card. Extrapola-

tion to zero cards gives an intercept of 2.2 x 10 The













\

--\







\ 3 Milliwatt Helium-Neon
\ Laser Characteristic


Experimental


S 3
4 10



S102
10



101


0
4-1 00
r-I


0
l



10-1



10- 2
10



10-
|-


Attenuating Cards


Figure 10. Intensity calibration.


Raman Level
\ (10-6 of Laser)
\







available excitation for Raman spectra, however, is a little

more than this, because the laser diameter of 1 mm covers

more than the slit width of 0.1 mm. A characteristic laser

line then, corrected for this overlap, would have an intercept

at 2.2 x 10 up by a factor of 10, but with the same slope

as the experimental curve.
-6
If the recorder noise level were a fraction, 106 that

of a fictitious recorder level due to total laser input, then
-i
typical Raman radiation would appear at F = 2.2 x 101 with

S/N = 1. This assumes complete utilization of the excitation

radiation and no Raman energy loss between the scatterer and

the d2 signal channel.

Experimental results are in reasonable agreement with

this analysis. During the Raman spectrum run with carbon

tetrachloride, for example, there was a noise level of F =
102 -I -2
3 x 102, which should have given S/N = (2.2 x 101)/(3 x 102)

= 7.3. The observed S/N was about 4, which appears to be a

very good agreement. But the agreement simply ignores losses

from multiple laser reflections in the scattering cell, losses

which are due to the optical acceptance angle at the entrance

slit, and losses due to the angular distribution of the Raman

radiation.

The helium-neon laser also has a spectrum of neon lines

of low intensity associated with the conventional gas dis-

charge, and Rayleigh scattering from these relatively weak

lines can compete with the Raman scattering from the stimu-

lated laser line. An estimate of their strength can be








obtained by applying the absorber method of intensity cali-

brations. Experimentally, the factor F is about 101 for

many neon lines in this particular laser, so that without an

optical filter, the Raman lines must be differentially picked

out from the Rayleigh neon background. This also means that

the ratio of laser light to a typical neon background line is

about 2.2 x 104/101 2 x 105.



Tuned Amplifier


The tuned amplifier is required to be sensitive only to

the second harmonic of the modulated light signal. The degree

to which dO and dl signals are rejected at the tuned amplifier

is thus critical for d2 performance. Experimental character-

istics of the tuned amplifier are shown in Figure 11. where

the tuned amplifier was effectively isolated, excited by a

test sinusoid oscillator, and the output measured with an

oscilloscope. The insert circuit diagram shows a test resis-

tance, R", added as a parameter for evaluating the detuning

effect as the Q of the circuit becomes modified. Otherwise,

circuit constants are those used in U7 of Figure 7. Experi-

mentally, the center frequency for R" = 0 is 86.2 Hz compared

with the 60 Hz power line frequency.

The tuned amplifier has a double feedback mechanism, a

so-called "double-T" filter, as pointed out earlier, and shown

in Figure 11. A patent for this double T-network was granted

to Augustadt [16] in 1938, and the first literature description





















500 -





400 -


R"= 0

.H300-
R" = 2.5 K


R" 5 K


200 R" = 10 K





100 -






60 70 80 90 100 110 120
Frequency, Hertz



Figure 11. Tuned amplifier characteristic.








was given by Scott [17], also in 1938. The device has been

subsequently developed and miniaturized [18-21], but with

apparently limited applications, perhaps because it is most

effective at very low frequencies which are seldom used.

The objective of the following analysis is to develop a

mathematical model for the observed frequency response of the

tuned amplifier, and the purpose is to acquire perspective

for application of these data to the instrumentation. Two

steps are required for a simple model -- first, the reduction

of the double T-network to an equivalent double n-network; and

second, the formation of an amplifier circuit which uses the

equivalent network [22].

To develop an equivalent H-network, consider an approach

similar to that of Stanton [18]. In steps of evolution, a

single T-network, Figure 12(a), can be expressed as a single

n-network, Figure 12(b). Then two equivalent n-networks can

be arranged as a double f-network, Figure 12(c), and finally

the double n-network can be arranged as a single 1-network

which has terminal impedances which are identical with the

original double T-network.

The general relation for the T-network to H-network con-

version is well known and easily derived [23]. The result is


7 7 = 7 7 = 7 7 = H
A 2 B 3 C 1 H

where iH is defined for convenience as the function


H = ZZ2 + Z 1 3 Z23

















Single T-Network Equivalent
Single n-Network


Addition of Two
Single n-Networks










Equivalent I-Network
of Double T-Network


Figure 12. Equivalent network for tuned amplifier analysis.







For one branch (primed quantities) and the other branch

(double primed quantities), the composite equivalent H-network

(triple primed quantities) components are

ZA, = ZXZX/(ZX + ZX)

ZB' = ZlZ"/(Zh + Z")
B BZ B

Z', = Z IZ /c(ZL + Z1)


To find the frequency where there is maximum gain, the feed-

back must be zero -- either Z vanishes, or Z"' becomes

infinite at some particular frequency. The first case is

denied because of the finite resistance of elements in the

circuit. However, Z"' has a denominator which can become

zero when both real and imaginary components vanish indepen-

dently. That is

71- Z"/ (7+ "
"B ZBZ B B

z = Z + Zi + 2/
B B 1 2

= (R1 + R2) + j (R1R2/X3)

Z1 = Z7' + Z7 + z7 Z7 /z1
B 1 2 1 2 3
= -(X1X2/R3) j(X1 + X2)

where the real part of Z is R, and the imaginary part is X,

in general.

For resonance, the double condition for maximum ZB is

(I) Re (ZB + ZB) = R1 + R2 (XX2/R3) = 0

(II) Im (Z' + Z') = -(X + 2) + (RI1R/X3)= 0
_' (X1 + X2) + 1 2/X3) =







For the actual double T-network used in the amplifier,

the values are R1 = 357 K, R2 = 88.7 K, R3 = 73 K, C1

.005 vf,C2 = .02 pf,C3 = .024 pf. Either (I) or (II) can be

used for determining the resonant frequency under these cir-

cumstances, since one condition implies the other if all

circuit components are known and compatible. Assuming that

X x = 1/woC at resonance, then using the nominal circuit

element values,

2 -6 2
(I) 1/2o = (R1 + R2) C1 C2 R = 3.256 x 106 sec


(II) 1/2o = C1 C2 C3 R1 R2/(C2 + C1) = 3.050 x 106 sec2


The average of these values gives f = w /2i =

pared with the experimental value of 86.2 Hz.

quency, there will also be a theoretical upper

the gain.

