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A ., _ v . .2 r.vl..‘ nu T— LIBRA R Y MiChigan State University Vvv This is to certify that the thesis entitled "A Computer-Interfaced Fourier Transform Spectrometer with Applications to Some Aspects of Solid State Spectroscopy" presented by Thomas Michael Niemczyk has been accepted towards fulfillment of the requirements for _Emfl._degee in _£hemistry_ 07/76.: “ C Majo professor \ Date DEC. 2941972 (I? . m 0-7639 ' BOOK BINDERY INC «I l was av HUM} & SDNS‘ LIBRARY BINDE RS srnmsroahflfllsul "\n b— 1| 1 ABSTRACT A COMPUTER-INTERFACED FOURIER TRANSFORM SPECTROMETER NITH APPLICATIONS TO SOME ASPECTS OF SOLID STATE SPECTROSCOPY BY Thomas M. Niemczyk A computer-interfaced Fourier transform spectrometer for use in the far-infrared has been constructed. Because of poor sources and detectors available, the far—infrared region is relatively inaccessible. Interferometric techniques possess several advantages over conventional dispersive methods, which are discussed with particular emphasis on the far-infrared. However, the experimental interferogram is the Fourier transform of the desired power spectrum, and a computer must be used to perform the necessary mathematical analysis. In order to minimize the time required for the data reduction, and to provide the additional advantages of automated control of the instrumental operating parameters, a commercial RIIC FS-720 interferometer was interfaced to a PDP 8/1 digital computer. The major portion of this thesis is concerned with the general considerations for interfacing experimental apparatus to a small laboratory computer, and the particular choices of hardware and software developed for the present application. The programs used to move the interferometer mirror, sample the data points, average and/or ratio the results, and transform the interferograms are described, and listings provided in the Appendices. The computer-interfaced instrument has been combined with complementary Raman techniques in the investigation of the solid state properties of some small molecules. The first project involves the Thomas M. Niemczyk infrared and Raman investigation of the lattice spectra of a-FZ, the low temperature phase of solid fluorine. The results of these experiments were used to evaluate the predictions of a theoretical study, and indicate that improved calculations are required. The instrument was also used in the study of the temperature dependence of optical lattice vibrations, for which it is predicted that the frequency shift with temperature of a given low-frequency mode should be slightly different in the infrared and Raman spectra. This prediction is experimentally verified in a study of the librational lattice mode of OCS. A COMPUTER-INTERFACED FOURIER TRANSFORM SPECTROMETER WITH APPLICATIONS TO SOME ASPECTS OF SOLID STATE SPECTROSCOPY By Thomas Michael Niemczyk A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry T972 f"\ 1‘“! AL In?“ t) 4) («A ACKNOWLEDGMENTS This author gratefully acknowledges the guidance, encouragement, and friendship of Drs. C. G. Enke and G. E. Leroi during this course of investigation. Thanks are also given to Dr. R. R. Getty, Dr. S. R. Crouch, fellow group members, and the Chemistry Department staff members who have provided help and suggestions during the course of study. This author thanks Michigan State University and the National Science Foundation for granting him assistantships, and the U. S. Department of Health, Education and Welfare for granting him an NDEA fellowship. Finally, this author wishes to thank his parents and his wife, Susan, for their unfaltering support and encouragement. ii II. III. Introduction Fourier Transform Spectroscopy A. "106W MUOW>>TI TABLE OF CONTENTS Historical .................... Fourier Spectroscopy ............... . ,The Michelson Interferometer ............ Apodization, Sampling and Spectral Recovery . . . . Advantages of Fourier Transform Spectroscopy . . . l. The Multiplex Advantage ............ 2. Etendue Gain ................. 3. Other Advantages ............... Disadvantages of Fourier Transform Spectroscopy . . . . Computer-Interfaced Fourier Transform Spectrometer. . . . Introduction .................... Interface Design Considerations .......... Overview of the System .............. The Computer Interface Buffer ........... Input/Output Transfers .............. 1. Timing of I/O Transfers ............ 2. The Operation Decoder ............ e. I/O Instructions ............... Timing of Data Transfers ............. l. Flag Checks .................. 2. The Gated Driver ................ iii Page T3 T4 T4 16 T8 T8 20 20 21 25 27 28 32 IV. 6. Interface Construction ................ 34 1. General Criteria ................. 34 2. The Control Interface ............... 35 3. The Measurement Interface ............ 38 H. System Software ................... 4] 1. Introduction ................... 4l 2. The PS/8 System ................. 4l 3. PS/8 Fortran ................... 42 4. The PAL8 Assembler ................ 43 5. PHASE] - The Control Section ........... 44 6. PHASET - The Measurement Section ......... 46 System Characterization and Performance ......... 48 A. Introduction ..................... 48 8. System Characterization ................ 48 l. Noise ...................... 48 2. Response Time of the System ............ Sl C. Water Vapor Spectra ................. 54 D. Comparison of a PDP 8/1 and a CDC 6500 Transform . . . 54 E. Ethane Spectrum ................... 58 The Infrared and Raman Spectra of a-Fluorine ....... 60 A. Introduction ..................... 60 B. The Structure of a-Fluorine ............. 61 C. The Raman Spectrum of a-Fluorine ........... 68 D. The Far-Infrared Spectrum of a-Fluorine ....... 72 E. Conclusions ..................... 72 iv VI. Temperature Dependence of Optical Lattice Vibrations: Crystalline OCS ...................... 75 LIST OF REFERENCES ....................... 83 APPENDICES ........................... Appendix A. Program Spectra ................... 87 A. Introduction ...................... 87 8. Program Listing .................... 87 Appendix 8. Programs for the PDP 8/I .............. 95 A. Program PHASEl ..................... 95 1. Introduction .................... 95 2. Listing of PHASEl ................. 96 8. Program PHASZ3 .................... l06 I. Introduction .................... 106 2. Listing of PHASZS ................. l07 C. Program PHASE4 ..................... ll5 l. Introduction ................... 115 2. Listing of PHASE4 ................. ll6 LIST OF TABLES Table Page I Determination of noise in an interferogram ......... 50 II Frequency shift with temperature of the lattice mode of OCS ..................... 78 vi LIST OF FIGURES Figure Page l Diagram of the Michelson interferometer .......... 9 2 Output of the Michelson interferometer as a function of mirror displacement X ................. ll 3 Block diagram of computer-interfaced Fourier transform spectrometer .................. 23 4 Computer connections for programmed data transfer ..... 26 5 Generation of DS 36 with a dual octal decoder ...... 29 6 The timing of the IOP pulses relative to the 05 pulse. . . 30 7 Connections for a status flag check ........... 3l 8 Schematic of a gated driver ............... 33 9 The control section of the FTS-720 interface ....... 37 lo The measurement section of the FTS-720 interface ..... 39 ll Generalized flow diagram of the control section software for the FTS-720 interface ............ 45 l2 Flow diagram of the measurement section software for the FTS-720 interface ................ 47 l3 Time response of the system ............... 53 14 High resolution spectrum of water vapor ......... 55 l5 Comparison of a spectrum produced on the CDC 6500 to a spectrum produced on the PDP 8/I .......... 56 l6 Spectrum of the lattice region of ethane at 20°K ..... 59 17 Unit cell of a-F2 .................... 62 18 Projection of a-F2 unit cell onto the ab plane ...... 63 vii T9 20 21 22 23 24 25 26 27 Projection of the a—Fz unit cell onto the ac plane for the C2/m structure .............. 65 Projection of the a-Fz unit cell onto the bc plane for the C2/c structure .............. 66 Correlation diagram for a-F2 ............... 67 Raman spectrum of the fundamental and overtone of a-FZ. . . 69 Raman spectrum of the lattice region of a-F2 ........ 70 Far-infrared spectrum of the lattice region of a-F2 . . . . 73 Raman spectra of the lattice mode of OCS at l0°, 60°, and 120°K ...................... 79 Far-infrared spectra of the lattice mode of OCS at lDD° and 25°K ..................... 81 Frequency verses temperature for the lattice mode of OCS. . 82 viii I. INTRODUCTION Although no precise definition of the term "far-infrared" has been generally accepted, it might be taken to mean the spectral region covering lO-4OO cm']. Thus the far—infrared encompasses the region between the microwave and the usual infrared covered by normal laboratory instruments. Even though this is a narrow frequency range, it has tremendous significance in many areas of chemistry. Attesting to this are several recent review articles (l-6) and books (7,8). Various types of far-infrared absorption may be observed, and these often depend on the phase of the system studied, g,g,,pure rotation in the gas and lattice modes in the crystalline state. To a rough approximation the frequency of any vibration is given by var/T71?— (T.T) where f is the relevant restoring force constant for the atomic or molecular motion, and u an appropriate reduced mass. Frequencies in the far-infrared will be expected for relatively small values of f/u. Clearly, this will come about if either the value of the reduced mass is large, that is the masses involved in the motion are heavy, or if the force constant is relatively weak compared to those found for normal chemical bonds. Both considerations are commonly satisfied in chemistry. In inorganic chemistry many such situations arise, the former for heavy-metal-to-metal, and also metal—to-ligand bonds, and the latter with the relatively weak bonds found in donor-acceptor complexes of various types (7). Torsional modes have been extensively investigated using far-infrared methods. In gases and liquids the torsional mode may be the only low-frequency absorption, and provided the intensity is sufficient, identification is relatively easy (7)- A large amount of work has also been done on the study of ring conformations and associated vibrational modes, especially in four- and five-membered ring systems (8). Far-infrared studies can also give direct information about the strength of a hydrogen bond, an inadequately understood phenomenon that is of great interest (9). Currently a great deal of effort is being expended in the investigation of hydrogen bonding in biologically interesting molecules (T0)- Of special interest here in our laboratories is the study of lattice vibrations in molecular crystals. The ultimate objective of such studies is to learn more about intermolecular forces. Very simple molecules are chosen because they are most amenable to model calculations, and of the condensed phases, the solid state is chosen because the molecules are in relatively well-defined positions, so that a wide range of intermolecular geometries need not be considered. When a molecule is condensed the internal vibrations are perturbed, and they may in addition be split by interaction with neighboring molecules. The translational and rotational degrees of freedom of the gas phase molecules become highly hindered, and are observable in the vibrational spectrum as so-called lattice modes. The intermolecular forces are considerably weaker than interatomic forces, and since a molecular grouping is involved the masses are relatively high; thus the lattice modes generally occur in the far-infrared region. Although it is an area of great interest, far-infrared spectroscopy has been an alien study in many chemical laboratories for a number of reasons. Two principal problems have been the low intensity of the sources currently available for this spectral region, and the insensitivity of detectors available for the low energies associated with these long wavelengths. Because conventional spectrometers use prisms and/or gratings for the selection of monochromatic radiation, much of the originally weak light intensity coming from the source is lost through dispersion and/or diffraction, and the intensity of the radiation being received at the detector is greatly diminished. Obviously any loss of intensity with far-infrared wavelengths is critical, and therefore very wide slits must be used to obtain a workable signal-to-noise ratio. Because of the large slit-width