Advances in Infrared Technology1

M. Czerny and H. Röder, Frankfurt a/M.

I. Sources of Radiation

1. From the theory of black-body radiation. The most important sources of infrared radiation are thermal radiators. As is known, Planck’s radiation law is valid for them:

\[ E_\lambda\, d\lambda = c_1 \frac{\lambda^{-5}}{e^{\frac{c_2}{\lambda T}}-1} \, d\lambda, \]

where \(c_1\) and \(c_2\) are constants, \(\lambda\) is the wavelength, and \(T\) is the absolute temperature. In studying the distribution of intensities over the spectrum, the function

\[ c_1 \frac{\lambda^{-5}}{e^{\frac{c_2}{\lambda T}}-1}, \]

is investigated, and it is by no means always emphasized that the conclusions are valid only for such a spectral decomposition when the spectral interval \(d\lambda\) remains constant. This latter assumption, however, is in general not in accord with experimental data; the interval \(d\lambda\) changes (for example, in prism spectrometers when passing from one wavelength to another). Under certain conditions it is considerably more correct to regard as constant the quantities \(\frac{d\lambda}{\lambda}\), or \(d\nu = \frac{d\lambda}{\lambda^2}\), and on this basis to investigate the functions:

\[ \frac{\lambda^{-4}}{e^{\frac{c_2}{\lambda T}}-1} \quad \text{or} \quad \frac{\lambda^{-3}}{e^{\frac{c_2}{\lambda T}}-1}. \]

For the short-wavelength infrared region, the number of quanta \(dn\) contained in the spectral interval \(d\lambda\) may be of importance. From the relation

\[ E_\lambda\, d\lambda = h \frac{c}{\lambda} dn = c_1 \frac{\lambda^{-5}}{e^{\frac{c_2}{\lambda T}}-1} \, d\lambda \]

we obtain

\[ dn=\frac{c_1}{hc}\cdot \frac{\lambda^{-4}}{e^{\frac{c_2}{\lambda T}}-1}\,d\lambda . \]

The survey of functions

\[ \frac{\lambda^{-m}}{e^{\frac{c_2}{\lambda T}}-1} \]

is facilitated by the following circumstance: if the logarithm of the function is plotted as a function of the logarithm of the wavelength for constant values of \(T\), then a family of curves is obtained, which are called isotherms. With such a doubly logarithmic representation, all the curves take the same form (Fig. 1) and are obtained one from another by parallel displacement along a straight line. The tangent of the angle of inclination of the direction of displacement with the axis of abscissas is equal to the exponent \(-m\). The temperature values on this straight line form a logarithmic temperature scale.

The same relation also holds for the isochromats (curves corresponding to identical wavelengths) in a doubly logarithmic representation. Such a representation is the content of Wien’s displacement law in its most general form. Only, usually, the displacement of the maximum of the isotherms is denoted as a consequence of this law.

Fig. 1. Isotherms corresponding to Planck’s radiation law in a doubly logarithmic representation

From Fig. 1 it is clear that raising the temperature of the source brings a substantial advantage only in the short-wave, but not in the long-wave region.

2. Thermal radiators. In the field of thermal radiation sources no serious successes have been achieved. The Nernst lamp in the short-wave infrared region, the Auer mantle in the long-wave region, and the mercury-quartz lamp in the region of the very longest waves still play the most important role. American investigators have replaced the Nernst lamp with the Globar lamp. It is distinguished by a longer service life in comparison with the former.

There has been no lack of experiments on replacing the Auer mantle with other radiation sources \(^{1,2}\). But all these experiments have shown how exceptionally successful the spectral distribution of the radiation of this body is. Its not too great emission in the long-wave visible region, and also its almost vanishingly small emission in the short infrared region between 1 and \(7\,\mu\), make it the most successful source of radiation for the long-wave infrared region.

Several years ago Pfund³ described a method in which an Auer mantle was excited and radiated in a tube under the action of an electric discharge. This investigator succeeded in obtaining enhanced emission in the short-wave infrared region, at least equal to that given by a Nernst lamp.

1. Electromagnetic radiators. Apparently it has proved possible to construct such generators of short electric waves as give radiation down to the long infrared waves⁴,⁵,⁶. However, if, on the one hand, no one doubts that there is a continuous transition between these two regions of the spectrum—the infrared and the region of short electric waves—then, on the other hand, it would be possible to speak of the filling of the intermediate region only if it were possible in this region to obtain sufficiently intense and constant radiation both with infrared sources and with electromagnetic radiators, so that the properties of both kinds of radiation could be compared with one another.

It would be necessary to carry out measurements of the absorption of both radiations in the same substances. This, however, has not yet been accomplished. In this sense the infrared region approximately between 1.3 mm⁴ and 400 μ has not yet been investigated.

II. METHODS OF REGISTRATION AND MEASUREMENT

All methods of registration and measurement of infrared rays are divided into two groups: in the first group a light quantum causes a photochemical or photoelectric process (photographic registration, photoelement); in the second group—in the so-called thermal receivers—the radiation is first converted into heat by absorption, and then the rise in temperature of the receiver is measured. In principle, a third group of instruments is also conceivable, in which light pressure could be used, i.e., from the quantum point of view—a change in the momentum of the quantum, and from the electrodynamic point of view—the direct ponderomotive action of the electromagnetic field of the radiation on the receiver.

A. Photochemical and photoelectric methods

1. Infrared photography. In recent years great successes have been achieved in the field of photochemical methods. Efforts directed toward making ordinary photographic plates sensitive to the rays of the infrared region by means of suitable sensitizers have led to excellent results, indicated in many reports⁷,⁸,⁹. A comparative review of various types of Agfa and Kodak plates and their regions of sensitivity is given by Kinle in Handbuch der Experimentalphysik¹⁰. It is necessary to point out that commercial plates are applicable up to 1.2 μ, and, if necessary, also up to 1.3 μ. The maximum sensitivity of varieties sensitized to the farthest infrared

region, lies, for Agfa plates, at about \(1.05\,\mu\) ^8, and for Kodak plates at about \(1.09\,\mu\) ^7. Plates surpass all thermal receivers by several orders of magnitude. Precise comparative data are not yet available; however, the following approximate relation holds. If radiation in the region of \(1\,\mu\) is so weak that it produces in a good thermal receiver, with a receiving area of several square millimeters and with an equilibrium-establishment time of 10 sec., a barely perceptible deflection, then with the same 10-second exposure the radiation can be recorded by a sensitized plate as well. But since with photographic plates the exposure time can be brought to a value on the order of 100,000 sec. (28 hours), it is possible, as calculation shows, to record by means of plates radiation ten thousand times weaker than by means of thermal receivers. Thermal receivers have for the most part already been brought to the theoretical limit of sensitivity; it must therefore be acknowledged that plates sensitized to the infrared region have a great advantage. Unfortunately, despite all achievements in the field of sensitization, plates have access to approximately half an octave of the infrared spectrum, whereas the entire infrared spectrum comprises nine octaves.

As for the hope of sensitizing photographic plates considerably farther into the infrared region, it was pointed out ^11 that there is a certain theoretical limit here. The farther into the long-wavelength region the plates are sensitized, the more rapidly they must fog under the influence of dark reactions. In passing to longer waves, even at room temperature an ever larger number of quanta of black radiation appears, to which the plate must respond just as to the same quanta sent by a special source. Likewise, in the plate itself, owing to thermal oscillations, there will occur an accumulation of energy, which will cause a photochemical process all the more strongly the more the plate is sensitized to the long-wavelength region, i.e., the smaller the energy required to induce the photochemical process.

