C. Burgess and K.D. Mielenz (Editors), Advances in Standards and Methodology in Spectrophotometry

© 1987 Elsevier Science Publishers Β. V., Amsterdam — Printed in The Netherlands

DETERMINATION O F THE OPTICAL CONSTANTS O F SOLIDS BY DISPERSIVE

FOURIER TRANSFORM SPECTROMETRY

T.J. PARKER

Physics D e p t . , Royal Holloway and Bedford New C o l l e g e , Egham,

Surrey T W 2 0 O E X (England)

ABSTRACT

A review is presented of techniques for determining the optical constants of solids by dispersive Fourier transform spectrometry ( D F T S ) . The experimental criteria which must be satisfied to realise the advantages over more conventional methods are discussed, and a brief review of the theoretical background is given. The most common experimental configurations used in DFTS are described, and the advantages of the technique are illustrated with examples of measurements on solids in the far infrared and visible. References to similar work on liquids and gases are given in the bibliography.

INTRODUCTION

The interaction of a beam of electromagnetic radiation with a

sample of m a t e r i a l , whether a solid, a liquid, or a g a s , can be

completely characterised by the frequency dependence of the

optical constants. If w e consider first isotropic m a t e r i a l s ,

these constants comprise two numbers which are each functions of

frequency, namely the refractive index, n, and the extinction

coefficient, k, which together define the complex refractive index

η = η + ik. (1)

Other important related parameters are the absorption

coefficient

α = 47Tvk, (2)

where ν = Ι/λ is the wavenumber and λ is the w a v e l e n g t h , and the

dielectric response functions

ε = ε' + ί ε " = (η + i k )2. (3)

376

The importance of these parameters is that on the one hand

they can be related in a simple way to the results of reflection

and transmission measurements on suitable s a m p l e s , and on the

other hand their frequency dependence can be derived theoret-

ically from microscopic models of the elementary excitations in

the samples.

When the interaction of a b e a m of radiation with a sample is

considered in the most general t e r m s , either in reflection or

transmission, each frequency component can b e regarded as under-

going an attenuation in intensity and a change in phase. In a

particular measurement these changes are related to the optical

constants by the appropriate form of the Fresnel relations, but

only rarely does an experiment permit a complete determination of

the frequency dependence of both η and k from a simultaneous

determination of the changes in both the intensity (or amplitude)

and the phase.

Dispersive Fourier transform spectrometry (DFTS) is a powerful

technique for making simultaneous determinations of both optical

constants of suitable materials from direct measurements of their

amplitude and phase response functions, either in reflection or

transmission. This is usually done by placing the sample in the

fixed arm of a two-beam interferometer such as a Michelson inter-

ferometer, rather than in the output beam as in conventional, or

power, FTS. The configurations most commonly used in DFTS are

illustrated schematically in Fig. 1. The advantages of each

configuration will be considered later, but it can be seen that

in each case the sample interacts with only one of the partial

beams in the interferometer, and the effect of this on the rec-

orded interferogram can be understood by considering the case of

amplitude reflection spectrometry (Fig. l a ) . If the interfero-

meter is perfectly symmetric, with mirrors in each arm, the

measured interferogram should have perfect symmetry as shown in

Fig.2a. (The interferogram shown in Fig. 2a is antisymmetric

rather than symmetric for technical reasons determined by the

method of observation w h i c h are not relevant h e r e ) . If the fixed

mirror is now replaced by a specimen, as shown in Fig. la, with

the specimen surface in the same plane as that of the reference

mirror, the symmetry of the instrument will be lost. The position

of the moving mirror corresponding to zero optical path difference

between the two arms of the interferometer for a particular

377

Fig. 1. The b a s i c interferometer configurations used in DFTS. (a) reflection, (b) double pass transmission, (c) single pass transmission. Key: MM moving, FM fixed m i r r o r , BS beam divider, S specimen, i input beam, ο output beam.