The general condition for resonance found

w2 from (I) and (II) is
o


89.6 Hz, com-

At this fre-

limit, A, for



by eliminating


l/x3R3 = (1/x1 + 1/x2)(1/R1 + 1/R 2)


To simplify computations, introduce the dimensionless

parameters, p, q, s, a, which are defined in terms of the

impedances at resonance,


p = R1/(R1 + R2)

q = xa/(xl + x2)

s = (xi + x2)/(RI + R2)

a = m/W0







Then the values of the circuit components in terms of these

parameters are

R1= p R

R2 = ( p) R

x1 X2 2
R3= R1- 2 = q(l q) s R


X1 = x1/a = (qs/a) R

X2 = x2/a = [(1 q)s/a] R

R1 R2
X =X1 2 [p(l p)/sa] R

The n-network equivalent impedances in terms of these param-
eters leads to

ZB = R1 + R2 + j R1 R2/X3 = (1 + jsa) R

Z = -(X1 X2)/R3 j(X + X2) = -(1/a2)(1 + jsa) R

= -(1/a2) Z

Z = R1 j X3(R1 + R2)/R2 = (p/sa)(sa j) R

S= R3(X2 + X1)/X2 j X1 = (qs/a)(sa j) R
= (qs2/p) Z

Z = R2 j X3(R1 + R2)/I1 = [(1 p)/sa](sa j) R

ZI = -j X2 + R3(1 + X)/X1 = (1 q)(s/a)(sa j) R

= [ i -q s2
[1 p; s z







Substitution of these values gives the following simplifica-

tion for the single 1-network equivalent impedances:

ZA' = [(sa j)/(aW)] R

ZB' = Z' [a/(l a2)] j w j W ZX'

Z'' = (1/sa) [(sa j)] B R = B W Z"'

B = s [1/(1 q) + s2/(1 p)]-l

a = c/(l C2)


W = (p + qs2)/(pqs)

a = u/a0 *

For the second step of formulating a circuit where the

H-network is included with the amplifier, the entire network

must be considered. For simplification, however, allow the

excitation source and the output system to be totally uncoupled

from the tuned amplifier. Figure 13 indicates the relationship

between circuit elements and circuit variables. The triple

primed quantities on the diagram indicate the equivalent

1-network values for the double T-network. The current

through the operational amplifier, which has amplification,

A, is

I = A I1


0 IB + IC A V)/Z' VcC '

11 A -B VA/ZX' (VA VC/Z
















































Figure 13. Tumed amplifier circuit model.








Substitution, and collection of terms in VA ahd VC, gives the

gain, G, of the system,


Z B A
G= /V A = A L + A



To retain conventional interpretation of a feedback amplifier,

introduce an effective amplification, A*, and an effective

feedback function, F*,


A* = A Z' /Z{'

F* = Z"' /Z'

G* = A*/(l + A*F*)


Then the gain becomes a product of two functions -- effective

gain, G*, and a modifier function, (1 + F*) ,


G = G* (1 + F*)


The insertion of physical resistors at critical locations

modifies the gain; for example, in series with ZX" or in

shunt with Z' Z"' or Z' In each case, G* is different.

Resistors across Z"' or Z"' are least influential in the
A B
tuned amplifier of U7. However, a resistor of the order of

R', R' = R1 + R2, decreases the gain substantially, and should

be modeled into the circuit as a realistic value for the

internal resistance of the operational amplifier.

Consider the gain versus frequency characteristic where

the resistor R' is included, and let Z"' Z*"'
B B'







Z "' = Z '' R'/(Z'' + R')

= ZB Z R'/(Zi Z" + R' Z" + R' Z)


The resonant frequency is shifted with thb addition of R',

so that new dimensionless parameters are required. Returning

to conditions (I) and (II), and requiring that the denominator

of Z*"' become zero at resonance,
-B

(I') R' [R1 + R2 X1X2/R3] + = 0

(II') R' [-(Xi + X2) + R1R2/X3] + y = 0

B = (R1 + R2)(-X1X2/R3) + (R1R2/X3)(X1 + X2)

Y = -R1R2X1X2/(X3R3) (X + X2)(R1 + R2)

The coefficient of R' represents conditions (I) and (II),

whereas 6 and y are corrections for shunting Z"'. To find

the resonant frequency, use X3 from (II'),


RR3 ~ A X1X2
X = [R1R2/2RR3 ( X+ X Case R' = R1 + R2 = R.
3 12 3X1 1+ X2 1 2


Substitution of X3 in (I') gives the relation for the resonant

frequency, wo,


1/o + [R(C1 + C)2 3 R C RC2R3/2] 1/ 2

+ 2 1 R2/2 = 0

Substituting values fo the circuit constants gives
Substituting values for the circuit constants gives








1/2 = 3.828 x 106 sec2

f = 81.4 Hertz
0

The peak of the response is broad, with its center at about

83 Hz when R' = 2 R, experimentally. The corresponding band-

width is about 20 Hz. These values compare well with f =

89.6 Hz calculated for the case of R' = .

The peak gain was lowered from 500 to 270 by the addi-

tion of R' = 1 M, which is considered as a justification of

the model performance in the vicinity around the tuned fre-

quency. Therefore, in summary, a suitable model for the tuned

amplifier U7 consists of a f-network with Z"' Z"', and Z'7
A B
where Z*"' is the effective value of Z"' shunted with R' = 1
B B
megohm. A simpler first approximation model would ignore R'

(i.e., R' = o), but would require the peak response to be

reduced by a ratio of Z*"' /Z'' This simpler model also

would indicate correctly an appropriate frequency shift that

occurs near maximum gain.

The diminished performance of U7 for varying R" is very

similar to that when R' is varied. This can be shown by

taking derivatives of G, letting AZ"' = Z*"' Z"', and

AZ' = Z*"' Z"' The result is that R' R" u constant.
A A A
An unusual and unexpected effect in the tuned amplifier

performance is a phase shift between input and output which

depends on the amplitude of the input signal. The shift was

observed for a sinusoidal test signal input, and was approxi-

mately linear, 6 degrees over a 10-volt output when the input








was changed over 15 millivolts. For normal d2 Raman operation,

where signal levels of 1 microvolt or less are used, this is

an unimportant effect.