Czerny and Mollet noted in one paper ^12 that the low stability of photographic plates sensitized to the far infrared region, even at room temperature, points to this effect of dark reactions. Conversely, J. Eggert showed that, in the existing regions of sensitization, the indicated effect may be disregarded, because recently it has proved possible to prepare plates that are significantly more stable at the same sensitivity (see also ^9). Thus, one may hope to push sensitization somewhat farther into the infrared region.

5. Photoelements. Approximately the same region of sensitivity as the photochemical methods is covered by methods based on the use of various photoelectric effects (photoelements are meant). Whereas pure alkali metals are sensitive chiefly to ultraviolet and blue rays, by means of appropriate treatment or by depositing several layers it is possible to shift the sensitivity of photoelements into the red-

or infrared spectral region approximately up to \(1.2\,\mu\)^{13, 14}. Well-insulated photocells, at high gains, make it possible to reach \(1.4\,\mu\).

As examples one may cite cesium photocells, which have a typical layered structure \((\mathrm{Ag}, \mathrm{CsO}, \mathrm{Cs})\)^{14}, whereas the “Phonopress” photocells of Infram G. m. b. H. consist of a homogeneous mixture of many components^{15}. The recently introduced design of photocells with amplification by secondary emission, understandably, produces no shift of sensitivity toward the red; it is only another solution to the problem of amplification. The so-called “thallofide” cells, for many purposes, cannot be taken into consideration, despite their relatively high infrared sensitivity, because they do not operate linearly^{14}.

The importance of photocells for infrared spectroscopy, in comparison with the possibilities of photographic plates, is slight. Plates surpass photocells in sensitivity. Only where rapid response and the need for short-time recording of radiation are involved is the use of photocells appropriate.

The above-mentioned limit of infrared sensitivity of commercial photocells is not, however, the limit of the theoretical possibilities of the photoelectric effect. In the literature there are data by Fischer, Gudden, and Troy on the Becquerel effect with galena^{16} and on a light detector made of galena^{17}. In these works it is shown that twice-dispersed radiation acts on the instrument at wavelengths almost up to \(3.4\,\mu\).

B. Thermal receivers

6. Absorbing media. The most important group of instruments for recording and measuring infrared radiation are thermal receivers. For them, above all, a substance is required that converts radiation into heat by absorption. In addition to the substances previously known and still used, such as soot or platinum black for the short-wave infrared region and sodium liquid glass or ordinary powdered glass for the long-wave region, a new group of substances should be mentioned. A. H. Pfund showed^{18} that when a metal is sputtered in a space filled with air or another neutral gas at a pressure of \(1\) mm Hg, many metals are deposited not in the form of a shiny mirror, but in the form of gray or, in favorable cases, deep-black layers. The transmission curves of these layers in the short infrared region, presented in Fig. 2, are taken from Pfund’s work^{18}. Since the optical behavior of the layers depends essentially on the conditions under which they were deposited, the proposed curves give only an approximate picture.

Of the blackening for thermal receivers there has always been required the fullest possible absorption of the wave of the wavelength that it is desired to measure, as well as the smallest possible change of the absorbing

ability in the wavelength interval under consideration. Recently, two further requirements have come to be imposed on these substances: the smallest possible heat capacity of the absorber and the smallest possible absorptivity with respect to all waves of other lengths not under study. The first of these requirements acquired the greater significance the more people strove to construct a receiver with a short time for the establishment of equilibrium, as is required for recording instruments or for methods with flickering illumination. The second requirement, for the least possible absorption of wavelengths not studied in the measurement, followed from the need to establish the smallest possible heat loss by the absorbing site through back radiation. This leakage takes place in the wavelength region of approximately 5–20 μ. If the absorbing area has a small absorptivity, then its emissive power is also small (in the sense of Kirchhoff’s law). A receiver for the short-wave infrared region can be blackened in such a way that in the region 5–20 μ it will already possess a rather small absorptivity. Kerckhoff has recently dealt with this in detail.^19

Fig. 2. Transmission of Se-, Te-, Bi-, and Zn blackenings as a function of wavelength. The thickness of the layers was chosen so that transmission begins at identical wavelengths.

With respect to this last requirement, shiny metals deserve particular attention. If one imagines a metallic film whose thickness varies, starting from zero, then it is evident that the radiation incident on the foil, as its thickness increases, will at first be absorbed more and more appreciably. At the same time, however, the share of reflected radiation also increases, and so strongly that at a certain thickness a maximum of perceived radiation occurs. With still thicker foil the reflection is so strong that only a very small share of the radiation is perceived. This circumstance is especially noticeable in the long-wave infrared region, where the optical behavior of metals is determined by their electrical conductivity. These relations were studied experimentally and theoretically by H. Murmann^20 and W. Woltersdorff^21. If by \(d\) we denote the thickness of the metallic layer, by \(\sigma\) its specific electrical conductivity, measured in electrostatic units, and by \(c\) the velocity of light in vacuum, then in the long-wave infrared region, for the fraction of radiation \(R\) that will be reflected, for the fraction \(D\) that will be transmitted through, and for the fraction \(A\) remaining in the layer,

the following relations hold (Fig. 3):

\[ D=\frac{1}{\left(1+\frac{2\pi\sigma d}{c}\right)^2};\qquad R=\frac{1}{\left(1+\frac{c}{2\pi\sigma d}\right)^2}; \]

\[ A=1-D-R=2\sqrt{DR}. \]

These are approximate formulas, obtained by expansion in a series in one parameter containing the thickness \(d\). What is interesting in these formulas is the absence of dependence on wavelength, although the refractive index and the absorption coefficient are, in the derivation, assumed equal to

\[ n=k=\sqrt{\frac{\sigma\lambda}{c}}. \]

Fig. 3. Theoretical relation between the reflectivity \(R\), transmittance \(D\), absorptivity \(A\), and the product of the specific conductivity \(\sigma\) by the layer thickness \(d\). Valid for metals in the long-wave infrared region

Experimental verification within certain limits confirms the formulas given. Layers whose absorption maximum \(A\) reaches 50% are, for good conducting metals, transparent foils; for poor conductors they are situated at the boundary of opacity. These pieces of foil therefore make it possible to create gray absorbing layers with very small heat capacity. Fruitful experiments with such sheets, used as bolometric surfaces, have recently been carried out by G. Teinson, but have not yet been published. These sheets were also used by Czerny and Mollet\(^{12}\) in their experiments on infrared photography.

In the violet region, for each metal there is naturally a thickness at which the greatest amount of radiation can be absorbed in the metal. In this case the phenomenon depends on the wavelength.

A particularly illustrative experiment on eliminating the radiating ability of a receiver is the construction of K. H. Cartwright\(^{22}\), in which the thermocouple is cooled to the temperature of liquid air. Such an instrument, however, has not yet been used for serious measurements.