Fourier component is shifted away from the beam divider by an

amount which is determined by the phase response function Φ(ν) of

the sample. Since Φ(ν) is generally frequency dependent,

different Fourier components will be shifted by different amounts

x(ν) = φ(ν )/4πν , (4)

as well as being attenuated by the amplitude reflection coeff-

icient, r ( v ) , of the sample. Consequently the interferogram,

which is the sum of all the Fourier components, becomes asymmetric

as shown in Fig. 2b, with pronounced structure at positive path

differences (i.e. on the side of the interferogram furthest from

the beam d i v i d e r ) . Since both the shift x ( v ) and the attenuation

are recoverable from the two interferograms, it follows that the

amplitude and the phase response functions of the sample can both

be determined.

An extensive review and a bibliography of the subject have been

published by Birch and Parker (Refs. 1,2) and more recent devel-

opments have been reported by Birch (Ref. 3 ) . In the present

article the aim will be to give a brief account of the principles

and some aspects of the more b a s i c theory of the technique, and

to present a small selection of measurements on solids to i l l -

ustrate the capability of the technique in the far infrared and

its potential at shorter w a v e l e n g t h s .

378

(a)

ι 1 1 r

O P T I C A L PATH D I F F E R E N C E

Fig. 2. Comparison of a symmetrical background interferogram and an asymmetric specimen interferogram in reflection DFTS.

THEORETICAL BACKGROUND

As with most spectroscopic m e a s u r e m e n t s , the most suitable

configuration is determined primarily by the optical properties of

the specimen, and the most common geometries used in DFTS are

illustrated in Fig. 1. Samples must be prepared with an optically

flat surface for reflection m e a s u r e m e n t s , or in the form of plane

parallel lamellae for transmission m e a s u r e m e n t s . In the case of

solids, samples can b e directly inserted in the fixed arm of the

interferometer in the appropriate configuration. H o w e v e r , for

measurements on liquids or gases suitable cells and retaining

windows are required to define the geometry of the samples. This

considerably complicates both the design of the apparatus and the

analysis of the results because of the interactions which occur at

the additional interfaces. These points are fully discussed in

Refs. 1-3.

The general case of the interaction of a beam of radiation of

379

unit amplitude incident on a lamellar specimen of complex refrac-

tive index n 2 immersed in a medium of complex refractive index η χ

is illustrated schematically in Fig. 3. Series of reflected and

transmitted partial w a v e s are generated by the

t12 â | ?2 i t 2 i

^12^2^21^21

Fig. 3. Generation of multiply reflected and transmitted partial waves by a medium^of refractive index ί ϊ 2 immersed in a medium of refractive index ί ϊ 1 .

multiple reflections which occur at the interfaces. For DFTS it

is usually sufficient to consider the case of normal incidence,

and the coefficients r^ , t 1 2, etc, in Fig. 3 are then the Fresnel

reflection and transmission coefficients for radiation incident

normally from m e d i u m 1 onto m e d i u m 2, and

a 2 = exp ( - a 2d / 2 ) exp (27Tin2vd) (5)

is the complex propagation factor and d is the thickness of

medium 2. For the purposes of illustration, it w i l l b e sufficient

to consider the case of a solid specimen in a vacuum, so that

n ^ n and η-^1. B e f o r e considering any p a r t i c u l a r measurement it

is convenient to follow the procedure of Chamberlain (Ref. 4) and yv

introduce a complex quantity L ( v ) , known as the complex insertion

loss, which describes the changes which occur in the amplitude

and phase of an e l e c t r o m a g n e t i c w a v e propagating in the fixed arm

of the interferometer when the arm is changed to accommodate the

specimen. It can be shown that if I Q( x ) is the symmetric back-

ground interferogram of the interferometer, and I g( x ) is the

asymmetric interferogram obtained after introducing the sample,

380

then

L(v) = L ( v ) exp ί φ Ε( ν ) = FT I g( x ) , ( 6 )

FT I 0( x )

wh e r e FT indicates complex Fourier transformation. This procedure

enables the spectroscopic part of the operation, which is similar

for all m e a s u r e m e n t s , to be conveniently separated from the

ensuing analytical procedure. The remaining part of the exercise

is to establish the relationship between n, k and L in each case

and to solve the equations for η and k.