requirement, resolution is greatly reduced. When the source energy is low, it is a common practice among physicists to use interferometry to increase the efficiency with which the radiation can be utilized because of an interferometer's inherently greater light gathering power. For this reason interferometry has been very important in astrophysics. Interferometry also lends itself to applications in the far-infrared region of the spectrum, because of this increase in light gathering power. Furthermore, there is an additional advantage that is gained by the utilization of an inter- ferometer in the far-infrared, the so-called multiplex advantage. Because many frequencies are incident on the detector instead of just one, as is the case with conventional spectrometers, the frequencies are said to be multiplexed and the resultant signal-to-noise ratio of the measurement is increased. There is, however, one major drawback to the use of interferometry; the output of an interferometer is not a typical spectrum relating the intensity at the detector to frequency or wavelength, but an interferogram, and must be appropriately analyzed to generate the spectrum to be interpreted. The major operation in this data analysis is to take the Fourier transform of the interferogram, a step which gives Fourier transform spectroscopy its name. Fourier transformation is a complex mathematical operation and as such is very difficult to carry out without the aid of a computer. Unless there is immediate access to a computer, this step can cause considerable delay in the elucidation of the results of an experiment, a fact which can lead to considerable wasted time and effort if various experimental parameters must be adjusted in order to find the optimum conditions. With these arguments in mind, it was decided to take an existing Fourier transform spectrometer and interface it to a small laboratory computer. Having the spectrometer on-line with a computer not only offers the advantage of nearly instant availability of the spectrum of the system being studied, but also the ability to control the spectrometer with the computer, freeing the experimenter for more productive tasks. Some of the basic principles of Fourier transform spectroscopy are discussed in Chapter II of this thesis. Especially emphasized are the advantages possessed by this technique. A description of the computer-interfaced spectrometer is given in Chapter III along with a discussion of some of the general methods and technology of interfacing small laboratory computers. A detailed description is given of the actual interface design and the information that is transmitted between the computer and the spectrometer. In Chapter IV an evaluation and analysis of the performance of the spectrometer is presented. The last two chapters of this thesis deal with the application of the computer-interfaced Fourier transform spectrometer to studies of molecular crystals. Chapter V contains a study of the lattice modes of the low-temperature phase, the a-phase of molecular fluorine. Chapter VI discusses the temperature dependence of the lattice mode of OCS, comparing the frequency shift observed in the Raman spectrum to that observed in the far-infrared spectrum. II. FOURIER TRANSFORM SPECTROSCOPY A. Historical Interferometry is a very old technique, although it has been only very recently that it might be considered a standard spectroscopic technique. The earliest application of interference spectroscopy was by H. Fizeau in 1862 (ll)who used Newton's rings to show that the yellow sodium radiation was a doublet. The Newton's ring apparatus was provided with a means for separating the lens and plate slowly, and the fringe contrast was observed as a function of the separation distance. The fringe count itself was used to measure the distance; it was observed that the contrast went through maxima and minima with a period of 980 fringes. Fizeau concluded from his observation that the line was actually a doublet whose separation was l/98O of the average wavelength and that the two components were of roughly equal intensities. Michelson invented the type of interferometer that bears his name sometime in the late 1800's (l2). He used his interferometer in several important studies including his ether drift experiments, his determination of spectral profiles by the visibility technique, and in his search to find a line sufficiently monochromatic for use as a length standard (13). In his search for the length standard he discovered that the red Balmer line of hydrogen is a doublet, the green line of natural mercury is a complicated multiplet, and that the red line of cadmium is exceptionally narrow. It was this line that he chose for 6 the length standard, a standard that stood until l960, when it was replaced by the orange line of krypton produced by a lamp operated at the triple point of nitrogen. The first true interferogram was published in l9ll by Rubens and Wood (14). They were investigating the far-infrared radiation emitted by a Nelsbach mantle, and chose to use an interferometer because a quartz prism with sufficient dispersion also absorbed too much of the radiation they were studying. For the next few decades interferometry was a specialized tool used only in rare cases, such as above, where the source of radiation was extremely weak or the resolution of conventional spectrometers was not sufficient. In l95l Fellgett published in his thesis (IS) the first numerically transformed interferogram. About the same time Jacquinot (l6) pointed out the fact that an interferometer has a greater energy throughput than a conventional spectrometer of the same resolution. These two facts, along with the invention of the digital computer with which one could transform the interferograms, brought about renewed interest in interferometry. B. Fourier Spectroscopy The end results produced by an interferometer and a conventional dispersion spectrometer are the same, a spectrum or a plot of intensity versus frequency. To produce the spectrum of a beam of polychromatic radiation its Fourier transform must be taken, and the manner in which this step is done is very different for the two types of spectrometers. In a conventional spectrometer the polychromatic radiation must be dispersed or separated into bundles of almost monochromatic radiation because the frequencies are so high the detector cannot discriminate between them. This separation of frequencies is a physical Fourier transformation, 1,3, a prism or grating is a very powerful Fourier transformer. By mechanical arrangements the monochromatic bundles are slowly swept past the detector, which responds only to intensity, and a spectrum is produced. The optical system of an interferometer does not disperse the polychromatic radiation, but performs a frequency transformation. The incoming signal is uniquely encoded so that the frequencies of the optically transformed signal fall within the time response of the detector being used. The detector can then respond to both the frequency and intensity information present in the signal. A signal when so encoded is called an interferogram and when appropriately analyzed, Fourier transformed, yields the spectrum of the signal. The overt presence of the Fourier transform steps leads to the name Fourier transform spectroscopy. C. The Michelson Interferometer A simplified diagram of a Michelson interferometer is shown in Figure T. In its most common form it consists of two plane mirrors at a right angle to one another and a beamsplitter at an angle of 45° to the mirrors. One mirror is normally fixed and the other can be moved in a direction perpendicular to its front surface. The beamsplitter serves to divide the incoming light from the source and ideally should transmit 50% of the light and reflect 50%. The compensator serves to equalize the optical path lengths of the two arms of the interferometer. To understand how the interferometer works imagine that the source is monochromatic and that the interferometer is set so that the SOURCE l BEAMSPLITTER MOVABLE '1 N ATO MIRROR COMPE s R C2222 ~ ta <.__, - ' 2> DETECTOR L. L ] FIXED MIRROR Figure l. Diagram of the Michelson interferometer. l0 optical path length of each arm is identical; then the two light beams will be in phase when they return to the beamsplitter. They will constructively interfere and the detector will record a maximum. Now, if the movable mirror is moved l/4 of a wavelength the optical path will have changed by 1/2 wavelength and when the two beams meet back at the beamsplitter the waves will be l80° out of phase and thus will destructively interfere. The detector will record a minimum. If the mirror is moved farther the output will be a cosine wave with a period of one half the wavelength of the source and appear as shown in Figure 2A. The equation for the output, the interferogram,is I(X) = B(V) cos (2nXV) (2.l) where I(X) is the intensity of the output as a function of the mirror movement X; B(V) is the intensity of the source as a function of optical frequency V, j,_, B(V) is the spectrum of the source. The frequency of the observed cosine wave produced by the detector depends on two factors: the frequency of the incoming electromagnetic radiation and the velocity with which the mirror is moved. The frequency of the detector signal is given by the equation f = 2vV (2.2) where V is the wavenumber of the source and v is the velocity of the mirror movement. Thus, for constant velocity v there is a linear relationship between the frequency V of the incoming monochromatic radiation and the frequency of the detector signal. For example, with Tl 'Xl (I +)( E3 2 '-X 0l +)( Figure 2. Output of the Michelson interferometer as a function of mirror displacement x. (A) Monochromatic source (8) Broadband source TZ a mirror velocity of O.l cm/sec and radiation of 100 micron wavelength (lOO cm"), a frequency of 3 X lO12 Hz, will produce a detector signal 20 Hz. A signal of high optical frequency is thus encoded into a signal some eleven orders of magnitude lower in frequency. In practice a monochromatic source is not used but hopefully a source of constant intensity across the whole frequency region of interest. To visualize what happens in this case imagine each frequency component being treated independently and the output being a summation of all the cosine oscillations caused by the different input frequencies. Figure 28 shows an interferogram that might result from a polychromatic source. At zero path difference all of the waves are in phase and as the mirror is moved away from the zero position they rapidly sum out to a steady value. The resulting ac signal that is obtained by moving the mirror is the interferogram and is represented by the equation: I(X) = f + B(V) cos (2nXV)dV (2.3) Mathematically equation 2.3 is one half of a cosine Fourier transform pair. The other half is B(V) = f+ m I(X) cos (2nXV)dX (2.4) .00 Equations 2.3 and 2.4 provide a relationship between the interferogram I(X) and the spectrum B(V). Measuring the interferogram, the spectrum can be found by taking its Fourier transform, the mathematical operation indicated by equation 2.4. Interferograms are seldom as symmetrical as shown in Figure 28. Assuming the electronics and optical alignment of the system are perfect, an interferometer is seldom compensated perfectly across the entire wavelength range being used. Compared to the width of the beamsplitter, l3 the wavelengths of far-infrared radiation are so long that the compensator is generally left out of an interferometer designed solely for use in this region. The error that this introduces is small compared to the error that is caused by not sampling at exactly zero path. Mathematically this leads to the introduction of sine components into the interferogram. Thus the interferogram and the spectrum must be related by the complex Fourier transform pair +00 I(X) = I B(V) e2"lxvdv (2.5) + co . B(V) = I I(X) e'2"‘xvdx (2.6) In practice two facts must be taken into account: the interferogram is not sampled from +m to -w, and the interferogram is only sampled at discrete points. Thus the actual representation of equation 2.6 is X B(V) = E I(X) e'2“lxvdx (2.7) which is referred to as the discrete Fourier transform (l7). D. Appdization, Sampling and Spectral Recovery The effects of not being able to move the mirrors from - to +~ must now be considered. This truncation of the interferogram might be described mathematically as multiplying the true interferogram by a boxcar function that is 0 outside the sampling interval and l everywhere inside it. This truncation causes a scanning function to be imposed on the spectrum, exactly analogous