Random Noise and Interference


The following list of items have been considered, evalu-

ated or represent modifications leading up to a condition

where the Raman lines of carbon tetrachloride are observed

with 3 milliwatt laser excitation:

(1) Electrical transients: The insertion of a 1:1 iso-

lation transformer greatly reduces transient interference

which comes through the power line into the long time con-

stant stages of the operational amplifiers.

(2) Scan motor switching: Most switches were shunted

with a 0.25 pf capacitor. Special low-noise switches instead

of conventional wafer switches are suggested, but none were

used. Also, judicious relocations of the switches and

switched circuits were not attempted.

(3) Intermittent wobble: Some frequency drifting was

corrected by changing the natural frequency. Overheating of

circuit components was corrected by reducing the modulation

power demand. Phase overcontroll" was corrected by electric-

ally loading the coil with huge capacitors (225 uf). Inter-

mittent mechanical friction between the drive coil and field

magnet was corrected by mechanical realignment.







(4) Noise potentiometers: Noise was traced to potenti-

ometer components in the square wave amplifier (U3) and the

preamplifier (US), but the components were not replaced.

(5) Parasitic oscillations: The preamplifier stage

required strong negative feedback for the higher frequencies

(1 to 10 KHz) -- .01 pf was used for degenerative coupling.

(6) Jitter due to zener diodes: Corrective measures

were either to remove them functionally, or to by-pass them

with small capacitors.

(7) Operational amplifiers: These units were sometimes

unbalanced, or had irregular output in time, or simply "gave

up." Four out of eight positions have been replaced with

more than four units, although sometimes the units have

remained partially effective in operation.

(8) Power supply coupling: Each amplifier or transistor

acts as a load to the power supply -- a loading which varies

over each cycle. All circuits, particularly the drive circuit

with Q4 and Q3, are reduced to a minimum drain required for

constant, consistent operation. In this way, variations in

the power supply load not only reduce the demand on the power

supply regulator so that it works more effectively, but also

these variations are less of a disturbance to other circuits

located along the line between the load and the regulator.

Further isolation from the power supply is provided by RC

filters (47 1'f x 1 Kt = 50 ms) at each of the operational

amplifier power terminals, including the dc amplifiers in the

second detector. Not one unit could be ignored in obtaining








quiet operation. Power supply ripple has been less than 1

millivolt throughout the performance; 1 microvolt sensitivity

is required for the Raman signal channel; and ripple follow-

ing any of the filter units has not been measurable.

Isolation between each stage and the power supply serves

as a partial isolation between stages. However, several

interstate leads which appeared as printed circuitry on the

card were physically removed because they contributed to

crosstalk or feedback. An empirical approach to isolation of

troublesome circuit elements has reduced the noise level by

an order of magnitude.

(9) Feedback: A significant feedback problem exists

between the preamplifier and the tuned amplifier due to in-

phase feedback between the output and input of the combined

two units. If the inverting input of the preamplifier is

used for the photomultiplier signal, and a decoupling resis-

tor of 22 K is used between stages, the "noise" is reduced

by about an order of magnitude.



Interstage Decoupling


Since the Raman scattering produces small signals, sen-

sitive amplifiers are needed to record them. If an amplifier

system contributes too much noise, Raman signals would not be

observed. Random noise effects can be integrated out with

the use of long time constant circuits over many cycles, but

this can only be done when the events are of equal positive








and negative content during the observation time. Interstage

coupling can be an effective source of nonrandom noise which

cannot be integrated, but since it is identifiable, it can be

minimized or eliminated.

For example, consider a 120 Hz ripple in the power supply.

If either the wobble frequency, which is derived from the

mechanical vibration of the slit, or the 60 Hz power source

changes, then a beat frequency is generated. This beat could

appear at the chopper, which is located at the juncture of

the sync and signal channels, and the second detector would

proceed to average out positive and negative rectified por-

tions of the beat frequency wave forms. Since it is not a

Raman signal, the beat frequency ideally contributes nothing

to the signal channel if all frequencies are constant; but

practically, if the input to any stage of the signal channel

is not isolated, or balanced with respect to power supply

ripple or neutral potential (ground), or both, then the stage

accepts the beat signal as a real signal input. The beat

frequency therefore appears at the recorder, perhaps as a

regular tracing, but generally it is overwhelming to the weak

Raman line recording.

Other examples of interstate signal coupling include

square wave, fundamental or harmonic frequencies, parasitics,

and power line transients. The means of decoupling varied

greatly to accommodate the different waveforms. Successful

solutions have included negative feedback, resistor damping,

isolation, and stabilization (thermal and frequency).












CHAPTER IV

RESULTS AND DISCUSSION



The circuitry and instrumentation described in Chapters

I and II allow for the detection of a Raman spectrum of car-

bon tetrachloride, as shown in Figure 14. This is a poor

Raman spectrum, but it permits evaluation of the d2 method.

Generally speaking, the Raman lines for carbon tetrachloride

are strong lines, appearing with wavenumbers of 217 (70), 313

(80), 459 (100), 760 (20) and 791 (20) cm-1, the parenthetic

numbers indicating relative intensity at 4358 A excitation

[18]. These Raman lines correspond to Stokes lines at 6416,

6456, 6517, 6648 and 6661 A using helium-neon laser excita-

tion. Figure 14 is very similar to that obtained by Darling

and Williams, who used much stronger excitation, and obtained

corresponding Stokes lines of 4932, 4956, 4992, 5068 and 5076

A with argon laser excitation. For reference and identifica-

tion, a characteristic d2 profile of a highly attenuated

primary 6328 A line is shown in Figure 15.

Figure 14 shows a series of reasonably sharp features

which are spectral lines, or specifically their d2 equivalent.

The largest features are marked A to I; with wavelengths as

shown in Table J. The position of the Stokes lines of carbon

tetrachloride is also shown, and designated a to k. They




51











S- --- r-- --




ftI J

i --ILL
. . ....... "- ... ... .. ...





S *__ i -- -- i :. i. l .

it 1 :-'r c :. i ;v+,+, lti' I




-- i ; '- !-- -: --:- -- +; .----- -- -
hA I .Tr-^ ^

Initial d 2 Rama i spectrum o' carboI t.tr-















cloride, 3 m 6328
. I . ..
r I _i _l i i r ..
chloi- e 3 mw 6328 -ij-
Ir "~~ ~ i i ` . .;" C r --z _L 4:
I lL - -vif +- t+'




/~-.~.~ -lf~--~-F--
6500 6600~;- L~-- C

Iniia d Rmanspctumo[ arontera
ch orde 3 w638


Figure 14.