If the sample is completely opaque in the region of interest

only the first reflected partial wave can be observed, and the

measurements must be m a d e by the technique of amplitude reflection

spectroscopy illustrated in Fig. la. Since one of the partial

beams interacts with the sample once only, the amplitude

reflection coefficient

r = r exp i<j> ( 7 )

rather than the power reflection coefficient

R = J ?* = | Ç | 2 ( 8)

is determined. (The symbol * indicates the complex c o n j u g a t e ) .

However, since the amplitude reflection coefficient of the

reference mirror is

? o = exp ÎTT , (9 )

it follows that the complex insertion loss in this case is given

by

L ( v ) = r exp ΐ(φ-π ) (10)

so that r and φ can be readily determined from the two measured

interferograms. η and k can then be calculated from the Fresnel

relations for normal incidence:

η + ik = (1 + r exp ίφ)/(1 - r exp ΐφ) (11)

381

If the sample has a very low absorption coefficient (i.e. if

η » k ) it can be conveniently inserted in the form of a plane

parallel slab in the beam in the fixed arm, and if it is suffic-

iently thick, the signatures associated with the different trans-

mitted partial waves will be separated as shown in Fig. 4. If we

consider the first signature it can be seen that it is shifted by

approximately 2(n-l)d from I Q, where η is the mean value of the

refractive index in the measured range, and highly asymmetric as

w e l l . It is often helpful to associate the shift w i t h a mean

value of the refractive index, n, in this way, and the asymmetry

with the dispersion of η about n. In transmission measurements

it is usually convenient to record the two interferograms first

and then to measure the shift separately.

Fig. 4. The background interferogram and the signatures generated by the first two transmitted partial w a v e s in single pass transmission D F T S .

If the signatures are well separated as shown, it is sufficient

to record the first signature only, and it can b e shown that the

complex equation relating η and L can b e separated into real and

imaginary p a r t s , with

n(v) = 1 + L_ C4>T ι (v> + 4 τ τ νΒ ± 2 m 7 T

3

2-iïvd

(12)

382

k ( v ) = 1_ In

2πνα

4n(v)

{1 + n ( v ) l2L ( v ) J

(13)

In E q . 1 2 , φ^' is the principal value of the p h a s e , the factor

2πιπ , where m is an integer, is required to remove discontinuities

between adjacent branches of the phase spectrum, and 2B is the

shift in optical path difference between the two interferograms.

For more absorbing specimens thinner samples are required. The

signatures from the different transmitted partial w a v e s then m o v e

closer together and eventually overlap. When this occurs the real

and imaginary parts can no longer be separated and the complex

equation relating L to η must be solved numerically.

In reflection DFTS the measured phase angle is very small:

0 < φ—π < π, (14)

which leads to a very small shift between the specimen and

background interferograms, as shown in Fig. 2. Consequently, a

small systematic error in the determination of the relative

positions of the two interferograms can lead to a very large

phase error in reflection D F T S , particularly when λ is small.

From Fig. 4, on the other hand, it can be seen that in t r a n s -

mission DFTS the two interferograms are usually very widely

separated in optical path difference so that the shift can be

easily measured. It follows that when it is feasible, η and k

can be determined more accurately in transmission than in reflec-

tion. This can be difficult to realise with heavily absorbing

samples, but an amplitude advantage can be achieved if an instru-

ment is designed to allow one partial beam to pass through the

specimen once only as in Fig. 1c. If we compare Figs. 1b and 1c,

it can be seen that if the complex single pass transmission coeff-

icient is

t(v) = t(v) exp ίθ (15)

then the double pass transmission coefficient is

T ( v ) = t ( v )2, (16)

so that with suitable specimens it can be advantageous to use the

geometry of Fig. 1c.

