Naturwissenschaflen

280

Fourier Transform Spectroscopy M. J. D. Low Department of Chemistry, New York University New York, N. Y. USA

Fourier Transform spectroscopy is beginning to flourish. However, unlike the almost explosive growth following a discovery in some fields, such as gas chromatography or lasers, the use of scanning interferometer systems to measure spectra has had to pass through a long period of quiescence. The latter was, essentially, enforced through the lack of technology, and it was the emergence of electronics and computer science that made Fourier Transform spectroscopy feasible. Further advances in technology, especially the recent advent of the minicomputer, are now rapidly raising Fourier Transform spectroscopy from obscurity. The success story, then, goes back for three quarters of a century (or even further, if one thinks of Robert Boyle's observation in t663 of what are now termed "Newton's Rings" Et~ and Fizeau's use of interference to study the yellow sodium doublet ~2~). In considering this technique of spectroscopy, it is interesting and useful to begin with Michelson's "visibility curves"; briefly outlining the basis of Fourier Transform spectroscopy, and then to take a giant step in terms of time and technology.

plate B. A fine screw passed through the carriage bearing mirror M1, so that when the handle H was rotated, the mirror could be moved a known amount. If the position of M s was adjusted so that the optical paths of the reflected and transmitted rays were equal, then the two beams would be in phase when they return to the beamsplitter. The field at the output of the interferometer as viewed through the telescope would therefore appear bright. If M1is now moved toward or away from the beamsplitter b y a distance equal to t/4 of the wavelength i of the light, then tile optical path of the reflected ray will be changed by 4/2. The two beams will then arrive at the beamsplitter 180 ~ out of phase, will interfere destructively, and the field will be dark. Continuing the motion of M s in either direction will cause the field to brighten and darken in succession, an oscillation occurring for each quarter-wavelength movement of tile mirror. If monochromatic radiation of frequency v, intensity I, is observed, the brightness of the field I (X) is then a simple function of the optical path difference X,

I(X) = 1 ( t +cos 2~ ~ x ) . Michelson's VisibiEty Curves Fig. I shows the apparatus used b y Michelson. A spectral line was isolated in the manner shown, and a beam of light was led into tile simple device. The beam was evenly divided upon striking a semitransparent beamsplitter plate B, one ray being reflected to the movable mirror M 1, the second being transmitted to the stationary mirror M 2. The two rays, after being reflected b y the mirrors, were recombined at the beamsplitter, and were observed through a telescope by a detector, D. The plate C was used to compensate for dispersion introduced b y

(t)

Suppose, now, that the supposedly monochromatic light entering the interferometer really consists of two components differing slightly in wavelength. Each component will undergo the interference phenomenon, and the brightness of each will be described by Eq. (1). As M s is moved, however, the two components will interfere with each other and, after M s has moved through a certain distance, there will be destructive interference. This is shown schematically b y the two curves at the top of Fig. 2. Further movement of M s will then cause partial overlapping, and so on. The field brightness or "visibility" (or detector signal) is then summation of two effects. This simple case is illustrated by Michelson's observations of tile red Balmer line of hydrogen. He observed the visibility curve (a plot of intensity

Oglmo0

Mirror

Fig. t. Michelson's interferometer

Displacement

Fig. 2. The top two curves represent two rays differing slightly ill wavelength, like the red B a l m e r line of h y d r o g e n shown on the left, b o t t o m . The v i s i b i l i t y curve is on the right, b o t t o m

