The design and evaluation of a selectively modulated interferometric dispersive spectrometer

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Title:
The design and evaluation of a selectively modulated interferometric dispersive spectrometer
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iv, 179 leaves : ill. ; 28 cm.
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English
Creator:
Fitzgerald, John J., 1950-
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Subjects / Keywords:
Spectrometer   ( lcsh )
Interferometers   ( lcsh )
Fourier transform spectroscopy   ( lcsh )
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theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1986.
Bibliography:
Includes bibliographical references (leaves 175-177).
Statement of Responsibility:
by John J. Fitzgerald.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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oclc - 17689607
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Full Text












THE DESIGN AND EVALUATION OF A
SELECTIVELY MODULATED
INTERFEROMETRIC DISPERSIVE SPECTROMETER













By

JOHN J. FITZGERALD


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




UNIVERSITY OF FLORIDA


1986















TABLE OF CONTENTS


Page

ABSTRACT ............................................... iii

CHAPTERS

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

II THEORETICAL CONSIDERATIONS ........................ 9

Fourier Analysis and the Michelson Interferometer.12
Theoretical Treatment of SEMIDS .................. 23

III INSTRUMENTAL DESIGN................................ 43

IV ALIGNMENT PROCEDURES.............................. 76

V SYSTEM PERFORMANCE EVALUATION .................... 86

VI ANALYTICAL EVALUATION ........................... 132

VII DISCUSSION OF RESULTS ........................... 155

VIII ADDITIONAL DEVELOPMENTS......................... 160

APPENDICES

I DERIVATION OF FOURIER INTEGRAL .................. 166

II FIGURES OF MERIT ................................ 171

III EXPERIMENTAL MEASUREMENT OF ..................... 173

SIGNAL-TO-NOISE RATIOS

BIBLIOGRAPHY ........................................... 175

BIOGRAPHICAL SKETCH .................................... 178














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




THE DESIGN AND EVALUATION OF A
SELECTIVELY MODULATED
INTERFEROMETRIC DISPERSIVE SPECTROMETER

By

JOHN J. FITZGERALD

August, 1986

Chairman: James D. Winefordner
Major Department: Chemistry

In approaching the problem of rapid simultaneous

multielement analysis, the large light gathering power,

wide spectral range and high resolution of a Fourier

Transform Spectrometer (FTS) should be of benefit. The

severe mechanical tolerances required in the construction

and operation of a classical Michelson interferometer for

use in the UV-Visible spectral region have limited

investigations in the application of simultaneous trace

quantitative analysis. Theory is presented demonstrating

that replacement of the fixed mirror in one arm of the

Michelson interferometer with a rotating grating preserves

most of the FTS advantages and results in a greatly

simplified detector system. No mathematical Fourier

transform is required. The need for a computer is


iii








eliminated. An instrument, SEMIDS (SElectively Modulated

Interferometric Dispersive Spectrometer), was constructed

to investigate the mathematical model. Design criteria and

basic operational performance as a flame emission

spectrometer are presented. SEMIDS achieved high

resolution, high throughput and greatly simplified

operation compared to a Michelson interferometer.

Performance as a trace quantitative tool was disappointing

because of unanticipated noise contributions from flame

background. A summary of the noise component contributions

is discussed.














CHAPTER I
INTRODUCTION

In the history of analytical chemistry, there has

always been a strong tendency to use the best available

methods to develop techniques for rapid multielement

analysis. There are a wide variety of analytical problem

areas where the capability of analyzing a sample for a

number of different elements is a great asset. These

problem areas include the fields of clinical,

metallurgical, geochemical, biological, environmental and

industrial chemistry. The progress over the last decade in

electronic equipment and in technology has been rapidly

utilized in the construction of new systems for

multielement applications. Most of the new systems use the

available technology to improve on the data acquisition

rates and the parameter control of already existing

analytical tools. The work presented in this dissertation

describes a new multielement analysis tool which does not

employ technology to improve on previous system performance

but which rather uses some basic optical considerations to

provide improved spectral isolation characteristics over

grating monochromators. The available technology is

employed to keep the operating simplicity of the device

called SEMIDS comparable to the devices which it is

intended to replace. SEMIDS is an acronym for SElectively








Modulated Interferometric Dispersive Spectrometer. The

prototype device was built as a result of investigations by

Winefordner and his research group into a variety of

techniques for rapid multielement analysis by atomic

spectroscopy.

A partial survey of activity in this area supports the

contention that most developments in multielement analysis

represent applications of new technology to old methods

and places the development of SEMIDS in perspective. The

objective in multielement analysis, whether atomic

absorption AAS, atomic fluorescence AFS, or atomic

emission AES, is to record one or more components of the

UV-visible spectrum for each of several species of

interest during a single sampling cycle. This goal

requires the use of either rapid single channel or

multichannel detection systems. There are three major

classifications of multielement detection devices:

temporal devices, spatial devices, and multiplex devices.

The information collection methods may also be loosely

grouped into three categories including data collection in

a sequential mode, in a simultaneous parallel mode, or in

a simultaneous multiplexed mode.

The temporal devices use only one detector and the

information is encoded in the time domain so only one

spectral element falls on the detector at one time.

Despite a wide variety of mechanical methods used to

achieve the multielement capability, the most successful








and widely applied techniques are those of rapid scanning

dispersive spectroscopy and programmable dispersive

spectroscopy. The rapid scan techniques collect

information from all the spectral components in a very

short time interval and excellent reviews on the methods

employed are available in the literature (1,2). The

programmable scan spectrometer uses the fact that large

areas of the spectrum do not contain useful information and

uses logic control to step rapidly through these regions.

Malmstadt and Cordos (3) have described a modular system

for AFS and D. J. Johnson et al. (4,5) have published

several articles describing a programmable system for AFS

using a continuum source. A variation of the programmable

monochromator has been described by Golightly et al. (6)

using an image dissector photomultiplier tube to

effectively generate a moving slit. In each case, the

system was designed around the "state of the art"

technology: in the case of rapid scanning, it was the data

collection system that provided the rapid scan; in the

programmable scan it was the presence of computers and/or

new intense sources that were the keys to success; the

system was totally dependent on a new type of detector.

This trend continues with spatial devices.

Spatial devices depend on multiple detectors.

Historically, the first method using this approach was the

emission spectrograph using a photographic emulsion as

detector. The next improvement in the field was to replace







the emulsion with electronic detection and this led to the

direct reader spectrometer. Aside from some application

work in AAS (7,8), further development was halted until new

detectors became available. These detectors were

electronic image devices and can be separated into TV

tube-type devices (9-23) and solid state devices (24-31).

Each device has some special characteristics but invariably

shares the problems of poor quantum efficiency, poor

signal-to-noise ratios, poor spectral response, and limited

linear range. In every system, it is the presence of a new

detector and associated technology that differentiates-them

from the classical spectrograph.

Multiplex systems can be classed as dispersive and

nondispersive, but again it is the available technology

which permits data acquisition and treatment as well as

system control. The dispersive multiplex techniques have

all involved the Hadamard transform (32) and a number of

papers have been published describing various systems

(33-37). The multiplex approach appears to have limited

usefulness in the UV-visible spectral region (38).

Nondispersive multiplex systems have generally been based

on the Michelson interferometer. Fellgett (39) was the

first to point out the potential of the multiplex devices

in high luminosity designs. The multiplex disadvantage,

derived from the noise components over the entire

spectrometer bandpass, limits the uses of these devices in

the UV-visible. All multiplex systems rely on computers,








either for real-time data analysis or for data

transformation and would not be practical without digital

devices.

The fact that a particular multielement system was

made possible through technological advances does not mean

that the system cannot function acceptably. The initial

work of Winefordner's group was directed towards the

comparison of theoretically predicted signal-to-noise

behavior for a number of approaches including programmable

scanning systems (4,5), Hadamard transform systems (38) and

image devices (40). The preliminary work indicated that

the optical image device would probably have the best

signal-to-noise profile of the systems investigated, with

the multiplex/Hadamard system having the worst behavior

because of the previously mentioned multiplex noise

disadvantage in the UV-visible spectral region. The

experimental signal-to-noise behavior of each approach was

then determined with the appropriate device constructed in

Winefordner's laboratory. F. W. Plankey built the Hadamard

system and confirmed the S/N ratios were worse than those

obtained with a comparable dispersive grating monochromator

operated in a sequential scanning mode (34). D. Knapp

constructed a rapid multielement system using a

commercially available image vidicon, the Optical

Multichannel Analyzer available from SSR Instruments,

Princeton, NJ (40). This system in the laboratory

environment with light sources typically found in atomic








spectroscopy had limited dynamic range and poor S/N ratios.

The limitation in the system was the nature of the vidicon

tube; should an imaging tube with better characteristics be

built, the system should realize the predicted S/N

behavior. The best overall performance was achieved by the

programmable system built by D. Johnson and F. W. Plankey

(4,5). In the original configuration, the system consisted

of a conventional 1/3 m grating dispersive monochromator

(GCA-McPherson, Model 218, Acton, MA) as the spectral

isolation device. The radiation detection was performed

with a photon counter package (Model 1105, SSR Instruments,

Princeton, NJ), and overall system control was exercised

through the keyboard of a PDP 11/20 minicomputer (Digital

Equipment Corporation, Maynard, MA).

Assuming from the above evaluation that some type of

programmable scanning system is the best available atomic

multielement analysis system, the obvious question is how

to improve its performance. As the brief survey indicated,

the established approach would be to substitute one or more

of the components in the original system with a device

representing a higher level of technology. Reference to

the description of the Johnson-Plankey system shows that

this would require the substitution of one of three

components, the monochromator or spectral isolation device,

the photon counter or the computer. The computer has

vastly more potential than is used in this system and to

replace it with a better or more powerful device would be








difficult and unnecessary. Similarly, the photon counter

is a powerful tool representing almost state of the art

technology and would be difficult to replace with a better

detection system. By a process of elimination, the last

device to be considered is the grating monochromator,

historically the oldest design concept in the system.

The common figures of merit for a monochromator are

the resolving power, R, and the luminosity, L, or the

throughput. For a particular grating, the resolving power

has fixed maximum value given by the equation R=Nm, where N

is the number of grating grooves illuminated and m is the

spectral diffraction order. The luminosity is a function

of the optical configuration of the spectrometer. To

improve the performance of a particular monochromator, it

is not possible to increase arbitrarily either R or L

because they have a constant product, i.e. RL=constant.