to the slit function in conventional spectroscopy. It is often convenient to modify the scanning function to one that produces spectra more acceptable in appearance. This l4 process is called apodization (18,l9) when done in the Fourier domain, and one type of apodization when applied to the spectrum itself is called smoothing (20). The ability to easily modify the scanning function of the spectrometer is a unique characteristic of Fourier spectroscopy (Zl). One must also take into account the fact that the interferogram is only being sampled at discrete points. It can be shown that the interferogram must be sampled at a rate that is twice the bandwidth of the system in order that the spectrum be accurately recovered (22). Thus, to determine the sampling interval necessary for a particular interferogram the sampling interval must be set so that the optical path difference of the interval is one half or shorter than the wave- length of the shortest wavelength to be recovered. E. Advantpges of Fourier Transform Spectroscopy l. The Multiplex Advantage_ Because the interferometer only converts the frequency content of the incoming waveform to a much lower frequency and not to a spectrum as a conventional spectrometer would, it might seem that it is a somewhat more complicated and troublesome method of obtaining a spectrum. However, there are certain advantages that make Fourier spectroscopy a powerful technique. One advantage that might be realized is the multiplex advantage, or Fellgett's advantage (15). In any spectrometer information smaller than the resolution of the spectrometer is not seen. Thus, the number of resolution elements in a spectrum is a measure of the amount of information contained in the spectrum. The number of resolution l5 elements, m, in a spectrum can be defined as Ama - Amin divided by the x resolution, 6A, of the system used to obtain the spectrum. In a conventional scanning spectrometer each resolution element is observed for only a fraction of the total scanning time, T, that being T divided by the number of resolution elements m. The signal will add as the first power of the time spent observing it, and, if the noise is assumed to be white and random, the noise will add as the square root of the time spent observing it. Thus for the conventional scanning spectrometer the signal is proportional to T/M, the noise to (T/M)”2 and the signal-to-noise ratio (S/N) to (T/M)]/2. With an interferometer each resolution element is being observed all of the time. All optical frequencies are incident on the detector at once and in such a situation it is said that the spectral information is multiplexed. Thus the signal adds as T and the noise as TI/z, and the signal-to-noise ratio S/N is proportional to Tllz. Comparing the multiplex case to the conventional spectrometer on the basis of signal-to-noise ratio the multiplex spectrometer is better by a factor of m],2 , the square root of the number of resolution elements. It should be pointed out here that Fellgett's advantage is realized only in regions where detectors are detector-noise limited. As the signal level increases there can be no increase in the noise level. Thus, in a spectrometer utilizing a photomultiplier tube, for which the shot noise increases as the square root of the signal level (23), Fellgetts advantage would be cancelled. But in the infrared and far-infrared, the region in which the interferometer used in this study is employed, thermal detectors are used and fall into the detector-noise limited category (24,25). l6 2. Etendue Gain The second major advantage that an interferometer possesses over a conventional spectrometer is the etendue of the optical system (l6). The etendue is in general constant for an optical system and it determines the amount of light which can be transmitted by the system. It is therefore sometimes referred to as ”throughput". One can easily see how this advantage arises since a conventional spectrometer must have slits as entrance and exit apertures. An interferometer doesn‘t need slits, and its entrance and exit apertures are usually determined by the size of the mirrors used in the system. Comparing areas of entrance apertures one would get a gain of several thousand for an interferometer, but it isn't quite that simple. The etendue of an optical system is defined as E = A9 (2.8) where A equals the area of the collimator and n is the solid angle subtended by the detector. Using the following relations: do l/ZL (2.9) 30 H 0/60 (2.l0) where 60 is the resolution, R the resolving power and L the path difference, the solid angle subtended by a Michelson interferometer can be shown to be (26) a” = 2n/R (2.11) T? To arrive at a corresponding equation for a grating spectrometer we note that the solid angle subtended by the exit slit is _ 2 RG - WC/f (2.12) where w and t are the width and length of the exit slit respectively, and f is the collimator focal length (27). For a resolution do and a dispersion de/do, the exit slit width is given by w = f --Go = f gfl'g (2 l3) do do R ' making 2. l 96 "’ 7F}? 0 (2'14) an. Ga: It can be shown from the grating equation that de 33- = tan 6 3 l (24l5) This makes %e%% (2M) Comparing etendues EM = ADM - 2;A (2.17) E6 = AOG = é-Q- (2.18) Even for a very fast grating spectrometer l/f does not exceed l/3O (8), which makes the Michelson interferometer appear to be better than the grating spectrometer by a factor of 200, for equal collimator area and resolving power. T8 The gain in etendue is especially important in energy-limited situations. One of these situations arises in far-infrared spectroscopy because of the very poor sources available for use in that region. Indeed, much of the work developing interferometry as a spectroscopic tool has been done by spectroscopists who wished to perform studies in the far-infrared region (28-32). 3. Other Advantages There are other less important advantages: the resolution of a measurement can be increased by simply increasing the maximum path difference of the scan, the resolution function of the measurement can be altered by data treatment only, and the gain in signal-to-noise ratio can be traded-off for speed. The trade-off for speed allows the Fourier spectrometers to be used as fast scan spectrometers in applications not possible before (33,34). F. Disadvantages of Fourier Transform Spectroscopy The major disadvantage of Fourier transform spectroscopy is that the initial data is in the form of an interferogram and a complex data treatment must be performed before one can see the spectrum. From the interferogram one can tell whether the instrument is aligned or not, or whether there are many or few peaks in the spectrum, but is impossible to predict very much about the spectrum that will result. The need for data processing in Fourier spectrosc0py has two immediate implications: the cost of the computer time necessary and the fact that one may have to wait hours, even days, before it can be determined if the experimental conditions used were correct, 1,2, was the sample too thick, too thin, the right concentration? The cost of l9 Fourier transformations has been largely circumvented by fast transform techniques (35), but the second factor can be circumvented only by immediate access to a computer. Analog techniques suffer from inflexibility, which leaves the obvious solution of putting the instrument “on-line" with a digital computer. With such a setup, one can not only take advantage of being able to see experimental results immediately, but also be able to utilize the computer's ability to control experimental systems. III. A Computer-Interfaced Fourier Transform Spectrometer A. Introduction As pointed out in Chapter II, the major drawback of Fourier transform spectroscopy is the fact that the initial result of each experiment is an interferogram. This interferogram must then be taken to a computer and transformed before the results of the experiment can be analyzed. An obvious solution to this problem is to interface the instrument to a computer so that the results of a scan might be made available after only the computation time. Further, the computer can be used to control the instrument, 1,2, the instrument can be fully automated so that the experimenter can be freed to do more meaningful tasks. This is an important feature for many instruments and especially so for the one discussed here, as it can take many hours to gather enough data to produce spectra with the desired signal-to-noise ratio or resolution. Further data enhancement advantages, such as averaging interferograms, can be more readily realized also. This chapter will discuss the interfacing of a Research and Industrial Instruments Co. model FTS-720 Michelson interferometer with a model F.S.-820 stepper motor to a Digital Equipment Corporation PDP 8/1 computer. The design considerations of the hardware built as well as the development of the software for the system will be discussed. 20 21 8. Interface Design Considerations There are many facts to be taken into account when interfacing any instrument to a computer. One must consider the size of the computer, what control functions must be performed, what measurement functions must be performed, the distance between the instrument and the computer, the logic levels used in the computer and in the instrument to be interfaced, 339, These considerations all have to do with the hardware of the interface and overlook, as very often happens, the second half of any interfaced system, the program or software that controls the flow of information in the system. The software is almost never the minor partner in any system and much care must be given to the software portion when any interface is designed. When designing an interface various trade-offs between hardware and software are possible. One can build more or less of the complexity of the system into either component, depending on the tasks that must be performed and the speed with which they must be done. A simple interface will require greater software support than a complex one, which may need only one instruction to initiate a whole sequence of operations. There are, of course, limiting situations such as the case where too many functions must be performed too quickly for the computer to possibly handle, where the designer has no choice into which component the complexity has to be built. In general, however, this is not the case and careful consideration must be given to this problem. In any experimental system flexibility is an important feature. This is particularly true for a computer-interfaced system and very easy to incorporate in the design if the software-hardware trade-off 22 is taken into account. For the greatest flexibility one should design a system such that as many functions as possible are performed by the software. When this is done, changes in the system can be made by simply changing a few of the instructions in the software routines. On the other hand, the level of the language required to write the programs ought also be a factor when making this choice. If complex programs must be written in a very low-level language it might be considerably easier to design and build the complexity into the hardware. A tremendous amount of time might otherwise be spent programming in an assembler language, which might be the only language reasonably used on the computer at hand. C. Overview of the System A block diagram of the computer interfaced system is shown in Figure 3. As can be seen from the diagram, the computer is one of the central parts of the system. The computer controls the flow of information, control signals, and data records to all parts of the system. The interferometer is an R.I.I.C. model FTS-720 Michelson interferometer equipped with a model F.S.-820 stepper motor and control. The amplifier is tuned to the chopping frequency of the source, a l25 watt high pressure mercury vapor lamp. The detector used is a Unicam model SP-SO diamond windowed Golay cell. The R.I.I.C. system also includes an analog-to-digital (A/D) converter and paper tape punch for the recording of the interferograms. The computer used in this study was a Digital Equipment Corporation PDP 8/1. The PDP 8/1 is a general purpose computer using transistor- transistor-logic (TTL) integrated circuit modules and parallel data 23 SOURCE ] * ‘ ‘ MIRROR _ DETECTOR INTERFEROMETER DRWE % - DRIVE _ AMPLIFIER CONTROL . AID _ A COMPUTER ’ paws 1 CONVERTER INTERFACE _& INTERFACE BUFFER 'NTERFACE _ i ‘ LINE- CARD PRINTER i PUNCH ‘ PDP 8/I COMPUTER e A PAPER TAPE PLOTTERS PUNCH _& READER REAL TIME CLOCK DEC TAPE LTELETYPEJ Figure 3. Block diagram of computer-interfaced Fourier transform spectrometer. 