7. Comparison of the sensitivities of different receivers. Among thermal receivers proper one should distinguish the classical types—the thermocouple and the microradiometer, the radiometer and the bolometer—and, on the other hand, certain new designs, which we shall briefly mention below. In the evaluation of receivers in recent years a change has occurred since, in connection with the fundamental work of G. Ising\(^{23}\), it became clear that these instruments have in part already been brought to the limit of thermodynamic fluctuations. This fact must in the future form the basis for comparing the capabilities of these instruments. If one considers earlier attempts

...comparison of various instruments, it turns out that there is no flawless method for comparison, but that methods are being proposed for determining sensitivity which are supposed to show that a newly constructed instrument is one or two orders of magnitude more sensitive than earlier ones. The person who has constructed an instrument with an especially small receiving surface emphasizes that it is necessary constantly to reduce the deflections of the instrument to \(1 \text{ mm}^2\) of receiving area; the person who has built an instrument with a large internal resistance indicates how many volts can be obtained under the action of a definite unit of radiation, while the person who has built an instrument with a small internal resistance convincingly indicates how many amperes can be obtained under such irradiation; the person who has built an instrument with a very small mirror will require that the deflections be reduced, for removing the scale to a distance of \(1 \text{ m}\), while the designer of an instrument with a large mirror, on the contrary, will refuse reduction to a distance of \(1 \text{ m}\), etc.

The exact characterization of the capability of an instrument consists in answering the question: what amount of energy must be supplied to the receiving instrument in order to cause a deflection equal to, or somewhat greater than, the mean “natural” deviation from zero (Moll and Burger \(^{24}\), Czerny \(^{25}\), Cartwright \(^{26}\), Teissig \(^{27}\)). Here, by “natural” deviations from zero one should understand those deviations which are due to thermodynamic fluctuations. In practice, however, it is often impossible to create such favorable conditions that no other external actions cause large deviations from zero. In that case this must be stipulated, but then it is impossible to obtain comparable data that are fundamentally characteristic of the given type of instrument. Connected with this is a serious difficulty in comparing the actual effectiveness of various instruments. It is the reason why, in fact, truly reliable data are rarely encountered; however, this is not a fundamental objection to the method. Cartwright \(^{26}\), who from this point of view carried out a careful comparison of instruments of different types, inclines in favor of the vacuum thermoelement as possessing the greatest effectiveness. The difference between individual instruments, however, is not very marked, and, on reviewing the literature, one can establish that, along with the vacuum thermoelement, many investigators use air thermometers and radiometers for the most precise measurements. The bolometer is now less popular, but there are nevertheless indications that it may again come into use.

Scarcely less interesting than the question of which of the instruments is more sensitive is the question of how, with the most diverse designs of instruments, approximately the same highest sensitivity is always obtained. The properties of a thermoelement are determined by the thermoelectric emf of a pair of metals, those of a bolometer by the temperature coefficient of electrical conductivity, and those of a radiometer by the gas-kinetic coefficient. Thus, the matter concerns three effects,

between which no connection has hitherto been established. If, nevertheless, equal sensitivities are obtained, whereas they might even have differed by several orders of magnitude, then the empirical material likewise testifies that some general regularity is hidden here. With respect to the thermoelement and the radiometer, the following considerations apply.^25 Both these instruments are heat engines. Let us imagine a connecting rod attached to the wing of a giant radiometer and leading to the crank of some shaft. By periodically interrupting the irradiation of the radiometer wings, one obtains a periodically operating heat engine. Exactly the same can be done with a galvanometer connected to a thermopile. The fact that there is no connecting rod here and that one must be satisfied merely with the elastic torsion of the suspension thread and the creation in it of a mechanical stress changes nothing in the evaluation of the instrument as a heat engine. However, for a periodically acting heat engine there is a valid proposition according to which the optimal efficiency is

\[ \eta = \frac{\Delta T}{T}, \]

where \(\Delta T\) is the temperature difference between the heater and the cooler, and \(T\) is the temperature of the heater, measured on the absolute temperature scale.

For the thermoelement and the radiometer, \(\Delta T\) depends on the intensity of the incident thermal radiation. At the smallest radiation intensities that have to be measured, \(\Delta T\) is of the order of \(10^{-6}\) to \(10^{-7}\ ^\circ\mathrm{C}\). If for \(\Delta T\) one takes the value \(3\cdot 10^{-7}\) and for \(T\) the value \(3\cdot 10^{2}\), then one obtains \(\eta = 10^{-9}\). Thus this is the most favorable useful effect that can be expected at the given radiation intensities. If one compares the amount of heat supplied to the instrument with the resulting energy of elasticity of the twisting thread, then in fact, at the very smallest radiation intensities, the ratio obtained is of the order of \(10^{-10}\). In reality neither the thermoelement nor the radiometer reaches the optimal efficiency, but they approach it (let us say, to give a number) by approximately one order of magnitude. The most essential point in these considerations is that they lead to the conclusion that, with no design that would likewise be a heat engine, is there hope of obtaining significantly better results than is possible with a radiometer or a thermopile, and that the discouragingly small useful effect is a consequence of the second law of thermodynamics.

Unfortunately, from this point of view the bolometer cannot be studied. The bolometer is not a heat engine; its bridge only controls the energy flow of the accumulator as a result of a change in the resistance of the bolometric strip. Therefore, for the bolometer one should have expected a considerably higher sensitivity. The fact that this does not occur, and that, on the contrary, for the bolometer the sensitivity has the same order of magnitude as for heat engines, shows that precisely here something is still not entirely clear.

Advances in Infrared Technology

One more remark should be made about the relation between vacuum and air thermopiles. In the literature one can find many data indicating how many times more sensitive a thermopile becomes if it is placed in a high vacuum. The figures quoted vary approximately between 10 and 400. This must create the impression that a vacuum thermoelement is much better than an air one. This, however, is not true. Only a thermopile that works exceptionally poorly in air gives such a large increase in sensitivity when evacuated. There are as yet no fully exact comparative data, but estimates show that a properly designed vacuum thermopile is only about three times more sensitive than a properly designed thermopile in air. This relation is understandable even without an exact calculation, if one takes into account that in designing a thermopile one has to accept a familiar compromise: if its wires are made long and thin, then the heat loss from the irradiated spot is small, but the electrical resistance is large, and conversely. Therefore, for an air thermoelement considerably thicker wires are used than for a vacuum one, since there is no point in making the heat loss through the wires smaller than that through the surrounding air. As a result, a small internal resistance is obtained and the possibility arises of using galvanometers with high voltage sensitivity. Therefore the same galvanometers cannot be used for air and vacuum thermoelements. These circumstances are especially clearly manifested in the Boys microradiometer, which, as is known, is a moving-coil galvanometer to which the thermoelement is connected directly. Since here the metal rings formerly used, which supplied current to the moving coil and always had several ohms of resistance, are eliminated, this advantage makes it possible to obtain a moving-coil galvanometer with an internal resistance of 0.1 ohm or less. This entails the necessity of making thermoelements with thick wires and using them in air. Evacuating the microradiometer then gives an increase in sensitivity of only about a factor of two, which does not justify the effort expended, especially since other technical difficulties also arise.

Thus, a rationally designed and properly used air thermoelement can stand comparison with a vacuum thermoelement; the latter has an advantage in cases where maximum sensitivity is required and, in addition, no galvanometer with very small internal resistance is available. However, one should never forget to mount an air thermoelement in an airtight vessel, since otherwise the operation of the instrument will be affected by temperature fluctuations associated with fluctuations of atmospheric pressure. Unexpected are the observations that the system vacuum thermoelement—galvanometer is also slightly sensitive to fluctuations of atmospheric pressure.

For the rational design of thermoelements it is necessary to know the thermo-emf, thermal conductivity, and electrical resistance

materials. Cartwright^28 has developed a device by means of which these quantities can be determined, using small pieces of metal employed for constructing thermoelements.