Therefore, while either term is interchangeable up to the

diffraction limit of the grating, it is not possible to.

increase both terms independently. Logically, it is always

possible to construct a monochromator with larger optics

and a grating with more grooves per unit of surface area in

order to increase R and L. Practically, however, the

chromatic and stigmatic aberrations encountered with the

large optics require more elaborate and expensive

instruments.

If it is desired to improve the system's optical

performance, then an alternate spectral isolation device is








desired. In particular, such a device should have both

greater R and greater L and, if possible, these parameters

should be functionally independent of each other. The

operating complexity of the alternate spectral isolation

device should be on the same order as the operational

complexity of the grating monochromator. These goals are

precisely those that the device called SEMIDS was designed

to achieve. The SEMIDS construction employs no new

technology but operates in a totally different manner from

conventional grating dispersive monochromators.














CHAPTER II
THEORETICAL CONSIDERATIONS

SEMIDS utilizes interferometric optics. This is

significant because basic interferometric techniques, often

referred to as Fourier spectroscopy, have two potential

performance advantages over more conventional dispersive

monochromators: the Fellgett, or multiplex advantage (39),

and the Jacquinot, or throughput advantage (41). The

potential signal-to-noise ratio, S/N, improvement from the

multiplex advantage is, in practice, realized only where

detector noise predominates, typically in the IR spectral

region. The Jacquinot advantage, which does not directly

involve noise considerations, persists in all spectral

regions.

The theory of the Jacquinot advantage can be derived

from physical arguments involving the second law of

thermodynamics or from purely geometrical considerations

using an invariant relation in two planes. This

relationship is commonly called the Helmholtz-Lagrange

Invariant or the Smith-Helmholtz Formula, although it was

actually used in simpler form by earlier workers (42).

Simply stated, these arguments require that in a lossless

optical system, the brightness of an object must equal the

brightness of the image; therefore, the flux throughput








and the brightness can be considered at any point in such a

system (43). This observation applies to any series of

lossless optical elements and can be expressed in terms of

the luminosity, L:


L =[dB] = dSld1 = dS2d2 = ... dS dn


B(1)


where the subscript, i, refers to the flux increment do, in

W, between the source, and the first optical element and

the subscript, n, refers to the same quantity between the

last optical element and the detector; B refers to the

source radiance in Wm sr The solid angle of collection

for each optical element, n, is in sr and the area, S, of

each device is in m2. Jacquinot noted that for

interferometers the term dSdn was a constant, and therefore

it was possible to have a single optical system with both

high resolution and high luminosity.

While these advantages of high optical throughput and

high spectral resolution have been known for some time, a

number of severe physical restrictions in addition to the

distributive noise multiplex disadvantage have precluded

widespread use of interferometric techniques in UV-visible

atomic spectroscopy. Optical tolerances must be kept to

within small fractions of the wavelengths of interest; in

the UV-visible region such tolerances require extremely

precise optics and correspondingly precise mechanical

tolerances on all parts of the interferometer. In








addition, the spectrum is obtained as an interferogram

which must be mathematically processed to recover a useable

power density spectrum. This process requires access to a

computer or, more generally, the dedicated use of a

minicomputer or hard-wired Fourier transform analyzer.

These combined considerations necessitate a practical

interferometer being both complex and expensive.

It is correct to state that the instrumental profile

of all types of spectrometric systems can be described with

Fourier techniques, whatever the operational principle. It

is interesting to note that the simpler mechanical devices

like dispersive grating monochromators which use a grating

to transform information encoded in terms of frequency to

terms of position on a focal plane require very complex

mathematical expressions, while the expressions for

interferometers are quite simple. Nevertheless, it would

seem quite plausible that by various manipulations, the

spectroscopist could design a device in which the transform

was neither completely mathematical, as in the

interferometer, or completely physical, as in the

monochromator. The advantages of such a hybrid approach

would be selective retention of some of the advantages of

each approach and elimination of some of the limitations.

SEMIDS uses precisely this approach. In order to explain

the innovations in SEMIDS, a brief description of

conventional Fourier spectroscopy is given.








Fourier Analysis and the Michelson Interferometer


It seems likely that no single instrumental

development has had a more profound effect on modern

physics and scientific research than the interferometer

constructed by Michelson. The basic instrument and its

derivations have found applications in spectroscopy,

metrology, refractrometry, and optical component testing as

well as microscopy. Although Michelson was aware of the

concepts of Fourier transform spectroscopy (44, 45), the

complexity of the procedures with the limited technology

available at that time prevented extensive developments in

this area. However, the Fourier transform integral is

fundamental to all interferometric spectrometers and, as

such, a brief derivation is instructive. The Fourier

transform integral theorem states that given a function,

F(x), provided it has certain properties, it may be

mathematically expressed as

-1
F(x) = f'J 0 A(y) exp(-i2ryx)dy T -1[A(y)] (2)



if F(x) is known and A (y), the Fourier transform of F(x)

is desired, it is uniquely given by


A(y) = f F(X) exp(+i27yx)dx = [F(x)] (3)



where the second integral is called the Fourier transform

and the first integral is called the inverse Fourier








transform. The conditions of validity are

(1) F(x) is a finite function with a finite number of

discontinuities;

(2) the derivatives of both F(x) and A(y) must exist

except for a finite number of points, and the

derivatives must exist on either side of these

points; and

(3) F(x) must be absolutely integrable i.e.,

J | F(x)ldx <-.

The application of the theorem to spectrometers is usually

performed in five sections: establishing the definition of

Fourier integrals, establishing the law of superposition of

amplitudes for waves, establishing the Hermitian properties

of light expanding the integration limits from -o to +o,

demonstrating that the amplitude (position dependent) can

be written in terms of the electric field (frequency

dependent), and finally combining wave expressions from the

two arms of the interferometer, computing the flux density

from the resultant electric field and taking the Fourier

transform of the resultant expressions to obtain the

spectrum as flux versus wavenumber.

A simpler derivation can be given using the Michelson

interferometer as a concrete example. In this derivation,

proper units are assumed to be provided by the omitted

normalizing factors, and since the Michelson interferometer

is symmetrical the effects of reflection and transmission








will be assumed to be equivalent in each arm. Let the

incident amplitude on the beam splitter be


A(z,o) = a(c)exp i(wt-27zo) (4)


where z is the position variable, t is time, and w is

frequency. In the Michelson interferometer after amplitude

splitting, there are two beams which have traveled

distances z and z2 before recombination. After

recombination, the amplitude expression is

Ar(Z ,21,o) = a(o) [exp i(at-2Tozl)+


exp i(wt-2"oz2)] (5)


The intensity for the spectral range do after recombination

can be defined as

I(zl#,z2', )do = Ar(zl,z2,o)A*(zlz2,a)

= 2a2(o) {1 + cos[2r(zl-z2)o]}. (6)


The total flux at any path difference z = (zl-z2) is given

by the expression

I(6) = Jf I(6,o)do
0

= 2 Jf a2 ()da + fJ a2 ()cos(2ao6)da (7)
0 0

The interferogram itself is a function of the flux versus

path difference and the expression is obtained by solving

for the case 6 = 0,









1 a 2
[I(6)- 2I(0)] = 2 fJ a (o)cos(276o)do (8)


and since the radiation is, of course, real and the

interferogram is symmetric, the spectrum is obtained with

the Fourier cosine transform

21
B(a)a2 (a) = fJ [I(6)- I(0)]cos(27 6)do. (9)



Equation 9 gives the irradiance or flux density B(o) as a

function of path difference at a given wavenumber. For a

complete derivation, see Appendix I. To obtain the

complete spectrum, the integral must be calculated for each

wavenumber.

A schematic diagram for a Michelson interferometer is

given in Figure 1(A). The path difference 8 is changed by

translating the mirror M1 parallel to the optical axis of

one arm of the interferometer. Radiation from the source

is incident on the beam splitter at 45. The beam

amplitude divides and half goes to each reflector M1 and

M2. The beams recombine at BS, and fringes are observed at

the detector plane. Optically, the system as viewed from

the detector consists of two sources S and S2 behind each

other. If the two image planes M and M' are parallel,

the geometry is equivalent to two sources in line behind

each other, and the characteristic circular fringes of

parallel plates are observed. If M and M2' intersect, the

crossover point is the point of zero path difference, and




















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the fringes will appear as straight lines parallel to the

line of intersection. If the two planes are inclined but

do not intersect, then the fringes will appear to be

hyperbolic sections with the direction of curvature

changing with the direction of the wedge apex, a.

The theory of fringe shape can be elucidated with

reference to the diagram in Figure 1(B). The two image

planes M1 and M' producing the interference are inclined

at a small angle a. The line extending from R to the point

0, the observation point, is perpendicular to the plane MN

and is the z axis of the coordinate system with the x and y

axes in the plane as shown. To an observer at 0, the angle

of interference is e, and the path difference of rays from

the front and rear planes reaching 0 from P is 2dcose,

where d is the separation of the planes at an arbitrary

point, P, on M Expressing the length of OP in terms of

x, y and z, the coordinates of P in an orthogonal system

with R at the origin give

OP2 = (x2 2 + z2) (10)



and therefore can be expressed as


cos = z/(x2 + y2 + z2). (11)



If the wedge thickness at R is k, then the thickness at P

is (k+xtana), and because the conditions for interference

require that the path difference between the two planes be








equal to an integral number of wavelengths X, the

expression for fringe shape is

2(k+xtana) z
m ~ (12)
(x2 +y2+z2




Consider the special case where the planes intersect

at R, then k=0 and equation 12 reduces to


2xz tana
rm = (13)
/ 2 2 2
(x +y +z )



If z is large compared with x and y and a is small, then

equation 13 can be simplified to mX = 2x tana = 2xa. This

is the equation of a straight line, and so for a given m, x

is constant; therefore successive fringes will give

straight lines parallel to the axis. These fringes appear

localized on M1 and are equidistant, separated by the

distance X/2a.

This fringe behavior exists only when z >> (x+y). If

the point 0 is closer to the plane MI, then x+y is no

longer negligible and the equation for the fringe location

becomes that of a hyperbola instead of a straight line. In

this case, the line of intersection with the plane becomes

the axis of the hyperbola, and the degree of curvature of

the fringes becomes dependent on the wedge angle.






19


In the case where both planes are parallel, i.e. o=0,

equation 12 reduces to

2kz
mA = -
/ 2 2 2 (14)
(x +y +z )

Manipulating this expression yields


2 2
2 2 2 4k z (15)
(x +y +z ) = 2 2
mA

which simplifies to


2 2 4k 2-m X21 z 2
x +y = -2 2 (16)



If the observation point 0 is a constant, then z is also

constant. Because the planes are parallel, k is a

constant, and for one fringe, m is constant; therefore, the

term x 2+y is also a constant and is the equation of a

circle. For values of k less than X/2, no circular rings

form, and the field at point 0 appears to have regular

illumination.