24 transfer. The computer is organized into a central processor, a core memory, and input/output (I/O) lines. The core memory consists of two fields of 4096 twelve bit words. In addition to the core memory two DECtape transports are available as memory extension devices as well as I/O devices. In addition to the I/O lines and the DECtape units, input devices to the computer include a Teletype and a high-speed paper tape reader.’ Outputs include the Teletype, a high-speed paper punch, an analog plotter (Heath Model EU-205-ll), a cathode ray tube display (Tektronix Model 603), a X-Y plotter (Varian Model F-80), a card punch (I.B.M. Model 526), and a line printer (RCA model 301). A real time clock is also available to provide computer-controlled time measurement for the timing of experiments (36). For an experiment to be "on-line" with a laboratory computer a flow of data and control signals between the computer and the experiment is necessary. This flow of data and control information is carried out over the computer I/O lines. Control signals and binary data words in the form of buffered TTL voltage levels can be exported and imported by the computer over its I/O lines to and from the experiment. When obtained from the manufacturer, the PDP 8/1 1/0 lines are not at all easy to access, a fact which can make interfacing, physically joining the computer I/O lines with the experiment, rather a difficult and tedious task. Further, the experiment may be distant from the computer, a fact which can add complexity to the problem. 25 D. The Computer Interface Buffer In the past it was necessary for each experimenter to design his own specific interface to bridge the gap between the computer and the experiment. The relative inaccessibility of the computer I/O lines caused each experimenter to build up a complex individual interface within the computer. The Heath EU-80l-E Computer Interface Buffer (CIB) used in this system eliminates the difficulty of the 1/0 line connections to PDP 8 computers as it transports these lines outside the computer. It greatly reduces the complexity of design and wiring for any single interface, consequently eliminating much of the time spent designing and building interfaces. By transporting the I/O lines from the computer the C18 serves as a basic link between the computer and the outside world. The structure of the computer and the I/O signals as they appear at the C18 are illustrated in Figure 4. The boxes and signals on the left represent things inside the computer and those on the right represent signals as they appear at the C18. All data are transferred into or out of the computer as l2 bit binary words. The input transfer occurs over the AC O-ll or "AC IN" lines and all output transfers go from the accumulator to the "AC OUT" lines, the BAC O-ll. Other important I/O lines present in the C18 are the buffered memory bits, BMB O-ll; the skip line, SRPI clear the accumulator, C_A3 the program interrupt, PT} the input-output pulses, IOPl, IOP2, and IOP4; egg, The IOP pulses are especially important as they are used to time all I/O transfers as well as generate any control pulses that are needed for the system. 26 If ACCUMULATOR (AC) I X . O-H BUFFER / \>[ 1% MEMORY BUFFER (MB) BUFFER REGESTER fl OPERATION A I DECODER I CORE llO MEMORY V I IOP I GENERATOR I SKIP LINE I ( CLEAR AC I CPU t INTERRUPT I OPERATION INITIALIZE I > CONTROLLER I RUN , TIMING SIGNAL L) ‘ TIMING SIGNAL I , Figure 4. Computer connections for prograImIed data transfer. O—ll GATE 1g XE 0-11 '62? O-ll BMB O-ll IOP l TOP 2 IOP 4 WOR|.D 27 E. Input/Output Transfers l. Timing of 110 Transfers It is mandatory that all data transfers into and out of the computer be carefully timed. If not, the computer may not be ready to accept a data word when it is present at the AC IN lines or it may input erroneous information if it loads the value at the AC IN lines before the experimental system has presented the binary word to the inputs. 2. The Operation Decoder The timing is synchronized by the computer activating the I/O lines only when an I/O instruction is encountered. The computer "understands" instructions only as 12 bit binary numbers. The operation decoder looks at the first three bits, bits 0-2, of each instruction word to identify what kind of operation the instruction calls for. There are eight unique combinations for the three bits which fall into three types, memory reference instructions, operate microinstructions, and input-output (I/O) instructions. It is the I/O instructions that are of interest here. 3. 110 Instructions The 1/0 instructions all have operation code ll02(68). Bits 9 to ll of an I/O instruction form the code for the IOP generator, which puts out pulses used in the timing of I/O transfers. These pulses are IOPI, 2, and 4 corresponding to the bit in the IOP code section of the I/O instruction. The remaining bits in the I/O instruction, bits 3-8, are used to generate an address for the I/O instruction. Each I/O device is assigned a unique address called a device select code (05), 28 1,3, the teletype is 03 and the paper tape punch is 02. Thus in designing an interface one simply chooses a unique device code for his particular interface, or section thereof, and then, by a system of logic gates called an octal decoder, the proper interface is activated each time an I/O instruction is encountered by the computer. The generation of a DS pulse using an octal decoder is illustrated in Figure 5. The octal decoding is done with two integrated circuits, ICT and 1C2, which are Texas Instruments Inc. model SN 7442N (37). The IOP generator is activated by the operation decoder when it detects an Operation code of 6. The IOP generator then generates the IOP pulses called for by bits 9-ll of the I/O instruction. The timing of these pulses with reSpect to the DS pulse is shown in Figure 6. The IOP pulses and DS pulses can then be gated together to perform certain operations at appropriate times in the computer cycles. F. Timing of Data Transfers l. Flag Checks As was mentioned above all data transfers must be accomplished at a time when both the computer and the experiment are ready. Most devices have a status flag, a register that is high or low depending on the state of the device. An A/D converter for example might have a status flag that indicates when a conversion is being done and then changes state when the conversion is complete and the data word is ready for transfer. The status flag state can be acquired with an I/O instruction by gating an IOP and 05 with the status Signal as shown in Figure 7. The gate in Figure 7 is a NAND gate (38) and will go from l-O only when all three inputs are a logical l.. The output of this gate can be connected to the SKP line of the C18. The SRP line, 29 on 8.. .Emuoumu Pmuuo Pasu a saw: on me Go cowueemcmo .m mgamwm o m 2 A _ o 8 _ 2 n 8 .um an. — .v 9. on o m 8 . , E .56 2. 50 2.883 m3<> Ma 92.. 30 Ds IOPI . IOP2 . IOP4 ‘ __1 ____1 O-I- dd)- mm- 091'- 5 1- t 2 Figure 6. The timing of the IOP pulses relative to the 05 pulse. 31 [)5 COMPUTER STATUS Figure 7. Connections for a status flag check. 32 when momentarily connected to a 0 signal will cause the computer to skip the next instruction. To check the status of a device the computer usually enters a two-instruction loop, the first an I/O instruction to check the status and the second, an instruction that tells the computer to jump back one instruction. When the IOP, DS, and status signal cause the computer to skip out of the loop the device is known to be ready and the transfer can be carried out. 2. The Gated Driver A O-level signal at an AC IN causes the corresponding AC bit to go to l during any I/O instruction. When there is more than one device which might be used to transfer data into the accumulator, g,g, the Teletype and an A/D converter, it is necessary that each device's output signal be connected to the AC IN lines only when data is to be transferred into the AC from that device. This is accomplished by connecting the devices'output signals to the AC IN lines through gates that are active only at the appropriate time. This system of gates is called a gated driver and a schematic of a gated driver is shown in Figure 8. Gates O-ll will be "open“ only when the output of gate A is l, or in other words when the output of gate A is l the outputs of gates O-ll will correspond to the data inputs. The output of gate A is only T when the proper DS and IOP are generated. Thus if one wanted to load the output of an A/D converter into the AC the status of the A/D would be checked and when the converter was ready (the data word would be present at the inputs of the gated driver) the I/O instruction opening the gates would be given. The data would then be loaded into the AC and stored in some appropriate memory location. 33 [NARA CMJT [NADA Ibl 0 o I l fig 1 __.C] \& l0 ll ll (II; Figure 8. Schematic of a gated driver. 34 Most I/O transfers, whether into or out of the accumulator, are handled in an analogous fashion. This forces the data transfers to be timed such that both the computer and the I/O device are ready for the transfer and thus data is never lost or masked out. G. Interface Construction I. General Criteria The interface was designed to meet several general criteria. First, it had to be compatible with the instrument such that the existing stepper motor power amplifiers and the detector amplifier might still be used. Compatibility is a factor which one must consider when interfacing to a computer any instrument that was not specifically designed for such a purpose. If very extensive work must be done to force compatibility with a computer interface it might be more efficient to start over with a new instrument designed for the purpose. The FTS-720 system was very easily interfaced from this point of View, as only two components had to be added to the system to insure compatibility. In the control section the O and +l2 V logic levels of the motor power amplifier had to be shifted to the O and +4 V TTL logic levels. This was accomplished using only one integrated circuit on the outputs of the TTL section of the control interface. In the measurement section an operational amplifier was used between the output of the detector amplifier and the A/D converter input. The operational amplifier, which served several purposes, will be discussed later. A further criterion for the design was that the instrument could be switched easily from the computer control mode to the manual control mode. In this way the instrument would never completely depend on the 35 computer to be operational. Finally, the interface was designed so that as much as possible of the system control is done by the computer software so that changes in the control or measurement system might be made by rewriting the software. Finally, the interface must provide at least a certain minimum number of pathways for the flow of information between the computer and the instrument. If the computer is to be used to control the instrument as well as log the data output, there must be provisions for the transfer or generation of control signals in the interface. The specific signals needed for both the measurement and control sections of the interface will be discussed in the following sections. 2. The Control Interface The interface to the instrument was divided into two sections, a measurement section and a control section. The control section must fulfill two functions: the pulses that increment the mirror drive must be generated and the direction of the mirror movement must be controlled. The necessary timing mechanisms and pulse generators could be built into the interface, so that upon receiving a begin command from the computer the mirror would automatically be scanned over the required distance at the proper rate. The actual connection to the computer would be simple, just the begin pulse would need to be transferred outside of the computer, but it would not be as flexible as would an interface that depended on the computer software to fulfill all the necessary control functions. 