Spectroscopic Instruments

Spectroscopic Instruments


devices used to study the spectral composition, with respect to wavelength, of electromagnetic radiation in the optical region, which extends from 10–3 to 103 micrometers (μ,m) (seeSPECTRUM, OPTICAL), to ascertain the spectral characteristics of radiators and of objects that interact with radiation, and to perform spectrochemical analysis. Spectroscopic instruments may be classified according to, for example, the spectrometric techniques employed, the radiation detectors used, or the working range of wavelengths.

The operating principle of most spectroscopic instruments may be explained by means of the simulator shown in Figure 1. The shape of the aperture in the uniformly illuminated screen 1 corresponds to the function f (λ) describing the spectrum under study—that is, the distribution of the radiant energy with respect to the wavelengths λ. The aperture in screen 2 corresponds to the function α(λ – λ’) describing the ability of the instrument to isolate from the light flux narrow portions δλ in the neighborhood of each λ’. This very important characteristic of a spectroscopic instrument is called the instrumental, or transmission, function. The process of measuring the spectrum f (λ) with an instrument whose instrumental function is α(λ – λ’) can be simulated by registering the variation in the luminous flux passing through the aperture as screen 2 is moved relative to screen 1—that is, as

Figure 1. If the spectrum under study f(ʎ) is measured with an instrument having the instrumental function a(ʎ – ʎ’), then the result of the measurements F(ʎ) is described by the integral F (ʎ) f a(ʎ — ʎ’) f (λ) dλ, which is called the convolution of f and a. The convolution process can be simulated by the change in the aperture area during the relative movement (scanning) of screens 1 and 2. The smaller the width δλ of the function a(λ — λ’), the more accurate the reproduction of the true contour of f(λ) by the instrument. The identity F(λ)= f(λ) is achieved only for an infinitely narrow instrumental function (δλ→0).

screen 1 is scanned. It is clear that the smaller the width of the instrumental function, the more accurate the measurement of the shape of the spectrum contour and the finer the structure that can be detected in the spectrum.

Along with the working wavelength range, the width of the instrumental function is a basic characteristic of a spectroscopic instrument. This width determines the spectral resolution δʎ and the spectral resolving power R= λ/δλ. The wider the instrumental function, the poorer the resolution and the smaller the value of R. On the other hand, a wider instrumental function means the instrument transmits more radiant flux—that is, the optical signal and the signal-to-noise ratio M are greater. Noise (random interference) is unavoidable in any measuring equipment. This noise is in general proportion to Spectroscopic Instruments, where f is the passband of the detector. The larger ∆f, the higher the instrument’s speed of response and the shorter the measuring time. A larger ∆f, however, means greater noise and a smaller M. The relation between the quantities R, M, and ∆f is given by the equation

(1) Rα M(∆f)β = K(λ)

The exponents α and β take on different positive values depending on the particular type of spectroscopic instrument. The constant K, which is a function of λ only, is determined by the design parameters of the given type of spectroscopic instrument and imposes restrictions on R, M, and ∆f. In addition, the possible values of R are limited by diffraction and the optical aberrations of the instrument, and the values of Δf are limited by the time lag of the detection and recording portions of the instrument.

The principle of operation that has been discussed with the aid of Figure 1 pertains to the single-channel methods of spectrometry. Extensive use is also made of multichannel methods, in which scanning is not employed and radiations of different wavelengths are recorded simultaneously. This approach corresponds to the superposition on screen 1 of a stationary screen from which N instrumental-function profiles have been cut out for the different wavelengths; the flux from each aperture (channel) is recorded independently.

Figure 2 presents a general classification of the spectrometric methods that underlie the various schemes and designs of spectroscopic instruments. The classification is based on two fundamental criteria: the number of channels and the physical methods of isolating λ in space or time. The methods of groups 1 and 2 involve the spatial separation of λ (selective filtering). Known as the classical methods, these methods were the first to be developed and are the ones most commonly used. In the single-channel instruments (group 1), the flux under study with the spectrum f (λ) is passed through a spectrally selective filter, which isolates from the flux certain intervals δλ in the neighborhood of each λ’. The filters used in such instruments can be tuned either continuously or in discrete steps so as to scan the spectrum in time according to some law λ’(i). The isolated components δλ are transmitted to the detector, and the detector signals are recorded to yield a function of time F(t). By converting from the argument t to the argument λ, the function F(λ), which is the observed spectrum, is obtained.