8. Newest design details. Of the many technical details that lead to the constructive improvement of classical thermal receivers, only a few can be mentioned here. In the field of thermoelement manufacture, the work of K. Möller is especially important. He proposed^1) evaporating metals in a high vacuum and depositing them on thin nonconducting films. If, by introducing suitable diaphragms, one ensures that the metals overlap one another only in a small zone, then thermoelectrically active “junctions” are obtained, which can be made as thin as desired. Independently of him, similar proposals were later made by other investigators.

A later proposal by Möller^29 consists in the following. To make a thermoelement, a homogeneous thread is coated galvanically, up to half its length, with another metal; then the entire thread is strongly heated, so that the deposited metal diffuses into the principal metal of the thread. In this way a thermoelectrically active alloy is obtained. In this method the difficulties of making an ordinary junction are likewise avoided; from hairlike threads one can make thermoelements of very small heat capacity.

New constructions of bolometers are considered in the works of Bosworth^30 and Moon and Steingart^31.

9. Installations free from vibrations. One cannot conclude the chapter on classical thermal receivers without making remarks concerning vibration-free installations and methods for observing small deflections of a galvanometer mirror; only when sufficient attention is paid to these circumstances can the natural boundary of measuring technique, generally speaking, be reached. Among the large number of proposals for installing galvanometers and radiometers free from vibrations, one may note the work of R. Möller^32; the point of view developed in it led to constructions that proved themselves in tests in many laboratories. Möller started from the well-known Julius suspension design (installation of the receiving instrument on a stand suspended from the ceiling by three long wires). He showed that for galvanometers one may completely neglect the vertical component of vibrations, contrary to what is intuitively considered most essential, and that the task consists only in eliminating the horizontal component as completely as possible. Instead of placing the galvanometer on a board suspended from the ceiling by three wires, one may also place the board on three rods (1 m long, 7 mm thick), mounted on the floor on a heavy stand. In this way a very weak coupling is obtained for rapid horizontal oscillations of the floor.

^1) A brief reference is contained in the report on the activities of the Physikalisch-Technischen Reichsanstalt in Z. Instrumentenkunde, 46, 176, 1926.

To calm the natural oscillations of a Julius suspension or an installation on rods, Moll used the principle of internal damping by means of a rocking vessel, which proved quite satisfactory. Beneath the board carrying the galvanometer there was fastened a flat tin cup about 40 cm in diameter, filled with paraffin oil to a height of about 8 mm. Owing to internal friction, the oil suppresses possible natural horizontal oscillations of the installation or suspension. Rotational oscillations about the vertical axis are also damped thereby. The previously adopted external methods of damping a Julius installation readily admitted disturbances, because these methods produced an undesirable coupling of the external damping device with the oscillating building. Moll’s rod installation is more convenient, but not more productive, than the Julius suspension. With regard to the latter, Moll’s cited work also contains valuable data.

Let us briefly mention two further methods: the installation on bearing balls proposed by Czaph33, which is intended to eliminate horizontal oscillations, and the shock-free installation of Gercke and Focht34 with an air cushion, which represents a further improvement of Moll’s rod installation, since it also brakes the vertical oscillations still present in the latter. Thus preference should be given to this installation if the elimination of vertical oscillations is in fact important. For galvanometer installations, however, this is not necessary, as was already indicated above. As for Czaph’s installation, which appears very attractive because of its simplicity, there are as yet no favorable reports from other sources.

10. Measurement of small deflections. For the reading of very small deflections of galvanometers and radiometers, Moll’s thermorelay35 and other related designs have found practical application, such as, for example, Bergmann’s differential photoelement with a blocking layer36, 37. It is necessary, of course, to realize that the use of these methods makes sense only when the instrument installation is so good that, under direct observation with telescope and scale, no irregularities whatever in the zero position are noticeable. These methods are of special importance when it is desirable to record objectively the deflections of a galvanometer. A refinement of the usual method of reading with telescope and scale was used in one work by Cartwright and Czerny and was then discussed in greater detail by the latter38, 39. In productivity and equipment requirements, this method lies approximately midway between the usual method of reading with scale and telescope and the relay method.

11. Methods with variable illumination. Since Herschel’s time, the generally accepted practice for radiation receivers has been the use of the differential method, in order, to a first approximation, to eliminate the effects of fluctuations of room temperature (irradiated and non-irradiated junctions of thermoelements, two wings of a radiometer, two bolometric strips). From this basic principle there follows—

are now being produced when methods with variable illumination are used. Let us imagine a bolometer constructed with such a thin foil that, after only \(1/10\) sec of irradiation, it practically reaches its final temperature. If the radiation falling on the bolometer is interrupted by means of a sector rotating ten times per 1 sec, then periodic voltage oscillations with a frequency of \(10\ \mathrm{Hz}\) will appear at the ends of the bolometer foil. With the aid of a transformer these can be fed to a tube amplifier, the amplified alternating current rectified and measured with a comparatively insensitive direct-current ammeter. If, in constructing the amplifier, measures are taken so as to pass only the frequency of \(10\ \mathrm{Hz}\), then changes in room temperature will be vanishingly small, because, in comparison with a frequency of \(10\ \mathrm{Hz}\), they proceed slowly. If one represents the decomposition of these changes in a Fourier series, then only terms in the region of frequency 10 will be non-vanishing. This principle of detecting the radiation being measured among all the other interfering radiations by means of a modulating frequency is beginning to be introduced more and more widely into the technique of radiation measurement. It may be said that the spatial differential principle hitherto customary is being supplanted by the temporal differential principle.

The method of variable illumination has found applications in various directions. It is possible, for example, to eliminate the bridge in a bolometer and to measure the voltage oscillations of one single foil (Lehrer \(^{40}\)), which gives an experimental simplification. It is also possible to combine the temporal principle with the spatial one, in order to eliminate, to a greater degree than by means of one method alone, the influence of interfering radiation and of changes in room temperature. To this group belong the resonance radiometer proposed by Pfund \(^{41,42}\), and the Firestone apparatus \(^{43}\). The simultaneous application of both methods is justified by the fact that neither of them by itself operates quite perfectly. Methods with variable illumination have acquired importance because, with their aid, certain methods of recording radiation have become feasible which had not been used before. From this group we shall mention the “Fluff”—the instrument of Hayes \(^{44,45}\). The construction is as follows. Let us imagine an air-impermeable window, transparent to the radiation, placed tightly against the membrane of a condenser microphone, the space between the window and the membrane being filled with a substance containing much absorbed air and giving off air upon slight heating. If this substance is heated by absorption of radiation, then the gas pressure in the space increases, and the microphone membrane will be deflected. If the radiation is periodically interrupted, then a corresponding alternating voltage can be taken from the condenser microphone and measured after sufficient amplification. In Hayes’s construction, vegetable pith is used as the absorber \(^{1}\), and it must be especially well tested.

\(^{1}\) For similar purposes, burnt vegetable cotton wool, possessing great adsorptive capacity, is used. Translator’s note.

Such a construction implements the spatial differential principle comparatively poorly; however, the first reports give grounds to hope that it will yield useful results by means of the temporal differential principle.