36 To obtain the greatest flexibility possible, the interface was designed so that the software commands all of the necessary functions for this section of the interface. In order to accomplish this there must be three information channels between the computer and the instrument, one to set the mirror drive to right, one to set it left, and one to increment the drive. A diagram of the control section is shown in Figure 9. The AC OUT lines are brought from the C18 to the experimental interface via a Heath model EU—80l-21 I/O Patch Card. The octal decoder is a Heath model EU-800-SA Dual Octal Decoder Card which generates the DS 64 and DS 65 used in this circuit. These two 05 signals separate the instructions for the interface into two sections, one to control the direction of the mirror movement and the other to generate the pulse train to drive the stepper motor. All of the measurements with the interferometer must be made with the mirror moving to the left (towards the beamsplitter), so one of the commands to the interface (05 65 and IOPl) sets the mirror drive to the left (as determined by FF] and the first AOI gate). The other command to this section (DS 65 and IOP4) changes the mirror drive to the right so that the mirror can be moved back to the starting position at the end of a scan. FF2, activated by DS 64 and IOPl, is used to generate the pulse train that steps the motor. FF3 and FF4 and the two remaining AOI gates generate the proper pattern on the motor coils so that the motor moves in the desired direction. The inputs to the power amplifiers of the stepper motor operate on O and +12 V logic levels so that the +5 TTL level had to be shifted to the +12 level by using a level shifter. The 37 .mumwempcw ownumhu 6:» mo cowuumm poeucou as» .m mesmAC I314... I- >9. [ fitim ma: H $5 _ O A , ,I. O .. _ 2. a0. 2.. IIF _ .20. I. a , 3 mo , .— HHIIIIIIJW O LFII "Hue-..” 9%. O 22. no mo _ _ 9.5 1:: «888 Oh ._<.—UO 32... OH mthmZOU 38 level shifter used is just a single integrated circuit, a Texas Instruments Inc. SN74l7 (37). 3. The Measurement Interface Besides the connections for the parallel transfer of the data words from the A/D to the computer, the measurement section of the interface must provide for the transfer of two further signals: the convert command to the A/D converter and the flag check, used to inquire whether or not the A/D has finished a conversion and is ready for transfer. The measurement section of the interface is illustrated in Figure 10. Perhaps the major component of this section is the A/D converter. The A/D converter used in this section is an Analog Devices, Inc. series ADC-U 12 bit converter. The converter has an input range of O to +10 V, an input impedance of 2.5 KD, and a nominal conversion time of 10 nsec. These specifications dictate some of the design specifications for the rest of this interface section. Again BMB 3-6 are decoded by an octal decoder to produce the DS 36 and DS 37 used in this section of the interface. 05 36 and IOPl are gated together to form the "Convert" command, a stroke pulse to the A/D converter that resets the converter and then initiates the conversion. This pulse of about 600 nsec duration, even though within the specifications of the converter, did not trigger the converter properly when applied directly to the converter. It was empirically found that the converter worked properly when the convert pulse was approximately 1 usec long, so a monostable was used to increase the length of the convert pulse. 39 .wuewgmpcw omn-m22 mcp Co =o2uuwm ucmsmesmame Us» .o2 mesm22 . ,u. .55 b 2.22.2322... 20.322252. 22.5 20.2.28 .28 .ZOU m._.<0 522.228 2.2.225 a? 82.2.0 2:20. 2.350202 2 20. Am 8 22.228 8 8 9m 9222 9.5 O? 32: O\ H mash—ECU 40 The instrumentation amplifier was used for several reasons. First, it was desired that the detector amplifier settings, when in the manual control mode, be the same as when in the computer control mode. The input range to the A/D converter present in the FTS-720 system is 0 to -8 V, so the output of the detector amplifier was designed to fit this range. Thus, to use the A/D in the interface, the output of the detector amplifier had to be inverted, and to take advantage of its full input range a gain of 1.25 was desired. When the system was being set up it was found that the signal common was not 0 V exactly, but floating 12 to 15 millivolts above ground. When this connection was tied to ground the detector amplifier ceased to work properly, so an operational amplifier with differential inputs and programmable gain, 1,2, an instrumentation amplifier, was needed. The instrumentation amplifier used in this system is a Heath model EU-900-DA. The amplifier was programmed to have a gain of 1.206 :_ 0.002 and found to be well within its 1.0.05% gain nonlinearity specification over the entire 0 to -8 V input range. The instrumentation amplifier solved two other problems as well. Because of the relatively low input impedance of the A/D converter, 2.5 Kn, loading of the detector amplifier may have been a problem if its output had not been properly isolated from the input of the A/D. The instrumentation amplifier had an input impedance of 20 MD which effectively isolates the detector amplifier from the A/D inputs. Further, the bandpass of the instrumentation amplifier is relatively low, down 3 dB at 15 KHz, so that it acts as a low pass filter when in the circuit. This can be an effective aid in reducing any high - frequency noise that is present. 41 The A/D outputs are connected directly to the inputs of a gated driver, a Heath model EU-800-TL. In addition to the data outputs of the converter there is a status output which is a logical 1 when a conversion is taking place. The status output returns to 0 when the conversion is completed. The status signal is inverted and then gated together with DS 37 and IOPT onto the SKP line to form the "flag check" for the converter. The outputs of the gated driver are connected directly to the AC IN lines and DS 37 and IOP4 are used to form the "Gate" command. H. System Software 1. Introduction The hardware of the interface was designed so that the software would handle all timing and control functions in the system. In this manner the system was designed to be as flexible as possible. The software was developed so that all measurement parameters are variable and can be established at the beginning of each experiment. 2. The PS/8 System The computer used in this study, a PDP 8/1, was equipped with a TCO8 DECtap controller and two TU56 DECtape transports (39). These peripherals can operate as memory extension devices and as such allow one to operate under a monitor system, in this case called the PS/8 Keyboard Monitor (40). The Keyboard Monitor accepts commands from the Teletype keyboard to create logical names for devices, to run system and user programs, and to save programs. The Keyboard Monitor is present in core at all times and provides communication between the user and the PS/8 executive routines. The PS/8 system is very powerful 42 and makes the PDP 8/1 many times more potent than it would be without the DECtape systems and the monitor system. The PS/8 system includes routines to handle all the peripheral devices as well as programs used to edit and debug user programs. It also contains two different compilers, one called PAL8 which uses an assembly language, and the other a version of FORTRAN II. 3. P818 FORTRAN The FORTRAN in the PS/8 system is in many ways a substantial advance in small computer high-level languages. It has a very useful feature that allows the user to intersperse FORTRAN statements with assembler language statements, which makes it possible to generate all the I/O signals needed to operate an interface. High-level languages in general are very inefficient in small computers; the compilers take up most of the available core which limits the size of the user's program, or else compiler length is sacrificed for inefficient compiling. With the PS/8 system, programs can be more or less of any length since sections of the program can be swapped in and out of core from the DECtapes. The FORTRAN compilations are very inefficient in their use of core and in the speed with which they can perform tasks. In most situations these inefficiencies are not critical and the time saved in program development over that of a more efficient assembler language more than compensates the additional time needed by the computer to run the less efficient program. One limitation that the PS/8 FORTRAN has is that it does not have the ability to service program interrupts, a limitation that in some situations would be critical. 43 4. The PAL8 Assembler All the programs for this system were written in the PAL8 language. This choice was made only with reluctance for it is a mammoth task to do extensive programming in any assembler language. FORTRAN might have been used to write all parts of the programs, except that the number of points that could have been Fourier transformed under such circumstances would have been limited to 512, in contrast to the 2048 that can be transformed with PAL8. This is due to FORTRAN'S inefficient use of core; even though programmed sections can be swapped in and out of core the Fourier transform section along with the data array must fit into core at the same time. The ability to transform only 512 points would be a severe limitation to the system. PAL8 is an assembler language; the instructions are written in a nmemonic code and have a one-to-one correspondence with the machine language instructions the computer understands. Because of this one-to- one correspondence a skilled programmer can write programs that are as efficient as theoretically possible. PAL8 has some very useful features that are not common to most assembler languages. These stem from the fact that it is a part of the PS/8 system, so the ability to access the system device handlers has been built into the assembler. This feature is handled by a routine called the User Service Routine (41), which allows the user to read data or programs into or out of core to any of the peripheral devices present in the system. In particular, it allows the user to read data onto or off of the DECtape units using only a few program instructions. This feature was extensively used in the software developed for this system. 44 The software developed for the system is divided into three parts, the measurement and control section, the Fourier transformation section, and the plotting routines. The measurement and control section, entitled PHASEl, will be discussed here as it is an integral part of the interface system. 5. PHASEl - The Control Section In general PHASEl controls the interferometer, records the interferogram, and stores it on DECtape. The program begins with a dialog on the Teletype to establish the scan parameters. A sample dialog is as follows: PROGRAM TO RUN THE FTS-7ZD HOW MANY SCANS? ROW MANY POINTS PER SCAN (POWER OF 2)? SNMELE INTERVAL IN 5 MICRON UNITS HOW MANY 100 MSEC WAIT PERIODS? HOW MANY SAMPLES PER POINT (4095)? 29 EAEEL FOR INTERFEROGRAMS DATATDLDA This experiment would consist of five scans, each of which would have 1024 points at a spacing of 20 microns path difference. The computer would wait 2 seconds for the detector to settle after the mirror was moved before sampling the point, then sample it 2000 times, average the results, store the individual points, and finally store the whole interferogram on DTAl (DECtape unit 1) in a file called DATATD.DA. A generalized flow diagram for the control section of the software is shown in Figure 11. The first block sets the step counter to allow for variable sampling intervals and the delay routine sets the maximum 45 SAMAPLE RCNUTNNE INC) SCLAPJ EXDONE YES REPCMNTKDDI AAHUKDR LOAD DATA ’ ON DECTAPE Figure 11. Generalized flow diagram of the control section software for the FTS-720 interface. 46 speed with which the mirror can be stepped. The maximum speed was selected to match the maximum speed attainable under manual control. Once the mirror is moved to a new sample position the computer jumps to the sampling routine which is discussed below. Once the scan is completed the mirror is moved back to the starting position of the scan and the data is stored on the DECtape. Upon return from the routine that stores the interferogram the file name is incremented,1,g, the second interferogram would be stored as DATAll.DA. 6. PHASET - The Measurement Section A flow diagram of the measurement section of PHASEl is shown in Figure 12. Once the mirror is moved to a new position a delay routine is initiated in order that the detector and the electronics have a chance to stabilize at the new value. Then, proceeding down the flow diagram, a register is set to count the number of times the point is measured. The convert command is given to the A/D converter and the computer then waits for the converter to finish the conversion. Upon completion of the conversion the value is gated into the accumulator, the value is added to the sum for that sampling position, and the computer checks to see if that point should be sampled again. If so, it jumps back and executes the same steps again; if not, it computes an average value for that sampling position, stores the value, and then returns to the control routine. A complete listing of PHASEl is given in Appendix B of this thesis. The remaining software developed for this system is also discussed and listed in the Appendices. 