75. ]g., He/t 6, 1970

lXl. J. D. Low: Fourier T r a n s f o r m Spectroscopy

28t Transducer

White r Light

-q

"I R

C:2-.,-Detectot-~n

Start

Zero

Fig. 4. A "fringe-referenced" system. The radiation to be examined is processed by the interferometer on the right. The second interferemeter is used to provide trigger and time-base signals. One interferometer can be used for both functions : one part of the beamsplitter is used for the laser and white lights, the rest for the IR signal. This, however, reduces the light-gathering ability of the interferometer Fig. 3. Interference patterns produced by various simple spectra

versus mirror displacement) shown at tile lower right part of Fig. 2, and from this obtained the distribution of light shown at the lower left, concluding that ... Since the curve is periodic, we m a y be pretty sure that this red line o/hydrogen is a double line. This/act, I believe, has never yet been observed ... I31. Tile separation of the lines was 0.14 ~. Some more complex curves produced b y radiation of different line shapes, numbers of lines, and so on, are shown in Fig. 3. I t is readily apparent that tile complexity of the signal, termed inter/erogram, increases rapidly as the spectral features multiply, so that the inverse procedure -- reconstructing a spectrum from the interferogram -- becomes even more difficult. Michelson was able to examine and determine tile structure of a number of lines [4~ and constructed an 80-channel analog device to aid the process Ehl. Michelson's "computer" consisted of 80 gears driving 80 wheels to rotate at speeds proportional to the integers 1 to 80. Each wheel rocked a lever which in turn produced a simple harmonic motion in an adjustable arm. Each arm was linked b y springs to an axle,tile composite motion of all 80 motions then moving a pen. The device, now in the Smithsonian Institution, was obviously incapable of handling tile complex interferogram of an intricate multicomponent spectrum. Nothing much more could be done with what appeared to be an interesting and promising spectroscopic technique, until the passage of time brought about the improvements in detectors, optics, and electronics with which an interferogram could be measured and also brought about the development of tile devices with which the signal could be stored and processed. Outline o~ Fourier Trans/orm Spectroscopy When polychromatic radiation enters the interferemeter, each component can be treated independently, e.g., Eq. (t), and the output or detector signal will be the summation of all of the cosine oscillations produced b y all of the optical frequencies of the source. Such an interferogram is shown schematically

as trace A in Fig. 4. When the optical path difference or retardation X is zero, all waves are in phase and the signal is large. As the mirror moves away from this zero position, the signal declines rapidly. The total signal can be expressed by, +co

_r(X) = f I (v) cos (2

x v dr)

(2)

--OO

where I ( X ) is the interferogram and I(v) is tile spectrum, i.e., the intensity of tile source as function of frequency. Eq. (2) is one of a cosine Fourier Transform pair, the other being, +co

z(v) = f_r(x) cos(2

dX.

(3)

--OO

In theory, then, one would use a suitably automated Michelson interferometer to measure intensity as function of mirror displacement or retardation, and then perform the mathematical operation indicated b y Eq. (3) in order to obtain the spectrum. In practice, however, it is very difficult to construct a perfectly balanced interferometer for use over an extended wavelength range, and this leads to the appearance of sine components in the interferogram. A complex pair, +co

I(X) = f

(4)

--00

+co

•

= f z (x) e-

dX

(S)

--CO

must be used. Note also that the integration limits require an obviously unattainable infinitely long mirror motion. T h a t and other corrections (see Connes [63 or Vanasse and Sakai [71 for comprehensive treatments of the theory) lead to a formidable and forbidding data reduction procedure which, until the advent of the modern digital computer, has been a practically insurmountable obstacle. The development of computers and fast Fourier Transform programs [8 3 has now made Fourier Transform spectroscopy feasible. Only a small part of the obstacle remains: it is tedious, inconvenient, time-consuming, or just unsatisfactory, unpalatable, or unacceptable to m a n y experimenters, to record data and then take the data

282

M.J.D. Low: Fourier Transform Spectroscopy

to someone else's computer for processing. The residual hurdles, including the psychological ones, are now being rapidly eroded through the use of minicomputers. It is now possible to carry out all operations in-house, rapidly, conveniently, and

economically. The previous equations show that it is possible to describe a spectrum -- encoding the intensity and frequency relations of a source -- by measuring intensity as function of mirror position. It is equally valid to consider time and mirror velocity, and such an aspect is useful because it points to some of the requirements of the instrumentation used to produce and process interferograms, e.g., detector frequency response, digitization rates, etc., although such items are outside the scope of this article. Consider again monochromatic radiation entering an interferometer such as that shown in Fig. t. It is obvious that the rate at which the field is made to oscillate between light and dark depends on how fast the handle H is turned. If tile mirror M~ is moved through a total distance X/2, the retardation is X, and with light of wavelength, ~, the number of fringes or oscillations produced is X/1. If the mirror motion occurs in time T, frequency, [, of the fringes is X/,tT or