In the multichannel instruments (group 2), the information regarding the spectrum under study is obtained by simultaneously recording (without scanning over λ) with several detectors the radiant fluxes at various wavelengths (λ’ λ“, λ’”, . . .). These wavelengths may be isolated, for example, by means of a set of narrow-band filters or by means of multislit monochromators (polychromators). If the separation between channels is not greater than δλ and the number of channels N is sufficiently great, then the information obtained is similar to that obtained when the spectrum is recorded with a single-channel scanning instrument (if the δλ are the same, the detectors are identical, and other conditions are equal). The measuring time, however, may be 1/N of that for the single-channel instrument. The greatest number of channels is achieved when multielement photoelectric detectors and photographic materials (in spectrographs) are used.

The principle of operation of the newer methods (groups 3 and 4 in Figure 2) has been developed since the mid-1960’s. These methods are based on selective modulation, where the wavelengths are separated not in the optical portion of the instrument but in the electrical portion.

Figure 2. Classification of spectrometric methods according to ways of separating wavelengths. The profiles of width δλ symbolically depict the instrumental functions. In the classical methods (1 and 2), these profiles describe the ability of an instrument to separate wavelengths spatially. In the new methods (3 and 4), the instrumental function describes the ability of an instrument to separate electrically wavelengths that have been coded in various ways in the optical portion of the instrument. Scanning, symbolized by →, is used in the single-channel methods (1 and 3). In the multichannel methods (2 and 4), there is no scanning, and radiation intensities of a series of wavelengths λ’, λ”, λ’”, … are measured simultaneously. For each group, the principal types of spectroscopic instruments in the group are named.

In the simplest single-channel device of group 3, the flux under study with the spectrum f (λ) is passed through a spectrally selective modulator that is capable of modulating with a certain frequency f0 = const only the interval δλ in the neighborhood of λ’; the remainder of the flux is left unmodulated. The scanning of λ’(t) is achieved by tuning the modulator so that different wavelengths are modulated successively by the frequency f0. By isolating the component f0 in the detector’s signal with an electric filter, a time function F(t) is obtained whose values are proportional to the corresponding intensities in the spectrum f (λ).

The multichannel systems using selective modulation (group 4) are based on multiplexing, that is, the simultaneous detection, by a single detector, of radiation from many spectral elements δλ in a coded form. In this approach, the wavelengths λ’, λ”, λ’”, … are simultaneously modulated by different frequencies f’, f”, f’”, . . ., and the corresponding fluxes are superimposed in the detector to produce a complex signal, whose frequency spectrum with respect to f carries information about the spectrum with respect to λ that is under study. When the number of channels is small, the components f’, f’, f’”, ... are isolated from the signal by means of electric filters. As the number of channels is increased, the harmonic analysis of the signal becomes more complicated. In the limiting case of interference modulation, the desired spectrum f (λ) can be obtained from the Fourier transform of the recorded interferogram. One of the possible methods of multichannel coding, the Hadamar mask matrix, has been put to practical use (see below).

The only methods beyond the scope of the classification given in Figure 2 are those using the nearly monochromatic radiation of tunable lasers (seeSPECTROSCOPY, LASER).

The groups of methods described above have all been used in constructing spectroscopic instruments, but to different extents. For example, the sisam spectrometers of group 3 have been employed only in a few experimental laboratory situations. On the other hand, the classical devices based on monochromators have become the principal means of analyzing the structure and composition of substances. There follows a discussion of the most commonly used types of spectroscopic instruments; the classification given in Figure 2 is adhered to.

Figure 3. Optical schematic of a spectroscopic instrument in which wavelengths are spatially separated by means of angular dispersion: (1) collimator, (2) dispersing element having angular dispersion ∆Φ/λλ, (3) focusing system (camera); (ES) collimator entrance slit, (Oi) collimator objective, (Ci) focal length of collimator objective, (O2) objective of focusing system, (C2) focal length of focusing-system objective, (F) focal plane. The objective of the focusing system creates in the focal plane images of the entrance slit in radiation of different wavelengths with the linear dispersion ∆x/∆λ. If a single exit slit is in the focal plane, the instrument is called a monochromator. If there are several slits in the focal plane, the instrument is known as a polychromator. If a human eye or a photosensitive layer is in the focal plane, the instrument is a spectroscope or spectrograph, respectively.