383

PHASE ACCURACY

The determination of the phase spectrum in D F T S imposes a

number of constraints which are not so readily apparent in power

FTS. If we take as a simple criterion the requirement that all

systematic phase errors should be completely eliminated, i.e.

reduced to the random noise l e v e l , then a signal-to-noise ratio

of s leads to random noise levels of 1/s and 1/s radians in the

amplitude and p h a s e , respectively. In the case of the p h a s e , this

is equivalent to an error in optical path difference of

Αχ ~ Δφ/4πν (17)

Thus if Δ φ - 1 / s - O . O l , then in the far infrared ( v < 3 0 0 c m ~1, s a y )

Δχ~0.03μηι. This defines the precision with which a number of

important parameters must be specified if systematic phase errors

are to be eliminated. These include

(i) T h e reproducibility of the sampling points in the measured

interferograms.

(ii) The geometry of the samples (i.e. the flatness of the

surface in reflection m e a s u r e m e n t s and the thickness in

transmission m e a s u r e m e n t s )

(iii) The relative positions of the reflecting surfaces of the

specimen and reference m i r r o r in reflection measurements

In most far infrared work it has been p o s s i b l e to achieve the

required phase accuracy by using an accurate sampling device on

one arm and taking precautions to eliminate differential thermal

expansion between the two arms. However, at shorter w a v e l e n g t h s ,

and particularly in the near infrared, visible and u l t r a v i o l e t ,

this becomes impossible, and it becomes necessary to use an

interferometer with a subsidiary laser channel passing along the

same path as the b r o a d band radiation beam to m o n i t o r the optical

path difference. Further precautions must be taken in reflection

spectroscopy to compensate for irregularities in the sample

surface since the required tolerance is beyond the best specimen

preparation techniques.

REVIEW OF EXPERIMENTAL RESULTS

DFTS w a s first developed in the far infrared because of the

difficulties of measuring the phase spectrum. The vast majority

384

of measurements have been carried out in this region, and only

recently have the first efforts been made to extend the technique

to much higher frequencies. In this section a small selection of

far infrared measurements will be presented to illustrate the

capability of the technique, followed by a description of some of

the more recent work in the visible to illustrate the potential

for further development. Although many very accurate measurements

have been reported at millimetre w a v e l e n g t h s , this work will not

be discussed here as it is too far removed from the scope of this

conference. For a more complete survey of published work,

including reviews of measurements on liquids and g a s e s , Refs. 1-3

should be consulted.

In some of the earliest work Chamberlain and Gebbie (Ref.5)

used double pass transmission spectroscopy to determine the

optical constants of polytetrafluorethylene (teflon) in the range

70-450 c m "1 at room temperature. After subtracting out the

Fig. 5. (a) The absorption coefficient and (b) the dispersion Δη in the refractive index of teflon in the region of 200cm

1( A f t e r

Ref. 5 ) .

dispersion in the refractive index due to an intense absorption

band at 5 1 6 c m_ 1, they investigated the anomalous dispersion in

the region of weak bands at 202 and 2 7 7 c m_ 1 and showed that the

dispersion in the region of 2 0 0 c m_ 1 (Fig.5) followed very closely

the behaviour expected from a damped simple harmonic oscillator.

At about the same time, Russell and Bell (Ref. 6 ) used single

385

pass transmission spectroscopy to determine the optical constants

of crystal quartz for both the ordinary and extraordinary ray in

the range 1 0 - 4 0 0 c m_1 at room temperature (Fig. 6 ) . For this

Fig. 6. The refractive index and absorption coefficient of quartz for (a) the extraordinary ray and (b) the ordinary ray (After Ref. 6 ) .

work they used both very thin (75ym) and comparatively thick

(d~several mm) samples to cover the full range of values of α, so

that in the analysis it was necessary to take account of the

situations in which either only the first or all transmitted

partial waves were present. The accuracy of the refractive index

measurements was about one part in 2000, and the results were

used to obtain accurate dispersion parameters for the absorption

b a n d s . Similar measurements were later reported on sapphire

(Ref. 7 ) . This work illustrates one of the most useful features

of transmission DFTS. The displacement in optical path difference

between the specimen and background interferograms is usually very

large, as shown in Fig. 4, and can be measured very accurately.

