Advisory Panel Jonathan W. Amy Glenn L. Booman Robert L. Bowman
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INSTRUMENTATION Jack W. Frazer Howard V. Malmstadt William F. Ulrich
J
Infrared Fourier Transform Spectroscopy New technology will greatly increase the capabilities of Fourier Transform spectrometers so that the impact of these high resolution instruments will be felt i n all areas and applications of infrared analysis
By
M. J. D. Low,
ITcopy has flourished that infrared spectroswithin the past IS A TRUISM
two decades and has found applications in a wide variety of analytical situations. A glance at the literature makes this as obvious as the connection between the spread of infrared spectroscopic techniques and the increased availability and improved quality of commercial spectrometers. It is also obvious and pertinent that the spread and success of “infrared” have so far been predominantly associated with spectrometers operating on the principle of dispersion. Such instruments, using prisms and/or gratings to disperse radiation mixtures, a t present make u p the bulk of the world’s spectrometers. It is important to note that dispersion spectrometers constitute just one general type of instrument system which can be used to measure spectra. Alternate, nondispersive systems based on filters or on interferometers have been available for quite some time, but these have not been used very much because the technology required to build adequate instruments was not available. However, this situation appears to be changing rapidly and, with the use of improved electronics and data handling techniques, there have been significant advances in the use of scanning interferometers for the measurement of infrared spectra. It is the purpose of the present article to outline the basis of interferometric or Fourier Transform spectroscopy, and to point out the advantages and disadvantages as well as the potential of this nondispersive method of analysis, Optical Transformation
The end results produced by a Fourier Transform spectrometer and a conventional dispersion spectrometer are the same. Each type of instrument yields a spectrum-a plot of intensity versus frequency-but there are drastic differences in the way the spectrum is produced. In the conventional spectrometer, the polychromatic radiation
New York University, New York, N. Y. 10453
must be fanned out or separated into bundles of (almost) monochromatic radiation because the frequencies are so high that a detector cannot discriminate between them; the detector can only respond to intensity, and not frequency. Then, by some suitable mechanical arrangement such as a tilting mirror, the series of bundles is slomly swept past a suitable detector. Each bundle can be termed a resolution element. The detector of the dispersion instrument then produces a simple electrical signal which is proportional to the intensity of the (almost) monochromatic radiation striking it. The spectrum produced in this fashion is thus the result of a series of radiometric measurements. Conversely, the optical system of the Fourier Transform spectrometer does not disperse polychromatic radiation, but performs a frequency transform. The incoming signal is uniquely encoded so that the frequencies of the optically transformed signal fall within the time range of response of detectors, which can then pick u p both the frequency and intensity information present in the signal, The “transformed” or coded polychromatic radiation falls on the detector throughout the entire observation period, and a complex signal termed a n interferogram is produced. The original signal (the incoming polychromatic radiation) and the interferogram are complementary and constitute a Fourier pair. Consequently, by “transforming the interferogram,”2.e.. subjecting it to Fourier analysis (hence the term Fourier Transform spectroscopy )-it is possible to obtain intensity-frequency information about the original signal. ,4 precise description of the transforms requires fairly involved mathematics (see Selected Reading), but the way interferograms are produced and processed can be readily understood if one considers monochromatic radiation or a mixture containing just a few wavelengths. Suppose a beam of monochromatic
radiation of wavelength u: enters a Michelson interferometer, shown schematically in Figure 1, and is divided into two equal components a t a beamsplitter. Each is reflected at a mirror and returned to the beamsplitter, where their amplitudes will add, If the rays a, and a2 arrive at the beamsplitter in phase, they will interfere constructively and a signal proportional t o the sum of their amplitudes will be produced by the detector. The rays a, and a2 will be in phase when the mirrors are equidistant from the beamsplitter. If MI is displaced by a distance w/4, the path of a, is changed by w/2, so that, on recombination a t the beamsplitter, a, and u2 will be 180” out of phase. There will then be destructive interference,
Figure 1. Optical system of Fourier Transform spectrometer A simplified diagram of a Michelson interferometer (only the rays leading to the detector are shown, and a compensator plate was omitted). The mirror, MI, is mounted on a suitable carriage and is mechanically or electrically moved. If monochromatic radiation enters the interferometer, the detector produces the signal shown below the optical system VOL. 41, NO. 6, M A Y 1969
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INSTRUMENTATION ~
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A research instrument for the colloid and surface scientists involved in studies of particle interactions and research in electrokinetic phenomena