The discussion at this point has involved only the

optical path length and not the effects of geometrical path

considerations. Consider the equation for zero optical

path length difference in the two arms of the

interferometer,
n n
E n .d = Z n2 d j (17)
i=l l li j=l 2 2j








where n is the refractive index and d is the geometrical

path length in each segment of the respective arm. When

this equation is fulfilled at a particular wavelength, then

the phenomena described for equation 16 occur, and no

circular fringes appear. Furthermore, as the path

difference becomes progressively larger than zero, the

number of circular fringes increases and their diameter

decreases. In the original Michelson design in Figure

1(A), it can be seen that the rays incident on the mirror

M1 pass through the beam splitter only once while those

incident on M2 pass through the beam splitter twice. It is

possible, at one wavelength, to adjust the geometrical path

length so that the conditions in equation 17 are met.

Because the index of refraction is a function of

wavelength, there is no single geometrical path length

difference which gives an equal optical path length in each

arm of the interferometer for all wavelengths. As a

result, an uncompensated interferometer can only be used

with monochromatic light. The customary approach to

correcting this problem is shown in Figure 2, i.e., in the

field compensated Michelson interferometer. A transmitting

plate, CP, of the same dimensions as the beam splitter, is

inserted in one arm of the interferometer. This causes the

rays in each arm of the device to undergo the same number

of transitions, and even though the total optical path

length differs for different wavelengths, the optical path

length difference remains a constant.

























Source


Compensat:
Plate


Beamsplitter


Detector


Figure 2. Field-compensated Michelson interferometer
schematic. If all reflection occurs at the front surface
of the beamsplitter, then radiation reaching the detector
from both Mi and M2 is refracted three times.








The use of a compensating plate has an additional

advantage in terms of the maximum allowable field size. In

an uncompensated design the field is limited by the

restriction that


R = 8F2/h2 (18)


where R is the resolving power, F is the focal length of

the collimator, and h is the diameter of the source. This

condition results from the fact that the two rays derived

from the marginal ray have a different path length in the

two arms than the two rays derived from the paraxial ray.

The intensity at the detector due to a monochromatic ray

from the edge of the field stop will be modulated at a

different rate than the intensity due to the same

monochromatic ray at the center of the field. Because the

field compensating device causes rays from all parts of the

field to have the same optical path difference in both

arms, larger fields can be obtained. In this type of

design, the practical limit on field size for a fixed

resolving power, R, is usually caused by the spherical

aberration of the optics and may be expressed as

2F4
4n F (19)
R 4 (19)



where n is a refractive index of the compensating plate.

The above basic treatment of the characteristics of

the Michelson interferometer is useful in describing the








instrumental function of SEMIDS and the deviations from

conventional Fourier spectroscopy.


Theoretical Treatment of SEMIDS

The basis for the requirement that optical and

mechanical tolerances in the UV-visible spectral region be

much more stringent than in the IR spectral region can be

seen in equation 9. The transform contains a term

cos(2n'6). In the IR spectral region, an example of good

resolution would be the separation of the absorption bands

at 2960 cm and 2930 cm- due to the C-H stretching in

methyl and methylene groups, respectively. This requires

that the operational characteristics be stable enough to

allow the Fourier transform to recover two cosine terms

separated by one part per hundred. Correspondingly,
0
average performance in the UV-visible region at 2000A
+4 -1
(5x10 cm ) would be the resolving of the spectral
o -1
intervals IA (25 cm ) apart. The two cosine terms in

this case would differ in frequency by one part in two

thousand. Because the method of spectrum recovery is a

fairly rigid mathematical process, any inharmonicity in the

interferogram generation will give spurious results after

transformation.

The use of the "monochromatic" radiation in an

interferometer would decrease the distributive noise

problem of multiplex systems and simplify the

interferogram. The detector waveform would be a single

unconvoluted cosine term making a mathematical Fourier








transform unnecessary. Physically, however, the method of

producing "monochromatic" radiation, such as with

monochromators and filters, provides limited throughput and

limited flexibility. The use of such devices would limit

the light-gathering power of the interferometer.

In fact, the operational concept of SEMIDS internally

limits the number of interfering wavelengths in order to

obtain the simplified output. The work described in this

dissertation is based directly on the interference

selective modulation spectroscopy system described by T.

Dohi and T. Suzuki (46). In a less direct manner, SEMIDS

is derived from the SISAM (Spectrometre Interferentiel a

Selection par l'Amplitude de Modulation) techniques

pioneered by Professors Piere and Janine Connes at the

Centre National de la Recherche Scientifique in Paris,

France (47, 48).

A basic schematic of SEMIDS is illustrated in Figure

3. The most obvious modification from the basic Michelson

(Figure 1A) is the use of a rotating grating G in place of

the fixed reflector M2. The polychromatic radiation from

the source S passes through the aperture H and is
o
collimated by lens Ls. This type of arrangement is

generally referred to as the Fizeau collimator after H.

Fizeau who first used the design in 1862 in an

interferometer to investigate thin films (19). The

amplitude of the collimated radiation is split by the beam

splitter BS. In one arm of the device, the radiation


















S
0
SH







Ls




M
BS




Ld







g


Figure 3. Schematic of SEMIDS. Source radiation (S )
passes through the aperture (H) and the collimating 0
lens (L ) before splitting at the beamsplitter (BS).
The radiation is reflected from the oscillating mirror
(M), returns through the beamsplitter and is focused on
the detector (D) by the collimating lens (Ld). Radiation
diffracted from the grating (G) is also focused on the
detector.








behaves precisely like the normal Michelson; i.e. it is

incident on the translating reflector M and returns to the

beam splitter. In the other arm, the radiation is incident

on the diffraction grating inclined at an angle e from the

normal to the incident radiation. The only radiation that

is returned along the axis of the device is that which

fulfills the grating condition


mA = 2d sinO (20)



where m is the spectral diffraction order and d is the

distance between adjacent grooves of the grating. The

recombined wavefronts interfere and are then imaged on the

detector surface by the lens Ld.

When the schematic in Figure 3 is examined with

respect to the operating principle of a diffraction grating

monochromator, the internal use of the grating in SEMIDS as

a spectral isolation device appears logical. However, with

respect to the conventional Michelson design, it is not at

all apparent that the modification will produce the

required results particularly when considering the wedge

effect of tilted reflectors on fringe shape. The angle 8

that the grating makes with respect to the translating

mirror M would seem to prohibit the formation of circular

fringes. The explanation of why the grating can be used

lies in the fact that it is not simply a reflecting device

but is interferometric in nature. Equiphasic monochromatic

radiation incident on the grating will be diffracted at









some angle dependent on wavelength, but it remains

equiphasic since the path difference between adjacent

parallel rays must be an integral number of wavelengths.

Nevertheless, the substitution of the grating requires a

new derivation of the interferometric instrument function

in order to predict all the effects of grating rotation.

There exist a number of independent variables in the

treatment of SEMIDS which are held constant at various

points in the derivation in order to simplify the stepwise

elucidation. Initially, the mirror translation effects are

ignored so that any changes in the path length difference

result from grating rotation. In addition, the complex

amplitudes of the wavefronts will be treated at an

imaginary plane, labelled OX in Figure 4, which corresponds

to the locus of equiphasic radiation returning from each

arm of the device. Figure 4 can be derived from Figure 3

by rotating the axis defined by CO to coincide with the

axis defined by CO The term S is the source as seen
m om
from the mirror while S is the source at the grating.
og
The terms Z and ZG refer to the wavefronts from the mirror

and grating, respectively, while ZR is the resultant

wavefront incident on the detector. Following the

treatment for the Michelson, a(c) is the spectral amplitude

distribution of the source. The variable x represents the

displacement along the observation plane OX and 9 is the

grating angle. The amplitude of the wavefront IM incident

on the mirror is given by the expression,


































r'4







4-4






0













4-.4



E 0
0
*)



.,.









A M(o,s) = a(o)exp(2rnioxsinO) (21)

and after reflection, the amplitude is modified by the

reflection coefficient of the mirror, r(')


AM' (o,x) = r(o)AM(o,x) (22)



Analogously, the amplitude of the wavefront incident on the

grating IG is given by


A G(o,x) = a(o)exp(-2rrioxsine) (23)



and after diffraction by


A' (o,x) = b(o)A (o,x)exp(2Timx/d) (24)



In the last expression, b(a) is the "mth" order spectral

diffraction coefficient of the grating and d is the spacing

between adjacent grooves on the grating. After

recombination, the amplitude of the resultant wavefront ZR

is given by the law of superposition of amplitudes. That

is,

AR(o,x) = [A'(o,x) + A'(o,x) ] (25)


The intensity I (Ur,x) is again defined as

I(o,x) = AR(o,x) A*(o,x) (26)
R R


for the spectral range da. Integrating equation 25 over








the entire spectral range yields


I(x) = J a (a) cose[r 2(o)+b 2(o)+2r(o)b(o)
0

cos 2n(2osin9-m/d)x]do (27)



If the grating is considered as the field stop and the

width of the flux is 2W, then the total energy passed by

SEMIDS can be obtained by integrating equation 26 from the

limit -W/cose to +W/cose


I = W/cosI(x)dx (28)




Performing the indicated integration over the flux width,

the expression for the total energy transmitted by SEMIDS

is obtained as a function of wavelength,

= 2 2 2
I = j 2a (o)W{r (a)+b (o)+2r(a)b(c) since 2

[(2osin9-m/d) W/cos6]}do (29)


Equation 28 is the instrumental profile of the spectrometer
2
and indicates that the spectrum a (0)r(U)b(o) may be

obtained as a function of e, the grating rotation angle.

Inspection of equation 28 shows that the intensity is

attenuated by the third term in the bracket

f6 = sinc2[(2osin9-m/d) W/cos]l (30)



The since z function is defined as (sin z)/z. The plots in

Figure 5 show a normal sine function graphed on the same







31







































0
(4









































/ o
U
4-I
C0
Cl)
U)


U)




(a
0




U)




:3
0




0

I -,"-
-1-4
\ / 5" g








where N is the total number of grating rulings illuminated

and m is the spectral order. The results of equation 30

are identical with the diffraction limit of the grating.