47 ‘ SET NO. OF— MEASURES STROBE lCONVERTER CONVERT R NO GATE VALUE INTO ACC - ADD VALUE TO SUM GET AVERAGE VALUE I YES 3 STORE ‘ VALUE I I I Figure 12. Flow diagram of the measurement section software for the FTS-720 interface. IV. System Characterization and Performance A. Introduction Having an instrument on-line with a computer often offers the possibility for more completely characterizing the instrument's performance than might otherwise be possible. The computer does not tire when systematically changing one parameter from a list of many and recording the results of the change. It also allows the experimenter to sample data points very rapidly and to store vast amounts of data for later analysis. These tasks are often possible without a computer, but often too tedious to carry out. However it is, for example, much easier to optimize a system for such things as noise rejection if the character of the noise present is completely understood. 8. System Characterization 1. Noise Noise can be a problem in any measurement if care is not taken to eliminate it from the signal. This is especially the case in far- infrared spectroscopy because of the poor sources and detectors available. As previously pointed out the interferometer,by taking advantage of the multiplex principle, helps to increase the signal- to-noise ratio but does not completely solve the problems inherent to doing spectroscopy in this region. 48 49 An analysis of the noise on an interferogram can be made when the interferometer is interfaced to a small computer and a fast A/D converter is employed to digitize the interferogram. With the Analog Devices ADC-U converter the sampling rate can be conveniently set as high as approximately 50 KHz, allowing a measurement to be made and stored as often as every 20 nsec. To get some idea of the noise level on an interferogram the instrument was set so that the gain of the amplifier was at 20 dB, a level that is typical of the gain needed to record the background interferograms for the types of cells used in the spectrometer, and the resulting signal output sampled at various rates. The signal was sampled 2000 times at each rate, the high and low value found, and the average and standard deviation for the measurements calculated. The results of this study are summarized in Table I. When this study was done it was found that the least significant bit of the gated driver was bad, 1,g, the least significant bit of the number recorder was always 0. The bad integrated circuit was replaced and the study was redone. The results of the second test were essentially the same as the first test, but the first test points out a very interesting fact so it is those results that are presented here. With the least significant bit of the gated driver gone, the value stored was equivalent, or almost so, to that which would be recorded by an eleven bit converter. However by sampling many times and storing the average value of the many measurements, the number of significant bits in the value stored can be increased as long as there is some noise in the signal being measured. In this case the value stored had twelve bit resolution, just the same as the value that was stored when the gated driver was working properly. 50 momm.o moon oomm.o momm wam.o momm 22mm.o momm co2pm2>mo .III ULevemum 2o. momm momm momm momm now: Pm.momm mm.nomm Fm.nomm m¢.Nomm ms2m> mmo2m>< .Ememoemycmuc2 cm :2 mm2o: Co =o22m=252mumo .H apneh com cop m.om m.- 6mm: :2 2e>2m2c2 m2aeem 51 In this system the increase in resolution that can be gained by averaging is not utilized, as the values are stored as single precision integers, or in twelve bits, and the resolution of the converter used is already twelve bits. Nevertheless the averaging can be used to eliminate noise from the signals. As indicated in Table I there is a certain amount of noise on an interferogram. The standard deviation is an indication of the noise on a signal and for all the sampling rates it was close to 1 bit. The noise recorded didn't seem to change with the different sampling rates nor did there appear to be any high frequency (>1000 Hz) noise present. This is quite reasonable as the detector amplifier is tuned to 13 Hz and there are at least two low pass filters in the circuit. Noise of this level and in this frequency range can be completely eliminated from the signal as long as enough measurements are made and the sampling time, the time from the first measurement to the last, is long enough to adequately sample the low-frequency noise oscillations. The sampling routine, as it now operates, digitizes a point in the interferogram approximately every 40.5 usec. This rate is more than adequate to sample noise of 1000 Hz, and if 1000 points or more are averaged it should adequately sample the lower frequency noise on the signal. 2. Response Time of the System The ability to sample very fast also enables one to easily measure the time response of the system. This is important because the detector used in this instrument, a Golay cell, is quite slow. The detector response time is on the order of 20 msec. Because of this slow response time the detector amplifier was not designed to respond 52 to high-frequency signals, and has a minimum time constant setting of 0.5 sec. Thus a measurement of the instrument response time will be a product of the amplifier response time and the detector response time, but dominated by the response time of the amplifier. To measure the response time of the system the movable mirror of the interferometer was set very near zero path so that there was a reasonable signal change when the mirror was stepped. The mirror was then stepped and the changing signal sampled every millisecond. A plot of signal level verses time of measurement is shown in Figure 13. As can be seen from Figure 13, the time constant setting on the detector amplifier is only a nominal value as the signal has come close to reaching the final value in the 0.5 sec that the "time constant" was set at. In a more critical analysis than Figure 13 allows, it can be seen that the value is approximately 98% of the final value, which corresponds to four time constants. After one additional time constant the value is greater than 99% of the final value, and for practical purposes, might be considered to have reached the final value. The instrument response time was measured in an analogous fashion for higher "time constant" settings of the detector amplifier. Very similar results were obtained for all settings, 1,g, the "time constant" setting of the detector amplifier corresponds to approximately four actual time constants. Thus, optimum results might be obtained by waiting 25% longer than the "time constant" setting of the detector amplifier before sampling an interferogram point. The noise on the signal appeared to be independent of the time constant setting, a fact that might be taken to mean that the noise on the signal is being picked up in the interface. Even so, it can be eliminated by sampling the point many times and averaging. A/D CONVERTER VALUE N OCTAL 53 3100 T o o o a 8 m 01 8 o N 8 9 g 1 l 1 L L L L L '- 0.2 0.4 0.0 0.8 TIME IN SECONDS Figure 13. Time response of the system 54 C. Water Vapor Spectra The sample used to demonstrate the performance of any far-infrared spectrometer is water vapor. This is so because H20 has many rotational transitions in the far-infrared, numbering at least 278 between 12 and 305 cm" (42); most of the absorptions are very strong, and it is an ”easy to obtain" sample. Although these properties make it an easy sample to study, they also make water vapor a tremendous interference when trying to study other samples with frequencies that lie in the far-infrared. Figure 14 shows a spectrum of water vapor obtained by filling the sample compartment with water vapor to a pressure of about 10 torr. This is a pressure low enough so that there should be little collision broadening of the peaks. The spectrum illustrates the resolution that can be obtained with the instrument set up in the present manner. Peaks A and B are at 107.1 and 107.7 cm.1 respectively, and peaks C and D are at 116.6 and 117 cm'] respectively (42). 0. Comparison of a PDP 8/1 and a CDC 6500 Transform An interferogram was obtained of a sample that consisted simply of the sample compartment filled with air. A 2048 point interferogram was obtained, the maximum number of points that can be transformed on the PDP 8/I and transformed on both the PDP 8/1 and the CDC 6500. The resulting Spectra are shown in Figure 15. As can be seen from Figure 15 the spectra produced on the different computers are nearly identical. When compared to the 6500 it might be expected that the PDP 8/I calculations would suffer from round-off error since the 6500 has 60 bit words and the PDP 8/I has 12. It appears 55 .Loao> Loam: Co Eacuuwam :o2uapomme now: .22 m23m22 ..Eu 0: m: O: NO— <—— NOISSIWSNVUL 56 POP 8/ I M CDC 6500 W 75 85 95cm" Figure 15. Comparison of a spectrum produced on the CDC 6500 to a spectrum produced on the PDP 8/I. 57 that round-off error is not a problem, at least within the resolution of the plotters. It is interesting to compare the manner in which the calculations are done on the two computers. The calculations on the 6500 are done in double precision floating point, so they might be accepted as an "absolute" standard. The calculations on the FWN’8/Iare done in a pseudo-floating point (43), 1,g, all numbers in the input data must be scaled so that they are less than 1. The transform routine then handles all data in double precision, always maintaining the decimal point between bits 0 and l. The final output is scaled back to 12 bits and exported in the same format as the input data. The absence of a significant round-off error in the transformations done on the PDP 8/Iis also due to an additional factor. The Cooley- Tuckey algorithm used to perform the transforms increases the speed of a Fourier transformation by reducing the number of complex multiplications and divisions that must be done (44). By the same factor, it also increases the accuracy of the transform, as the round-off error is directly proportional to the number of operations that must be done. Without the fast transform algorithm the main advantage of having the interferometer on-line would be eliminated, for it would not in any reasonable length of time be possible to examine the spectrum produced from an interferogram. A FORTRAN Fourier transform program was written to do a straightforward transformation, just as the integral implies. An interferogram of 500 points was selected, but when the transformation was not complete after eight hours the attempt was aborted. The length of time, whatever it would have been, to do the straightforward transform, is longer than it need be due to several 58 factors: the inefficiency of the PDP 8/I FORTRAN compiler, calculating each sine and cosine instead of using a lookup table, and not using the hardware multiply/divide option on the computer. Eliminating these factors would decrease the time needed to do a transform by a factor of at least 10. But, even so, the time necessary would in all likelihood still be too long to make it reasonable. The Cooley-Tuckey routine used in this study can transform a 2048 point interferogram in approximately five seconds, making it easily possible to examine each spectrum as it is produced. E. Ethane Spectrum Most of the studies made using the FTS-720 are of solid state samples. Spectra of this type are in general much harder to obtain than the water vapor spectra already presented as the absorptions are often very weak, some solid samples scatter light making their spectra noisy, and the absorptions are generally quite broad compared to the rotational transitions observed in a gaseous sample. However, with proper care, good spectra can be obtained using the FTS-720 as evidenced by the spectrum of the lattice modes of ethane shown in Figure 16. The sample was 4 mm thick and at a temperature of about 20°K. The Spectrum shown is the ratio of the summation of ten sample spectra to the sum of six background spectra. The inconsistency in the baseline between 75 and 80 cm"1 is due to the absorption in this region of the thick polyethylene windows used. The polyethylene absorption is so much stronger than the ethane peaks that it doesn't ratio out very well. The spectrum agrees well with that previously reported, considering the difference in temperature at which the experiments were done (45). Indeed, at the lower temperature of the present work, these bands due to the translational lattice modes are narrower and better defined. 