It follows from Eq. 12 that the accuracy of the refractive index

determination is usually limited in practice by the uncertainty

in the measurement of the specimen thickness. Consequently, when

suitable samples are available, the uncertainty in the refractive

386

index can be reduced to levels of the order of 1 part in lCr .

Reflection DFTS has been widely used to investigate the far

infrared lattice response of ionic crystals in the region of the

reststrahlen band where bulk specimens are o p a q u e , and two

approaches have been used to eliminate systematic errors in the

phase measurement. Instruments which permit the specimen and

reference mirror to be mechanically interchanged with very high

precision have been constructed in several laboratories (Ref.

8 - 1 0 ) . With careful design work the reflecting surfaces can be

located with remarkable precision. Birch and Murray (Ref. 9) have

achieved a reproducibility of about O.Olym with an interferometer

constructed for measurements at room temperature, and Zwick et al

(Ref. 11) have used a mechanical replacement technique for

measurements at liquid helium temperatures. However the diffic-

ulties of mechanical replacement can b e avoided if part of the

specimen surface is metallised for use as a phase reference

surface, and this approach has been followed by several research

groups (Ref. 1 2 - 1 4 ) . It has the disadvantage that larger spec-

imens are required, but is more easily adapted for measurements

at low temperatures and high frequencies.

Measurements by Staal and Eldridge (Ref. 15) of the optical

constants of NaCl at 48K are shown in Fig. 7. On either side of

the reststrahlen band (see Fig. 7b) the reflection measurements

Fig. 7. The calculated and measured refractive index (a) and

absorption coefficient (b) of NaCl at 48K (After Ref. 1 5 ) .

387

w e r e supplemented with power transmission m e a s u r e m e n t s because in

these regions the phase is very close to that of the reference

mirror and difficult to m e a s u r e . The measurements w e r e compared

with calculations w h i c h took account of damping of the transverse

optic resonance by t w o - and three-phonon decay p r o c e s s e s , as w e l l

as by one-phonon isotope-induced absorption. It can be seen that

good agreement w a s obtained between measurement and theory, and

that the measurements are sensitive to weak structure in the

region where the absorption coefficient is very large.

Maslin et al (Ref. 16) have compared the sensitivity of DFTS

and power FTS for studying w e a k features in imperfect crystals.

They chose a polycrystalline sample of KBr containing 0.3% CI for

their investigation, and showed that weak one-phonon and two-

phonon structure could be observed at room temperature by r e f l -

ection DFTS on a bulk specimen, in addition to the expected CI

gap m o d e , as shown in Fig. 8. Most of the observed features w e r e

assigned to processes which are dipole forbidden in pure single

crystals, indicating that the samples w e r e either disordered or

highly strained. The authors were unable to observe the same

features at room temperature by power transmission spectroscopy,

even with samples thinned to about lOOym.

Fig. 8. (a) The measured amplitude and phase reflection spectra of KBr:CI at 300K, and (b) the anharmonic damping function of KBr:CI calculated from (a) (After Ref. 1 6 ) .

Reflection DFTS has also been used extensively for m e a s u r e -

ments on semiconductors. Gast and Genzel (Ref. 17) have reported

measurements on InAs and InSb and, in the latter case (Fig. 9 ) ,

both the free carrier response and the lattice response were

388

ι ι ι ι ι ι Ί IE Hh λ ^ ν 1.0 - a - LU C — - - ^ / -J ξ 0.8 - Χ/ Ν.φ - Ο

Ρ 0.6 - /\\ η - <

Ο) 0 50 100 150 200 250 3 0 0

10 .0 [ - \ 1 1 1

Γ"1 1 1

n , k2° V Y J

0.5 - \ / \ / \

0.21 1 AJ L _ i 1 ι r

( b ) 0 50 100 150 200 250 300

W A V E N U M B E R ( C M "1)