The resolving power of SEMIDS should therefore be primarily

limited by the characteristics of the grating.

The discussion to this point has indicated that the

introduction of a diffraction grating to a conventional

Michelson interferometer would result in a successful

spectral isolation device. Despite the irreducible

geometrical path difference encountered by rays at either

edge of the inclined grating, the nature of the

interference is not significantly altered. This is because

the diffracted radiation from the grating is always

equiphasic with respect to a normal to the optical axis of

the arm. Therefore, the effects of mirror translation

should be equivalent to the case of the conventional

Michelson.

In order to calculate the solid angle of collection, n,

it is necessary to modify the treatment somewhat. The

aperture, H in Figure 3, is not an ideal point source and

the source, So, itself has finite size. As a result, some

off-axis radiation will also reach the collimating lens,

Ls, and pass through the device. The effect of this

off-axis contribution will be to diminish the fraction f

in equation 29. In order to calculate the magnitude of

this contribution and the maximum acceptable aperture, it

is necessary to include the off-axis contribution in








scale as a normal since function. It can be seen that the

since function has the same frequency as the sine function

but damps rapidly to zero. A plot of the f8 function is

given in Figure 6. The data used to calculate the values

shown were typical of UV-visible spectroscopy; the a was

50,000 cm-1 (200.0 nm); the grating spacing d was 0.001695

cm/groove; and the width of the flux was taken as 4.0 cm.

The value of f6 approaches zero rapidly as the value of

2usin9 deviates from m/d. The fraction has its first zero
-6
at an angle approximately 8 x 10 rad from the first

maximum. The second maximum occurs at approximately 2 x
-5
10-5 rad from the first and is only 0.128 times the

magnitude of the highest value. The function continues to

oscillate at values of e larger than this but the magnitude
-2
of the fraction remains less than 10 of the peak value.

Because there is a unique e, for a given wavenumber a,

which gives a maximum intensity, and a wide range of angles

that give minimum signal, the expression for f may be used

to estimate the theoretical resolving power, R of SEMIDS.

The Rayleigh criterion that two spectral lines are

completely resolved when the maximum of one falls on the

minimum of the other has little theoretical foundation but

is often used as a measure of resolving power performance

(49). Using the Rayleigh expression and substituting the

f6 term gives a theoretical resolving power of


R= o m= 2m W
R ( ) 2 ) ( W ) = Nm, (31)
o o cose





34


1.0







0.8-







0.6







0.4


fe



-0.2-








50 200

-7
6(radians x 10 )



-0.
Figure 6. Plot of SEMIDS since function using typical grating
and 20.0 cm focal length collimator.









equation 26 and to rederive the subsequent expressions.

Figure 7 shows the different paths traveled by the paraxial

ray and by the marginal ray in a device with a finite

aperture H. The marginal ray intersects the optical axis

at a small angle a. The path difference between the two

rays prior to interference is therefore equal to the path

length of the paraxial ray multiplied by the cosine of a.

The diagram in Figure 8 is the same as that in Figure 4

expanded to include the off-axis wavefronts, Z a and ZaG'

from each arm of the interferometer. The intensity

distribution of the interference caused by the two off-axis

conjugate wavefronts can be expressed along the equivalent

grating plane OX:

I (x) = JO a2 () cosO[r2 ()+b2 () (32)

+2r(o)b(o) cos 2n (2osin6coso-m/d)x]do



This expression is analogous to equation 26. Using the

small angle approximation and expanding the cosine term in

a series and simplifying terms gives I(x) as


I (x) = fJ a2(o) cos6{r (o)+b (0)

+2r(o)b(o) cos 2i[2o(sin9) (1-a2/2)

m/d]x}do (33)


Substituting the expression for solid angle, Q = na2, into

equation 32 and integrating the resultant expression over

the solid angle gives






















Marginal Ray


Paraxial Ray


Beamsplitter


Source


Figure 7. Schematic of optical paths for rays passing;
1) through the center and 2) tangent to the edge, of the
source aperture










o 2 2 2
I(x) = Jf a (o)?cosO{r (o)+b (o)+2r(o)b(o)


since (oxS/w7 sin6)} cos 2nr[2oa(l-/47)sin6


-m/d]x do (34)



Equation 33 can be compared to equation 28. The intensity

of the interference from a finite source is modulated by

the term since ('xQ/nsine) and the wavenumber of maximum

modulation is shifted from m/(2dsin9) in equation 28 to

[m/(2d(l-0/4n)sin9]. The first zero of the since function

occurs when


Qxosin6 =I; (35)


therefore the maximum permissible solid angle Qm of the

source is limited by


Q M< i/(osinOX) (36)


where 2X is the width of the grating. If the expression

for the wavenumber of maximum modulation is substituted

into equation 35, it can be rewritten as

m < 4 (37)
mX + (d/2) mN (37)



where N is again the total number of illuminated grating

grooves. A sample calculation using these relations and

some typical parameter values can be instructive. For a

diffraction grating with 590 lines/mm and 25.44 mm








illuminated width and a collimator with a 200 mm focal

length, the maximum acceptable solid angle 0m is 8.39 x

10-4 sr with an angle of 1.63 x 10-2 rad and a maximum

acceptable aperture of 6.52 mm diameter. These figures

compare very favorably with those obtained from

conventional dispersive monochromators with the same size

optical elements. The actual instrumental function using

the off-axis condition is obtained by integrating equation

33 over the limits -W/cose to +W/cose.

Having demonstrated the applicability of the grating in

SEMIDS and obtained the expression for the limiting

aperture conditions, the final topic to be elucidated is

that of the signal modulation mechanism. Considered from

the purely theoretical approach using an ideal

interferometer, the interfering radiation should produce a

pure monochromatic sinusoidal waveform at the detector

output. The expected signal behavior is shown graphically

in Figure 9A. All waveforms are plotted against time. The

lowest plot in Figure 9A is the voltage, V, applied to the

piezoelectric transducers on the translating mirror. A

triangular wave is used to give a linear displacement, and

the path difference, A, also varies linearly with the same

frequency as the applied voltage. The signal obtained at

the detector, S has the same frequency as the driving

waveforms but is a cosine wave. The area under the curve,

So, is the estimate of the radiation intensity at the

wavelength of interest.




















































































U) I


0 0


r-
S0

o0 0
0-- -H

N )
4J1 I -J


U) 0 0









e> o


04) 0
o c4-

14 H r







(0 1
D- 0 U) 0

S 04-
0a










-H

4-1 4C
-H C -i

0 4 ) U)


















U0 >1
-4 U -1
4) -r4


) 4-0)









-) -)

r-4
(U-0








-H U)








rd0
0 ty








0 --I
W 0 H






40 -H
4V C1








In the operating SEMIDS system, the theoretically

predicted modulated signal was not observed. The cause of

some additional modulation was mentioned briefly in the

section on conventional Michelson interferometers. In an

uncompensated Michelson system, it is not possible to

adjust the geometrical path lengths so that the optical

path length difference remains constant at more than one

wavelength at a time. As a result, there exists some

finite equilibrium path difference, A at each wavelength

as the system is scanned. This equilibrium path difference

is the remaining optical path length difference between the

true zero path difference condition and the smallest actual

path difference. Because this equilibrium path difference

is a function of wavelength, it is not a constant during a

spectral scan. The effects of the changing equilibrium

path difference can be shown by expanding the expression

for the signal waveform in a Fourier series. In general,

all periodic functions can be expressed using the relation


I() = o + Z a cos[2lnA]
2 n=l n

+ Jn1 8n sin 27nA (38)
n=(38)

In the SEMIDS case, because the intensity function is

symmetric, the summation of the cosine terms is sufficient

to characterize the waveform. The terms a and A are
o o
dependent on the equilibrium path difference. Because

these terms are not constants during scanning (the

equilibrium path difference is wavelength dependent), the








intensity waveform is modulated by a periodic waveform of

lower frequency (see Figure 9B). The mirror is still

displaced by the applied voltage, V, with the triangular

waveform. The path difference, A, does not always reach

zero. When the equilibrium path difference is not zero, a

distortion on the detector output waveform, S results.

The method used to eliminate the effects of this

equilibrium path difference and other low frequency noise

problems introduced by instrumental artifacts is simply to

bias the applied triangular waveform with a low frequency

sine wave voltage which modulates the low frequency

waveform distortions. The resultant signal, Sm, has a

cosine waveform, and the area under the curve is again a

measure of the intensity of the interfering radiation at a

particular wavelength. Further discussion of the specific

instrumental considerations in dealing with this problem

will be given in the next chapter dealing with design

problems.















CHAPTER III
INSTRUMENTAL DESIGN

The paramount consideration in the design of SEMIDS

was that it must have reliability of results and simplicity

of operation comparable to or better than the class of

dispersive grating monochromators it was designed to

replace. In the actual construction of the device, these

aspects received much more consideration than either the

resolving power or luminosity. It was felt that to achieve

high performance at the cost of increased complexity of

operation or decreased reliability would not be desirable

because in many applications the full potential of SEMIDS

would not be expanded and that in these cases an exotic

operating system would result in an unfavorable comparison

with monochromators.

The device, as built, is a prototype instrument and

suffers from difficulties typical in systems that undergo

an evolutionary developmental procedure. The system was

built with flexibility in the design concept to permit

modifications in a simple manner, and as a result, it is

much larger and more complex than actually necessary for

the operation of SEMIDS. This is readily apparent in the

size of the base plate used to support the optical

components. This plate is approximately 1.3 m square

despite the fact that the only functional distance between








the components is the focal length of the lenses, 20 cm.

Therefore, it is important to remember during the following

description of SEMIDS construction that a much smaller

device could be constructed with the same performance

qualities and even better operational qualities.

All the components of SEMIDS are supported by a single

aluminum alloy plate approximately 1.3 m on each edge and

2.5 cm thick. The plate weighed approximately 115 kg. All

of the optical components in the system rest on this

structure although the top surface of the plate was not

used as a position reference plane. Figure 10A shows the

physical details of the plate. Permanently attached to the

surface are aluminum tracks, 1 cm square, to facilitate

movement and alignment of the translational stages. These

parallel tracks bisect the plate surface from the center of

each side to the center of the opposite side. On two

adjacent edges, the tracks terminate at upright aluminum

plates of the same thickness as the base plate and 20 cm

high. These plates serve as rigid supports for the

variable entrance and exit apertures and the

photomultiplier housing. The apertures were variable iris

diaphragms pressed into holes milled in the upright plates

with a minimum aperture diameter of 0.5 mm and a maximum of

13.6 mm. The potential advantages of using such a massive

support plate were to decrease the sensitivity of the

system to ambient vibrations and to increase the thermal

inertia that a large heat sink can provide. In practice,
















aperture support
and detector
housing


air-filled balls


Figure 10. Schematic of SEMIDS support plate; (A) top
surface and (B) vibration-damping support locations


tracks


rubber
stacks


L__j


0


0
IN


l0








the system was easy to maintain in thermal equilibrium but

the flexibility of the plate did introduce vibrational

problems.