59 oo— .¥oom pm mcmcum Co cowmme muwpum2 mg» mo Escuumam 2.26 z. 262222.82... .Oo d #I .22 m23m22 om *— NOISSIWSNVHI V. The Infrared and Raman Spectra of a-Fluorine A. Introduction The solid phases of fluorine have been examined by x-ray diffraction (46,47), heat capacity techniques (48,49), and by NMR (50). The crystal structure of B-fluorine, which is stable between the melting point (53.5°K) and a solid-solid transition point at 45.6°K, has been determined to be cubic, space group Pm3n with eight molecules per unit cell, very similar to the structure of y-Oz (51). The molecular orientations on the sites are random so that no discrete Raman scattering or infrared absorption is expected in the low-frequency region. The structure of the low-temperature phase of fluorine (a-fluorine), which is stable below 45.6°K, has never been uniquely determined despite theoretical interest in the problem of lattice stability of the halogen crystals (52). From an x-ray powder diffraction investigation (47) the structure is known to be monoclinic with four molecules per unit cell and a probable space group of C2/m, although C2/c could not be ruled out completely. The structure is similar to o-02 (53), and along with other similarities between oxygen and fluorine, points out the fact that solid fluorine is much more similar to solid oxygen than to the other crystalline halogens. Theoretical predictions of the lattice frequencies of a-fluorine have been made (54). The far-infrared and Raman spectra can be used to 60 6T critically evaluate these predictions, because fluorine is a simple enough molecule that one might expect the theoretical treatment would give meaningful results. Indeed, if the frequencies observed matched those predicted for one of the two possible structures very well, one might with reasonable confidence be able to assign the correct structure. In addition, the data gained from this study should be useful in further theoretical studies and provide useful information about the forces that hold a molecular lattice together. B. The Structure of a-Fluorine The unit cell dimensions of a-fluorine are a = 5.50 A, b = 3.28 A, c = 10.01 A with B, the angle between the a and c axes, being l34.66° (47). A diagram of the unit cell is shown in Figure 17. It depicts one unit cell drawn in solid lines which has four molecules and a primitive cell (see the dashed lines) which contains two molecules. It is the orientation and packing of the fluorine molecules in the two possible structures that is of interest. The ab projection is the same for both structures and is shown in Figure 18. The molecules are drawn to scale at the 0.002 electron density contour. This particular contour was selected by the x-ray workers because it helped them analyze the experimental diffraction pattern, which was not simply interpreted. They noted that the experimental packing in other simple first row diatomic solids such as N2 and 02 was reproduced by placing the nuclei so that the 0.002 electron density contours touched. Arranging the calculated fluorine electron densities in similar fashion revealed some unexpected extinctions in the powder diffraction intensity. The two structures differ in that the tilts of the molecules in different ab layers are not the same. In the C2/m structure the 62 Figure 17. Unit cell of a-Fz. 63 81 ”O? Figure 18. Projection of a-F2 unit cell onto the ab plane. 64 molecules are rotated about the b axis, each ab layer in the opposite direction. In the C2/c structure the different layers are tilted out of the ac plane by alternate opposite rotations about the a axis. The ti It (for both structures) improves the nesting of the molecules of one layer into the molecules of adjacent layers. Figure 19 shows the unit cell for the C2/m structure projected on to the ac plane. Molecules centered at the y = 1/2 positions are 1‘ nd icated as dashed lines. The molecules, as determined from the X-ray results, are tilted 11° _+_ 1° from the c axis. A projection of the unit cell onto the bc plane for the alternate s t ructure, the C2/c structure, is shown in Figure 20. The angle of t 1’ ‘l 1: out of the ac plane was found to be approximately 10°. Again th e molecules at the y = 1/2 positions are indicated with dashed lines. An interesting feature of the F2 lattice, for either possible 5 thucture, is that the molecules lie on two non-equivalent sites. As a Y‘esult, each of the sites can be treated as belonging to a separate 3". b 1 attice in a group theoretical analysis of the crystal. The two be S u‘lting correlation diagrams can be superimposed to give the CO hrelation table for oI-fluorine shown in Figure 21. Thus, in the Raman spectrum there should be one intramolecular fundamental, which may be split by interaction of the two molecules in the primitive Ce 1 1 , and four intermolecular librational lattice modes. Subtracting t h Q three zero frequency translational modes corresponding to the d ‘i S placement of the entire lattice, three infrared active translational 1 6. tt‘ice modes are to be expected. 65 .m232632um E\Nu mg» 20» mcm2a um mcp case 2266 p2:: N218 any we :o2uumn022 .m2 m23m22 '0 \ .’ \ 66 Figure 20. Projection of the a-F2 unit cell onto the bc plane for the C2/c structure. 67 2xa.Nxa mNm.xm Nxa.-a.2xa.xxa 22m 222>2pu< .N215 20C Em2mm2u :022m262200 .FN m23m22 3 2um2mm F.om m.mm m.¢m «.mm 312223 22.62.2392“. umgegmcH um>2mmao .muo Co Duos muwupep 6:» mo meageLOQEOO gu2z uypzm 26cm30622 ¢~.o m~.o om.o ~m.o Pe.o m¢.o wv.o vm.o vn.o mm.o om.o 00.2 22m2a= 22m. casem «>2ue26m o.mw c.5m N.mw o.mw m.om n.2m m.~m m.em m.mm m.mm e.om m.om «pusuq2ucmsam22 :msem uw>2mmao omp owp opp oop om om mm on om o¢ om mm ow op Axov meaueemasm» .HH mpnmh 79 10° 60° 120° 1 I l L L 1 110 90 70 cm' Figure 25. Raman spectra of the lattice mode of OCS at 10°, 60°, and 120°K. 80 The far-infrared spectrum of the lattice band of OCS was obtained for samples of OCS frozen from the liquid. The cell was constructed of copper sides with polyethylene windows sealed to the copper with indium gaskets. The results of the far-infrared study are also given in Table 11. Figure 26 illustrates the frequency shift with temperature of the band in the far-infrared. However, in this case the plotting routine used scales the spectra in a manner such that comparison of intensity (either area or peak height) is not directly possible from this figure. Figure 27 is a graph of frequency versus temperature for the Raman and infrared bands. The squares represent peaks obtained from the Raman spectra and the circles represent the far-infrared data. It may be noted that the Raman and infrared librational peaks have almost identical frequencies at the low temperatures, as expected (only V = O significantly populated), but at higher temperatures there is a definite difference. The difference at 100°K is 1.1 cm"1 and the difference at higher temperatures should be greater. Thus it appears that the differing contributions of the anharmonicity of the librational mode to the infrared and Raman band intensities expected theoretically is experimentally discernible. More far-infrared data is needed for higher temperatures, but these data are difficult to obtain because the band becomes exceedingly broad above 100°K. Now that these experimental observations are available, it would be most interesting to test the various models for the inter- molecular interactions in simple molecular crystals to ascertain whether the lattice dynamical calculations of crystal energy levels can predict frequencies, temperature shifts, and infrared-Raman splitting obtained for OCS. 81 0% - f / « ‘v E 100’ 25° L. .L, I L l 70 90 110 FREQUENCY IN CM" Figure 26. Far-infrared spectra of the lattice mode of OCS at 100° and 25°K. 82 TE U S _- B I (D m a b 8 m 9 o _ a 0 o D 83 #2 ”T 4? I~ i~ ;; i- if 42- i ’f‘* 1 t O 20 40 60 80 100 120 'K Figure 27. Frequency versus temperature for the lattice mode of OCS. 6 Raman 0 Infrared l0. ll. 12. l3. T4. 15. 16. (LIST OF REFERENCES G. R. Wilkinson, S. Inglis, and C. Smart, "Spectroscopy," Rept. Conf. organized by Inst. Petrol. Hydrocarbon Res. Group, London, 1962, p. 157. J. L. Wood, 0. Rev. Chem. Soc., 12, 111, 362 (1963). F. A. Miller, "Proceedings of the 4th Conference on Molecular Spectroscopy," Hydrocarbon Research Group, Inst. Petroleum (London), 1968. . R. Ferraro, Anal. Chem., 36, 24A (1968). . W. Brasch, Y. Mikawa, and R. J. Jakobsen, "Appl. Spec. Rev." Vol. 1, . G. Braume, Jr., Ed., E. Arnold and M. Dekker, New York, 1968. MMLC... . D. Palik, J. Opt. Soc. Am., 66, 1329 (1960). Finch, P. N. Gates, K. Radcliffe, F. N. Dickson, and F. F. Bentley, "Chemical Applications of Far-Infrared Spectroscopy," Academic Press Inc. , New York, 1970. K. D. Moller and W. G. Rothschild, "Far-Infrared Spectroscopy,“ John Wiley & Sons, Inc., New York 1971. G. C. Pimentel and A. L. McClellan, "The Hydrogen Bond,“ Freeman and Co., San Francisco, 1960. S. N. Vinogradov and R. H. Linnell, "Hydrogen Bonding,“ Van Nostrand Reinhold Co., New York, 1971, Chapter 9. H. Fizeau, Ann. Chim. Phys., 66, 429 (1862). A. A. Michelson, Phil. Mag., 61, 256 (1891). A. A. Michelson, "Studies in Optics," University of Chicago Press, Chicago, 1927. H. Ruben and R. W. Wood, Phil. Mag., 61, 249 (1911). P. B. Fellgett, thesis, University of Cambridge, 1951. P. Jacquinot and C. Dufour, J. Rech. du Centre Nat. Rech. Sci. Lab. Bellevue, (Paris) 6, 91 (1968). 83 T7. 18. 19. 20. 21. 22. 23. .24. £25. £26. £27. 228. 229. £330. 331. E32. :33. 334. 235. 336. 537. 84 G-AE Subcommittee on Measurement Concepts, "What is the Fast Fourier Transform?" I.E.E.E. Trans. Audio Electrocoustics, AU-15, 45 (1967). P. Jacquinot and B. Roizen-Dossier, ”Progress in Optics Vol. III," E. Wolf, Ed., North Holland Publishing Co., Amsterdam, 1964, p. 31, 162-171. J. Connes, Rev. Opt., 40, 45 (1961). Translation by C. A. Flanagan, NAV-WEPS Rept. No. 8099: U. S. Naval Ordinance Test Station, China Lake, Calif., 1963. A. Savitzky and M. J. E. Golay, Anal. Chem., 66, 1627 (1964). G. Horlick, Anal. Chem., 16, 943 (1972). R. Bracewell, "The Fourier Transform and Its Applications." McGraw-Hill Book Co., New York, 1965. "RCA Photomultiplier Manual,“ RCA Corporation, 1970. R. C. Jones, J. Opt. Soc. Am., 61, 879 (1947). P. B. Fellgett, J. Opt. Soc. Am., 62, 470 (1949). E. Loewenstein, "Fourier Spectroscopy." presented at 1970 International Conference on Fourier SpectroscOPy. March, 1970. F. A. Jenkins and H. E. White, "Fundamentals of Optics." John Wiley & Sons, Inc., New York, 1971. A. Anderson and H. A. Gebbie, Spectrochimica Acta, 61, 8831 (1965). J. Strong, J. Opt. Soc. Am., 61, 354 (1957). P. L. Richards, J. Opt. Soc. Am., 61, 1474 (1964). H. A. Gebbie, "Advances in Quantum Electronics," Columbia University Press, New York, 1961, p. 155. W. J. Hurley, J. Chem. Ed., 66, 236 (1966). P. R. Griffiths, C. T. Foskett, and R. Curbello, Appl. Spec. Rev., 6, 31 (1972). M. J. 0. Low and S. K. Freeman, Anal. Chem., 62, 194 (1967). For several references see I.E.E.E. Trans. Audio Electroacoustics AU-15 (1967) and AU-l7 (1969). B. K. Hahn and C. G. Enke, to be published. "The Integrated Circuits Catalog for Design Engineers," Texas Instruments Inc., Dallas Texas. 38. 39. 40. 4T. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 85 H. V. Malmstadt and C. G. Enke, "Digital Electronics for Scientists," W. A. Benjamin, Inc., New York, 1969, p. 163. "The Small Computer Handbook," Digital Equipment Corp., Mass., 1970, p. 95. ”OK Programming Systems User's Guide," Digital Equipment Corp., Mass., Order No. DEC-P8-MEFA-D. "PS/8 Software Support Manual," Digital Equipment Corp., Mass., Order No. DEC-O8-MEXB-D. Moller and Rothschild, op, 611,, p. 317. E? J. E. Rothman, DECUS Program Library, N0. 8-143,1968. ‘ ‘ J. W. Cooley and J. W. Tukey, Math. Comput., 16, 297 (1965). Y. A. Schwartz, A. Ron, and S. Kimel, J. Chem. Phys., g, 99 (1971). H I. T. H. Jordan, W. E. Streib, and W. N. Lipscomb, J. Chem. Phys., 41, 760 (1964). L. Meyer, C. S. Barrett, and S. C. Greer, J. Chem. Phys., 66, 1902 (1968). E. Kanda, Bull. Chem. Soc. Japan, 16, 511 (1937). J. H. Hu, 0. White, H. L. Johnston, J. Am. Chem. Soc., Z6, 5642 (1953). D. E. O'Reilly, E. M. Peterson, 0. L. Hogenboom, and C. E. Scheie, J. Chem. Phys., 66, 4194 (1971). T. H. Jordan, W. E. Streib, W. H. Smith, and W. N. Lipscomb, Acta Cryst., 11, 777 (1964). I. H. Hillier and S. A. Rice, J. Chem. Phys., 36, 3881 (1967). C. S. Barrett, L. Meyer, and J. Wasserman, J. Chem. Phys., 11, 592 (1967). J. Laufer, thesis, Princeton University, 1968. A. E. Douglas and J. W. Raymonda, Paper G7,Presented at the 27th Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, 1972. J. E. Cahill and G. E. Leroi, J. Chem. Phys., 61, 97 (1969). O. Schnepp, "Advances in Atomic and Molecular Physics," Vol. 5, Eds. D. R. Bates and I. Eastman, Academic Press Inc., New York, 1969, p. 155. 