Table I

Features Appearing in Figure 14


Observed Calculated Stokes
Wavelength AX Wavelengths AX

A 6358 (11) 30 a

B 6380 (15) 52 b --

C 6414 (25) 86 c 6416 (70) 88

D 6448 (14) 120 d 6456 (80) 128

E 6467 (12) 139 e -- --

F 6512 (37) 184 f 6517 (100) 189

G 6597 (30) 269 g -- -

H 6616 (20) 288 h -- --

I 6650 (13) 323 i 6648 (20) 320

J 6660 (11) 332 j 6661 (20) 333

K 6686 (38) 358 k


Notes: (1) The amplitudes of the observed lines as
they appear in Figure 14 are shown in
parentheses. The scale is chart units.

(2) AX is the difference between excitation
wavelength and observed wavelength inA.





53










-44



S .L.
S --7-










F-ur-e-15c i--i"i--.







4-- - I
























Figure 15. Typical d2 line response.







also appear in the table. It is evident that.the calculated

Stokes lines c, d and f fall near large features of the spec-

trum, namely the features C, D and F, respectively. On the

other hand, the features A, B, E, G, H and K which are

observed are not predicted as Raman derived lines of carbon

tetrachloride. Stokes lines i and j, which in fact may be

concluded to appear in the spectrum, are of low intensity as

predicted from the literature.

Wavelengths of lines can be determined directly from

the recorded data of Figure 14 by establishing a scale in

units of chart divisions. Eight chart divisions cover pre-

cisely 100 K, so that the wavelength of an arbitrary line is

determined by adding or subtracting from 6328 A, the laser

excitation indicated by the broken line. Wavelength scales

indicated on the figures are, therefore, only approximate.

Within some error limits, the large number of features

that appear in Figure 14 could perhaps match peaks of any

known spectrum, although there is apparently excellent agree-

ment in wavelength and intensity with predicted values for

some specific peaks. For this reason, it would be desirable

to seek confirming data that C, D and F of Figure 14 are in

fact Raman lines in the carbon tetrachloride or sample spec-

trum. Consider the following arguments:

a) Apparent Raman spectra may occur because of other

scatterers, where any feature that appears in the data could

be properly ascribed to the illumination source or to the

instrumentation. F-or example, helium and neon spectral lines








may be elastically scattered; such scattering'would produce

Rayleigh lines of the laser gas with an intensity that could

be high enough to produce features as large as those of

Figure 14.

b) Corresponding to each Stokes line of any Raman spec-

trum, on the long wavelength side of the laser line, an anti-

Stokes line should also appear on the short wavelength side,

with a difference in wavelength from the laser light which

departs in a predictable manner from the difference observed

for the Stokes line. Features failing to show this differ-

ence in separation from the laser light might be expected to

originate from imperfections of the grating. Such features,

commonly referred to as "ghosts," are well known to be char-

acteristic of ruled gratings, and presumably also of replica

gratings from the ruled gratings. Their intensity is normally

negligible, but night be sufficient to show up here.

Both of the possibilities were investigated as described

below. With reference to the anti-Stokes lines, it is impor-

tant to note that the Stokes and anti-Stokes lines are differ-

ent in amplitude as well as wavelength. For example, appar-

ently the origin of the Raman spectrum is a nonlinearity of

the molecular polarization, p, with applied electric field, E.

Bulk polarization per unit volume, P, is an observable, the

average of all molecular polarization, P = , and can be

defined as the difference between electric displacement, D,

and the applied electric field,







P = (D e:E)/4T

p = E [eo(k 1)/4rn] E/Eo = k

= E .


is then an average molecular polarizability, where k is

the dielectric constant of a bulk of the material. For a

point charge model of a molecule, the dipole formed by charges

+q and -q at a separation distance d gives an electric field

at large r,


Er 2 q Ar/r3 = 2 q p cos 6/r3

=2 p/r3


p = |q| d

a = 0, for all binary encounters.


For such an approximation, the molecular polarizability is


a = p/Er = r3/2


For a general case where the charge is distributed in space,

however, assume that a = a(r), and that a Taylor expansion is

possible around the equilibrium position, ro,


a(r) = a + (aa/ar) r +.


Classical electromagnetic theory gives the radiated energy,

I, as


1 = 2[d2 P/d t2]/3 c2







To formulate the time dependence of the polarization on time-

varying fields, the excitation is E = E cos vt. The dipole

oscillates with a frequency v' about ro, and r = ro cos v't.

Then


P =E cos vt a + (aa/r) r cos v't + .


= [E a cos vt] + Er /2 ( (aa/r) [cos(v v')t


+ cos(v + V')t] + . .


The first term accounts for the Rayleigh scattering, the

second for Stokes and the third for anti-Stokes scattering

of the incident radiation. Higher order terms exist, but

each order with less amplitude.

The anti-Stokes components represent higher energy pho-

tons than the exciting photons. This is because the molecule

originally is in an excited state and drops to a ground level

after the photon collision. The classical radiation depends

on the fourth power of the frequency, so that the ratio of

the intensity of the Stokes line is


anti-Stokes _v + v) 4e-hv'/kT
Stokes (v v'J


The Stokes bands (lower frequency) are always the stronger.

For carbon tetrachloride, for example, the use of the Stokes

bands at room temperature should give increased intensity by

factors of 1.11, 1.17 and 1.26 for the Raman lines 217, 313

and 458 cm-1
{nd 458 cmi







Carbon Tetrachloride versus Toluene


After obtaining the Raman spectra data of Figure 14, the

system was changed -- optimized to make a comparison between

carbon tetrachloride and toluene Raman spectra. Figures 16,

17, 18 and 19 show the results of runs which cover the Stokes

and anti-Stokes ranges of each material. Except for changing

the material in the scattering cell, all instrumentation con-

ditions remained identically the same for both runs, but dif-

ferent from Figure 14.

Five toluene lines in the anti-Stokes spectrum were iden-

tified and marked A, B, C, D and E in Figures 16 and 17 --

6134, 6037, 5958, 5490 and 5888 A. According to the litera-

ture [24], the dominant lines in the region should be 6126,

6028, 5949, 5941 and 5879 A, which correspond to wavenumbers

521 (15), 786 (43), 1004 (91), 1030 (26) and 1208 (26) cm 1

The lines were identified by using data from both Stokes and

anti-Stokes sidebands, and exploiting an asymmetry in wave-

length difference between observed wavelength and excitation

wavelength. Equal displacements for the Raman Stokes and

Raman anti-Stokes lines cannot occur because frequencies are

additive, not wavelengths. Other observed "lines" are remark-

able in that they are displaced the same amount above and

below the excitation wavelength of 6328 A. Furthermore, it

is also reiiarkable that the equally displaced lines have simi-

lar amplitudes on both sides of 6328 A where the photomulti-

plier characteristic is known to vary rapidly -- 3% quantum




59






rr .- I- -


VA- 11



md i )i
_: _-- .l ..l '--.-----i-- -
:-_[ 7 rI .-- i t -rTl i -- ;-.--.- h-.! | l s I
"e ..B | 4 I.