1. Recording by evaporation (evaporography). Finally, the group of thermal receivers also includes a special method of infrared photography developed by Czerny, Vildenberg, and Mollet11, 12, 46, 47, 48. In this method the energy of infrared radiation is likewise first converted into the heat of a body. This localized heating is then detected by the evaporation, from the irradiated place, of a certain substance. The technique acquires the required sensitivity owing to the fact that a thin celluloid membrane, \(0.1 \mu\) thick, is coated on one side with a suitable absorber of radiation, while on its other side there is deposited, by evaporation, a layer of a special paraffin oil of such a thickness that the membrane together with it shows intense interference colors (thickness about \(0.5 \mu\)). If some portion of the membrane is irradiated and, because of this, heated above the temperature of the surrounding medium, the paraffin oil will distill from the irradiated places to the nonirradiated ones. This distillation process takes place very rapidly if the membrane is placed in a space from which the air has been pumped out and in which there are only vapors of paraffin oil (about \(0.01\) mm Hg). Since a change in layer thickness of the order of \(0.01 \mu\) is already recognized from the change in the interference colors, considerable sensitivity is attained. The sharpness of the signal is also quite satisfactory, owing to the small thickness of the membrane and of the paraffin layer. Spectral lines separated from one another by \(0.1\) mm are still distinguished. Commercial plates sensitized for the infrared region considerably surpass this method in sensitivity when wavelengths accessible to sensitized plates are involved. However, the advantage of the method under consideration is that, in principle, it is not subject to any limitation with respect to wavelengths. Up to now, photographs have been made approximately up to \(10 \mu\). This method makes it possible to photograph infrared spectra at a speed unattainable by any other method. In sensitivity the method does not yet surpass the best thermal receivers; however, it comes close to them. Unfortunately, this method cannot yet be regarded as technically simple. The difficulties here are the same as there would be in the ordinary photographic process if there were no production of photographic materials, but only recipes for preparing photographic plates.

III. METHODS OF SPECTRAL DECOMPOSITION OF INFRARED RAYS

Methods for the spectral decomposition of infrared radiation are based either on the use of the interaction of radiation with solid bodies, or on the capacity of radiation to interfere. But

The latter methods—this refers chiefly to various types of diffraction gratings—usually require the greatest possible preliminary decomposition by means of other dispersion methods. The dispersion methods include, chiefly: the prism, Christiansen filter, the residual-rays method, the quartz lens, and absorption filters.

13. Imaging systems. In spectral decomposition, imaging optical systems are always used, and therefore it is necessary first to say a few words about them. For the infrared region, concave mirrors are used predominantly. Their essential advantages over lenses are: absence of chromatic errors, uniformly high reflectivity—in contrast to the difficulties connected with absorption in lenses—and, finally, the possibility of making systems of large diameter. When concave mirrors are used, difficulties arise chiefly from the fact that either the rays are directed obliquely with respect to the axis of the mirror and no stigmatic imaging is obtained, or auxiliary mirrors must be used in order to achieve incidence as nearly perpendicular as possible.

Fig. 4. Arrangements of auxiliary mirrors for achieving perpendicular incidence on concave mirrors

In many spectral instruments for the infrared region, oblique incidence of the beam of rays is used. With a skillful combination of two concave mirrors of a spectral apparatus, part of the reflection errors from the first mirror can be eliminated by means of the second. These circumstances were noted in two short communications by Czerny, Turner, and Plettig[^49][^50] and later taken into account in a number of instrument designs.

When it is necessary to image the exit slit of a spectrometer onto the receiver, it is customary to place the receiver in front of the concave mirror on the axis of the latter. If the receiver is small and the concave mirror is large, the receiver covers only a small part of the mirror, and the loss of radiation is compensated by good convergence of the rays. Naturally, when receivers are manufactured, attention must be paid to this from the very beginning. This applies especially to thermoelements.

If it is desirable to place the spectrometer slit also on the axis of the concave mirror, then a special auxiliary mirror is used, as shown in Fig. 4, a or b. Both constructions achieve the goal and are often used. When the concave mirror has a large aperture, the use of construction a encounters difficulties, since in this case the auxiliary mirror screens from the slit a large part of the beam of rays. Construction b is free from this error, but has

that drawback, namely that a long “parallel” path of the rays arises in it. This would do no harm if the rays were truly parallel, but they are not. Usually, in spectrometers, only the horizontal section shown in Fig. 4, b is noted (and taken into account?). In this section the rays pass, to a certain extent, parallel. In the vertical plane, however, the finite length of the spectrometer slit makes itself felt. Here strongly diverging beams of rays are obtained.

When the “parallel” rays traverse a path equal to several focal lengths, as occurs in designs of the type shown in Fig. 4, b, they diverge in the vertical direction so much that a considerable fraction of them passes above or below the second concave mirror of the spectrometer (the second concave mirror is usually made of the same size as the first). The beams of rays meet the second mirror obliquely and eccentrically, which increases the error in the image, since from the first mirror there comes a far from perfectly plane wave.

Spectrometers with reflecting gratings are free from this error, associated with the long path of parallel rays, if the perforated plane mirror is replaced by a perforated diffraction grating. This includes Randall’s very successful spectrometer design for the long-wave infrared region[^51].

The tendency toward ever larger apertures inevitably led to the use of aspherical mirrors, especially mirrors with parabolic and elliptical sections. Indeed, with the aid of an elliptical mirror one can bring rays emerging from another point exactly to one point. However, this is true only for the focus itself. For neighboring points the image usually turns out to be strikingly poor, and in each individual case it is necessary to protect oneself, by exact calculation, from unpleasant surprises. The same applies to parabolic mirrors.

All this can be explained by an example. A mirror of diameter 140 mm is to project onto a receiver an image of the spectrometer slit, 20 mm long, reduced 6.25 times. The spectrometer slit and the receiver must lie on the axis of the mirror. The distance from the mirror to the slit is 500 mm, and the distance from the mirror to the receiver is 80 mm. For this a mirror is required with a radius of curvature at the vertex \(\rho = 137.931\) mm. The calculation is to be made for: 1) a spherical mirror, 2) a parabolic mirror, 3) an elliptical mirror. All the mirrors must have at the vertex the indicated radius of curvature. The spherical and parabolic mirrors are fully characterized by these data; the elliptical mirror, however, must have a major axis equal to 290 mm, so that the center of the slit and the center of the receiver are its foci. The three mirrors differ so little in transverse section that their difference can hardly be represented by a drawing. The spherical mirror has at the edge a height of 19.0825 mm, the elliptical one 18.3426 mm, and the parabolic one 17.7625 mm. The use of a parabolic mirror, strictly speaking, is not essential; it should only be established whether it is not better than a spherical mirror. So-

the relations in the image must be investigated for two points:

1. For the central point of the target, i.e., the point on the axis.
2. For the extreme point of the target, i.e., the point 10 mm above the axis.

The quality of the image can be investigated either with the aid of geometrical optics, in which case one calculates how the rays pass near the image point, or with the aid of wave optics, in which case one checks how equal the lengths of the optical paths are from the object point through the mirror to the image point. It is precisely this latter, less usual method that is set forth here. Figs. 5a, 5b, and 5c show the calculated data for points on the optical axis for ellipsoidal, parabolic, and spherical mirrors. For an ellipsoidal mirror the length of the optical path is the same for every point of the mirror surface. For a parabolic mirror it increases from the middle toward the edge; for a spherical mirror it decreases. To explain these differences in path lengths, curves have been drawn on the mirror surfaces connecting all points with a specified path difference1. At the central point the difference in path lengths is zero; on the first dotted circumference it is 50 μ, on the following circumferences 100, 200, 300 μ, and so on. At the edge of the parabolic mirror it is \(+956\,\mu\), and of the spherical mirror \(-1217\,\mu\). Thus, the spherical mirror is the least favorable, the parabolic mirror somewhat better, and the ellipsoidal mirror free from errors.