The size and flexibility of the plate required that it

be well supported to prevent warping. However, it was

found that most support materials, whether rigid or

semi-rigid, transmitted ambient vibrations from the support

table to the base plate. Sensitivity to vibration is

predictable in interferometers and unless isolation is

achieved the signal-to-noise ratios obtained are generally

unacceptable. The magnitude of the problem and the methods

used to evaluate SEMIDS performance will be discussed in

Chapter IV; however, the results of the investigation

indicated that most of the vibrational problems were caused

by the use of the large flexible support in the prototype

device and that a smaller optimized design with a rigid

support would have greatly decreased sensitivity.

Figure 10B shows the positioning of the inexpensive

dual-support system used to isolate the operational SEMIDS

from ambient vibrations and to minimize the effects of

direct physical perturbations to the device. The plate is

supported at eight separate points. At locations

approximately 30 cm from the center, the plate rests on

four stacks. Each stack consists of four #13 rubber

stoppers topped by two layers of Isomode rubber fabric

(Isomode is a composition rubber and fabric mat specially

formed for vibration isolation in heavy load bearing








applications; the material is manufactured by M. B.

Electronics Co., 782 Whalley Ave., New Haven, CT). These

stacks support the mass of the plate directly. The larger

circles in each quadrant of the schematic in Figure 10B

represent the position of four air-filled vinyl balls.

These balls perform a dual function: providing some mass

support and acting as vibration damping attenuators. The

support system rests on a conventional wood and plastic

laboratory bench. The use of the dual-support system

allows normal laboratory function in the close proximity to

the SEMIDS device with no observable degradation in system

performance. In addition, the support system performance

has proved stable over a period longer than one calendar

year.

All the optical elements are mounted on translational

stages to permit adjustment of position in the X,Y

directions on the plane of the plate. The basic schematic

of these devices is given in Figure 11. The stage consists

of two aluminum plates of the same outside dimensions and

1.9 cm thick. The lower section of the stage is grooved to

take the tracks mounted on the base plate. Two tracks of

the same dimensions as those on the base plate are mounted

on the upper surface of the lower translational stage

section. The upper translational stage section is milled

to slide over these tracks. Both the upper and lower

sections are provided with set screws so that they may be

securely locked into position on the aluminum tracks. All

























support plates


base track slots


Figure 11. Details of optical component translation stage








the devices attached to the stages are affixed with bolts

tapped into the upper plate.

Three of these stages support the collimating lens,

the focusing lens and the beam splitter. Adjustment in the

Z axis direction, that is, above the plane of the base

plate, is provided by the screw mechanism shown in Figure

12. The element is locked into position by a set screw and

changes in elevation are achieved by rotating the wheel on

the main section of the device. Stability is achieved with

a lock nut which can be used to fix the position at any

point. The construction of the device was performed in the

department machine shop with the screw mechanism

constructed of brass and the main section of aluminum.

The lens holders and the beam splitter support are

shown in Figure 13. All three devices were machined from

brass in the department shop. The basic concepts employed

in these devices as well as that used for the grating

rotation table were obtained from a monograph by James and

Sternberg on the design of optical components (49). Figure

13B is that used for the beam splitter support. This type

of support was chosen over any edge-mounted support because

it was found experimentally that even the slightest

asymmetrical pressure on the beam splitter would distort

the interference fringes and degrade overall system

performance. It should be noted however that this type of

support does decrease the effective diameter of the optical

element.





Figure 12. Details of adjustable elevation support device


50































(A)



D
0











0




(B)
Figure 13. Optical component supports; (A) lens holder
and (B) beamsplitter








The two reflecting elements, the mirror and the

grating, are not provided with an elevation adjustment

capability. The mirror is mounted on a large angular

orientation device (#10 503, Lansing Research Corporation,

Ithaca, NY). This device is constructed of aluminum and

has two concentric circular plates mounted on axes 900 with

respect to each other. Two micrometer screws with steel

shafts are coupled to the moveable rings with permanent

magnets and permit angular adjustments in the plane

perpendicular to the base plate as well as the parallel

plane. The device is equipped with set screws to fix the

proper orientation. However, the large diameter aluminum

rings tend to distort badly whenever the set screws are

used. As a result of this inability to "lock" the angular

orientation, the system alignment will degrade after

initial set up and must be monitored. The difficulties in

long-term system optical alignment are almost certainly

artifacts of the use of the devices and the choice of a

smaller device coupled with a more rigid structural

material would considerably reduce the problem. The mirror

assembly consisting of the mirror, transducers and supports

are fixed directly to the face of the angular orientation

device with a methyl acrylate adhesive.

The diffraction grating is supported directly by a

similar but smaller angular orientation device (#10.203,

Lansing Research Corporation, Ithaca, NY). This device is

mounted on a circular brass plate so that the geometrical








center of the front surface of the grating coincides with

the axis of rotation of the grating rotating axle table.

Figure 14 shows the construction details of this axle and

rotation table. The axle itself is machined from steel and

the exterior casing is aluminum. The axle is spring

mounted on two high-grade angular contact bearings. Figure

15 shows the motor coupling used to provide the scanning of

the spectrum. In this apparatus, all the parts except the

micrometer screw are made of aluminum. The micrometer is

high-grade steel. One end of the screw is fixed in the

grating table coupling. This device is constructed with a

small ball bearing to permit the micrometer screw to

maintain a constant tangent throughout the translation

procedure. The motor coupler is fixed to the shaft of a

stepping motor (Model HDM-15, Responsyn Motor, USM

Corporation, Goar System Division, Wakefield, MA). The

other end of the motor coupling is tapped for the

micrometer screw. Rotation of the motor shaft therefore

causes the micrometer screw to move into or out of the

coupler and causes the grating table to rotate. This

arrangement with the motor capable of resolving 480 steps

per revolution allows an angular increment on the order of
-6
5 x 10 radians.

The optical elements were obtained from a variety of

sources. The lenses used for collimation and focusing were

ground and polished (by ESCO Products, Oak Ridge, NJ) from

blanks of suprasil-fused quartz. This material was chosen














axle


fixed casing


Figure 14. Details of grating rotation table






micrometer screw


stepping motor


-micrometer coupling
grating rotation table


Figure 15. Grating rotation table motor mount coupling








because of its transmission characteristics in the

ultraviolet spectral region. The outside diameters of the

lenses were 76.2 mm and the focal lengths of the bi-convex

elements were 203.2 mm. This focal length determined the

distance between the lens holders and the entrance and exit

apertures and was the only functional separation in SEMIDS.

Therefore by changing the collimator characteristics and/or

geometry, it is possible to modify the overall dimensions

of a SEMIDS-type system.

The spectral transmission characteristics of the beam

splitter were the most important consideration in a

scanning system with a wide spectral range. Most

commercially available units have a fairly narrow bandpass,

generally less than 100 nm. The beam splitter used in

SEMIDS was coated on a suprasil-fused quartz blank 76.2 mm

in diameter and 6.3 mm thick. The surface of the blank was
0
tested flat to X/20 at the mercury green line (5460.7A).

The bandpass of the beam splitter was approximately
0
constant over the range of 2000-5000A and provided equal

division of the incident wavefront so that approximately

40% of the radiation was transmitted and 40% reflected.

Figure 16 shows the device's spectral characteristics

supplied by the beam splitter manufacturer, Dell Optics,

North Bergen, NJ.

The diffraction grating is ruled on a blank 10 mm

thick and 40 mm on each edge (Jarrell-Ash Division, Fisher

Scientific Company, Waltham, MA). It is a standard quality


























LO










E


Q)
4-1
4-)




















Eo 0
0




o 4







o>
4-J










on
0 011

















o >O
o CC



C0 Cr)
LI) r-











0)


0i)
-.1I


o o o o o o o o o o
o 0 0 ko 0n 0 m 04 -
-4









replica grating ruled with 590 grooves/mm and blazed at
0
3.90 to give a blaze wavelength of 2400 A. The substrate

material is fine annealed pyrex. The grating is attached

to the angular orientation device by a bolt glued to the

back of the blank and passed through a hole in the center

of the orientation device and secured with a nut.

The optical flat reflector was also obtained from Dell

Optics. The aluminum reflecting coating was vacuum

deposited on the surface of a fused quartz blank 16 mm

thick and 50.8 mm in diameter. The surface of the

reflector is coated with Dell's Alflex-A protective coating

and was tested flat to X/10. Figure 17 shows the mirror

and transducer assembly as mounted to the face plate of the

angular orientation device. The mirror is glued to the

ceramic portions of three Clevite PZT Unimorphs (Vernitron

Piezoelectric Division, Bedford, OH). A unimorph is a

small wafer, 2.54 cm diameter, of PZT5B ceramic mounted on

a thin brass plate of 3.43 cm diameter. The unimorphs are

glued to three brass rings of the same outside diameter and

a 2.2 cm inside diameter and 6.4 mm thick. These brass

rings are mounted tangent to each other in a triangular

arrangement on the face of the angular orientation device.

Each brass ring and its associated unimorph are

electrically isolated from the adjacent units to allow

individual voltage control. The principal advantage to

using this type of transducer rather than the more common





















Unimorphs


Mirror


Orientation Plate


Figure 17. Mirror displacement assembly








and more expensive bimorph ceramics is the relatively large

displacement (0.01 mm/V) at low voltages.

The entire optical system was enclosed and made

completely light tight because (1) stray light incident on

the detector would contribute to the total noise problem

and decrease the depth of modulation, and (2) the

difference in the index of refraction of air caused by

thermal inhomogeneities caused fringe distortion in the

interference pattern. This problem was first observed

during some preliminary alignment tests on the unenclosed

system. With a stable concentric fringe pattern centered

on the target, a person passed his hand under the optical

path in one arm of SEMIDS; the heat from his hand was

sufficient to cause the fringe pattern to waver like an

image of an object viewed over an asphalt parking lot on a

sunny day. Subsequent investigations showed that this

effect could be repeated or approximated in various ways,

including blowing cold air from a room air conditioner

along one arm and perpendicular to the other arm. The

effect disappeared when the system was sealed. Because the

total volume involved would be large if the entire plate

were enclosed a different approach was used to exclude

stray light. Box structures were constructed around the

mirror and the beam splitter as well as the grating angular

orientation device. A light baffle box was placed in front

of the exit aperture. This box consisted of parallel

aluminum plates with circular holes through the centers








aligned so that the focused radiation beam could still be

imaged on the detector but off-axis contributions would be

minimized. In addition, a sliding shutter was included to

protect the photomultiplier tube while aligning the system.