U I




S7 ---- I i I ,6 0




i7 ,,, I 6i0 I



..- "-- .. ; Ii
-I I I J 1 I




5700 600h 6300 I


Figure 16. Toluene, Raman anti-Stokes spectrum, 3 mwi
helium-neon laser 6328 A.




60




T T. T-7-- : ---- -' l- .. .. --- .. -


i~ j

*- ""- i ^ -- "- i,-_ i- .. --.- --+-H ---'
S I .; I .. I . -


71-

-. -- ._ .. - I-_*- 7 ._ '- I .... I.- - ]- --


... ..-- -"" -
-.,1i . .I 1.. .. -- i: + -




















Fi turo 17. Toluene Raman Stokes sp, ru, 3 ti, !elium,
neon lase 6328i A
i .. --










6300 6 6900 .




Figure 17. Toluene 1R"amar Stokes spct'rui,, 3 mt ., helium-
neon laser 6328 A.









3 r7~ Tr~7-E-~~----- -z ---~
-Ii1







'rr'. i -.n~--Vri!^- ri-n
Er r


H -. -;.
S~ I

7--

I !











--- i __ .t-;-----d- :---

St L. It, 7 i d
.... .._ . ... .,. i- ..
_. I -i


5700


6000


6300i A


Figure 18. Carbon tetrachloride, Raman pnti-Stokes spectrum,
3 mw helium-neon laser 6328 A.












'_ :r",L _i ":]- : : :+ -
rI-




1 t







I AI
I~:-: ir :,- -1 -- ii
tit ... .. ,



I LI i i I ,
-t


I 4 I t t
r r F


i L : T
__


~~LLi' -- -
.. .. _.....__.,_ ._ _____
S. . I ~ i:. ',+- 6 0 "- -.
| '- -i:I i. ; | | i ;-- :: .... r -, : ": i



i;l
o I _. _.l:.. .I . ::. . -j:--'V : --

9 -- 1 i ,L i rj?-



7- -
L'": i.~


6300


6600


Figure 19. Carbon tetrachloride, Raman Stokes spectrum,-
3 inm helium-noon laser 6328 L.


6900 A





63

efficiency at 5828 A (500 A below) to <0.1% at 6828 A (500 X

above the excitation).

Reduction and interpretation of the data are, therefore,

difficult because of the interfering "lines" which are inter-

spersed with the Raman spectrum. If Figure 16 (anti-Stokes)

and Figure 17 (Stokes) could be superimposed with the aid of

a fictitious mirror with properties which (a) folded the two

figures so that the 6328 line, Xo, became the origin for the

differential Stokes wavelengths, (Xs o), and differential

anti-Stokes wavelength, (XA a ), displacements, and

(b) flipped the folds over to match the curved base line of

the d2 recorded pattern, then each of the d2 spectrum lines

would still remain unmatched. This is because the top of a

line has "one peak," and the bottom of the line has "two

peaks" as shown in Figure 15 -- i.e., an overlay would also

be difficult to interpret.

However, an equivalent superposition can be carried out

using the tables constructed below, which reduces the data of

Figures 16 through 18. Estimates of peak amplitudes are

based on a mean measure from the top of a d2 line (maximum

position) to the bottom of a d2 line (mean minimum of two

positions). This is not a very satisfactory amplitude deter-

mination for a complicated spectrum, but at least it keeps

track of large and small features.

A display of the toluene data in Table II appears in

Figure 20; similarly, carbon tetrachloride data of Table III

appear in Figure 21. There are lines within each set of







Table II

Light Intensity in the Stokes and Anti-Stokes
Regions of Figures 16 and 17 for Toluene


Anti-Stokes "Stokes

a) (0o a (As) s -o)

5768 (25) 560 6466 (>10) 138
5798 (15) 530 6492 (>36) 164
5831 (12) 497 6520 (40) 192
5865 (20) 463 6547 (57) 219
5888 (38) E 440 6581 (-28) 253
5923 (08) 405 6607 (08) 279
5940 (10) D 388 6612 (28) 284
5958 (15) C 370 6646 (13) 318
5966 (08) 362 6668 (18) 340
6007 (15) 321 6685 (13) 357
6037 (42) B 291 6704 (13) 376
6049 (22) 279 6722 (09) 394
6071 (41) 257 6740 (11) 412
6104 (61) 224 6759 (20) 431
6134 (57) A 194 6793 (38) 465
6160 (74) 168 6820 (27) 492
6192 (28) 136 6848 (16) 520
6207 (29) 121 6883 (22) 555
6246 (>70) 82 6917 (19) 589
6276 (>14) 52


Notes: (1) Letter designation
on the figures.


corresponds with letters


(2) Designated lines are the closest match in
amplitude and frequency to Stokes side-
bands for published Raman modulation
frequencies.

(3) Stokes lines are weaker than the anti-
Stokes lines due to the photodetector
sensitivity in this range. They are too
small to be identified.










Anti-Stokes


-r -


B


-C B


C
D


D
-4


E ---mm


--- E


Figure 20.


Stokes


O-



eD


Amplitude of apparent line on the Stokes and
anti-Stokes sides of 6328 A excitation for
toluene (Ref. Figures 16 and 17, and Tables
II and IV).