In the same way, Figs. 6a and 6b present calculated data for an object point 10 mm above the axis and the corresponding image point 1.6 mm above the axis. Now even in the ellipsoidal mirror there appear large differences in path lengths, fluctuating approximately between \(\pm 200\,\mu\), although the object point is displaced from the axis by only 10 mm at a distance from the mirror of 500 mm. In Fig. 6b the curves for the spherical mirror are shown. Circumferences are obtained close to those in Fig. 5c, only all of them are shifted somewhat downward. Thus, the distortion for the spherical mirror is considerably smaller than for the ellipsoidal one. A very similar shift is obtained also for the system of rings of the parabolic mirror. This example shows both the advantage of the ellipsoidal mirror and the rapid deterioration of the image it gives for points off the axis.

The above-described method of representing image errors has significance in another respect as well. In passing from a mirror with a small aperture to large apertures, one obtains an increase in the illumination of the image points only so long as the path difference of the marginal rays, in comparison with the central rays, remains less than \(\frac{\lambda}{2}\)2.

The greater the wavelength of the radiation, the larger the aperture that can be used in this case[^52].

Mirrors are usually made of glass and coated, by evaporation in a high vacuum, with aluminum[^53] or so-called—

Fig. 5a. Elliptical mirror  Fig. 5b. Parabolic mirror

Fig. 5c. Spherical mirror

Fig. 5a, b, c. Curves of equal path differences for an object point on the axis

Fig. 6a. Elliptical mirror  Fig. 6b. Spherical mirror

Fig. 6a and 6b. Curves of equal path differences for an object point off the axis

the so-called Gocht alloy. Ordinary, formerly silver, coatings are increasingly falling out of use owing to their low durability; at the same time the reflectivity of silver in the infrared region exceeds that of aluminum only quite insignificantly. Experiments with mirrors made of stainless steel have also been successful.

Lenses, especially achromatic ones, are used in the shortest-wave infrared region, which is still accessible to ordinary photography. There are also spectrometers in which lenses not corrected achromatically are used, for example quartz lenses. In this case changes in the focal length must be compensated by mechanical means. If an autocollimating prism spectrometer is constructed, approximately corresponding to Fig. 7, then, in order to change the wavelength, it is necessary to rotate the prism and at the same time move the lens in the direction of its axis. By means of suitable mechanisms it is possible to connect the two motions in such a way that they can be produced by a single shaft with a drum calibrated in wavelengths.

Fig. 7. Spectral apparatus with a chromatically directed lens

If it is desired to obtain the best results with a reflecting system, the apparatus should always be tested by means of monochromatic visible light and several trial photographic exposures. Examination by eye—even when a magnifying glass is used—often leads to an overly favorable judgment, since the eye in general has a considerably smaller aperture than the reflecting system. For example, when testing by eye one may get the impression that sharp spectral lines are present, whereas on the photographic plate gross defects are revealed in them.

14. Prism methods. In recent years prism methods have been improved thanks to the fact that it has become possible to obtain synthetically larger transparent crystals of substances which until now had existed only in microcrystalline form. The crystals are obtained from molten material, and not from solutions, as was done earlier[^54],[^55],[^56]. Crystal growth is carried out by immersing a small crystal in the melt and then slowly raising it with careful cooling. Prisms of KBr have now come into fairly wide use. With them it is possible to work in the region almost up to \(25\,\mu\), whereas formerly, for KCl prisms, difficulties connected with absorption already appeared at \(19\,\mu\). With KJ prisms one can reach almost \(29\,\mu\), but nevertheless KJ prisms have not yet received the dissemination they deserve. They are apparently more difficult to prepare, and they are especially hygroscopic. Prisms of LiF and NaF have likewise not yet found any practical application. It may be expected that they will replace the hard-to-obtain and expensive fluorite. LiF is not hygroscopic.

To make possible the use of prisms for longer waves, Barnes^57 proposed cooling them to the temperature of liquid air; absorption at low temperature is significantly less. But, unfortunately, this proposal requires overcoming many technical difficulties and has not yet been properly tested.

It is known that the maximum resolving power of a prism is equal to:

\[ \frac{\lambda}{\Delta \lambda}= b \frac{dn}{d\lambda}. \]

Here \(\Delta \lambda\) denotes the minimum difference in wavelengths that two spectral lines of mean wavelength \(\lambda\) must have in order to be clearly separated (for vanishingly small slit width); \(b\) is the length of the base of the prism, \(\frac{dn}{d\lambda}\) is the dispersion of the prism for wavelength \(\lambda\).

Fig. 8. Minimum values of \(\Delta\lambda\), attainable with a prism with base length 5 cm

Fig. 9. Minimum values of \(\Delta\nu\), attainable with a prism with base length 5 cm

In Figs. 8 and 9 the course of \(\Delta \lambda\) and \(\Delta \nu = \frac{\Delta \lambda}{\lambda^{2}}\) is presented, with the adopted prism base length \(b = 5\) cm. The curves show that the value of \(\Delta \lambda\), attainable in the most favorable case, has for each prism material a characteristic, almost constant value. The more strongly a substance absorbs long waves, the larger \(\Delta \lambda\) becomes, and consequently the worse the resolving power. Hence follows the rule that, in passing to longer waves, for prisms it is necessary to use different substances in a definite sequence. An approximate value of \(\Delta \lambda\) is also obtained from the usual dispersion formula:

\[ n^{2}=\text{const}+\frac{C}{\nu_{0}^{2}-\nu^{2}}. \]

It follows from it that:

\[ \frac{1}{\lambda}\frac{\partial n}{\partial \lambda} = -\frac{C}{c^{2}}\frac{1}{n}\, \frac{\lambda_{0}^{4}}{\left(\lambda_{0}^{2}-\lambda^{2}\right)^{2}} . \]

Since in the interval under consideration \(\lambda^{2} \ll \lambda_{0}^{2}\) and \(n\) changes little, approximate values for \(\frac{1}{\lambda}\frac{\partial n}{\partial \lambda}\) and for \(\Delta\lambda\) follow from this.

Toward the short-wave side \(\Delta\lambda\) decreases, as Fig. 8 shows for the example of NaCl. The course of the curves for other substances need not continue toward short waves, since there they intersect chaotically. The curves for \(\Delta\nu\), i.e. for the maximum resolving power expressed in wave numbers, reveal an unexpected peculiarity, namely that for all substances absorption begins to appear as a disturbance where the resolving power reaches a value of approximately \(1\ \mathrm{cm}^{-1}\). This empirical rule does not follow from the dispersion formula.

Fig. 10. Minimum width \(\psi\) of a spectral line for a \(60^\circ\) prism with base length \(5\ \mathrm{cm}\). Its dependence on the wavelength \(\lambda\) and on the refractive index \(n\)

The meaning of both figures is that they show what can be achieved in the most favorable case with prisms having a base length of \(5\ \mathrm{cm}\). Some widening of the limits is still permitted by increasing the base length, but, naturally, not very much. It is another question whether these favorable values will be achieved in practice. Generally speaking, this should be answered in the negative.