Group 1: Single-channel instruments with spatial separation of wavelengths. The basic component in the optical system of instruments of group 1 (Figure 3) is the dispersing element, which may be a diffraction grating, echelette grating, Fabry-Perot interferometer, or prism. The dispersing element has the angular dispersion ∆Φ/∆λλ and permits the image of the entrance slit ES to be decomposed into radiation of different wavelengths in the focal plane F. Spherical or parabolic mirrors are generally used for the objectives O1 and O2 because their focal lengths, unlike the focal lengths of lens systems, do not depend on λ. Single-channel instruments have one exit slit in the focal plane F and are called monochromators. Scanning with respect to λ is generally accomplished by rotating either the dispersing element or an auxiliary mirror. The simplest monochromators use, instead of gratings or prisms, light filters having a circular wedge shape giving continuously a tunable narrow pass band. Alternatively, a set of narrowband light filters may be used that provide a series of discrete readings for different wavelengths.

Figure 4. Block diagram of a single-beam single-channel spectroscopic instrument: (L) radiation source, (M) optical modulator (chopper), (S) specimen under study, (F) scanning filter (monochromator), (D) photoelectric radiation detector, (A) amplifier and converter of signals from detector, (R) analogue or digital recorder

Single-beam and double-beam spectrometers are based on monochromators. In single-beam instruments (Figure 4), the functional elements are characteristically arranged one after another. When transmission or reflection spectra are measured, a built-in source of continuous-spectrum radiation is usually employed. When the spectra of external radiators are measured, provision is made for appropriate sources. For instruments of this type, equation (1) usually has the form Spectroscopic Instruments. The restrictions the equation imposes on R and Δf play an important role in the infrared region, where the luminance of the sources diminishes rapidly and the values of K are small. In the visible and near-infrared regions, energy restrictions play a smaller role, and the working values of R may approach the diffraction limit. For example, in diffraction-grating instruments they approach R,dif = 2kvL sin Φ where k is the orders of the diffraction, v = 1/λ is the wave number, L is the width of the grating, and <t> is the diffraction angle.

Double-beam designs are characteristic of spectrophotometers. A discussion of typical devices in group 1 follows.

HIGH-RESOLUTION SPECTROMETERS. High-resolution spectrometers for studying the structure of atomic and molecular spectra are nonportable laboratory devices that operate in accordance with the scheme shown in Figure 4. Their long-focus (up to 6 m) monochromators are contained in evacuated housings to eliminate atmospheric absorption and are located in vibration-proof and temperature-stabilized rooms. These instruments use twofold and fourfold diffraction on large echelette gratings and have high-sensitivity cooled detectors. As a result, values for R of 2 × 105 at × = 3µm can be achieved in absorption spectra. To reveal still finer structure, Fabry-Perot interferometers are incorporated in the design. In these interferometers, scanning with respect to λ over a narrow range is obtained by varying the pressure in the interferometer spacing or by varying the magnitude of the spacing with a piezoelectric device. The slit monochromator is used only for preliminary selection of the spectral range and for separation of superposed orders of interference. Such instruments are called Fabry-Perot spectrometers and permit the obtaining of R= 106 in the visible region.

DOUBLE-BEAM SPECTROPHOTOMETERS. In double-beam optical systems, the flux from the source is divided into two beams: a main beam and a comparison, or reference, beam. The optical null method is used most often. In this case, the instrument is in effect an automatic feedback control system (Figure 5). The modulator M sends the two photometer beams alternately to the entrance slit of the monochromator F. When the fluxes in the two beams are equal, the system is in equilibrium, and the wedge W is stationary. When the wavelength is changed, the transmission by the specimen changes, and the equilibrium is disturbed. As a result, an imbalance signal is generated. This signal is amplified and fed to a servomotor that controls the wedge movement and the associated recorder R. The wedge is moved until the attenuation produced by it in the reference flux matches the attenuation produced by the specimen S. The range of wedge positions (from completely closed to completely open) is coordinated with the recorder scale (from 0 to 100 percent) for the specimen’s transmission coefficient. A double-beam spectrophotometer usually records spectra on charts where the wavelengths λ or wave numbers v (in cm-1) are the abscissas and the values of the transmission coefficient T (in percent) or the optical density D = –log T (here 0 ≤ T ≤ 1) are the ordinates.