2v ( 2 / T ) ,

where v is the optical frequency, or

#

/ =2vV

(6)

where V is the mirror velocity. If V is constant, there is then a direct relation between the /requency o/ the

incoming radiation and the /requency o[ the detector signal. If V is chosen to be of tile order of mm/sec, then / falls in the low audio frequency range. For example, if V = 5 mm/sec, then 10-micron radiation (t000 cm -1, 3 • t014 Hz) will produce a detector signal of 500 Hz, some / t decades lower. Each frequency component of a polychromatic mixture thus becomes uniquely encoded at a much lower frequency (tile relations are like Eqs. (1) to (5)). The high-frequency incoming signal is, essentially, shifted "downstream" to a frequency range where detectors can operate. The resulting interferogram frequencies then fall into a range easily handled b y conventional radio frequency electronics. Note that, whether the interferogram is expressed directly as function of retardation or indirectly as function of elapsed mirror scan time, it is necessary to know the mirror position precisely. In the farinfrared range, where wavelengths are of the order of hundreds of microns, it is very easy to measure mirror position and changes of mirror position by means of ordinary mechanic's micrometers. At shorter wavelengths this is not practical, and Block Engineering, Inc. circumvented the problem b y using a constant velocity mirror drive in conjunction with an electronically generated time base. They have now replaced this method with a better one, by making the interferometer generate its own time base. This is shown schematically in Fig. 4. Two mirrors are mounted together and are moved b y the same drive mechanism. Tile radiation from the source to be examined is processed b y one interferometer and produces the interferogram A. Light from a laser is fed into the second interferometer and, being monochromatic, produces a cosine wave B. As

Naturwissenschaflen

the two mirrors are locked together, the interferogram and cosine signal are linked, and the latter functions as a precise time base. White light is also fed into the second interferometer and produces an interferogram C. The mirror positions are adjusted so that when the "sample" interferometer mirror is retracted and about to begin its sweep forward toward the " z e r o " position, tile mirror of the "reference" interferometer is near its zero point. When the sweep begins, the reference mirror goes to the position of zero retardation, and the central burst of the whitelight interferogram is used to mark the beginning of the sweep of the sample interferometer. These timebase and trigger signals of such a "fringe-referenced" system are then used to operate the associated electronics and computer.

Advantages The conventional dispersion spectrometer and the Fourier Transform spectrometer produce the same end result of interest to the spectroscopist or chemist -- a spectrum. It is consequently pertinent to ask why one should consider recording spectra in an apparently roundabout way with a complex technique, if high-quality dispersion spectrometers are available. Tile answer lies mainly in the high signalto-noise (S/N) ratio obtainable with the Fourier Transform spectrometer. This comes about in two ways. The Fourier Transform spectrometer, in distinct contrast to the dispersion instrument, does not have a "monochromator". Dispersion of radiation is not necessary, so that the energy-wasting slits of tile dispersion instrument are not needed. This greatly increases the light-gathering capability or throughput of the interferometer. The Block Engineering, Inc. Model 296 interferometer, for example, has a 50-mm diameter aperture compared to a slit width of a few microns necessary in a conventional spectrometer of comparable resolution. The second advantage also arises from the absence of the need to disperse radiation I9]. In the conventional spectrometer, each radiation bundle or resolution element of the spectrum is scanned across the detector in sequence. Consequently, if there are M resolution elements, the intensity of each element is measured for only a fraction T/M of the total scan time, T. The signal proper (the intensity of an element) is directly proportional to the time spent in measuring it, while noise, being random, is proportional to the square root of the observation time. The S/N is then proportional to (T/M)89 With the interferometer, however, all o/ the entering radiation is observed, so that eactl resolution element is observed throughout the entire scan period. S/N is consequently proportional to T89 This improvement b y a factor of M89 termed Fellgett's Advantage, is realized with detectors which are detector-noise hmited, and can be quite significant in terms of S/N. The advantage in S/N can be used to trade resolution for "speed". A spectrum can be measured with a Fourier Transform spectrometer in the same time as with a dispersion spectrometer but with better S/N, or in a much shorter time but with an equivalent S/N. Suppose that a spectrum is composed of 2000 reso-