Attainment of the limit presupposes a well-imaging system and a sufficiently narrow slit. When, then, is the slit sufficiently narrow? If monochromatic radiation is investigated with the aid of an entrance slit of vanishingly small width, then for a prism with base length \(b\), refracting angle \(\varphi\), and refractive index \(n\), with a symmetrical path of the rays, a spectral line is obtained whose width is determined by the angle \(\psi\) (cf. Fig. 10). For this angle the following expression follows from diffraction theory:

\[ \psi = \frac{2\sin\left(\frac{\varphi}{2}\right)} {\sqrt{\,1-n^{2}\sin^{2}\left(\frac{\varphi}{2}\right)\,}}\, \frac{\lambda}{b}. \]

In Fig. 10 the values of \(\psi\) are presented for \(b=5\ \mathrm{cm}\), \(\varphi=60^\circ\), and \(n=1.5\) and \(1.3\). Conversely, from this figure one may infer what should be understood by a “vanishingly small” slit width in each individual case. If one compares the recommendations available in the literature

about the width of slits with those in the figure, it follows that, in practice, larger slit widths are usually used in order nevertheless to attain sufficient intensity. (In reviewing the literature one may, however, find mention of a curious phenomenon: the concept of “sufficient intensity” depends on the wavelength. The shorter the wavelength of the radiation, the greater the losses required for them to be accepted as “satisfactory.”) The very small slit width to which the preceding formula leads does not correspond to ordinary radiation sources and receivers.

The calibration of the wavelengths of a prism spectrometer is usually carried out in such a way that, from the refracting angle and the refractive index of the prism, one calculates what wavelength emerges from the second slit. As the starting point, the Na wavelength from the visible region, or some other spectral line, is taken. It is highly desirable to check this calibration without fail by determining the position of a well-known and easily obtained absorption band. Shearin and Plyler^58 have recently proposed, for this purpose, the data given in Table 1.

Table 1

Normals of wavelengths (μ) for the infrared region

The problem of selecting wavelength normals for the infrared region is unquestionably important. Earlier, other investigators had already made various proposals. Draysh^59, for example, recommended the sharp absorption bands of fused quartz at 2.75 μ (cf. Fig. 22). K. Kort^55 proposed a quite sharp maximum in the reflection from crystalline quartz for the ordinary ray at 25.15 μ. However, the problem ought to be treated still more thoroughly. It is not enough that, at high resolution, one place in the spectrum

absorption is a characteristic indication for the wavelength. It is necessary to check whether, at small dispersions, this indication is not displaced to the side and whether it remains at all clearly noticeable.

15. Christiansen filters. If a plane-parallel vessel is filled with a solid substance transparent to the radiation, in the form of grains approximately of millimeter size, and this vessel is filled with a liquid whose refractive index for one wavelength coincides with the refractive index of the solid body, then for this wavelength the vessel behaves as a transparent plane-parallel plate. Rays of other wavelengths, for which this agreement of the refractive indices does not occur, undergo in the vessel a disorderly deviation in all directions. The greater the difference in the course of the dispersion of the two bodies, the more strongly the filter will act1. If the vessel is introduced into a parallel beam of rays, then rays of a narrow spectral region pass in the original direction, for which precisely the agreement of the refractive indices exists. Such a device is called a Christiansen filter. In addition to filtering, this device, as is known, can be used for calculating the unknown refractive index of some substance from the known refractive index of another substance.

Fig. 11. Course of the dispersion of NaCl

In the infrared region these filters have not yet found real application, but their significance has recently increased thanks to the investigation by Barnes and Bonner[^60]. In this work a fundamentally new application was made of the effect of the Christiansen filter in air2. This effect occurs where the refractive index of a powder passes through the value 1. This phenomenon is observed in various crystalline powders in the infrared region. A typical example of the course of the dispersion of a crystal in the infrared region is given, in its main features, by NaCl in Fig. 11. It is seen that the refractive index near \(\lambda = 32 \mu\) and \(\lambda = 54 \mu\) passes through the value 1. Owing to the proximity to the natural vibrations, the substance has strong absorption in the region under consideration. At \(32 \mu\), about \(35\%\) of the radiation still passes through a plate \(55 \mu\) thick; however, at \(54 \mu\), less than \(0.1\%\). A thin layer of powdered rock salt gives a sharp maximum of transmission only at \(32 \mu\). In Figs. 12a and 12b some examples of such transmission curves are presented.

Powdered salts are used in various ways for investigations in the infrared region. The above-mentioned Christiansen effect in air represents one of the few cases where there are easily surveyable relations. However, these relations—

...are nevertheless not so simple as in the Christiansen effect in liquids. For the value \(n=1\) there is a considerable value of the absorption coefficient, and in this case phase jumps of the waves appear

Fig. 12a. Transmission of a Christiansen filter made of powdered quartz: \(A\)—in \(\mathrm{CS_2}+\mathrm{CCl_4}\) (1:1), \(B\)—in \(\mathrm{CCl_4}\), \(C\)—in air

Fig. 12b. Transmission of powdered salt in air

in passing from one medium to another, which account for the low reflectivity.

16. Methods of residual rays. In the field of methods of residual rays, essentially nothing new has been published in the last ten years. These methods, in themselves, as the sole means of decomposition, have come to be used only in isolated cases. As methods of preliminary decomposition in work with a diffraction grating (and in individual cases also with a prism) they are acquiring ever greater importance, but in this case not 3–4 reflections are produced, but only 1–2. This rapid transition from the region of very low reflection to the region of very strong reflection here gives plates for residual rays an unquestionable advantage over absorption filters.

Fig. 13. Course of reflection from substances used as plates for residual rays

In Fig. 13 the course of the reflectivity is compared for a number of substances which in recent years have found application as plates for residual rays. From this figure it is evident which substances should be taken into account when one is concerned with some spectral region between 13 and \(200\,\mu\). For still longer waves...

no studies have been carried out. The data for LiF and NaF are based on the measurements of Korth[^61] and Holts.[^62]

Synthetically prepared single-crystal plates were used. This material substantially supplements the list of substances studied up to now.1

The curve for CaF₂, in its short-wavelength part down to 35 μ, is taken from the work of Rubens and Hettner.[^64] For this same region there are later measurements by L. Kellner,[^65] who found a uniform increase of the reflectivity in the direction of the principal maximum. For the descending part, over the entire range shown, there are only three points, obtained by Rubens[^66] by means of residual rays.

The course of the reflectivity for NaCl and KCl is taken mainly from Czerny.[^67] All the remaining curves are taken from the reports of Libisch and Rubens.[^66], [^68] In the latter measurements only the residual-ray method was used for spectral decomposition. Consequently, the course of the curves has been established only in its main features. For example, in KBr and KJ one should expect similar secondary maxima and as high a principal maximum as in the lighter alkali-halide compounds. For strontianite the course of the curve is not especially favorable, but in the corresponding region no other suitable substance is known.

17. Absorbing filters. Knowledge of the course of absorption of various substances in the infrared is of interest in many respects, and above all theoretically. However, infrared absorption is at least as important for experimental technique. The question of obtaining suitable absorbers for radiation receivers has already been discussed in the first part of this article. The use of substances as filters for radiation and windows in absorption vessels or in receiving instruments is a further question requiring exact knowledge of the course of absorption. These data are also necessary for the use of the “transparent valve” method.2

For the shortest-wavelength infrared region accessible to ordinary photographic methods, one should first mention the good glass filters that have been placed on the market in recent years. There is now a whole series of glasses that are opaque to the ultraviolet and visible regions, but transparent to long-wavelength radiation. The region of transmission of the various filters is very sharply bounded and lies in the red or in the short-wavelength

infrared region. Less satisfactory up to now are glasses that are transparent in the visible region and then at once become nontransmitting in the infrared region. In them the transition from the transmission region to the absorption region is not so sharp as in the first series.