Figure 5. Diagram of an optical null double-beam single-channel spectrophotometer: (W) optical wedge; the other symbols are as given in Figure 4

Numerous models of double-beam spectrophotometers are lot-produced by firms in many countries. The instruments can be divided into three basic classes: complex general-purpose instruments for scientific research (R = 103 –104), an intermediate class of instruments (R = 103), and simple routine-type instruments (R = 100–300). In instruments of the first class, provision is made for the automatic interchange of replica gratings, light sources, and detectors so that a wide spectral range can be covered. The most common ranges are 0.19–3 µm, 2.5–50 µm, and 20–330 µm. The designs of these spectrophotometers provide for a broad selection of values for R, M, and Δf and of recording speeds and scales for spectra of different objects. In instruments of the second class, the useful spectral range is smaller, and the choice of operating modes is limited. In simple spectrophotometers, one or two standard operating modes with a simple start-stop control are provided. Such instruments are portable devices weighing 20–40 kg.

Besides spectrophotometers whose operation is based on the optical null method, precision instruments are produced that are based on measurements of electrical ratios. In such instruments, the light beams of the double-beam photometer are modulated by different frequencies or phases, and the ratio of the fluxes is determined in the electrical portion of the device. Special types of spectrophotometers may include in their design microscopes (microspectrophotometers), devices for investigating fluorescence spectra (spectrofluorimeters) or polarized spectra (spec-tropolarimeters), devices for studying the dispersion of the refractive index (spectrorefractometers), or means for measuring the luminance of external radiators by comparison with a standard (spectroradiometers). Automatic spectrophotometers are the principal devices used in studying the spectral characteristics of substances and materials and in analyzing absorption spectra in laboratories.

SINGLE-BEAM NONRECORDING SPECTROPHOTOMETERS. Single-beam nonrecording spectrophotometers are usually simple and relatively inexpensive instruments for the region from 0.19 to 1.1 (µm. Their design is similar to that shown in Figure 4. The desired wavelength is set manually. The specimen and the standard against which the transmission or reflection is measured are inserted alternately in the light beam. Readings are made visually with an indicator or digital device. In order to improve their efficiency, such instruments may be equipped with digital printers and automatic specimen feeders.

RAMAN SPECTROMETERS Raman spectrometers may be of the single-beam or the double-beam type. Lasers are generally used as the source of radiation. In order to observe the Raman frequencies (seeRAMAN EFFECT) and to suppress the background created by the primary radiation, double and triple monochromators may be employed; holographic diffraction gratings may also be used. The instruments are provided with devices for observing Raman scattering in liquids, crystals, and powders at various angles and by transmission. In the best instruments, the ratio of the background to the useful signal has been reduced to 10~15, and Raman frequencies can be observed at distances up to a few cm-1from the exciting line.

HIGH-SPEED SPECTROMETERS. High-speed spectrometers operate in the manner shown in Figure 4. Unlike the previous types, however, such spectrometers are provided with devices for rapid cyclic scanning and with broadband (Δ/up to 107 hertz) detection and recording systems. For studying the kinetics of reactions, the scanning is carried out with a small duty cycle, which can be achieved, for example, by the traveling slit method. In this technique, the exit slit in the focal plane is replaced by a rapidly rotating disk having a large number of radial slits. Up to 104 spectra per second can be obtained in this way. If the lifetime of the object is too short for kinetic studies, then faster scanning by means of rotating mirrors is used. This approach provides a large duty cycle and requires that the start of the process be synchronized with the moment the spectrum passes through the slit. Examples of high-speed spectrometers are the SPV-U spectrovisor, which can record up to 500 spectra per second in the visible region, and the high-speed IKSS-1 (IKS-20) infrared spectrometer, which has an adjustable spectral range within the interval 1–6 µm and recording rates of 1 to 100 spectra per second.

Group 2: Multichannel instruments with spatial separation of wavelengths. Scanning is not used in the instruments of group 2. Instead, a discrete series of wavelengths (in polychromators) or parts of a continuous spectrum (in spectrographs) are recorded simultaneously. The optical portion of such instruments is usually constructed as shown in Figure 3. If a set of narrow-band light filters is used instead of a system producing an angular dispersion, the instrument is usually classed as a photometer.

Multichannel instruments are widely used to perform spectrochemical analysis of substances on the basis of selected analytical wavelengths λ. As the number of channels is increased, it becomes possible to study spectral distributions f (λ). A description follows of the most typical instruments of group 2, in the order of increasing numbers of channels.

