William J. Hurley Princeton University Princeton, N e w Jersey
Interferometric Spectroscopy in the Far Infrared
Although it is an area of great interest, far infrared spectroscopy has been an alien study in most chemical laboratories for a number of reasons. Two principal problems have been the low intensity of the sources currently availahle for this spectral region and the insensitivity of detectors availahle for the low energies associated with these longer wavelengths. Because conventional spectrophotometers use prisms and/or gratings for the selection of monochromatic radiation, much of the initially weak light intensity originating in the source is lost through dispersion and diffraction,and the intensity of the radiation being received at the detector is greatly diminished. Obviously any loss of intensity with the far infrared wavelengths is critical because of the detection problem, and therefore very wide slits must be used in order to obtain an optimum signal-to-noise ratio. Because of the large slit-width requirement, resolution is greatly reduced. Decreasing the slit-width to enhance resolution only further decreases the availahle light. I n the past, a few workers have skillfully managed the sensitivity and resolution problems and obtained very good spectra. However their methods were developed for specific problems and did not lend themselves to general or practical use. Consequently very little far infrared chemical information has been obtained. I n recent years instruments for use in the far infrared have become commercially available, hut some of them are grating instruments and suffer from the disadvantages mentioned above. Also the costs of these grating instruments are very high. A newer type of instrument, the interferometric spectrophotometer (or Fourier spectrophotometer), is much more efficient in its use of the availahle light than the conventional instruments because it does not use gratings, prisms, or narrow slits and is capable of affording excellent resolution. I n this paper the principles of interferometry and its application to far infrared spectroscopy will he discussed. Historical
When the source energy is low, it is common practice among physicists to use interferometry to increase the efficiency because of its light gathering power. For this reason interferometry has been very important in astrophysical studies. Other interferometric techniques have been developed for the accurate determination of wavelength and for index of refraction studies. Since there is poor efficiency in the far infrared region of the spectrum, interferometry lends itself to application, and many of the established techniques have facilitated the design of far infrared interferometric spectrophotometers. Another feature which makes interferometry attrac236
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tive for application with the long wavelengths of far infrared radiation is that optical tolerances are not so restricted as they are with the shorter wavelengths. To use interferometry in the visible or near infrared region would be a more formidable task. There are several types of interferometers hut all essentially have a coherent source, a beam or amplitude divider, and a detection system. The Michelson, lamellar grating, and Fahry-Perot interferometers have been used for far infrared measurements with the first being more popular in chemical laboratories. For this reason this paper will discuss only the Michelson instrument and the reader is referred to Richards (1)for adescription of the lamellar grating instrument and to Renk and Genzel (8) for a discussion of Fahry-Perot interferometers. It is of interest to note that Michelson (3) himself suggested that interferometric techniques could he applied to spectroscopy, hut, for reasons which were valid at the time, this idea was postponed. I n 1952 Rupert (4) realized the potential that interferometry had in the study of molecular structure, and in 1956 Gebbie and Vanasse (5) found experimentally that such work was possible. Since then techniques have been improved and commercial interferometric spectrophotometers have become availahle from the Research and Industrial Instruments Company (RIIC) and from Sir Howard Grubh Parsons and Company, Ltd. Instrumentation
A block diagram of a commercial Michelson interferometric spectrophotometer is shown in Figure 1. The entire optical systcm is enclosed and evacuated to a pressure less than 0.1 mm Hg in order to prevent atmospheric water vapor absorption. The source is a quarts jacketed mercury lamp which has been shown (6) to he better a t lower frequencies than a heated glohar source. Modulated light from the source is collimated and passes to a taut Mylar (polyethylene terephthalate) film about 12 in. in diameter which acts as a beam splitter. Part of the light is reflected onto the movable mirror iM1 and part is transmitted to the stationary mirror M S . The radiation which is rejoined after reflection by the mirrors has certain frequencies which constructively interfere and others which destructively interfere. The interference arises because of the difference in optical paths A M I A and AMzA shown in Figure (2). This difference is continuously changed by moving mirror M I at a constant rate, but usually slow enough to average the noise to an acceptable value. The mirror is mounted onto a shaft which is moved toward and through zero path diierence, i.e., where A M I A = AM2A, by an electric motor coupled to the shaft by a gear transmission. The motor is activated
by a manual control on the instrument. After the rays are recombined, the radiation passes to a Cassegrainian condenser consisting of convex and concave mirrors which focuses the light on the sample. The rays pass through the sample and are focused by another condensing system onto a Golay detector. The signal from
film is only 0.006 nim; hence a compensating film is unnecessary. ~nterfero~ra'ms
The difference in total path length traversed by the two halves of the beam before being recombined is a function of the position of the moving mirror which is twice the mechanical displacement of the mirror and will be called x. The intensity I(x) of the energy received by the Golay detector is a function of x because of interference between the two halves of the beam as they recombine. At x = 0 all frequenciesinterfere constructively so that all the far infrared energy of the source is incident upon the detector except for reflection losses and absorption by the samde. The hiaher freauencies do not cornpvtFl reach the detector because they are filtered by black polyethylene. If the radiation of the interfering beams conspectrum sists of the same wavelength AD, then the intensity of the light incident on the detector is given by (10)
J
Figure 1.