.57. Jg., Heir 6, 1970

M.J.D.

Low: Fourier T r a n s f o r m Spectroscopy

lution elements and that an observation time of I second per resolution element is required to obtain good S/N. The dispersion spectrometer requires a scan period of 2000 seconds or 33 minutes to make the measurement. The interferometer will make the same measurement in i second. Under the same conditions, improving S/N b y a factor of 2 would require four times the measuring time, or 2 hours t 2 minutes for the dispersion instrument, but only 4 seconds for the interferometer. The disparity in measuring times becomes greater if the resolution is to be improved b y a factor of 2. For the dispersion instrument, such an improvement would require that the slit widths be halved, so that its throughput is decreased b y a factor of 4. In order to regain the desired S/N, the measurement period must be increased b y a factor of t 6 to 8 hours 48 minutes. On the other hand, the resolution of an interferometer is a direct function of sweep length and is simply doubled b y doubling the mirror displacement. With an interferometer having a constant mirror velocity, the effect of increasing the resolution by a factor of 2 is to increase the measurement time from I second to 2 seconds. Such S/N advantages make it worthwhile to use the Fourier Transform techniques. Secondary advantages arise, also. One is that the relatively short scan times of an interferometer make it practical to carry out signal-averaging b y multiple scanning and addition of information. The signal proper is positive or negative, and the summation of signals is thus directly, related to the number n of signals added. Noise, however, is positive and negative at random, and is proportional to n89 S/N is therefore proportional to n89 Adding the data of a series of scans can thus be used to improve S/N -- if the individual scan period is short. Suppose that an interferometer scan of I second produces the entire spectrum at the same S/N as a 5-minute scan covering only a /raction of the spectral range produced b y a dispersion spectrometer. A 32-fold increase in S/N is obtainable b y adding 512 scans. For the interferometer, tile measuring period is increased from I second to about 8minutes; for the dispersion spectrometer, from

283

15 minutes to the impractically long period of 43 hours or almost 2 days. In a complete reversal, the previously formidable and cumbersome data reduction can now be used to advantage. The spectrum is obtained in digital form and is consequently easy to process. Using a built-in minicomputer, it is easy to use digital means to ratio spectra, scale-expand the ordinate or abscissa, go from one mode of presentation to another, e.g., from percentage transmittance to absorbance, and so on. The digitized spectrum is also ready for spectrum matching or identification -- in general, ready for data storage and retrieval b y large computers.

In/rared F TS While other manufactures have concentrated on the energy-starved far-infrared region, Block Engineering, Inc. has placed emphasis on the normal infrared or fingerprint region. Their most sophisticated instrument, the FTS-14 spectrometer system [101, is shown schematically in Fig. 5. A general-purpose digital computer is used to control the instrument and perform data reduction and analysis. Operator adjustments and interacting controls are virtually eliminated. The entire instrument is computercontrolled; programs optimized for any set of experimental conditions provide full-time monitoring of performance. The operator has access to the instrument only via Teletype. He m a y choose, for example, (a) resolution, e.g., 0.5 cm -1 over the entire spectral range for high resolution, or 2 cm -1 for a survey spectrum; (b) single-beam or double-beam operation, the latter resulting in a ratio-recorded spectrum; (c) normal presentation or scale expansion; (d) spectral range to be plotted (the spectral range covered is governed b y the beamsplitter -- for the fingerprint region, a scan results in a complete spectrum from 3950 to 400 cm -1 -- but the operator m a y choose to plot only a portion of the spectrum); (e) the number of scans.