FLAME (ATOMIC ABSORPTION) SPECTROPHOTOMETERS. Flame Spectrophotometers usually have one or two recording channels and measure the intensities of the absorption, emission, or fluorescence lines of the atoms of elements in the flames of special burners or other “atomizers.” In simple designs, the analytical wavelengths are isolated by means of narrow-band filters (flame photometers). More complicated instruments make use of either polychromators or monochromators that can be shifted to different wavelengths. Instruments of this kind are used in spectrochemical analysis to determine most elements of the periodic system. Such instruments provide high selectivity and a sensitivity as good as 10–14g.

QUANTOMETERS. Quantometers are photoelectric instruments for industrial spectrochemical analysis that are based on polychromators. The exit slits of the polychromator isolate from the radiation spectrum of the substance under study the analytical lines and the comparison lines. The corresponding fluxes are transmitted to detectors (photomultipliers) located at each slit. The photoelectric currents of the detectors charge storage capacitors, and the capacitor charges accumulated during the exposure interval are used as a measure of the line intensities, which are proportional to the concentrations of the elements in the sample. Presently available quantometer models are classified in various ways: according to the spectral range used (within the region from 0.17 to 1 µm), according to the number of simultaneously operating channels (from two to 80), according to the degree of automation, and according to the method of exciting the spectra (arc, spark, or laser). Quantometers are used to make rapid analyses of chemical composition. For example, the instruments are employed to analyze steels and alloys in ferrous and nonferrous metallurgy and to analyze metallic impurities in used lubricating oils from machines and engines in order to determine the amount of wear.

SPECTROGRAPHS. Spectrographs record simultaneously extended portions of a spectrum that has been resolved in the focal plane F (Figure 3). In photographic spectrographs, the spectrum is recorded with photographic plates or films. In other types of spectrographs, the spectrum may be displayed, for example, on the screen of a television camera tube or an image converter that “remembers” the image. When a good optical system is used, the number of channels is limited only by the resolving power (graini-ness) of the photographic materials or by the number of television scanning lines. To carry out spectrochemical analysis in the visible region of the spectrum by visual means, extensive use is made of simple spectroscopes and steeloscopes, in which the eye is the detector.

The wavelength range in which spectrographs are used begins at the short-wavelength boundary of the optical region and is gradually being extended into the infrared region as better photosensitive layers are produced and thermograph methods are developed. A great variety of spectrographs exist. For example, simple tabletop instruments are used for educational purposes, and compact rocket and satellite instruments are employed in investigating the spectra of the sun, stars, planets, and nebulas. Examples of large instruments include astronomical spectrographs, which are used in conjunction with telescopes, and laboratory IOmeter vacuum instruments, which have large plane and concave diffraction gratings and are used to investigate the fine structure of atomic spectra.

The linear dispersion of spectrographs (the portion of the focal plane Δλ occupied by the wavelength interval Δλ) is between 102and 105 mm/µm. The light power of spectrographs (the ratio of the illuminance in the image of the entrance slit to the luminance of the source that illuminates the entrance slit) can vary from —0.5 in high-transmission spectrographs to 10-3 or less in long-focus high-dispersion instruments.

HIGHSPEED MULTICHANNEL INSTRUMENTS. High-speed multichannel instruments are used to study the spectra of rapidly occurring processes. Such instruments are of various designs. For example, a spectrograph may be combined with a fast motion-picture camera (cinespectrographs), multisided rotating mirrors may be used in the instrument so as to scan the spectra at right angles to the direction of dispersion, or multichannel recording with multielement detectors may be employed. The terminology in this area has not yet been agreed upon. The terms “chronospectrograph,” “spectrovisor,” and “high-speed spectrometer” have been applied to the instruments discussed here.

Group 3: Single-channel instruments with selective modulation. Instead of spatial separation, selective modulation (coding) of wavelengths is used in the instruments of groups 3 and 4 in Figure 2. The separation of the wavelengths here occurs not in the optical portion but in the electrical portion of the instrument.