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and the detector output will be zero. This will also happen for all displacements which are odd multiples of to/& i.e., for retardations of t w / 2 , i - 3 ~ / 2 , i: 5w/2,and so on-where the plus and minus signs denote displacements on either side of the zero position. Similarly, constructive interference will occur at displacements of even multiples of w/4, with partial destructive interference occurring a t in-between displacements. If AI, were moved incrementally, the signal produced by the detector would fluctuate rhythmically and would, in fact, be a simple cosine wave. Suppose that, instead of being displaced step-wise, the mirror is moved smoothly with a velocity V . As the cosine wave produced by the detector goes through one cycle if M, is displaced by a distance w/2, the frequency of the detector signal is then, f=V/(w/2) =2vv Or, for a constant mirror velocity, there is a linear relation between the frequency Y (wave numbers) of the incoming monochromatic radiation and the frequency of the detector signal. For example, with a mirror velocity of 0.5 mm/sec, monochromatic radiation of 10 micron wavelength (1000 cm-l, frequency 3 x 1014 Hz) will produce a detector signal of 50 Hz; for 5 micron radiation, f = 100 Hz. The amplitude of the low frequency signal is proportional to the intensity of the incoming monochromatic radiation. The extension to a radiation mixture follows from
this: each frequency component of polychromatic radiation is made to undergo such a transformation in frequency and produces a detector wave of unique frequency. The signal or interferogram produced by the detector is then the summation of all such waves and is a complex signal like that shown in Figure 2 . The center peak in the interferogram occurs when M , and M, are equidistant from the beamsplitter, so that all components reaching the detector have the same phase. The peak amplitude of the interferogram is proportional to the total energy in the incident beam, The peaks of smaller amplitude along each side of the central spike carry intensity and frequency information. Data Reduction
Such an interferogram does not at all resemble a spectrum. I t is, in fact, not a spectrum, but the Fourier Transform of a spectrum, and as such carries the desired intensity-frequency information within it. I n principle, all the spectral information may be extracted by performing the appropriate inverse Fourier transformation. I n practice, reducing an interferogram has not been easily accomplished until recently. The computations involved in data reduction are so complex, lengthy, and tedious that manual computation is out of the question, This difficulty, as well as the absence of suitable analog conversion devices, was one of the factors which had kept Fourier Transform spectroscopy in obscurity. However, digital computer techniques and analog analysis are now readily available. The interferogram can be recorded on magnetic tape, punched cards, paper tape, or directlv in the core mem-
A quality control instrument for analyzing a wide range of industrial dispersions including heavy slurries havi n g u p t o 7 0 % of s o l i d s without dilution Zeta potential may be calculated from mobility data
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Useful in studying chemical processes involving coagulation, flocculation, deflocculation and flotation Price $2,420 Figure 2. Interferogram of polychromatic source The central spike corresponds to the position where the two mirrors are equidistant from the beamsplitter. The abscissa denotes time and, if the mirror velocity is constant, the mirror position. An electronically-generated time base is produced at the same time as the interferogram. The single sharp spike on the extreme left of the lower trace marks the start of the interferogram; the rest of the regular signal is used as time base. With fringe-referenced systems (see text), the time base is produced by the interferometer itself
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ANALYTICAL CHEMISTRY
A BURNINGQUESTION! ATOMIC ABSORPTION OR FLAME EMISSION? -
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ory of a suitable computer. The Fourier Transform is then performed by digital means. This has the advantage that a number of corrections can be made, spect,ra can be ratioed, and so on. Fast computer programs are available for these comput,ations, and the result is a normal spectrum. -4lternately, the interferogram can be scanned by a wave analyzer. The latter is, essentially, an audio-frequency spectrometer, and is used to extract the intensity-frequency information from the interferogram so that a spectrum results. A variety of such devices ranging from "real-time" to slow scanning ones are available. Analog data reduction is not as precise and nowhere near as flexible as the digital method, but has the advantage that data reduction and readout, are rapid. The time delay between the experiment and the reception of the results, frequently encountered if somebody else's computer is used, can be avoided. I n general, however, data reduction presents few problems and, with the increasing availability of small in-house or on-line computers, dificulties with data reduction are rapidly shrinking to the vanishing point (or at least, to a quite tolerable level). Advantages
Each ULTREX product is supplied with its lot Certificate of Analysis and is available i n 100 g. vials, priced at $50.00 per vial.