Figure 18 shows the schematic of the protected system.

Polyvinyl chloride tubing, 76.2 mm diameter, painted a flat

black was used to connect each box in the system to each

other and to the lens supports and entrance aperture. A

flexible tube of double thickness black felt was used to

connect the rotating grating mount to the end of a tube.

The completely closed system caused difficulty during

alignment procedures because the exit aperture was no

longer visible to the operator. This necessitated the

construction of a removable target placed in the beam

splitter box in the exit optical path. The use of this

device required that the top of the beam splitter box be

removable in order to observe the alignment and to remove

the target for system operation. Investigation showed the

use of this type of isolation system to be completely

effective. Figure 19 shows the effects of isolation on

noise levels.

There are two separate electronics packages necessary

for the operation of SEMIDS; the signal detection and

treatment package and the scanning and modulation package.

The scanning is achieved by rotating the grating and this

is done with a stepping motor. The power required to drive

the motor with the proper phasing is obtained through a
















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logic circuit supplied by the manufacturer. The logic

control necessary to provide precise and accurate grating

positioning is provided through an assembly language

program on a PDP 11-20 computer (Digital Equipment

Corporation, Maynard, MA). An alternate system of motor

control using a remote controller supplied by the motor

manufacturer was investigated. This device used a

potentiometer to adjust motor speed, a switch to change

direction of shaft rotation, and a digital thumb switch to

determine the number of motor steps. It was functional but

very cumbersome in the number of operator steps necessary

to effect a scanning cycle. The use of the computer

program was preferred during the evaluation'process because

it allowed more precise control of motor speed and was

capable of displaying the number of steps actually executed

if the scanning cycle were interrupted. Although the full

potential of the computer was not used in motor control and

was in that sense an inefficient use of the available

resource, the advantages of speed and scan control provided

by the teletype keyboard justified this approach.

The mirror displacement electronic package was

designed around the electrical characteristics of the

unimorphs. These wafers of ceramic are not matched in

performance and factory literature states that displacement

response may vary by as much as 20% between individual

devices. In addition, the unimorphs are primarily

capacitive devices with very high resistance. The
*








situation is further complicated because the electrical

behavior of each wafer is a function of the effective load

on the device. This makes the calculation of precise

driving circuit parameters impossible so provision had to

be made for individual transducer adjustment. Figure 20

shows a circuit diagram for the driving mechanism used in

the early system evaluation. The first stage of signal

summing and amplification is performed by a 171J

high-voltage operational amplifier (Analog Devices, Inc.,

Cambridge, MA). The waveforms to be amplified are summed

through 10 kQ resistors at the inverting input of the

amplifier. A 20 kf potentiometer in series with a -24 V

power supply at this input provides a DC offset at the

output. The offset is used to prevent the appearance of

spurious nodes in the detector signal caused by the mirror

striking the back of the unimorph support during

oscillation. Gain control is provided by a 200 kQ resistor

in the amplifier feedback loop. It was found necessary.to

use a transistor to isolate and provide voltage control for

each transducer because a voltage divider formed a complex

series of RC filters. A 100 kO trim resistor is used to

adjust the current on the base and the voltage at the

unimorph. Several difficulties were found with the system

described. The 171J operational amplifier is not a rugged

device. It has FET inputs which were quite sensitive to

high frequency sparks used to initiate electrodeless

discharge lamps. When operated near its voltage limits it


















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also becomes extremely vulnerable to switching transients

and since the module is expensive, these repetitive

failures contribute greatly to system costs. A more

fundamental problem derived from the instrumental function.

It was possible to align SEMIDS at any one wavelength and

tune in the detection system for the modulation frequency.

However a fixed displacement at one wavelength will produce

a modulation frequency dependent on the number of

wavelengths the displacement is equivalent to. If by

rotating the grating the interfering wavelength becomes

shorter, then the fixed displacement of the mirror is

equivalent to a different number of wavelengths and the

modulation frequency shifts accordingly. If the detection

system remains tuned to the original frequency, the effect

is of increased signal attenuation with increased scan with

spikes whenever a signal appears at a harmonic of the

original modulation frequency. The two alternatives to

solve this problem involve either varying the detection

frequency as a function of scanning wavelength or

decreasing mirror displacement with decreasing wavelength

in order to keep the modulation frequency constant. In

SEMIDS, the latter approach is more easily implemented, and

Figure 21 shows the modified circuit diagram. The system

is essentially a programmable amplifier. Two transistor

comparators are used to shape the command pulses from the

computer into clean step functions, one for forward pulses

and one for reverse command pulses. The output from the




















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comparators is fed into a Monsanto Model 160A Reversible

Counter (Monsanto Electronics, Inc., West Caldwell, NJ).

The counter automatically accumulates pulses in a forward

direction and subtracts the pulses in a reverse direction.

The counter displays the number of pulses the motor has

moved from some arbitrary reference point; this number is

also presented at an output in BCD (binary coded decimal)

format and is converted into analog form using a 12 bit

digital-to-analog converter (Analog Devices, Inc.,

Cambridge, MA, Model L12). This analog voltage is used to

scale the magnitude of the waveform signal by passing both

the waveform voltage and the DAC voltage through a

four-quadrant multiplier (Burr-Brown, Inc., Tucson, AZ,

Model 4094/15C). The control of amplification is obtained

in the following way. As the number of pulses in the

counter becomes greater (equivalent to shorter

wavelengths), the voltage presented to the multiplier by

the DAC is smaller and the product of this voltage and the

waveform signal is also smaller. Intermediate stages in

the device between the DAC and the multiplier use 741

operational amplifiers to provide a DC offset (the

intercept on a plot of voltage vs pulse number) and gain

control (the slope). The output of the multiplier is

passed through a two-stage transistor amplification circuit

with fixed gain. The final output stage is identical to

that shown in Figure 20. Substitution of the

two-transistor amplifier for the 171J op amp has not








limited system performance and has proven less susceptible

to component failure. Alignment procedures and performance

evaluations of both systems will be discussed in more

detail in Chapter IV. The waveforms used by the

programmable amplifier are obtained from a variety of

laboratory signal generators. The particular choice of

generator was not a significant factor in system

performance.

Signal detection circuitry is shown in schematic block

diagram in Figure 22. Radiation incident on the detector

was converted to an electrical signal with an RCA IP28A

photomultiplier tube (power supplied with a PAR Model 280

high voltage power supply mounted in an Ortec model 401A

bin (Princeton Applied Research, Princeton, NJ and Ortec,

Inc., Oak Ridge, TN). The signal was amplified first with

a current-to-voltage module constructed around an

operational amplifier (Analog Devices, Inc., Model 40J,

Cambridge, MA) which provided switch selectable gain from

104 to 108 V/A. The amplified signal was then processed by

a frequency selective amplifier (PAR, Model 210). This

device provided a fixed gain of 10 and a switch selectable

Q over the range of 1 Hz to 100 Hz. The frequency filtered

output signal was then further amplified with a wideband

unit (PAR, Model 211) and introduced into a signal

multiplier unit (PAR, Model 230). This was the first stage

of the integration process. The previous stages in signal

treatment provided amplification and some degree of noise


























































































,-I
E0
0

0
.1-
a4








rejection. It was noted in Chapter II that the area under

the curve obtained from the detector signal waveform was

the measure of the radiation intensity. Electronically

this area is obtained in an analog form by obtaining the

root mean square, RMS, of the detector signal. The PAR

multiplier was used to first multiply the signal by itself.

This unit also provided a series of RC filters on the

output side of the multiplier that were switch selectable.

The use of the filters was analogous to taking the

mathematical average of the signal. Figure 23 shows the

effect of the various stages on a time dependent signal.

Squaring the signal doubles the apparent frequency of all

components and introduces a DC offset. Filtering the

signal has the effect of "smoothing" the oscillations on

the signal. The filters effectively control the time

constant of the entire process, and as shown in the

diagram, the longer the time constant the more complete the

averaging process. In the operation of SEMIDS, a balance

was achieved between the time constant and the scanning

speed because at very high time constants, the spectrometer

has passed through a resolvable spectral interval before

the root mean square module can respond to the signal

change. This results in signal attenuation and increased

bandwidth of observed lines. In practice, the scanning

speed and the time constant were adjusted so that the

scanning time for each resolvable spectral component was at

least five times the value of the selected time constant.














Amplitude

0-




-1-





1 -




Amplitude





0


1 -


Filtered Signal

Amplitude




0


Signal


Figure 23. Signal waveforms at various stages in
detector electronics









It should be noted that the definition of resolvable

spectral component is not in this case the smallest

resolvable spectral component but is rather the operator

selected value. For many applications, resolution on the
0
order of 0.1 A is not necessary, and the operator may scan

at higher velocities and longer time constants without

signal degradation. The graph in Figure 24 shows the
0-1
relationship between scanning period (S A ), the time
0
constant -, (s) and the resolvable spectral interval (A)

AX. Any combination of scanning speed and time constant

that falls on one of the plotted lines will yield the

resolution of that plot. The operator of SEMIDS therefore

has the ability to alter the actual resolving power of the

instrument without altering the optics or aperture

diameter. The final stage of the RMS section of the signal

conditioning circuitry took the square root of the filtered

signal with a multiplier/divider module (Model 426A, Analog

Devices). The signal presented at the output of this stage

was a DC voltage representing the RMS area of the current

waveform output of the photomultiplier. The DC voltage was

exactly analogous to the output of more conventional

spectrophotometric systems and was treated in a similar

manner. The three output display devices used with SEMIDS

were an oscilloscope, a chart recorder and a digital

voltmeter. The oscilloscope was used primarily to examine

system performance during alignment and optimization

procedures, the recorder was used to obtain hard copies of








74















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75

spectral scans and stability studies, and the digital

voltmeter was used to convert and display the analog signal

to digital form for rapid data acquisition during

quantitative investigations.