C
- C
-4





- C
C"


A -






Table III

Light Intensity in the Stokes and Anti-Stokes
Regions of Figures 18 and 19
for Carbon Tetrachloride


Anti-Stokes Stokes
(Xa) (X a) (X ) (Xs Xo)
a o a s 5s o

5694 (19) 571 6441 (>08) 113
5704 (22) 549 6460 (>06) B 132
5790 (04) 538 6472 (05) 144
5838 (09) 490 6496 (48) 168
5868 (22) 460 6517 (10) C 189
5944 (15) 384 6531 (14) 203
5968 (24) 360 6536 (03) 208
6001 (11) 327 6556 (59) 228
6013 (05) 315 6584 (17) 256
6029 (20) E 299 6624 (26) 296
6048 (13) D 280 6642 (04) D 314
6074 (37) 254 6660 (05) E 332
6106 (37) 222 6686 (21) 358
6142 (24) 186 6694 (06) 386
6162 (47) C 166 6792 (26) 464
6191 (11) 137 6822 (12) 494
6209 (29) B 119 6849 (10) 521
6229 (14) 99 6870 (09) 542
6244 (18) A 84 6891 (25) 563
6252 (>04) 76 6916 (11) 588


Notes: (1)


Letter designation
on the figures.


corresponds with letters


(2) Unlike the toluene data, these carbon
tetrachloride data lines can be seen in
the Stokes region because they are nearer
to the excitation frequency where the
photodetector sensitivity is greater.
The amplitudes, nevertheless, are small.













Ani-tksSoe


A

B


C ---0


04











--o
0






-C






-C







Ln


C


I0-
NOW
ON


I _______________________________________


Amplitude of apparent lines on the Stokes and
anti-Stokes sides of 6328 A excitation for
carbon tetrachloride (Ref. Figures 18 and 19,
and Tables III and IV).


- A


B



C


D
E


D-0




-a


4


Figure 21.


Anti-Stokes


Stokes









data which have the same frequency difference around the

laser center frequency, as well as unmatched lines which are

Raman derived. On these figures, Stokes lines appear to be

"shifted" from the anti-Stokes lines, but fit expected pat-

terns for Raman spectra, while the interference patterns do

not.

Apparently the origin of the interfering lines, there-

fore, is not Raman scattering, nor Rayleigh scattering of the

neon laser line background. The most plausible assumption is

that the particular grating has a type of "ghost" which results

from a periodic error in the otherwise regular spacing between

the ruled lines. This effect is generally small, and is not

objectionable. It has an apparent amplitude here of about

1:103 to allow for the Rayleigh line to be the size of the

Raman line. This type of "ghost" and others have been long

known [25,26].

The grating "ghost effect" should vary with the particu-

lar grating in use, but any effect should be reduced sub-
0
stantially if an optical blocking filter for 6328 A, or the

excitation frequency, were inserted between the exit slit and

the photomultiplier. Choice of bandwidth for the blocking

filter would be governed by the proximity of the Raman line

to the laser line, and choice of attenuation would be governed

by the "mortal size of the ghost." No filters were available

to reduce this interference here at the time of this measure-

ment .









Table IV

Calculated Wavelengths Using Published Frequencies


Wavenumber Anti-Stokes Stokes
-1
(cm ) (a) (Xo Xa) (s ) (s -o)

Carbon Tetrachloride

217 (70) 6242 (80) 086 6416 (46) 088
313 (80) 6206 (77) 122 6456 (37) 128
459 (100) 6148 (235) 179 6517 (35) 189
760 (20) 6038 (155) 290 6648 (03) 320
791 (20) 6026 (103) 302 6661 (03) 333


Toluene

521 (15) 6126 (22) 202 6544 (03) 216
786 (43) 6028 (95) 300 6660 (03) 332
1004 (91) 5949 (279) 379 6758 (03) 430
1030 (26) 5941 (78) 387 6770 (01) 442
1208 (26) 5879 (106) 449 6851 (01) 523


Notes: (1)


The amplitudes have been corrected for frequency
(reported excitation was 4358 X), and also


corrected for the photomultiplier response for
each frequency.

(2) The photomultiplier correction indicates that
the anti-Stokes side is the more intense for
6328 X excitation.








Slit Modulation and Stability


Both the amplitude and the phase change during operation

of the modulator, and.this action contributes to a recorder

response, although in different ways. A frequency stability

of one part in 2.7 x 104 cycles has been attained with the

present mechanical system. This is good, but not especially

satisfactory because a line scan takes a relatively long time

of 0.5 minutes (1350 cycles). Such a variation represents an

uncertainty of 5% in Raman line amplitude due to a so-called

"stable frequency." Similar change occurs in the noise level

(i.e., where no Raman signals are present), so that the

recorder can experience amplitude excursions which depend on

frequency change as well as crosstalk.

In the present device, modulation amplitude is controlled

by a feedback system, where (a) the damping time is uncon-

trolled, and (b) crosstalk from the master oscillator feed-

back signal enters both the sync channel and the signal chan-

nel. Since the feedback is necessarily of different phase

from the sensor, and since the feedback phase varies accord-

ing to modulator needs, crosstalk effectively produces noise.

The modulator circuit is basically stable, but improvement is

possible, desirable, and would directly influence the d2

Raman Spectrometer sensitivity.

To avoid the mechanical modulator problems, it may be

possible to consider the use of an all-electric one. Such a

device does not exist at present, but could be developed.








For example, immediately after the second spectrometer slit

place a light amplifier element consisting of a photosensi-

tive surface which emits electrons. These electrons would

pass through an electric or magnetic field which is energized

at the wobble frequency. If the electron trajectories were

displaced in such a way as to scan a sensitive surface (e.g.,

a channeltron or electron multiplier), the electron beam wobble

would then replace the light beam wobble.

The important point to remember is that an effective

scan over the line profile is required, and not just an on-

off switch for the detector. In fact, it may be possible to

use a conventional photomultiplier if it can be modulated by

an external magnetic field up to a critical point where the

detector output remains independent of the position of a

light spot over its sensitive surface.

If an all-electric modulator were available, the limita-

tion imposed by the inertia or material coefficients of the

mechanical modulator would be removed. Frequency changing,

including electrical synchronous operations, are readily

available by state-of-the-art means. There is also the pos-

sibility of extending control with this method into the pulse

counting regime for high intensity signals by control of the

light amplifier sensitivity. Apparently pulse counting tech-

niques at high signal intensities are desirable for computer

purposes, but are very difficult to handle because too many

pulses jam the counters [8].









Modified Sync Channel and Second Detector


Development of this d2 Raman Spectrometer has been

hampered by crosstalk from the square wave amplifier output,

and in fact the square wave may not be essential to the d2

Raman operation. The purpose has been to supply a precisely

gated "chopper" signal to select out from the tuned amplifier

the cosine component which eventually appears at the second

detector (recorder). Consider an optional method which uses

cosine waveforms throughout as sketched in Figure 22.

For example, it is possible to use a second analog device

such as the AD/426 already mentioned, as a substitute for the

doubler function. The cosine waveform from the sensor would

be used as an input, and the same waveform as a second input,

so that multiplication of the input from both sources would

be the equivalent of a mathematical "squaring" operation.