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ANALYTICAL CHEMISTRY
-4s outlined, Fourier Transform spectroscopy is a complex, indirect, and occasionally quite disagreeable way to measure spectra, One may wonder n h y one should bother lvith something so complicated. . . . However, there are advantages. Remember that the interferometer brings about an optical transform. Essentially, radiation with frequencies of the order of 10'4 Hz is processed and heterodyned to yield signals in the low audio-frequency range. The original signal is shifted "down stream" in frequency by about' 11 orders of magnitude, thus drastically decreasing the demands on detector frequency response, The optical transformation moves the signal from a very high frequency range (one in which detectors cannot respond to frequency changes but respond only to intensity) to a Low frequency range where response to both amplitude and frequency is possible. This leads to significant, advantages in terms of signal-to-noise, based 3n the amount of signal which can be processed, and the time used to process it. Dispersion or filtering is not, re-
I
quired, so that energy-wast,ing slits are not needed. An interferometer has a relatively large, circular entrance aperture and relatively large mirrors (for example, in t,he mid-infrared ra.nge, a mirror diameter of 15 mm; in the farinfrared, several inches). The throughput, the amount of radiation which can enter the optics of the Fourier Transform spectrometer, is consequently quite large in comparison to that of a conventional spectrometer. The second major advantage is not quite as obvious as the throughput, gain, and also arises from the absence of the need to disperse or filter. I n the conventional spectrometer, each radiation bundle or resolution element of the spectrum is scanned across the detector. Consequently, if there are J4 resolution elements, the intensity of each element) is measured for only a, fraction T / d I of the total scan time, T . The signal proper (the intensity of a n element) is directly proportional to the time spent observing it, while noise, being random, is proportional to the square root of the observation time. The signal-to-noise ratio ( S / T ) is then proportional to (T/.lI)*, With the interferometer, however, the entering radiation falls on the detector, so that each resolution element, is observed throughoutt the entire scan period, with the result that S'A' is proportional to T + , The improvement by the factor of AI+ for the case of the interferometer, termed Fellgett's Advantage, can be quite large under conditions of relatively high, or high resolution, Fellgett's -idvantage is realized with detectors which are detector-noise limited --i.e.. as the signal level increases there is no increase in detector noise. The advantage in S / S can be traded off for rapid response. The scan time can be decreased. A spectrum can be measured with a Fourier Transform spectrometer in the same time as with a conventional spectrometer, but with a better S/iY. or in a much shorter time with an equivalent S1-Y. Disadvantages
The sources of disadvantages range from the economical (at present most Fourier Transform spectrometers are fairly eypensive in comparison to conventional instruments) to the psychological (Fourier Transform spectroscopy is neiv and therefore suspect; only the term spectroscopy sounds sort of familiar) One disadvantage, the necessity of a fairly complev data reduction procedure, has already been noted Others stem from the generally complex nature of the instrumentation The optical system of an interferometer is simple, but it must always be correctly and precisely adjusted Un-
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like a dispersion spectrometer, which will yield poor but still usable spectra if the instrument is misadjusted or mistreated, a misaligned Fourier Transform spectrometer yields nothing. However, the available commercial instruments appear to be quite stable and trouble from this source does not appear to be at all serious. The performance of the Fourier Transform spectrometer is also more dependent on the quality and performance of the electronic components than is the conventional spectrometer. Instrumentation
A rather large variety of spectrometer systems have been devised, mostly based on the Michelson interferometer. They differ little in principle, but vary greatly as far as the optical, mechanical, and electronic components are concerned. The spectral ranges covered depend on the nature of the beamsplitter and detector (and, of course, on the associated electronics). Commercially available instruments now cover the range from 40,000 cm-1 to 10 cm-1 (0.25 to 1000 microns). Scan times vary from about l/lOth second to several hours. Some instruments incorporate a small computer which is used for recording the interferogram and performing the necessary data reduction; others have a time-averaging computer used for multiple-scanning in order to enhance the signal-to-noise ratio when very weak sources are observed; still others are equipped with an analog data conversion device. All are quite sensitive. Applications 0