58. 59. 60. 61. 62. 63. 64. J. R. 86 E. Cahill and G. E. Leroi, J. Chem. Phys., 61, T324 (T969). H. Hester, "Raman Spectroscopy," Vol. 1, Ed. H. A. Szymanski, Plenum Press, New York, 1965. C. A. A. Scott Blackwell, private communication. Anderson and S. H. Walmsley,Mol. Phys., _7_, 583 (1964). Anderson and H. A. Gebbie, Spectrochimica Acta,_§1, 883 (1965). . Wagner, Z. Physik. Chem. B., 16, 309 (1941). . Vegard, Z. Krist., ZZ, 411 (1931). APPENDICES Appendix A. Program Spectra A. Introduction Program SPECTRA is a FORTRAN program for the transformation of interferograms from the FTS-720 to spectra. It consists of a main program and several subroutines. The main program reads the input data and then determines the path the calculations take depending on the information on the control cards input. The spectra produced can be averaged and/0r ratioed to a background spectrum and then output in any of three forms, punched, printed, or plotted. Subroutine FOURl is a fast Fourier transform routine based on the Cooley-Tuckey algorithm (44). Subroutine APOD performs a triangular or trapezoidal apodization on the interferogram. Subroutine PLOT scales the spectrum to be plotted and then plots the spectrum on the line printer. The control cards for the program are explained and other directions are given in the comment cards of the program. 8. Progpgm Listipg 87 88 ponGuaM quCTDA(Inpur:hG.DHIDUT=ZOOoPHNCH=65oTAPEDO=1NPUTSTAPE613 IDHTPUT) DODGHAM SPFCTQA DDFQ A FAGT FOURIFD TRANSFORM OF AN INTEPFFROGPAH FROM THF FTS-TRD FAD INFRARED SPFCTHUHETFR. IHF PHDGRAN WILL PLOT OUT THE DFSULTANT SPECTRA DH THF LINE PRINT?“ IF DFSIHED. THE INTFPFFPOGRAMS APP DFAD TN HExIDECIHAI. rDNVFuTEU T0 DFCIHAL FORM AND LOADED INTD THF DATA ARRAY. THFHE VAY HE ANY NUMBER OF POINTS IN THE INTERFEROGRANS A9 LONG ‘5 ALL THE DUNS DONE AT DNCF ARF NDUGHLY THE SAME. NTUO IS THE NUMRFPo A anEP 0F Two. TD wHTCH THF INTERFEPDGHAN HILL HE MADE UP TD. ALL HACKODDUNDG ARF ALI ADDED TNTD SHACK. IF SAHPLF RUNS ARE In at AVFRAGFD THFY APF ADDED IN ESAMP. UP TD 2000 POINTS CAN BE DUTPUT. DN THF GENERAL RUN PADANFTEH CARD GNHI To GNU? Is THF DFSIRFD OUTPUT RANGE IN HAVENUHBERS OELX-MIDRUR STEP DISTANCE FOP THE RUNS NTwo-A POWER OF TWO. GpFATER THAN THE NUHHER 0F POINTS 1N THF INTER. ISHTF FDR APODIT7ATION ROUTTNF PPnlN-PPINTG DUT SHACK IF EQUAL TO ONE HPLOT-PIUTS nUT sHACK IF EQUAL TD DNF SPHlN-PPINTG OUT SGAMP IF EQUAL TO ONE 5PTOT-P10TS DUT SSAHP IF EQUAL TD nNE SHUNCH-DUNCHS DUT SSAHD IF EUUAL Tn DNE SHATTD-RATIDS AND DLDTS SSAHP/SHACK It EQUAL To ONF RPUNCH-pUNCHS QSAHp/SHACK IF EQUAL Tn nNE IPnD-CALLS THE APOPIZATIDN HnUTINE IF EQUAL TO ONE ON THE INDIVIDUAL DUN PARAMETER CARDS IUACK-SFT EDUAI To nNF IF A HACRGRDUND HUN [PnlN-poINTs AN INDIVIDUAI SAMPLF IF EDUAL TO ONE [PLOT-PLOTS AN INDIVIDUAL SAMPLE IF EQUAL Tn ONF lSTDH-ADUS THE SAMPLE TD SSAHP IF EQUAL To ONE IRATIn-RATIns AN INDIVTHUAL SAMPLE AND PLOTS THE RFSULTS THE END OF EACH DATA DECK AND THE CONTROL CARD FOR THE NEXT Is TO BE SEPARATED RY A T-R-Q (ADO. 1F DOING UNLY ONE DATA DECK AT A TIME CALL IT A QAMDLE RUN PATHEO THAN A BACKGROUND RUN. nonnnnnnnnnnnnnnnnmnnnnnnnnnnnnnnnnn5.") DINENGIDN DAIA(?OAH)oVALHFlZOOO)oGNU1?0001oSBACKlZOOOToSSAMPTZOOOI DIMENSION HATCHAIIGIoMATCHRIIGIoNI(lhloNZTIGISNJIIGIoNBIlbloNQIIQI IONSIIQI COMMON GNu.GNUI. GNUz. KOIFF. KA CnHPLFx DATA INTFGFR RPPINoHDLDToSPOIN. SPLUTo SPUNCH.RPUNCH.GRATTD pFADT60.7001) MATCHA RFADIGU.70011 HATrHH 7001 FDQMATIIGRI. 64x1 c C DFAD THF GFREPAI DUN DADAHFIEQG C RFADIGO.IDUIGNUI.Gnu?.DFLx.NTwD.ISHIF.HPPTN.HPLDTosDRTN.SPL0T. I§DUNCH0 CURRENT PT [MAXVAL < CURRENT PT [STORE INDEX OF POINT [BEGIN SHIFTING /AC=NO. OF PTS TO SHIFT [LOOP TO SHIFT FIRST HALF [TO THE UPPER FIELD LOOPS: LOOP“: ARRAY: OUNTR: MAXVAL: INMAX: MPOINT: POINTR: FIELD 1 *2aaa DCL EV: TAD CIA DCA TAD DCA CLA TAD DCA ISZ ISZ ISZ JMP CLA TAD CIA TAD CIA DCA TAD DCA CLA CDF TAD CDF DCA ISZ ISZ ISZ JMP JMP 2400 88888 [ NTWO MPOINT ARRAY OUNTR HI [AC=NUMbER OF PTS REMAINING CLL [LOOP TO SHIFT SECOND HALF DOWN I POINTR I OUNTR POINTR OUNTR MPOINT LOOPS CLL ARRAY INMAX MPOINT ARRAY POINTR CLL IE I POINTR 00 I OUNTR POINTR OUNTR MPOINT LOOPA I CORECT [AC=NO. OF PTS TO SHIFT [LOOP TO SHIFT PTS BACK FROM [THE UPPER FIELD [OUNTR AT RIGHT PLACE [FROM PREVIOUS LOOP [SUBROUTINE TO REMOVE THE DC LEVEL FRON [THE INTERFEROGRAM [ O CLA DCA DCA TAD DCA TAD DCA CLL SUM! SUM2 (2400 OINTR (~20 COUNTR 112 STAVE: CLL [START OF DOUULL PRECISION TAD I OINTR TAD SUMl DCA SUMl RAL TAD SUM2 DCA SUM2 ISZ OINTR ISZ COUNTR JMP STAUL CLA CLL [ADDED FIRST 16 NUMBERS TAD SUMl RTR;RTR AND (@777 DCA SUMI CLL TAD SUM2 RTL:RTL:RTL:RTL TAD SUMI CIA DCA AVE TAD I M112 [GET NUM CIA DCA MNUM TAD (2400 DCA OINTR BEGAVE: TAD AVE TAD I OINTR DCA I OINTR ISZ OINTR NOP ISZ MNUM JMP BEGAVE CIF OD JMP I DCLEV CO U'J TR: 9: SUM 1: O SU’IZ: Q AVE: O M‘IUM: 0 OINTR: D 14112: 112 #2200 [SUBROUTINE ISHIF ISHIF: O [SUBROUTINE TO SHIFT THE ARRAY AND MAKE CLA CLL [UP TO NTWO POINTS wITH ZEROS TAD I N112 CIA TAD I N111 SNA .JMP FIXER AGAIN: OUT: LOPI: FIN: LOP2: DCA TAD TAD DCA TAD DCA TAD CIA DCA DCA ISZ SKP JMP CLA TAD DCA JMP CLA TAD RAR DCA TAD CIA DCA CMA TAD DCA TAD TAD DCA TAD CIA DCA TAD DCA ISZ SKP JMP CLA TAD DCA CMA TAD DCA JMP CLA TAD SNA JMP TAD DCA DCA ISZ JMP 113 SHIF [SHIF=NTWO-M (2400 I N112 ENDDAT ENDDAT SAVEL SHIF [LOCATION OF FIRST POINT AFTER ARRAY MSHIF I ENDDAT MSHIF [ZERO END OF ARRAY OUT IAC ENDDAT ENDDAT AGAIN CLL SHIF SHIFT SHIFT MSHIFT SAVEL POIPJl POINl SHIFT POIN2 I N112 [POINI IS THE LOCATION OF THE LAST [DATA POINT:POIN2 IS THE [LOCATION TO WHICH IT UILL [BE SHIFTED [JEGM I POINl I POIN2 NEGM [SHIFT THE ARRAY FIJ CMA POINI POIDJI POIN2 POIN2 LOPI MSHIFT CLA [DONE IFNO SHIFT FIXER (2400 POIN3 I POIN3 MSHIFT OO [ZERO THE bEGINNING OF THE ARRAY FIXER: OO: POINI: POINZ: N111: N112: SAVEL: POIN3: SHIFT} MS” I FT: SHIF) ENDDAT: N EGM: M S” I F: REDUCE: BAB: OPO: LEFT: XPX: INIT: ZAPER: CIF JMP ISZ JMP 0 O 111 (0 \GGQGGGSG [SUBROUTINE TO 114 DO I ISHIF POINS LOP2 REDUCE INTERFEROGRAM TO [NTWO POINTS WHEN NUM>NTWO / O CLA TAD CIA TAD CLL RAR SNA JMP DCA TAD DCA TAD TAD DCA TAD CIA DCA TAD DCA ISZ ISZ ISZ JNP CIF JMP CLL I N111 I N112 OPO [NUM ONLY 1 NTUO LEFT (240D INIT (ZAOO LEFT XPX [INDEX OF POINT TO BE SHIFTED I N111 BIGGER THAN ZAPER I XPX I INIT XPX INIT ZAPER BAB 00 I REDUCE [ZAPER USED AS COUNTER [BEGIN THE SHIFT 115 C. Program PHASE4 l. Introduction PHASE4 reads a spectrum into core from DTAl. selects the desired output points, calculates the power spectrum, scales the output values, and plots the spectrum on the Heath analog plotter. This program does most of the necessary calculations in floating point so the floating point package, DEC Floating Point Package A (EAE version), must be in core for the program to operate. The Fourier transform returns a complex spectrum and the desired power spectrum is calculated, in subroutine ARIM, by taking the absolute magnitude of each complex point. Subroutine DELNU calculates the output point spacing in wavenumbers, and SCALE performs the necessary scaling of the output points. Finally, PLOT plots the spectrum on the analog plotter by drawing a straight line between each output point. 116 2. Listing of PHASE4 [PROGRAM PHASEA.PA [THIS PROGRAM READS A FILE FROM DTA1 [AND PLOTS THE DESIRED PORTION ON THE [HEATH ANALOG PLOTTER [FLOATING POINT PACKAGE ACEAE VERSION) [MUST BE IN CORE [ PLOT=7ZOO INIT4=6QOO PEN=6071 STEP=6074 DALX=6072 DVI=7407 MQL=7421 MQA=7SOI FADD=1000 FSUB=ZOOO FMPY=3ODO FDIV=4ZOZ FGET=SOOO FPUT=6000 FNOR=7000 FEXT=OOOZ SQUARE=OOOl SQROOT=OOOB FIXTAB [PAGE 0 STORAGE *3 FILE4 (1186388 63W #20 GNU 1: 5:1112: DELX: NTWO: INDEXI: POUT: PO I I‘JTR: HSTORE: MPOUT: C13: COUNTR: FLAG: PONTR: THREE: TWELV: NOSCAN: [FIRST OUTPUT WAVENUMDER [LAST OUTPUT NAVENEMbER [SAMPLING INTERVAL IN MICROJS [NUMBER OF DATA POINTS [FIRST DESIRED OUTPUT INDEX [NUMBER OF OUTPUT SHQGSQ—‘GGSQSQQGQ 117 *62 M13: ‘ 13 [ [END FIXED POINT STORAGE [ FNTWO: O O O 1*1OTHO: 16 2342 O FLTl: 1 2000 O FDELIJU: O O O F2043: 14 2000 O FXN: O O O FZOAO: 13 377O O / [END STORAGE [ [SUBROUTINE LOAD [LOAD FAC WITH NUMBER [POINTER TO THE NUMDER IN THE AC [ LOAD: O DCA PONTR [POINTER TO NUMLER TAD I PONTR [GET EXPONENT DCA 44 ISZ PONTR TAD I PONTR [HIGH ORDER MANTISSA DCA 45 ISZ PONTR TAD I PONTR [LOW ORDER MANTISSA DCA 46 JMP I LOAD [ [SUBROUTINE DUMP [PUTS THE CONTENTS OF FAC INTO THE LOCATION [POINTED TO BY THE CONTENTS OF AC WHEN CALLED [ DUMP: O DCA PONTR 118 TAD 44 DCA I PONTR ISZ PONTR TAD 45 DCA I PONTR ISZ PONTR TAD 46 LCA I PONTR JMP I DUMP [ /SUUROUTINE TO FLOAT A NUMBER [CALL WITH NUMBER TO BE FLOATED IN THE AC [RETURNS WITH NUMBER IN FLOATING AC [ FLOAT: O DCA 45 DCA 46 TAD C13 DCA 44 JMS I 7 FNOR FEXT JMP I FLOAT [ [SUBROUTINE TO FIX A NUMBER [CALL WITH NUMBER IN FAC [RETURNS NI TH FIXED NUMBER IN THE AC [ FIX: O CLA CLL TAD 44 SZA SMA JMP .+3 CLA JMP I FIX TAD M13 SNA JMP DONE SMA HLT [ERROR DCA 44 GO: CLL TAD 45 SPA CML RAR DCA 45 ISZ 44 JMP GO DONE: TAD 45 JMP I FIX 119 [MAIN4.PA [MAIN PROGRAM FOR THE PHASE4 PROGRAM [ #200 CLA CLL CIF IO JMS INIT4 [INITIALIZE ZING: JMS READ4 [GET DATA FILE JMS SDELNU [CALCULATE DELNU JMS SGNU [CALCULATE OUTPUT INDEXES CLA CLL TAD (FDELNU JMS LOAD [PUT FDELNU IN FACC JMS 7200 [TYPE OUT FDELNU CLA CLL TAD INDEX] JMS FLOAT JMS I 7 FMPY FDELNU FEXT JMS 7200 [OUT PUT FIRST WAVENUMBER ISZ FLAG DODE: JMS UPDOUN [GET RED OF UNUANTED DATA &FLOAT JMS ARIM [A=SQRT(R**2+IM**2) JMS SCALE [SCALE FOR PLOT ROUTINE CIF IO JMS PLOT ISZ NOSCAN JMP ZING JMP 760O [DONE [SUBROUTINE SGNU [CALCULATES THE INDEXES OF [GNU1 AND GNU2 AND THE [NUMBER OF OUTPUT POINTS [ SGNLL O CLA CLL TAD GNU1 JMS FLOAT JMS I 7 FDIV FDELNU [FAC=GNU1[DELNU FEXT JMS FIX DCA INDEXI [INDEX OF FIRST DESIRED OUTPUT PT TAD GNUZ JMS FLOAT JMS I 7 FDIV FDELNU FEXT JMS FIX DCA POUT [INDEX OF LAST OUTPUT PT 120 TAD INDEX] CIA TAD POUT DCA POUT [NUMBER OF OUTPUT PTS JMP I SGNU [SUBROUTINE SDELNU [CALCULATES DELNU FROM DELX GIVEN IN [MICRONS AND NTWO BEING THE NUMBER OF POINTS / SDELNU: O CLA CLL TAD NTWO TAD (4000 [IF AC=O NTWO =2048 SZA [IF NTWO=2048 FLOAT WON'T WORK JMP .+6 JMS I 7 FGET F2048 FPUT FNTWO FEXT JMP .+7 CLA CLL [NTWO<2043 FLOAT WILL WORK TAD NTWO JMS FLOAT JMS I 7 FPUT FNTWO FEXT CLA CLL TAD DELX JMS FLOAT JMS I 7 FDIV F1OTHO [FAC=DELX IN CM FMPY FNTWO [FAC=DELX*NTWO FPUT FXN FGET FLTI FDIV FXN [FAC=1.0[(DELX*NTWO) FPUT FDELNU FEXT JMP I SDELNU [SUBROUTINE LARGE [SUBROUTINE TO FIND THE LARGEST [FLOATING POINT NUMBER IN AN ARRAY [RETURNS WITH SMALLEST NUMBER [IN LOCATION FXN [ LARGE: O CLA CLL TAD POUT CIA DCA MPOUT [NUMBER OR POINTS IN THE ARRAY TAD TWELV DCA POINTR [STARTING PT OF ARRAY JMS LOAD [GET FIRST IN FAC JMS 121 I 7 FPUT FXN FEXT ISZ CLA TAD TAD DCA TAD JMS JMS LOZ: MPOUT CLL POINTR THREE POINTR POINTR LOAD I 7 FSUB FXN FEXT CLA TAD SMA JMP ISZ JMP JMP CLA TAD JMS JMS LOX: CLL 45 LOX MPOUT LOZ I LARGE CLL POINTR LOAD I 7 FPUT FXN FEXT ISZ JMP JMP #400 [SUBROUTINE MPOUT LOZ I LARGE ARIM [STORE IN FXN [BEGIN TEST LOOP [PUT NEXT PT IN FAC [FAC'CURRENT PT - FXN [SKP IF CURRENT PTFXN [DONE7 [NO:GET NEXT PT [CURRENT PT’FXN [SO STORE IT INFXN [DONE7 [NO :GET NEXT PT [CALCULATES AsSQRT(R**2+IM**2) [FOR EACH DESIRED OUTPUT POINT / ARIN: 0 TAD DCA TAD CIA DCA TAD DCA CLA CMA DCA CLA TAD JMS ISZ JMP JMP JMS BACK: XXX: TWELV POINTR POUT MPOUT TWELV COUNTR CLL RAL FLAG CLL POINTR LOAD FLAG .+2 HERE I 7 [INPUT POINTER [NUMBER OF COMPLEX PTS [OUTPUT POINTER [SET REAL FLAG [GET POINT [REAL OR IMAG PART [REAL PART HERE: SQUARE FPUT FXN FEXT CLA CLL TAD POINTR TAD THREE DCA POINTR JMP XXX JMS I 7 SQUARE FADD FXN SQROOT FEXT CLA CLL TAD COUNTR JMS DUMP CLA CLL TAD POINTR TAD THREE DCA POINTR TAD COUNTR TAD THREE DCA COUNTR ISZ MPOUT JMP BACK JMP I ARIM [SUBROUTINE SMALL [SUBROUTINE 122 [GET IMAGINARY PART [FAC=SQRT(R**2+IM**2> [STORE POINT [INCREMENT POINTR [INCREMENT COUNTR [DONE? TO FIND THE SMALLEST [FLOATING POINT NUMBER IN AN ARRAY [RETURNS WITH SMALLEST NUMBER [IN LOCATION FXN / SMALL: LOOZ: O CLA CLL TAD POUT CIA DCA MPOUT TAD TWELV DCA POINTR TAD POINTR JMS LOAD JMS I 7 FPUT FXN FEXT ISZ MPOUT CLA CLL TAD POINTR TAD THREE DCA POINTR TAD POINTR JMS LOAD JMS I 7 [NUMBER OF POINTS IN ARRAY [STARTING POINT OF ARRAY [GET FIRST PT IN FAC [STORE IN FXN [BEGIN TEST LOOP [PUT NEXT PT IN FAC LOOX: *600 UPDOWN: ZIP: FSUB FXN FEXT CLA CLL TAD 4S SPA JMP LOOX ISZ MPOUT JMP LOOZ JMP I SMALL CLA CLL TAD POINTR JMS LOAD JMS I 7 FPUT FXN FEXT ISZ MPOUT JMP LOOZ JMP I SMALL 123 [FAC=PT-FXN [SKP IF CURRENT PT>FXN [CURRENT PT