CHAPTER IV
ALIGNMENT PROCEDURES

The complete alignment of SEMIDS, while not extremely

complex, includes a number of procedures not encountered in

the alignment of grating monochromators. There are

essentially two separate stages involved: (1) the gross

physical alignment of the optical components, and (2) the

electrical alignment of the transducers and the

programmable amplifier. In all cases, it is necessary to

align physically the optics first since the electrical

measurements are optimized to the functioning system's

performance.

In order to align the optical elements a small

helium-neon laser is used. In the prototype SEMIDS, the

laser is mounted permanently outside the system and is used

as a reference for all alignment. This approach was

necessary partly because the base plate was too flexible

for use as a reference plane. The initial step in the

procedure is to mount the grating, grating rotation table

and support, and the stepping motor and support on the

plate. The grating is mounted facing the entrance

aperture. Adjustments are then made to the grating angle

and the laser position until the laser spot is precisely

centered on the ruled surface of the grating and so the

reflected spot in the zeroth order passes out the aperture








in the same path as the entering beam. When these

conditions are achieved, it is necessary to adjust the

grating rulings so that they are precisely perpendicular to

the optical plane defined by the optical axis in all arms

of the interferometer. This is necessary to prevent loss

of alignment and signal as the grating is rotated. The

orientation is adjusted by loosening the lock nut on the

back of the grating orientation device and rotating the

central plate until the spots from the diffraction of the

laser beam in all orders are the same height above the base

plate. The next device to align on the plate is the

oscillating mirror assembly including the translation

stage, the angular orientation device, and piezoelectric

assembly, and the mirror. This unit is placed on the

tracks at approximately the same distance from the

geometrical center of the base plate as the grating

assembly. If the plate has been properly supported, the

addition of various masses to the plate should not affect

the previous grating alignment. With these two units in

place, the translational device and support containing the

beam splitter is placed in the plate center. Initial

adjustment of the beam splitter is performed with respect

to the grating. Because the beam splitter has finite

thickness, the spot from the laser beam will be laterally

displaced on the face of the grating. This is not critical

since the particular design to the collimator overfills the

grating. It is important, however, that the spot on the








grating is not displaced up or down indicating tilt in the

plane of the beam splitter. The elevation of the support

is then adjusted so that the spot of the laser is in the

geometrical center of the beam splitter. When these

conditions have been attained, the XY position of the

device and of the mirror translation stage are adjusted

until the following criteria are met:

a. The laser beam passes through the geometrical

center of the beam splitter,

b. The laser spot strikes the mirror in the

geometrical center,

c. The laser beam is incident on a horizontal axis

passing through the center of the grating, and

finally

d. The reflections off the mirror and the grating

pass out the centers of the entrance and the exit

apertures.

The final adjustment to insure the reflected beams

meet these criteria are performed with micrometers of the

angular orientation devices. At this point, the system is

essentially aligned with respect to the optical axis

defined by the laser beam. The collimating and the

focusing lenses with their translation stages can be

inserted. This is done by placing the lens unit in the

optical path and adjusting the position so that the laser

beam passes through the center of the lens. When this

condition is met, the lens has little effect on the








orientation of the beam, and the proper position can be

determined by checking the criteria a-d.

Once adjustments have been completed with respect to

the optical axis, it is necessary to adjust the separation

between the mirror and the grating and between the lenses

and the apertures. The collimating lens is easily adjusted

with a diffuse source placed outside the entrance aperture.

The aperture to lens distance is adjusted until a

collimated beam of constant cross section is observed. The

translational stage is then locked into position.

Similarly, the focusing lens is adjusted after the

collimating lens has been set until an image of the

entrance aperture is produced at the exit. The position of

this lens can be adjusted to view different portions of the

interference pattern and its position is not as critical as

the collimating lens.

The separation between the mirror and the grating is

important. As was mentioned in Chapter II, it is not

possible to adjust an uncompensated interferometric device

such as SEMIDS so that the optical path length is a

constant for all wavelengths. It is desirable, however, to

pick a reference wavelength and to adjust the geometrical

path length so that the optical path difference is zero.

This facilitates system alignment and minimizes the effect

of the equilibrium path difference at other wavelengths.

The reference wavelength for the prototype device is chosen

as the He-Ne laser wavelength 632.8 nm. A white card is








used as the observation screen and placed in front of the

focusing lens. With a ground glass diffuser placed in

front of the laser, the collimating lens produces a

homogeneous monochromatic field on the reflectors. Before

any path difference adjustments can be made, fine angular

adjustments with the micrometers are performed with the

reflecting mirror. The diagrams in Figure 25 show the

interference patterns produced with various orientations.

The basis for the alignment procedure can be seen in

equation 16. With the proper alignment, concentric

circular rings are observed on the observation field. 'The

number and size of the rings are a function of the path

difference, k, in equation 16. As the separation becomes

smaller, the conditions require that any particular fringe

also become smaller in diameter. Therefore, if one places

the reflectors at approximately the same distance from the

beam splitter and aligns the device to produce circular

fringes, the relative position of the point of zero path

difference can be obtained by displacing one reflector

along the optical axis and observing the direction in which

the fringes appear to move. If the rings appear to move

toward the center, then the path difference is larger than

the point of zero path difference. If the rings move

outward, then the separation is less. As the separation

becomes smaller, the thickness of the bright and dark areas

on the observation field becomes greater and there are

fewer fringes visible on the field. At separations very





Near 0 Path
Difference














Centered


Wedge


wI I III l


SEMIDS interference fringe patterns


81


Figure 25.








close to the point of zero path difference, the direction

of fringe movement becomes very difficult to ascertain for

two reasons: (1) there are usually only one or two rings

on the field at this point, and (2) the spherical

aberration of the collimating lens causes extreme

hyperbolic distortion of the fringes at small separations.

In practice, the procedure is to reduce the separation

until only two complete fringes are visible and to operate

the system from this point. This criterion is chosen

because it was easy to obtain and easily produced because

the spherical aberration was not large at this separation.

It is found easier to displace the mirror translation stage

than the grating stage and motor mount so all adjustments

are performed in this arm of the interferometer. This

completes the static alignment of the SEMIDS optical

components. The light baffles and protective box

structures are now installed. As was noted in Chapter III,

a target had been designed to transfer the position of the

exit aperture inside the beam splitter box, and this target

is used for the final alignment procedures.

Dynamic alignment of the mirror is necessary because

the displacement of all the unimorphs in the transducer

assembly are not equal. The procedure for dynamic

alignment is the same with either driving circuit since the

output isolation stage is the same in both cases. With

SEMIDS, statically aligned and using the diffused laser

beam to produce an interference pattern on the target, a DC








voltage is applied to the driving circuit. This produced a

displacement of the unimorphs proportional to their

response. With the unbalanced circuit, the result is to

displace the center of the interference pattern in some

direction on the target. In cases of extreme mismatch, the

concentric circular pattern was replaced with parallel

lines or hyperbolic shapes. By adjusting the potentiometer

in the voltage divider on the base of each isolation

transistor, the mirror orientation can be returned to the

same position as without the applied voltage. This is

monitored by the nature of the interference pattern on the

target. When properly adjusted, the voltage may be rapidly

switched on and off with no observed shift in the position

of the rings but with a phase change between light and dark

regions due to the changing optical path difference. The

final test of the unimorph alignment is to apply a low

frequency, on the order of 5 Hz, triangular wave to the

input of the driving circuit and observing the interference

pattern. If the alignment has been properly executed, the

rings move but stay centered. If the center of the moving

rings appear to "walk" back and forth on the target, then

the entire alignment procedure has to be repeated. With

the circuit shown in Figure 20, no further alignment is

necessary or possible, and SEMIDS can now be considered

operational. It is difficult to estimate the time

necessary for the alignment procedure because the expertise

and experience of the operator is a major factor in the


I








estimate. Nevertheless, the time necessary for alignment

is given to provide a "ball park" estimate of the

complexity of the procedure. To proceed from bare base

plate to operating SEMIDS requires the attention of one

operator for approximately 4 hours.

If the programmable amplifier shown in schematic

diagram in Figure 21 is used, one additional alignment is

necessary. For this step, two spectral lines are used,

either the laser and a hollow cathode lamp or two lines

from a single lamp. The procedure is to align SEMIDS with

one spectral line and to monitor the output of the

photomultiplier with an oscilloscope. A triangular voltage

is applied to the piezoelectric transducers and a sine wave

is visible on the face of the scope. By using a dual trace

scope, both the applied waveform and the output signal can

be directly compared, and the number of wavelengths the

mirror is displaced can be directly determined by counting

the number of sine waves in the period of the triangular

wave. By adjusting the offset "pot" in the driving

circuit, the displacement can be adjusted to any number of

integral wavelengths up to the maximum displacement voltage

of the circuit. The grating is then stepped to the next

spectral line. For simplicity, the procedure is always

performed on the longer wavelength-longer displacement

spectral line first. At the second wavelength, there are

invariably more sine waves in one period of the applied

triangular wave, since with a fixed displacement, shorter








wavelengths mean more fringes. The slope control in the

driving circuit is then adjusted to change the gain of the

amplifier until the circuit is displacing over the same

number of wavelengths with either spectral line. This

procedure sets the response of the driving circuit over the

entire scanning range because all the components of the

device have linear response.

The last adjustment to SEMIDS is the frequency of the

selective amplifier. This is determined by the frequency

of the applied triangular wave and the number of fringes

displaced. Once the approximate modulation frequency is

determined, the final adjustment is made with SEMIDS

operating on a spectral line from an external source. The

frequency selection dial is rotated until a maximum signal

is obtained. No further adjustments are necessary. The

time constant and the scanning speed are changed to fit the

conditions of various scanning cycles. The performance and

stability will be discussed in the next chapter.














CHAPTER V
SYSTEM PERFORMANCE EVALUATION

The first step in the system evaluation of SEMIDS was

to obtain measures of the stability and reliability. In

many respects, these were the most important parameters to

be determined because SEMIDS was intended to be

interchangeable with commercially available grating

dispersive spectrometers, and it was essential that the

device be comparable in overall reliability in order not to

prejudice the comparison unfavorably. The tolerances in

the system alignment, while not as critical to determine as

in a Michelson interferometer, were still too small to be

conveniently measured with mechanical devices. Therefore,

most of the evaluation was performed with the signal level,

the waveform and the shape of the fringes on the target as

the measurement criteria. This approach limits the amount

of quantitative data that can be obtained with respect to

transient system degradation from such sources as thermal

drift, etc. but readily allows qualitative estimates of the

severity of various problems.