The output contains an ac term of double frequency, and a dc

term which is blocked by a capacitor. Proper phase control

of the squarer output means that, at the electron multiplier

(or photodetector),only cosine terms are eventually selected.

A third AD/426 device, or its equivalent, could also be

substituted for the "chopper" function proper. If the

cos(2wt) output from the square were one of the inputs, and

the other input came from the tuned amplifier, then an analog

multiplication operation would result in the product of the

cosine component of the photodetector and the reference

cos(2wt) [unction.




































Z I f(t) cos 2wt

DIVIDER BIAS DIVIDER

Y



d2 RAPtAN RECORDER

OTE: (X) (Y) = (Z)


Figure 22. Raman Spectrometer, proposed option.









Furthermore, if the output from the multiplier is inte-

grated, by the use of long time-constant components, the

mathematical result would be proportional to the amplitude of

the second harmonic cosine terms -- i.e., a second Fourier

coefficient of the line profile which appears at the output

of the photodetector.

The amplitude of the signal which appears at the photo-

detector is proportional to I(x), x = x(t) as discussed in

Chapter I. Development of I(x) into component terms allows

the identification of second harmonic cosine terms, where the

Fourier coefficient contains the derivative contributions,

d2, d4, d6, etc. In this optional "Fourier" method with

AD/426 analog devices, the mathematics is exactly equivalent

to the d2 square wave "chopper" method. Only the electronic

technique is different, potentially capable of producing much

quieter operating instrumentation with less noise background.














CHAPTER V

SUMMARY AND CONCLUSIONS



Conclusions for this experimental study of d2 Raman Spec-

troscopy fall into essentially two categories, one which

records the state of d2 development at the time that the Raman

spectra were observed, and another which puts forth an esti-

mate for improved instrumentation based on results from the

study.

Raman spectra observed before and after the investiga-

tion show that a reduction in background noise can be accom-

plished by changes in the electronic circuitry. An improve-

ment of about four orders of magnitude in the background

level has permitted at least three carbon tetrachloride and

three toluene Raman lines to be observed with a weak helium-

neon laser of 3 milliwatts. Apparently moderate background

levels still exist, and are attributable to circuitry, but

it is more fruitful now to redesign the entire system where

location of parts, couplings and components are made accord-

ing to improvements based on present performance.

In general, the photomultiplier has not been a major

source of noise, but has limited the Raman signal response.

The present unit has a quantum efficiency of 0.8% at 6328 A,

which could be changed to one with about 15% efficiency.









Electronic coupling between amplifier stages has pre-

sented a major difficulty because levels of less than 1 micro-

volt interference are required. Operational amplifiers and

transistor circuits have been altered to offer minimum load-

ing to the power supply, thus reducing inductive coupling in

closed loop circuits, and capacitive coupling in open circuits.

In addition to the interstate coupling, an associated coupling

has been found between operational amplifiers and the power

supply. This coupling has served both to introduce power

supply ripple into the signal channels, and to allow varia-

tions in one stage to be conducted through the hard wiring as

an interference signal to another stage. A successful buffer

scheme has been devised which uses a series resistor with

capacitors across the amplifier power leads at each individual

amplifier. The time constant is as large as possible, 47 ms

(47 pf x 1 K), twice the wobble period. Buffering of all the

amplifiers was needed, and succeeded so that contributions

from the power supply ripple of 1 millivolt in 15 volts

became relatively ineffectual.

Electrical noise sources have been traced variously to

multiple ground loops, switches, potentiometers and thermal

excursions. Insofar as possible, contributions from the

noise sources have been minimized by physical isolation or

replacement of components.

'Modulator interference has been difficult to isolate

from the amplifier stages. The modulator feedback loop

includes a po%,erful transistor driver xihich is energized at









a phase that depends on an error signal for synchronism. The

error depends on wobble amplitude and frequency, which in turn

depend on the wobbler material coefficients. The entire

modulator then becomes responsive to ambient air currents,

temperature, power supply coupling and circuit feedback.

Nevertheless, the frequency has been stabilized to one part

in 2.7 x 10 Decoupling and reduction of the modulator

power have made a major reduction in the background noise.

A tuned amplifier is essential to the present system.

The particular type of tuned amplifier circuit is a double

T-network which is basically an active filter circuit. Per-

formance and analysis indicate that the feedback, input and

output circuits are unnecessarily dependent, and could be

improved if at least the feedback circuit included a buffer

for decoupling.

The Raman spectra have been influenced by optical com-

ponent performance -- "ghosts" due to grating imperfection

(periodic ruling line variation effect), and contributions

from the neon background of the helium-neon laser. Both of

these optical difficulties apparently can be remedied with

filters; line transmission filter at the entrance slit, and

line blocking at the exit slit.

The present system would probably give excellent Raman

spectra if a 50 mnv argon laser were used, and if a blocking

filter for 4880 A were inserted between the exit slit and the

photomultiplier. Assuming that the electronic noise back-

ground remains constant, the change to 4880 A improves the









photomultiplier efficiency 10/0.8 = 12.5 X, radiation effi-
4
ciency (6328/4880) = 2.83 X, power input 50/3 = 16.7 X,

giving an overall improvement of 592 X. The noise level

therefore would be approximately 1.6% of the Raman line

459 cm- of carbon tetrachloride. Without the blocking fil-

ter, however, the grating imperfections would contribute

interference lines as large as the Raman lines.

An optional design for a d2 Raman Spectrometer is pro-

posed which uses analog electronic devices to "square,"

"multiply," and integrate the output from a photodetector.

The method uses quiet low level sinusoidal signals, and the

mathematical orthogonal property of a Fourier integral to

select out the second harmonic coefficient, which in turn

approximates the d" profile of the Raman line. The method

does not require a tuned amplifier, although its use could

help noise rejection. The method is also compatible with a

proposed all-electric wobbler sampling technique.































APPENDIX A

WAVEFORMS OF SELECT POSITIONS IN
ELECTRONIC CIRCUITS OF d2 RAMAN SPECTROMETER





























Figure 23.


Modulator, sensor amplifier output, U2
(10 volt/cm x 5 ms/cm).


Figure 24. Master oscillator output, U1 (1 volt/cm
x 5 ms/cm).





























Figure 25.














A

11


C


Modulator, driver output to coil, Q4
(0.2 volt/cm x 5 ms/cm).


