[Analytical Spectroscopy Library] Advances in Standards and Methodology in Spectrophotometry Volume...
Transcript of [Analytical Spectroscopy Library] Advances in Standards and Methodology in Spectrophotometry Volume...
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)
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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.
REFERENCES
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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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