Fig. 9. (a) The power reflectivity and phase reflection coefficient, and (b) the optical constants of InSb measured at room temperature. (After Ref. 1 7 ) .

clearly revealed. More recently, Birch and Murray (Ref. 9) have

used amplitude reflection spectroscopy to study the far infrared

properties of CdTe at higher resolution, and the measured values

of the optical constants are shown in Fig. 10. The measurements

7.0 r

6.0 - /y\ 5.0 / 11

2.0 k

/ \ \

* ' 1 ι ^^-> • _ »

50 100 150 200

W A V E N U M B E R ( C M- 1

)

Fig. 10. The optical constants of CdTe at 290K. (After Ref. 1 8 ) .

revealed fine structure which had not been observed before by

more conventional techniques. The authors showed that the broad

features of the measured dielectric response functions followed

closely the behaviour expected from a damped simple harmonic

389

oscillator. The detailed structure was later shown (Ref. 18) to

arise from anharmonic interactions associated with the decay of

the transverse optic phonon at the centre of the Brillouin zone

into combinations of phonons elsewhere in the zone.

For most work in the far infrared it is sufficient to regard

metal mirrors as perfect reflectors, but for the most accurate

work, particularly when part of the specimen is metallised for

use as a reference mirror, skin effects must be taken into account.

However, Birch (Ref. 19) has demonstrated a useful technique for

determining the complex reflectivities of suitable transparent

samples by DFTS. The optical constants of a silicon crystal were

measured by transmission DFTS and the results were used to

calculate the complex reflectivity of the specimen with a

precision of about one part in ΙΟ1* , which is considerably better

than is usually achieved by reflection spectroscopy. The specimen

was subsequently used as the reference mirror in a study of Al

films vacuum deposited on optically polished glass b l a n k s , and

the dependence of reflectivity on film thickness was clearly

revealed. This technique should be particularly useful in the

visible and ultraviolet, where the choice of suitable materials

for use as reference mirrors also presents difficulties.

More recently, Burton and Parker (Ref. 2 0 ) have developed a

prototype interferometer for determining the optical constants of

solids in the visible and ultraviolet by DFTS. In this

instrument, the moving mirror w a s m o u n t e d on a high precision

hydraulic drive, and a He-Ne control laser and the w h i t e light

beam were both passed along the optical axis of the interfer-

ometer so that the laser fringes could be used to define the

sampling positions on the white light interferogram. Sampling

intervals of 39.55nm, which are small enough to avoid aliasing

problems in this frequency range, were obtained by subdividing

the natural fringe spacing of the laser by a factor of 8 using a

phase-locked loop circuit (Ref. 2 1 ) . It was found that the

reproducibility of the sampling points from interferogram to

interferogram was about 0.25nm, which is good enough for DFTS at

frequencies well into the ultraviolet. A simple measuring

procedure was developed which eliminated systematic phase errors

from most sources, including non-flatness of the specimen

surface, and the performance of the instrument in the reflection

mode w a s demonstrated with measurements on opaque metallic films

390

vacuum deposited on optically flat fused silica substrates. The

optical constants of gold determined with this instrument are

shown in Fig. 11 and compared with results obtained by Johnson and

Christie (Ref. 2 2 ) , who used a combination of power reflection and

transmission spectroscopy. It can be seen that there is good

agreement between the two sets of data, and it should be noted

that, for the determination by D F T S , the interferograms were

recorded in a few seconds and the computations were completed

in a matter of m i n u t e s .

ο J — . — . — . — , — . — . — . — . — . — . — . — . — . — . — k

1.5 2 .0 2.5 3 .0

P H O T O N ENERGY, eV

Fig. 11. The optical constants of Au in the visible. The points

are taken from Ref. 2 2 . Note that leV = 8 0 6 6 c m "1. (After R e f . 2 3 ) .