Figure 26. Signal channel, preamplifier output, U5
(0.2 volt/cm x 5 ms/cm). A right wing
of optical line, B optical line center,
C left wing of optical line.




























(a) Optical line center


(b) Optical line wing


Figure 27. Signal channel, tuned amplifier output, U7
(5 volt/cit x 5 ms/cm).






























Syncchannel, square wave amplifier output,
U3 (10 volt/cm x 5 ms/cm).


Figure 28.



























Figure 29.


Sync channel, doubler output, U4
(0.5 volt/cm x 5 iis/cm) Unequal rise
and fall times are due to di ferent (C
time constants in the wave shape gener-
at ion .




























(a) Total input


(b) Invcrting input only


Figure 30. Sync channel, doubler amplifier input, U4
(10 volt/cm x 5 ns/cm, total input;
5 volt/cm x 5 ms/ci, inverting input).



























Figure 31.


Sync channel, doubler amplifier output, U6
(10 volt/cm x 5 ms/cm).


Figure 32. Second detector, rectified tuned amplifier
output, US input (5 volt/cm x 5 ms/cm).















BIBLIOGRAPHY


1. Williams, D.T., "Spectrometer System," U.S. Patent
232,053, March 6, 1972.

2. Hager, R.N., Jr., The Theory, Design and Application of
a Second Derivative Spectrometer, Ph.D. dissertation,
University of Florida, 1970.

3. Spectrometrics of Florida, Inc. (subsidiary of ABA Indus-
tries, Inc.), P.O. Box 517, Pinellas Park, Florida 33565.

4. Lear Siegler, Inc., 1 Inverness Drive East, Englewood,
Colorado 80110.

5. Darling, J.W. II, "The Application of a d2 Spectrometer
for the Detection of Raman Spectra," paper presented at
the Southeastern Regional Student Conference, Atlanta,
Georgia, April 18-19, 1974.

6. Freeman, S.K., Applications of Laser Raman Spectroscopy,
John Wiley and Sons, 1974.

7. Panofsky, W.K.H. and Phillips, M., Classical Electricity
and Magnetism, Addison-Wesley, 1962.

8. Anderson, A., The Raman Effect, Volume 1: Principles,
Marcel Dekker, Inc., 1971.

9. Sushchinskii, M.N., Raman Spectra of Molecules and
Crystals, Israel Program for Scientific Translations,
19-7772.

10. Tobin, 1M.C., Laser Raman Spectroscopy, Wiley Intersci-
ence, 1971.

11. Spectra Physics, 1250 WI. Middlefield Road, Mountain View,
California 94040.

12. Jarrel-Ash, 590 Lincoln Street, Waltham, Massachusetts
02154.

13. EMI Electronics Ltd. (Distributors Whittaker Corp.,
Gencom Division, 80 Express Street, Plain View, Long
Island, New York).








14. Linear Integrated Circuits and MOS Devices, RCA Solid
State Series, 1972.

15. Analog Devices, Route #1, Industrial Park, P.O. Box 280,
Norwood, Massachusetts 02062.

16. Augustadt, H.W., "Electronic Filter," U.S. Patent
2,106,785, February, 1938.

17. Scott, H.H., "A New Type of Selective Circuit and Some
Applications," Proc. IRE, Vol. 6, pp. 226-235, February,
1938.

18. Stanton, L., "Theory and Application of Parallel-T
Resonance Capacitance Frequency-Selective Networks,"
Proc. IRE, Vol. 34, pp. 447-456, July, 1946.

19. Sallen, R.P. and Ken, E.L., "A Practical Method of
Designing RC Active Filters," IRE Trans. Circuit Theory,
Vol. CT-2, pp. 74-85, March, 1955.

20. Muschy, G.S. and Thelen, W., "Design of Hybrid Inte-
grated-Filter Blocks," IEEE Journal of Solid State Cir-
cuits, Vol. SC-5, No. 3, pp. 99-107, June, 1970.

21. Geffe, P.R., "Passive Q Sensitivities of the Twin-T
Selective Amplifier," IEEE Trans. Circuit Theory, CT-19,
No. 6, pp. 685-686, November, 1972.

22. Gray, P.E. and Searle, C.L., Electronics Princinles;
Physics, Models and Circuits, Wiley and Sons, 1969.

23. Everitt, W.L., Communication Engineering, McGraw-Hill,
1937.

24. Selected Raman Spectral Data, Report of American Petro-
leum Institute, Research Project 44, Thermodynamic
Research Center, Department of Chemistry, Texas A & M
University, College Station, Texas.

25. Wood, R.W., Physical Optics, Macmillan Co., 1936.

26. Sparrow, C.M., "Theory of Imperfect Gratings," The
Astrophysical Journal, Vol. 49, pp. 65-95, 1919.













BIOGRAPHICAL SKETCH


Wallace Dorman Kilpatrick was born at Worcester, Massa-

chusetts, on August 31, 1920. He was graduated from North

High School in Worcester, Massachusetts; attended Antioch

College in Yellow Springs, Ohio; and graduated from Clark

University in Worcester, Massachusetts, with the degree of

Bachelor of Arts in 1942. He studied Radio Engineering at

Harvard University, Cambridge, Massachusetts; Ultra High Fre-

quency Engineering at Massachusetts Institute of Technology,

Cambridge, Massachusetts; and graduate Physics at the Univer-

sity of California at Berkeley, California. He was graduated

from Florida Atlantic University at Boca Raton, Florida, with

the degree of Master of Science in Physics in 1970.

During WWII he was technical officer for airborne and

shipborne electronic equipment, including radio and radar,

aboard the light carrier CVE White Plains. He was Instructor

of Mathematics at Worcester Polytechnic Institute in Worces-

ter, Massachusetts. His experimentation background has been

obtained with the Lawrence Radiation Laboratory (both in

Berkeley and Livermore, California); with industrial research

at Electro-Optical Systems, Inc., Pasadena, California; and

with Franklin GNO Corporation, West Palm Beach, Florida.








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.




David T. Williams, Chairman
Professor of Aerospace Engineering


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.




Dennis R. Keefer
Associate Professor of
Aerospace Engineering


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.




Edward K. Walsh
Associate Professor of
Aerospace Engineering


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.




Thomas L. Bailey
Professor of Physics








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.




aiMes VW. Dufty
Associate Professor of (Ekysics


This dissertation was submitted to the Graduate Faculty of
the College of Engineering and to the Graduate Council, and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.

June, 1975




,Dea College of Engineering

\7


Dean, Graduate School




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