SPECTRAL >[ ,B-G,Tt ANALOG

IR SOURCE ~ , ~ (ELECTRONICALLY STABILIZED}

BLOCK ENGINEERING MODEL 296 FOURIER TRANSFORM SPECTROMETER

PYRO-ELECTRIC BOLOMETER DETECTOR

DATA

REFERENCE

ANALOG TO DIGITAL CONVERTER

CALIBRATION SCAN LASER AND CON-- REFERENCE TROL INTERFEROMETER

l

DIGITAL SPECTRAL DATA TO SIGNAL AVERAGER BA,r

WORD

OR

12,288 WORD I ADD[TIONAL CORE MEMORY (STANDARD)

(OPTIONAL) 72~000 WORD DISC FOR DATA AND PROGRAMS

Fig. 5. Schematic of Block Engineering, Inc. FTS-t4 Fourier Transform spectrometer system 20c Naturwissenschaften1970

284

3/i. J. D. Low: Fourier Transform Spectroscopy

Naturwisse~scha/ten

marked P. The movable mirror is mounted on a mount within the housing D. The bearing of the mirror drive shaft is kept drag-free by floating it on an air cushion within a close-fitting sleeve. The mirror drive is electromagnetic. Light from a H e - N e laser L is deflected b y a sinai, mirror M to a second interferometer mounted within the large cube (the mounting plate of the small interferometer can be seen on top of the cube). The laser, a white-light source, and the second interferometer constitute the fringe-referencing system. Wavenumber calibration is derived directly from the laser reference signal, and wavenumber marks are drawn on the chart b y the Fig. 6. Optical system, Block Engineering, Inc. Model 296 Michelson digital plotter. The optical system is coupled to a sampling compartment similar in layout to those of interferometer conventional spectrometers. The usual sampling cells and accessories can be accommodated. ~ ~ ~'~ In practice, then, one would place a sample i n s I /[ l/ I / / j ~ \ \ / ' ! I / V ~ suitable cell, put the cell in the sample beam, and t ~fl J tell the computer the operating and plotting pars! j C i meters via Teletype. The measurement and plotting 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,., 100 are then automatic. Some spectra obtained in this way, illustrating some of the capabilities of the ~system, are shown below. .-~ ~ Z~ ' - ~ z-~ ~ ; ' ~ Trace A of Fig. 7 is the single-beam spectrum of a I I . ~ ,,i' ~;l?"~lVv ~ t 01.... X/~ /] ~ ~ : sample of ethyl octanoa~e. The absorptions of the sample are superimposed on the spectrum of the source, and the spectrum suffers from all the disadvantages of single-beam spectra. On command, t-however, the instrument will measure the spectrum of the source (a " b a c k g r o u n d " spectrum) and ratio the sample and background spectra. Trace B of ....... io'oo' c~-i Fig. 7 is such a spectrum, and is similar to the doubleFig. 7. Ethyl oetanoate, between KBr plates. - - A Single-beam beam spectra produced b y conventional dispersion spectrum, 16 scans. B Spectrum A ratioed against a spectrum spectrometers. On command, the instrument will of the source, 16 scans. -- C Spectrum B scale-expanded then scale-expand all or any part of the spectrum (trace C, Fig. 7). Note that even with t6 2-second scans a spectrum of reasonable quality can be obtained. Better spectra can be obtained b y scanning for longer periods. This is shown b y the spectra of Fig. 8. Each of the ratioed spectra was obtained with the same sample, but with different numbers of scans. (The spectra are somewhat noisy above 2000 cm ~, because the beamsplitter had been damaged when these spectra were recorded. This is also the reason why the transmittance of the single-beam spectrum A of Fig. 7 is so low). However, the noisy spectra of Fig. 8 are well suited for showing the effects of multiple scanning. The decline in noise in the 3000 cm -1 region as the number of scans is increased is quite obvious. When a spectrum of acceptable S/N has been obtained, additional information m a y be extracted b y 3 000 2 000 1000 cm-1 means of ordinate scale expansion. This is illustrated Fig. 8. Eugeuol, between KBr discs. The number next to each b y the spectra of Figs. 9 and 10. After a spectrum of spectrum indicates the number of scans. Each spectrum was /ur/uryl alcohol had been recorded and the entire ratioed, but not scale-expanded spectrum plotted out (upper trace, Fig. 9), portions of it were scale-expanded. This can be done very simply b y commanding the computer to do so. One On command, the instrument will then carry out the measurement. The operator m a y then choose to plot types, for example, S E = Y , SP=3000, EP=3170, or replot portions of the spectrum which are of PLOT (meaning: scale-expand the spectral region interest to him, using suitable ordinate and abscissa from 3000 to 3170 cm -1 and plot the results) and trace A of Fig. t0 results. Within the range desired, expansion. The optical system of the FTS-14 system is shown in the part of the spectrum having the lowest transFig. 6. The interferometer itself is the massive cube mittance is placed at the bottom of the chart (the on the right. The exit port of the interferometer is zero % point), and the highest transmittance point is