Measurements with the same instrument (Ref. 2 3 ) have shown that

the optical constants of transparent solids can be determined

very rapidly in the visible by transmission D F T S . As in the case

of measurements in the far infrared, it was found that the shift

in optical path difference between the specimen and background

interferograms could be measured very accurately, in this case by

using fringe counting techniques, so that the accuracy of the r e -

fractive index determination w a s again limited by the uncertainty

in the specimen thickness.

Finally, it should be mentioned that an instrument for

measuring the refractive indices of gases in the visible region

by DFTS has been developed by Kerl and Hausler (Ref. 2 4 ) . This

work has been reported since the earlier reviews were published,

and the authors have obtained results on CH^ which are in good

agreement with measurements by scanning- wavelength interferometry.

391

SUMMARY

DFTS has several important advantages over alternative methods

of determining the optical constants or dielectric functions of

suitable samples, amongst which are

(i) Measurements can be made conveniently at normal incid-

ence, so that simple forms of the Fresnel relations can

be used.

(ii) The recorded information is complete in the measured

range, eliminating the need to extrapolate measured data

as in the case of Kramers-Kronig analysis of reflectivity

spectra. This is particularly important when there is

significant structure in neighbouring spectral ranges.

Furthermore, the method is capable of providing absolute

determinations of the response functions at high r e s o l -

ution more efficiently than is possible by ellipsometry.

(iii) An improvement of an order of magnitude or more in sen-

sitivity can often be obtained from measurements on very

weakly reflecting or transmitting samples by using

amplitude rather than power spectroscopy.

(iv) The measurements can be made rapidly. This is mainly due

to the multiplex and throughput advantages of F T S , but is

partly due to computational factors arising from the com-

pleteness of the recorded information and the simplicity

of the analytical techniques.

DFTS has been used extensively in the far infrared and many

results have been obtained in this region which s u r p a s s , in

accuracy and sensitivity, those attainable by more conventional

techniques. H o w e v e r , the technique has not yet been exploited at

shorter wavelengths mainly because phase accuracies of the order

of 1 0 ~2 radians are required to realise the advantages over a l -

ternative techniques. To achieve this the sampling combs of the

recorded interferograms must be reproducible from scan to scan

with an accuracy of better than 1 0 "3λ , and severe constraints are

also placed on specimen handling t e c h n i q u e s , especially in

amplitude reflection spectroscopy. Such tolerances are difficult

to achieve when λ is s m a l l , and this applies particularly to the

near infrared, visible and ultraviolet. H o w e v e r , the preliminary

work which has been reported in the visible has established the

392

feasibility of extending the technique to this region, and it is

anticipated that further work will enable the advantages which

have been demonstrated at longer wavelengths to be fully ex-

ploited in the visible and ultraviolet.

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1 J.R. Birch and T.J. Parker, in K.J. Button (Ed.) Infrared and Millimeter Waves, Vol. 2, Academic Press, New York, 1979,

pp 137-271. 2 J.R. Birch and T.J. Parker, Infrared P h y s . , 19 (1979) 201-215. 3 J.R. Birch, SPIE Vol.289 (1981) Fourier Transform'Infrared

Spectroscopy, 362-384. 4 J.E. Chamberlain, Infrared P h y s . , 12 (1972) 145-164. 5 J.E. Chamberlain and H.A. Gebbie, Appl.Opt., 5 (1966) 393-396. 6 E.E. Russell and E.E. Bell, J.Opt.Soc.Am., 57 (1967) 341-348. 7 E.E. Russell and E.E. Bell, J.Opt.Soc.Am., 57 (1967) 543-544. 8 E.E. Russell and E.E. Bell, Infrared Phys., 6 (1966) 75-84. 9 J.R. Birch and D.K. Murray, Infrared P h y s . , 18 (1978) 283-291.

10 J. Gast, L. Genzel and U. Zwick, IEEE T r a n s . MTT-22 (1974) 1026-1027.

11 U. Zwick, C. Irslinger and L. Genzel, Infrared Phys., 16 (1976) 263-267.

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