Diagram of the R1.I.C. Fourier Spectrophotometer.
the Golay is amplified and demodulated and the interferogram traced on a chart recorder. Simultaneously the Golay signal is digitized a t preset distances of mirror movement as determined by a Moire fringe system (7) and the digitized signal is recorded on paper tape or punched cards which serve as the input to a computer which transforms the data and traces the spectrum. At first inspection the complete system appears elaborate but in fact it can he purchased in "package" form or individual components may be purchased separately. A few workers have designed and assembled their own instruments. The mirror drive in the instrument described above is said to be aperiodic because the path difference between the two coherent and equally intense beams changes with a constant velocity without cyclic repet,ition. Some instruments have been designed so that the path difference is changed periodically at a certain set frequency, and this type of movement is called periodic. Genzel (8) has discussed these two approaches to interferometeric spectroscopy. It should be noted that there is no monochromater anywhere in the instrument. Radiation of many frequencies passes through the sample and only those frequencies which are not selectively absorbed reach the detector. Because many frequencies are incident on the detector instead of just one, as is the case with grating spectroscopy, the signal-to-noise ratio is very large and this feature is known as the multiplex or Fellgell advantage (9). Parenthetically it may be stated that a second film must be in position a t P in Figure 2 in many NIichelson interferometer applications in order to make the path in the film of the two rays equal, thus making interference possible. However in the far infrared the wavelengths are so long compared to the film thickness that the path in Mylar is negligible. For example 100 cm-' radiation has a wavelength of 0.1 mm whereas a 0.25 mil thick
where a represents the amplitude of the respective beams. Letting vo = lPawe have I(z)
=
at2
+ a? + 2aias cos 2rvoz
(2)
If the amplitudes are equal, as they should be in this case, I(z)
=
2a2(l
+ cos 2ruaz)
(3)
or letting 2a2 = I since a is a constant gives I(s) = 1(1
+ cos 2ruor)
(4)
When the radiation is polychromatic we must integrate the right hand side of equation (4) over all frequencies I(z) =
J_'z I ( v ) d ~+ J'z
I ( " ) cos 2ruzdu
(5)
G Figure 2.
Roy diagram rhowing the rplining and recombination of beams
The value of the intensity a t x
=
0 is
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and a t larger values of path differcnce x Z ( z ) = 1/21(0)
+ .r.+II(") cos 2ruzdu
For example if ,v (7)
The difference between I ( x ) and ' / J ( O ) is called the interferogram function, F ( z ): F(. )
=
I ( z ) - 1/2Z(0)=
I ( " ) cos 2ruzdv
(8)
and is obtained on a strip chart recording of the energy incident on the detector as the path difference between the two beams is changed. Figure 3 shows a typical interferogram. The value of ' / J ( O ) may be determined from the asymptotic value of the record.
ZERO
I PATH
were 400 cm-I,
DIFFERENCE
That is, the signal from the detector must be sampled at least every 1 2 . 5 ~of path difference. Because of the periodic sampling it can be shown that at the frequency v the computed spectrum contains false energies of frequencies where n is an integer. This effect is called aliasing. Therefore in order to obtain an unambiguous spectrum it is necessary t o use cutoff filters to reduce the spectrum to zero intensity at u,,, and to keep at zero the intensities of all higher frequencies. Such filtering is easily accomplished because v,,, can be chosen to be far away from any spectral feature anticipated. The theoretical resolution Av is set by the maximum path difference X of the interfering beams. These two quantities are reciprocally related (12) so that
As X approaches infinity thc resolution approaches the limiting value of zero. I t is obvious that one may obtain excellent resolution with interferometric spectroscopy. If one wishes a resolution of 0.5 cm-', which is certainly adequate for most chemical problems,
Figure
3. lnferferogrorn obtained for cry9tolline CHI of 4OK.
Equation (8) is recognized as a Fourier integral and its Fourier transform is I n practice F ( x ) can only be obtained over a finite interval -X to +X so the calculated spectrum I ( v ) is given by a truncated integral I(")
=
J.+$F ( z ) eos 2rvzdz
(10)
or sincc F(x) is symmetrical about zero path difference I n calculating spectra the Fourier cosine integral is allproximated by a summation I(")
= 2
x:
F ( z ) cos 2ruzAr
(12)
Since F ( x ) cannot be expressed analytically, numerical methods are used to determine its cosine Fouricr transform which gives the spectral distribution I(u). This is easily done by a general purpose, high speed digital computer. Information theory ( 1 1 ) tells that in order to obtain all the information in a spectrum from 0 < v