100,~--

~f~,a~

20o0 -

-

.

.

.

.

57. Jg., He/t 6, 1970

M.J.D.

.................

i..................

Low: Fourier Transform Spectroscopy

i

....................

i. . . . . . . . . .

1. . . . . . . . . . . . . . . . . . . . .

3 000

'"'"'"t .....

1500

I

t

2000

i

285

I000

c m -I

T Ill'Ill TlllllllllllllTiTr lT[TITllrllllllll]'lll'llllllllr ~I

1000

500 crr

Fig. 9. Furfuryl aIcohol, between KBr plates, 256 scans, ratioed. The upper trace shows the entire spectrum. The lower trace shows the portion below 1600 cm -I, scale-expanded. Portions of the spectrum were further expanded; see Fig. 10

placed at the top of the chart (the 100% point). The spectrum is multiplied by a suitable factor and the desired portion of it is plotted. The traces of Fig. t0 were obtained in this manner. At this stage it is important to note several points concerning resolution, S/N, and operation. The spectra of Figs. 7 - - t 0 were obtained at a resolution of 2 cm -1. Unlike dispersion instruments, the 2-cm -1 resolution was constant over the entire spectra range. Also, the resolution is unaffected by the number of scans taken, so that, unlike that of the dispersion instrument, the resolution is not degraded by shortening the scan period. Similarly, as the instrument is lasercontrolled, the wavelength accuracy is not degraded by shortening the scan period. As far as " q u a l i t y " or S/N is concerned, spectra meeting or exceeding the criteria for Class II spectra established by the Coblentz Society [ t t ] can be easily and routinely produced by unskilled operators. Similarly, precise, computer-controlled expansions of interesting portions of a spectrum are easily obtainable without rescanning. As the instrument is laser-controlled, wavenumber calibrations and corrections are not necessary. It is difficult, however, to generalize about the number of icans required to produce a " g o o d " spectrum, because the acceptability criterion depends on the user to a large degree. For routine, "survey" spectra of "reasonable" quality (meaning, one would see clearly the bands one is interested in) at 2-cm -1 resolution, even t or 4 or t6 scans of the sample suffice. In terms of time, this would mean, say, 4 scans of sample (4 • 2 seconds) plus 4 scans of background (4 • 2 seconds) plus data reduction (t minute) plus plotting time. The latter is variable, because all or only a portion of a spectrum might be desired (a few seconds to several minutes, depending on how noisy the spectrum is). Or, roughly, to obtain a reasonably good ratioed, scale-expanded spectrum at