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There is little point in using a Fourier Transform spectrometer to make a measurement which can be handled quite well with a conventional spectrometer. Using a Fourier Transform spectrometer must be worthwhile. Consequently, much of the literature describing applications of Fourier Transform spectrometers deals with measurements which are either very difficult or impossible to make with conventional dispersion instruments. Generally, energy-limited situations have been involved, so far--i.e., where the amount of radiation emitted by the source or transmitted, reflected, or emitted by the sample is very small. Fourier Transform spectrometers have consequently performed very well in the far infrared. They have also been very useful in astronomy for recording
I Analytical Chemistry A-PAGE REPRINTS FOR 1969 A special collection of A-page reprints of Volume 41 will be made available to interested readers. These reprints of the Reports for Analytical Chemists, Instrumentation Columns, Book Reviews, Editors’ Columns, and other special material of general interest will provide a convenience for those who bind ANALY TlCAL CHEMISTRY. Orders may be placed now for delivery in January of 7970. Price for set of A-page reprints is $3 To: Special Issues Sales American Chemical Society 1155 Sixteenth SI., N.W. Washington, D. C. 20036 From:
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Invest in a Series 5000 system now. It’s designed to be computer compatible. Make this system part of your analytical program . . and don’t worry about a newer G C . . if and when you computerize. Noisefree signals and reproducibility are vital to computer operation. The new solid state electrometer and improved thermal conductivity system provide freedom from noise, drift and shock. The electronic programmer and cool down controller, plus insulated flow controllers assure excellent chromatographic reproducibility. Series 5000 is versatile. . . unlimited modular expansion. . . 7 different detectors . . 6 dual detection systems. . packed, prep and capillary columns . . 5 inlet systems. Contact your Barber-Colman Chromatography Specialist today for details or write for Bulletin SB1
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the spectra of stars and planetary atmospheres; on a more mundane level, such remote sensing was used for the detection of SO, from smoke stacks, and promises to be useful in air pollution studies. The multiple-scanning instruments also appear t o have a great potential utility in the fingerprint region for a number of diverse applications including gas chromatography, surface effects, and the examination of micro samples, One example will suffice to point out the relatively high sensitivity, speed, and versatility as well as the potential of such instruments. During a study of diborane-trimethylboron equilibria it became desirable to characterize various compounds isolated from the equilibrium mixtures. Consequently, spectra were run with a Perkin-Elmer Model 521 instrument; spectra obtained with 30minute scans are shown in Figure 3. However, the changes in the spectra with time indicated that the sample
was decomposing and suggested the use of a Fourier Transform spectrometer. The simple, mainly self-explanatory setup shown in Figure 4 was used in conjunction with a Block Engineering Co. mutiple scanning spectrometer. A carefully prepared, pure sample of the order of mole was separated from the equilibrium mixture and immediately frozen out in the cell. The dewar was removed, and 50 consecutive scans, each of 1-second duration, were made when the sample had vaporized. The cumulative signal yielded spectrum ,4 of Figure 5 . Spectra B to G were obtained with a second sample of the same compound by similar methods, after the sample had been a t or near room temperature for various periods of time. The changes in the spectra speak for themselves. By the time the dispersion instrument had recorded the spectrum, the composition of the sample had already changed, There was even rela-
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Figure 3. Spectra of cis-1,2-dimethyldiborane Solid line: first scan. Dashed line: second scan of same sample. Each scan was about 30 min, measured with a Perkin-Elmer Model 521 spectrophotometer
Figure 4. Experimental arrangement 104A
ANALYTICAL CHEMISTRY
t,ively little correspondence between the first and last portions of the spectrum. This and other work suggested that much of the relatively voluminous infrared literature on alkyldiboranes was suspect, because it was probable that many of the spectra on which band assignments were based had been run with impure, partially decomposed compounds. The Fourier Transform spectrometer was thus extremely useful in this study. The other side of the coin is that it’ was not feasible to make new band assignments because the resolution of the available instrumentation was not, good enough. Potential