RASTER SPECTROMETERS. The design of raster spectrometers follows the general scheme shown in Figure 4 for single-channel instruments, but the slits in the scanning monochromator are replaced by rasters of a special form, for example, hyperbolic rasters. During the alternate operation of the entrance raster in transmitted and reflected light, amplitude modulation of the radiation occurs at that wavelength for which the image of the entrance raster coincides with the exit raster. As a result of angular dispersion, the images in the radiation of other wavelengths are shifted, and the amplitude of the modulation is diminished. Thus, the width Δλ of the instrumental function corresponds to a half period of the raster. Raster spectrometers provide greater flux than slit spectrometers (approximately 100 times greater when R ≈ 30,000). The use of raster instruments, however, is restricted by the exposure of the detector to the flux of unmodulated radiation and by the difficulty of fabricating the rasters and optical parts of the system.

SISAM. The sisam (Connes system) is an interference spectrometer with selective amplitude modulation. It is based on a double-beam interferometer, in which the end mirrors are replaced by synchronously rotating diffraction gratings and the optical path difference is modulated. Amplitude modulation is applied only in the interval δλ.dif corresponding to the diffraction limit in the neighborhood of λ that satisfies the condition of maximum diffraction for both gratings. The instrument always operates at the diffraction limit: R = Rdis= λ/δλdif. Because of the increase in the entrance aperture, the flux is about 100 times greater than in the classical instruments of group 1. The optical-mechanical portion of the instrument, however, is difficult to make and adjust.

Group 4: Multichannel instruments with selective modulation. In the instruments of group 4, a discrete or continuous series of wavelengths received by a single detector undergoes selective modulation (coding), and the electrical signals are then decoded. The most common types of instruments in the group are the Hadamar spectrometers and the Fourier spectrometers.

HADAMAR SPECTROMETERS. In Hadamar spectrometers, a discrete series of wavelengths is coded. The overall design is similar to that shown in Figure 4. Scanning, however, is not employed, and the slits in the monochromator are replaced by cyclically-changing multislit rasters of special design (the Hadamar mask matrix). The detector signals are decoded by a special device that produces a discrete spectrum of the radiation under study composed of about 100 point readings. Hadamar spectrometers are advantageous with respect to flux and speed of response and have been effectively used, for example, to make rapid analyses of exhaust gases from engines based on infrared spectra.

FOURIER SPECTROMETERS. In Fourier spectrometers, the wavelengths are coded continuously by means of interference modulation occurring in a double-beam interferometer when the optical path difference is varied (scanned). The detector at the interferometer exit produces an interferogram that is a signal in time. To obtain the desired spectrum, the Fourier transform of the signal is calculated with a computer. Fourier spectrometers are most effective for investigations of extended spectra of weak radiations in the infrared region and for solving problems requiring very high resolution. Instruments of this type exhibit a variety of designs

Figure 6. Infrared absorption spectra of water vapor in the range 200–250 cm–1. The spectra were obtained with a Fourier spectrometer with various optical path differences λ in the interferometer. The larger the optical path difference (that is, the longer the time expended in scanning with respect to λ), the greater the number of details that can be revealed in the part of the spectrum under study. When ∆ = 4 cm, the spectral resolution δ/∆ ... 0.5 cm–1.

and characteristics and range from large, unique laboratory apparatus with an optical path difference of 2 m (R = 106) to compact rocket and satellite spectrometers used for meteorological research, geophysical investigations, the study of planetary spectra, and other purposes. For Fourier spectrometers, equation (1) has the form Spectroscopic Instruments

The fundamental differences between the groups of instruments that have been discussed can be summarized as follows: in the single-channel instruments of groups 1 and 3, the experimental time is expended in accumulating information about new parts of a spectrum; in the devices of group 2, it is spent in increasing the signal-to-noise ratio; and in the devices of group 4, it is spent in increasing the number of structural details that can be discerned within a given spectral range (Figure 6).


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Tarasov, K. I. Spektral’nyepribory. Leningrad, 1968.
Zaidel’, A. N., G. V. Ostrovskaia, and Iu. I. Ostrovskii. Tekhnika i praktika spektroskopii. Moscow, 1972.
Optiko-mekhanicheskie pribory. Moscow, 1965.
Iakushenkov, Iu. G. Osnovy teorii i rascheta optiko-elektronnykh priborov. Moscow, 1971.
Mertz, L. Integral’nye preobrazovaniia v optike. Moscow, 1969. (Translated from English.)
Infrakrasnaia spektroskopiia vysokogo razresheniia: Sb. Moscow, 1972.
Cardona, M. Moduliatsionnaia spektroskopiia. Moscow, 1972. (Translated from English.)


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