8

o~

~

o

~

S

~

~ ~-~~176 ~~

Fig. 10. FurfuryI alcohol. Expanded portions of the spectrum of Fig. 9

F-

2000

1900

1800

cm"

Fig. I l. Spectrum of NO, at 0.5 cm -z resolution; t28 scans, ratioed, scale-expanded; NO at 10 Torr ill 10 cm eell

2-cm -1 resolution with a liquid sample at 0.025-mm pathlength would require a couple of minutes; a Class II spectrum would require 10 to 20 minutes. It is also possible to record spectra at higher resolution. The portion of the NO spectrmn shown in Fig. t I is an example. Such spectra can be obtained relatively rapidly and routinely b y unskilled operators.

286

M.J.D.

soo,ce

^ I/

= =

~

G0[,~

Detec

Mo

Naturwissenschaften

Low: Fourier Transform Spectroscopy

Fig. 12. Block d i a g r a m of MIR-2 far-infrared Fourier T r a n s f o r m spectrometer. A continuous mechanical, m i c r o m e t e r - t y p e drive is used. The fringe-referencing s y s t e m used is similar in concept to the one described in the text, b u t Moire fringes r a t h e r t h a n laser fringes are used

~e re

E

E1

Isl-~ ~Dis gttga I Ut

NO

1:5

Amplifier I

'1

i

,um

,o

~araboloid Mirror

200 Fig. 13. Schematic of MIR-2 far-infrared Fourier T r a n s f o r m spectrometer. The lower p a r t is the " s a m p l e s y s t e m " and can be modified for reflection and other measurements. The entire s y s t e m is evacuated

250 cm-t

Fig. 14. Spectra of I-I20 o b t a i n e d from d i s p l a y u n i t of M I R - 2 Fourier T r a n s f o r m spectrometer. As the scan is progressing, the c o m p u t e r produces a spectrum. The n u m b e r n e x t to each trace indicates the time ill m i n u t e s elapsed since the scan was begun

Far-In/rared FTS The FTS-14 will also operate in the energy-starved far-infrared region, but it is interesting to consider an instrument specifically designed for such measurements. The CODERG MIR-2 spectrometer [12] is shown in the largely self-explanatory Figs. 12 and 13. As with the FTS-14. a minicomputer is used to control and operate the instrument in addition to performing the data reduction. Computation of the spectrum is continuous while a single, slow scan is progressing, however, and the spectrum obtained from a portion of a single scan is displayed continuously. Fig. 14 illustrates this. It is thus possible to watch the spectrum improve as the scan progresses and, when a satisfactory S/N is achieved, plot the spectrum. After 45 minutes of scanning, the results were plotted and are shown in Fig. t 5.

HzO

1

RESOLUTION 0.25cm-t

B

I

200

I

2t0

I

2Z0

I

230

I

240

I

250

(m~-t Fig. t5. S p e c t r u m of H~O. This s p e c t r u m was p l o t t e d w h e n the s p e c t r u m shown on the display u n i t of the M I R - 2 h a d reached the stage i n d i c a t e d b y the 45 m i n u t e trace of Fig. t 4

C . S . B a r r e t t : I o n B e a m S c a t t e r i n g Applied to C r y s t a l l o g r a p h y

57. 9 Jg., H e l t 6, 1970

~oo - -

likely that there will be significant changes in the way spectra are measured and also in the way they are handled. The computer-controlled Fourier Transform spectrometer has high speed and sensitivity and its performance is always optimized, so that the Ph. D.-level instrument technician is not needed. Being digital, the data are in suitable form for all types of manipulations by large digital computers for data correlation, storage, and retrieval purposes. Individually, or together, these factors are important for both science and technology in terms of what spectra can be measured and how quickly and easily, or in simple economic terms of cost per spectrum. It seems likely, therefore, that the growth of Fourier Transform spectroscopy will increase.