Infrared dispersion spectrometers are well entrenched and, in view of some of the disadvantages of the Fourier Transform method, one may well wonder, Where do we go from here? Rapidly changing techniques point, to an answer. For example, inberferometers are generally used as single-beam spectrometers, and consequently the spectra have the inherent bad qualities obtained from single-beam operation, such as bands superimposed on a sloping background, and consequently must be corrected. However, dual-beam operation is also possible, and methods for using a single interferometer to yield spectra in which the background has been removed are developing rapidly. Rapid changes in data handling procedures have already been mentioned; further improvements seem likely. Of greater importance is the matter of spectral resolution, particularly for the type of multiple-scanning instruments used in the fingerprint. region. The resolution is mainly a function of the length of the sweep of the mirror and of the precision to which the position of the mirror is known as function of t i m e 4 . e . . with a constant velocity of mirror motion-the mirror should move as far and as smoothly as possible, If the velocity is precise, the mirror position is known, and consequently one can make an electronically generated time coordinate for the interferogram. These requirements lead to severe mechanical problems, with the result that the resolution has been relat,ively poor, for example, about 18 cm-x for an instrument covering the 2500250 cm-1 range. However, new experimental mirror drives have been developed, including drives in which the sweep length has been greatly increased but the linearity of the velocity has not been very much improved. I n such a case, the interferometer itself is used to generate its own time scale: in addition to processing infrared radiation, the interferometer is used to process a very narrow, almost, monochromatic line from a
The pushbutton GC Integrator for optimum accuracy Our GC Integrator has four pushbuttons that you won't find on any other electronic digital integrator. They make it easy to optimize integrator accuracy for different sample types, even for individual peaks. Because the pushbuttons let you change, instantly and simultaneously, all the adjustments that control integrator operation. In the control laboratory, this unique capability gives the chief chemist the opportunity to optimize integrator operation for each type of sample, while reducing the operating procedure to simple pushbutton instructions for technicians. In the research laboratory, the pushbuttons allow the experienced chromatographer to choose precisely the correct program for different sections of a chromatogram, switching back and forth a t will in order to optimize the integration of every section. Get a full description of the 3370A Electronic Digital Integrator by calling the nearest H-P sales office . . . or write for Bulletin 3370A. Prices start a t $4950 including built-in printer. Hewlett-Packard, Route 41, Avondale, Pennsylvania 19311. In Europe: 54 Route des Acacias, Geneva.
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105A
source such as a neon lamp or a laser. This produces a discrete signal which is time-locked to the mirror motion and hence to the interferogram. If the mirror velocity changes, the time-base signal changes, so that it is possible to derive a precise time coordinate for the interferogram and consequently improve the resolution. Such “fringereference” systems have been built, and will probably become commercial in the very near future. Fourier Transform spectrometers with 1 cm-1 and even 0.1 cm-1 resolution in the fingerprint range will become available. I n view of the new technology, it is probable that their cost will be of the same order of magnitude as that of high quality dispersion instruments. What then? The impact. of the high resolution Fourier Transform spectrometers will be felt in all areas of infrared analysis. The extrapolation from existing experimental prototypes is not great: the restriction of interferometers to low energy situations will be greatly decreased, and t.he emphasis of applications will shift, to include all types of infrared spectral measurements. The inherently high sensitivity of the Fourier Transform spectrometer will make it possible to record high quality infrared spectra in a matter of seconds; at worst, in a matter of minutes. Fourier Transform spectroscopy will therefore become profitable in all manner of scientific and analytical infrared applications. Selected Reading
The principles of Fourier Transform spectroscopy have been treated in detail by G. A. Vanasse and H. Sakai, in Chapter 7 of “Progress in Optics,” Val. VI, E. Wolf, Ed., John U’iley & Sons, Inc., S e w York, 1967. Short, general articles M. J. D. Low and I. Coleman, Spectrochim. Acta, 22, 396 (1966). M. J . D. Low, J . Chem. Ed., 43, 637 (1966). W. J. Hurley, J . Chem. Ed., 43, 236 (1966). G. Horlick, Appl. Spectr., 22, 617 (1968).
Remote Sensing M. J . D. Low and F. K. Clancy, Environ. Sci. Techn.. 1. 73 (1967): R. Beer, Physics Teacher, 6, No. 4 (1968); D. M. Hunten, Science, 162, 3B (1968).
Miscellaneous Applications M. J. D. Low, Anal. Letters, 1, 819 (1968) ; Appl. Spectr., 22, 463 (1968) ; Appl. Optics., 6, 1503 (1967); M. J . D. Low and I. Coleman, Appl. Optics., 5, 1453 (1966); M. J. D. Low and S. K. Freeman, Anal. Chem., 39, 194 (1967) ; J . Ag. Food Chem., 16, 525 (1968); M . J. D. Low and J. C. McManus, Chem. Commun., 1967, 1166; M. J. D. Low, R. Epstein, and A. C. Bond, Chem. Commun., 1967, 226; J . Chem. Phys., 48, 2386 (1968). C. H. Perry e t al., A p p l . Optics, 5 , 1171 (1966); J . Appl. Phys., 37, 1994 (1966); Spectrochim. Acta, 23A, 1137 (1967); A -4nderson and H . A. Gebbie, Spectrochim. Acta, 21, 883 (1965); D. M. Adams and H. A . Gebbie, Spectrochim. Acta, 19, 925 (1963).