The first topic investigated can be roughly classified

as static alignment degradation. This topic included most

of the potential difficulties that arose because of the

various engineering choices that were made during the

construction of the prototype SEMIDS. Of primary



86









importance was base plate warp and expansion. The presence

or appearance of warp over some finite period would lead to

degradation in the static alignment and therefore the

fringe pattern on the target. Because of the design of the

optical system, warp would affect some components more than

others. The system was designed so that only one element,

the grating, was the field stop. This effectively

prevented vignetting in the system. Vignetting causes the

intensity of an off-axis image on a field to decrease

because some areas of the optical elements are not filled.

The lenses have a diameter of 76.2 mm and the beam splitter

tilted at 450 to the axes has an effective diameter of 53.9

mm. The grating 40 mm on edge and the circular mirror has

a 50.8 mm diameter so that both reflectors were overfilled

by the collimator and a slight variation in the height or

position of the collimated beam would not be critical. On

the other hand, the position of the focusing lens would

critically affect the magnitude of the photomultiplier

signal and the angles at which all the optical elements

intercepted the collimated beam would affect the nature and

position of the interference fringes. Over a period of

more than six months, no system degradation was observed

that could be attributed to the base plate warping with the

support system previously described in Chapter III.

A problem was observed that could be directly assigned

to the size and composition of the base plate. A low

frequency drift was observed resulting from thermal







expansion of the plate which prevented any attempt to use

phase sensitive detection methods with the prototype

SEMIDS. The problem was observed with a diffuse laser beam

as the source when the system was aligned with the grating

in the first order. A normal fringe pattern of concentric

rings was observed on the target with the central fringe a

bright spot. Over a time period on the order of two

minutes, the central fringe intensity would drift through a

gray tone and become a dark spot. This drift corresponded

to an output wave phase shift and could be readily observed

on the oscilloscope. The severity of the problem with the

prototype SEMIDS could be limited by operating the system

in a constant temperature environment, but the problem

could not be entirely eliminated in this manner because of

thermal inhomogeneities caused by workers' body heat in

close proximity to the base plate. In the prototype

SEMIDS, the thermal drift was classified as a low frequency

noise and the second applied waveform in the modulation .

scheme compensated for the phenomena. The effects on the

fringe pattern were caused by the changing optical path

difference so the use of smaller geometrical separations

and support plates with low thermal coefficients of

expansion should allow phase sensitive detection methods.

Another problem encountered with the static alignment

of SEMIDS derived from the inability to lock the position

of the angular orientation devices used with the mirror and

grating. These devices were machined from aluminum and







exhibited some thermal drift and a slow alignment

degradation. Over an operating period on the order of one

half hour, the alignment would degrade so that the center

of the interference pattern was no longer in the center of

the target. This caused the focusing lens to image

segments of the concentric circular fringes on the detector

and, because the surface of the detector was covered by

both light and dark fringes at the same time, the depth of

modulation decreased and the signal intensity was

attenuated. In an optimized design of SEMIDS, these

devices would be replaced with supports constructed of much

more rigid material to allow the correct position to be

permanently fixed. The magnitude of the system degradation

was investigated in order to ascertain the overall effect

on performance of slight misalignment. The testing

procedure was to align the system properly with the diffuse

laser radiation and to scan the spectral line repetitively.

The peak heights were recorded on chart paper, and the

average of ten scans was used to obtain a measure of the

signal intensity. The scanning procedure was then repeated

with the same source but aligned at various points on

circles with radii 2 mm and 4 mm from the target center.

Figure 26 shows the target field with the test points and

results. The average of peak heights at each position was

used to calculate the percent of maximum peak height

obtained at each misalignment position. It was readily

apparent that displacements along the scanning axis did not





































51% 56% Scanning
Axis



30%





21%









Figure 26. Relative intensity of detector signal as a
function of reflector alignment.








degrade response or cause catastrophic failure of the

modulation scheme. The qualitative description of the

behavior is that a wavelength shift occurred, and the

signal attenuation resulted from measuring on the

"shoulder" of the line profile. Displacing the target

alignment in an up or down direction resulted in more

serious signal loss. This is logical because the scanning

of the grating cannot recover misalignment in these

directions. Investigation showed that most of the angular

orientation drifted less than 2 mm misalignment of the

image on the target, and therefore the signal from the

detector was never completely lost. Therefore, in a

qualitative determination, the aluminum angular orientation

devices had satisfactory stability and a quantitative

determination could be achieved by monitoring the

alignment. The procedure for checking and adjusting the

alignment was simple, consisting of placing the target in

the exit optical path and turning the micrometers on the

mirror support until the interference pattern was centered.

The entire cycle required less than 30 s. While the

performance of the present SEMIDS prototype was certainly

not nearly as good as could be obtained with improved

design, it was still sufficiently stable to permit further

investigation of system behavior without major

modification.

Vibration is always a major concern in interferometric

instruments whatever the nature of the detection system








because it can introduce spurious signals resulting from

the added modulation on the mirror displacement. The

primary sources of vibration in SEMIDS derive from external

causes. The vibration of the stepping motor fixed to the

base plate was also a potential problem source. As was

mentioned in Chapter III, a special support had to be

designed to minimize the effects of ambient vibrations.

The method for detecting and estimating the magnitude of

the problem was simple. With the system aligned and

operating with a line source, the photomultiplier signal

was displayed on an oscilloscope. With an unperturbed

system, the pattern on the scope was a simple sinusoidal

waveform subject to the low frequency phase drift

previously mentioned. Any vibrational perturbation to the

system resulted in the loss of the signal waveform on the

scope and the appearance of a trace composed of

nonperiodic, rapid oscillations. These oscillations damped

in some finite time and the sinusoid reappeared. As a

measure of the efficiency of vibrational isolation devices,

the time required for this damping effect was used. The

dual support system proved immediately successful when

compared to the previous supports for the base plate

because activities in the laboratory like slamming doors,

teletype operation, air conditioner operation, and workers

striking the support table were no longer observable on the

oscilloscope. With previous support design, SEMIDS

demonstrated susceptibility to acoustic noise. That is, if








a metal wastebasket were struck or any other loud noise

occurred, the scope would reflect the effects of that noise

on the system. With the dual support, the same type of

acoustic noise sources no longer affected the signal.

Additional investigations in this area were performed with

a signal generator coupled to a 6 in. speaker. With the

output voltage on the signal generator at 20 V, the speaker

was passed around all the optical elements and supports as

well as the base plate itself. Some points exhibited more

sensitivity than others. For example, when the speaker was

positioned directly behind the mirror support and the

generator frequency was less than 100 Hz, a stable

modulation was superimposed on the sinusoidal trace. In

all cases, SEMIDS responded to the acoustic noise at lower

frequencies, but the amplitude of the perturbation was less

than 10% of the modulated signal and the perturbation

damped below observable limits as soon as the speaker was

turned off or pointed in a different direction. Therefore,

it was felt that SEMIDS was sufficiently isolated from

ambient and acoustic noises to permit operation in a normal

laboratory environment with no extraordinary protection

measures necessary.

Because the initial investigation of the efficiency of

the dual support system indicated the system was successful

in eliminating or damping the effects of ambient

vibrations, an additional test was performed to obtain a

slightly more quantitative evaluation. The laboratory








where SEMIDS was constructed was primarily an analytical

spectroscopic research unit and access to vibration

measurement technology and equipment was severely limited.

The test was performed using a single pendulum arrangement

to impart a force of known magnitude at various points

along the perimeter of the base plate. The pendulum

consisted of a 0.2 kg mass supported by a wire 0.5 m long

attached to a support frame constructed of steel rods. The

pendulum bob was displaced 0.25 m from the equilibrium

position. The applied force can be calculated using the

pendulum approximation,


F = m g d (38)
L

where g is the gravitational acceleration 10 m/s 2, L is the

length of the wire, d is the lateral displacement, and m is

the mass of the bob. With the pendulum used in the

investigation, the applied force was 1 N. The measurement

of the perturbation was performed as before by observing an

oscilloscope trace. A stopwatch was used to obtain a

measure of the duration of the perturbation, and the signal

intensity before and after the application of the force was

used to determine if the system alignment was affected. In

all cases, the oscillations observed on the oscilloscope

damped below observable limits in less than 1 s. The

signal intensity as measured by the voltage on the scope

was in every case within 2% of the initial value. These

results indicated that SEMIDS prototype was fairly robust








in its resistance to external perturbations and its

performance in this area was certainly comparable to a

grating dispersive monochromator.

The first two investigations were primarily concerned

with the evaluation of the static support devices. Because

this evaluation was performed primarily with the optical

system operating, there was no possible method of

definitely assigning particular observed problems to one

device or even to one class of devices other than on a

logical and on a "most probable cause" basis. The third

investigation was of a different nature because it was'on a

component of the optical system, even though the evaluation

techniques remained the same. As was mentioned in Chapter

III, the motion transducer was somewhat unique in design.

The triangular arrangement of the three unimorphs was a

departure from precedent in this field and, according to

engineers at the manufacturing facility, had never been

used in a precision displacement application prior to

SEMIDS. As a result, extensive tests were performed with

the assembly to determine the limits of performance and

stability characteristics.

The first investigation in this series was to

determine the displacement and the frequency dependence of

the combined transducer assembly and driving circuit. The

displacement was measured with the diffuse laser beam as a

monochromatic source at 633 nm. The system was aligned

with the grating diffraction in the first order and a








triangular waveform with a 200 Hz frequency applied to the

input of the driving circuit. The applied voltage to the

piezoelectric transducers was monitored with an RMS

voltmeter and the displacement determined with an

oscilloscope. By displaying both the applied waveform and

the photomultiplier output simultaneously, the number of

fringes in each half of the applied wave could easily be

determined. It should be noted that the RMS voltage

displayed on the digital voltmeter used was not a true RMS

value because the circuitry was designed to measure

sinusoidal voltages, not triangular. However, because'the

frequency was held constant and only the voltage changed,

the displayed value could be used as a close measure of the

"true" RMS voltage. Figure 27 is a plot of data obtained

in this test. A slight modification was found necessary.

With no DC offset on the transducers, an asymmetric "dip"

on one side of the output waveform was observed. This

effect was explained by observing the fringe pattern at

various offset levels. The fringe pattern, while remaining

constantly centered on the target, did not always stay at

the same phase. That is, at certain voltages, the center

of the target would be neither a bright or dark fringe but

somewhere between. The offset was therefore adjusted at

all settings of the waveform amplitude in order to insure

complete fringes in each half cycle of the applied

waveform. As can be seen from Figure 27, the displacement

was linear over the entire range. The displacement can be