NaCI

/ ~

RESOLUTION ~

287

3cm4

60

c 50

100

150 200 250 300 FREQUENCY (cm-1)

:350

I 400

Fig. 16. Reflection s p e c t r u m of NaCI

The MIR-2 covers tile 400-t0cm 1 region with a maximum resolution of 0.t cm -1. Single- or doublebeam operation is possible. Scan times depend on the resolution and operating mode selected. Another example, showing a spectrum obtained by a reflection technique, is given in Fig. t 6.

Prospects The advantages of Fourier Transform spectroscopy have already been outlined, and are seen to be significant. It is apparent that not only is a new method of spectroscopy now available, but a new type of instrument system is emerging. The system is digital rather than analog, and the brain of the skilled operator is being replaced by the computer core. As far as spectrometric measurements are concerned, especially in the fingerprint and infrared regions, it seems

Acknowledgment. Partial support from the National Center for Air

Pollution Control is acknowledgment. [11 See the discussion in J. Strong: Concepts of Classical Optics. London: W. H. Freeman & Co. 1958, pp. 222ff. - - [2] Fizeau, H.: Compt. Rend. 54, 1237 ( 1 8 6 2 ) . [3] Michelson, A . A . : Light Waves and Their Uses. University of Chicago, 1902; reprinted, Phoenix Science Series. University of Chicago Press; p. 78. - [47 Michelson, A . A . : Studies in Optics. University of Chicago Press, 1927; reprinted, Phoenix Science Series, University of Chicago Press, 1962; pp. 34ff. - - [5] Michelson, A. A., Stratton, S. W.: Amer. J. Sci. 5, I (1898). - - [61 Connes, J.: Rev. Opt. 40, 45, 116, 17t, 23t (1961). An English translation is available: document AD 409869, Clearinghouse for Federal Scientific and Technical Information, Cameron Station, Virginia. - - [7] Vanasse, G. A., Sakai, H., in: Progress in Optics, Vol. 6, E. Wolf, ed. Amsterdam: North-HoIIand Publishing Co. 1967, pp. 261 ff. - - [8] Cooley, J. W., Tukey, J. W.: Math. Comput. 19, 297 (1965); G-AE Subcommittee on Measurement Concepts: W h a t Is tile Fast Fourier Transform? I E E E Trans. Audio and Electroacousties, AU-15 (2), 45 (1967); lKlahn, R., Shively, R. R.: Electronics 41 (8), 124 (1968); Forman, M.L.: J. Opt. Soe. Am. s6, 978 (t966). - - [9] Fellgett, P.: 1~*[.S. Thesis, University of Cambridge, 1951. - - [t0] Block Engineering, Inc., Cambridge, Mass. - - [11] Specifications for Evaluation of Infrared Reference Spectra. Analyt. Chem. 8, 27A (1966). - [t21 Soei6t~ de Conversion des l~nergies, Cliehy, France; distributed by Scientific Instrumentation, Ine., Palo Alto, California. Received J a n u a r y 16, 1970

Ion Beam Scattering Applied to Crystallography C. S. B A R R E T T

James Franck Institute, University of Chicago, Chicago, Illinois, U.S.A.

Introduction The interaction of a beam o~ charged particles with a crystal is a field of study relatively neglected by crystallographers. Compared with the older fields of X-ray, electron, and neutron diffraction analysis of crystallographic problems, it has very definite limitations, yet a considerable amount of crystallographic information can be derived directly from the geometry of the pattern of scattered rays, and more can be obtained if approximate or rigorous methods of interpreting the energies and intensities of the scattered particles are applied. Experimental work in the field has been done chiefly with accelerators operating in the t to 4 MeV range,

but work can be done also with small accelerators in the t00 keV range, with equipment comparable in cost to X-ray diffraction units. Some work can be done even without the use of solid state detectors and energy analysis of the scattered beams, by merely recording the scattered beams on photographic film. The studies of ranges of ions in solids, rates of energy losses, excitations associated with ion beams, implantation, channeling, blocking, and radiation damage