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COMMENTARY by Ralph H. Muller
Analytical chemists will be grateful for Professor Low’s outline and discussion of infrared Fourier Transform spectroscopy. I n so carefully outlining the advantages as well as the present limitations of the interferometric approach to infrared spectroscopy, we believe the conclusion is inescapable that these techniques will seriously rival spectrometers operating on the principle of dispersion, however elegant and highly developed the latter class of instruments happens to be. We are happy to note Dr. Low’s observation of the “connection between the spread of infrared spectroscopic techniques and the increased availability and improved quality of commercial spectrometers.” We think it is clearly demonstrable that in all ages, the amount of scientific information was at’ all times governed by the techniques, resources, and instruments available for the problem. At present,, the vast amount of publications is ample proof that most information has been obtained with elegant instruments, most of them automatic or semi-automatic. It is probably demonstrable that a smaller proportion of all investigators who publish today are concerned with the development of new methods, new techniques, and new instruments than some thirty years ago. The information explosion does not run parallel to the population explosion-it exceeds it and not by working overtime at, time-anda-half remuneration. We suspect that sharp inflections in the growth curve arise about once every twenty years. Someone then gets a Nobel Prize and during the new cycle publications increase at a rate proportional to the improvement. in equipment developed for the new phenomenon. We are reluctant to dwell upon the boredom which sets in after the 1961st paper on the phenomenon has appeared. Considering the question of improved resolution, we note that this is a function of the length of the sweep of the interferometer mirror and the constancy of its velocity. T o achieve the highest precision is an undertaking requiring the best resources of physics and engineering, and the effort has been going on for about three quarters of a century. When Henry iZugustus Rowland, at’ Johns Hopkins, built his first engine to rule diffraction gratings, he spent several years in perfecting the lead screw used to advance the diamond cutting tool. This was done by running 108A
ANALYTICAL CHEMISTRY
a split-nut,, lapped with fine abrasive, back and forth along the screw in order to eliminate periodic errors in pitch. It is not quite certain who first suggested the use of an interferometer (counting of interference fringes) as a criterion of perfection. As a rough benchmark of the dimensions which are involved, the distance between fringes for the median wave length of the sodium D lines (5893 A ) is about 11 microinches. Several decades ago, Dean George Harrison a t M I T developed the Compander, an ingenious system for the automatic and continuous correction of tool position for second order correction of residual screw errors. With an interferometer mirror placed on the cutting tool carriage, the moving fringes were detected photoelectrically -giving rise to a sinusoidal voltage which was constantly compared with a similar voltage derived from the rotation of the feed screw. The two sinusoidal voltages were adjusted to equal amplitude but for corrections, the phase relations were utilized. A slight error in pitch would cause a phase shift and this difference, after amplification, was used to advance or retard the cutting tool position momentarily. One hundredth of a fringe displacement could be measured with this system, which corresponds to a mechanical displacement of X/200. The source of light for the interferometric monitor was the 5461 Hg line obtained from an arc using the .O*Hg isotope. This had been developed by Meggers, and in other aspects, the line is of such high spectral purity that it may well serve as an absolute alternate standard of length. It would not surprise the chemist to be told that the achievement and maintenance of such high metrical precision required the control of the partial pressure of CO, and water vapor in the air surrounding the dividing engine because these determine the refractive index of the air and, therefore, the velocity of light in the measuring arm. These factors, along with temperature fluctuations and vibration, determine the precision which can be attained. Present day resources in electronics, computing, and in engineering are vastly better than when these requirements were established. Probably the technique will be competitive or superior to conventional methods when it can provide equal or greater precision per unit time, cost, and operation ease. The principles of interferometry have other, including unexplored, uses.
Ordered Fluids and Liquid Crystals ADVANCES IN CHEMISTRY SERIES No. 63 Twenty-two studies on characterization, properties, and occurrence of these phenomena in many substances, including: e the polymorphism of tristearin 0
characterization of mesomorphic phases by nmr spectroscopy
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interfaces in nematic liquids
0
liquid crystals as ordered components of living substances
e liquid crystalline nature of phospho-
lipids 0
the structure of synthetic polypeptides in solution by polarization of fluorescence
0
order and structure in concentrated polymer solutions and gels
e field dependence of the magnetic sus-
ceptibility of the liquid Crystal phase of pazoxyanisole
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