The classical substances used in the infrared region as windows and filters are quartz in crystalline and

Fig. 14. Transmission of LiF according to Kh. V. Khols (Ann. Physik, 29, 433—440, 1937)

Fig. 15. Transmission of NaF according to Kh. V. Khols (Ann. Physik, 29, 433—448, 1937).

fused forms, fluorite, and some crystals of alkali-halide salts. In recent years the absorption behavior of these materials has been subjected to precise investigation. In Figs. 14—19 the absorption behavior of these substances is presented. In calculating the transmission, in addition to absorption proper, losses due to reflection were also taken into account. The transmission

Fig. 16. Transmission of fluorite according to earlier measurements

Fig. 17. Transmission of NaCl according to L. Kellner (Z. Physik, 56, 215—234, 1929) and according to other, older measurements

data are given for layer thicknesses of 10 mm, 1 mm, and 0.1 mm. Values for other thicknesses can be obtained from the figures with sufficient reliability by interpolation. For relatively exact values of the extinction coefficients it is necessary to consult the original works. A large part of them can also be found in the Landolt-Börnstein tables.

The transmission of crystals of alkali-halide salts in the long-wavelength infrared region, i.e., on the other side of their

own frequencies has been studied many times in recent years. Unfortunately, the hope of finding among these substances filters suitable for the longest-wavelength region has not been fully realized. The absorbing power of these substances decreases toward long waves extraordinarily slowly. Moreover, the comparatively large value of the refractive index causes considerable reflectivity. The latter, in turn, reduces the transmittance even in the absence of absorption and leads to clearly expressed interference maxima and minima of transmittance. For example, a NaCl plate \(0.15\) mm thick at \(100\,\mu\) transmits about \(15\%\), and at \(200\,\mu\) approximately \(38\%\). And only for the wavelength region

Fig. 18. Transmission of KCl according to A. Mentzel (Z. Physik, 88, 178—196, 1934) and according to other, older measurements

Fig. 19. Transmission of KBr according to A. Mentzel (Z. Physik, 88, 178—196, 1934)

Fig. 20. Transmission of crystalline quartz, cut perpendicular to the optical axis

above \(300\,\mu\) should one expect that crystals of alkali-halide salts will provide suitable filters.\(^{69}\) And yet LiF, which in this respect ought to be placed first, unfortunately has an especially high refractive index (\(n=3.1\)).

There have been attempts to grind alkali-halide salts into powder and then, dispersed in paraffin or enclosed in paraffin, to use them as a filter. The results are not entirely satisfactory.\(^{70}\)

Of greater technical importance is the course of absorption of crystalline and fused quartz. Figs. 20—24 are detailed

review. Measurements in the short-wave region were given by Drummond^71; curves in the long-wave part were obtained by Barnes^72, Cartwright^70, and B. Koch^69. Recently W. Stein made the astonishing—

Fig. 21. Transmission of crystalline quartz cut parallel to the optical axis

—observation that crystalline quartz, in the vicinity of 17 μ, possesses a transmission region previously unknown, which is clearly noticeable in layers of thickness less than 1 mm. Plates of paraffin are often used.

Fig. 22. Transmission of fused quartz

In visible light paraffin scatters more than it absorbs. Up to now there have been no exact investigations of how paraffin behaves in the infrared region.

Fig. 23. Transmission of crystalline quartz

Fig. 24. Transmission of fused quartz

In the short-wave region there is absorption corresponding to the natural vibrations of the paraffin molecule, but apparently scattering also takes place. In Fig. 25 some transmission measurements are compared. They relate partly to paraffin

with a melting point of 68–72°, partly with a melting point of 42–44°. Measurements with the latter are given by Barnes^72; the rest, in the region 50–240 μ, by Cartwright^70. Both worked with grating spectrometers. Barnes used a large dispersion. The bands which he finds in the vicinity of 100 μ may also appear in other grades of paraffin. Cartwright also finds that the more fusible paraffin absorbs more strongly below 100 μ, but that above 100 μ the difference becomes imperceptible. The remaining measurements in the short-wave part were made by L. Kellner^65.

The importance of paraffin lies in the fact that no other solid is known which has a higher transmission than paraffin (small dielectric constant). Its low transmission in the long-wave region makes paraffin at the same time a good filter for radiation.

Fig. 25. Transmission of paraffin: — melting point 68–72° C, - - - melting point 42–44° C

Especially thin layers of paraffin are obtained by lowering thin films of celluloid into molten paraffin. When removed, a thin layer of paraffin adheres on both sides. These layers still attenuate the short-wave region quite strongly.

Among the other filters that absorb the short-wave part and transmit the long-wave part, the long-known filters made of layers of soot and of paper remain in use. The application of these substances is unsatisfactory in that they do not have a completely definite composition. Measurements of the transmission of these and analogous substances in the region 20–240 μ are found in the already mentioned works of Barnes^72 and Cartwright^70. Fig. 26, concerning the transmission of various grades of paper, is taken from these works.

18. Gratings. The greatest successes in decomposing infrared radiation have been achieved by means of diffraction gratings. Their use is possible for all wavelengths of the infrared spectrum.

The use of diffraction gratings in the infrared region cannot be compared with that for the visible or ultraviolet regions without additional remarks. In the latter cases the grating serves chiefly to reveal individual lines or the structure of emission spectral bands, and also to provide high dispersion and extreme accuracy in determining wavelengths. An infrared grating, on the contrary, is inserted into a monochromator and must decompose a continuous spectrum as cleanly as possible. For this purpose, however, the grating by its very nature is not very suitable. It must be remembered that each individual line element of the grating first of all scatters, to a greater or lesser extent, all waves and, moreover,

so that scattered monochromatic waves travel in some definite direction. Only as a result of interference between the elementary beams scattered by a large number of regularly arranged linear elements of the grating is there obtained extinction of all undesirable waves and summation of a small number of desirable ones. Practice shows that this is accomplished to a considerable degree; however, the experimenter will do well to remember at all times that every irregularity in the structure of his grating manifests itself in the fact that the interference suppression is no longer faultless; he must therefore always reckon with an admixture of all other wavelengths as stray radiation. This remark does not apply to the well-known superposition of the spectra of different orders, corresponding to the basic grating formula \(m\lambda = g \sin\varphi\), according to which all waves \(\lambda\) for which the product \(m\lambda\) has the same value overlap one another. Here the circumstances are less favorable than when a prism is used, in which, as is known, stray radiation is also observed. With regard to the interfering effects that cause the appearance of “ghosts,” no information whatever can be found in the literature on infrared spectra; nor are there data on the strange intensity anomalies in diffraction spectra first observed by R. W. Wood[^73],[^74].

Fig. 26. Transmission of paper. \(A\)—black silk paper, \(0.025\) mm; \(B\)—white filter paper, \(0.13\) mm; \(C\)—black paper, \(0.13\) mm (for packing photographic plates).

For the very short-wave infrared region, ordinary optical gratings are used with the greatest success. Only for somewhat longer wavelengths are specially manufactured infrared gratings employed. A large grating constant allows further technical possibilities for giving the individual rulings of the grating a definite shape and thereby makes it possible to increase the intensity.

In recent years, wire, laminar (plate) and echelette gratings have become characteristic of infrared technique and have been successfully used. If one considers the advantages and disadvantages of each of these three types, one may arrive at the following result. We shall compare wire, laminar, and echelette gratings (with one and the same grating constant) with respect to the intensities of the first-order spectrum; in doing so we assume that the incident radiation is directed perpendicular to the surface of the grating. Let us first imagine a plane grating in which reflecting strips of width \(a\) alternate regularly with nonreflecting strips of width \(b\) (Fig. 27). Then the grating constant is \(g = a + b\). If

fix the grating constant and vary the ratio of \(a\) and \(b\), then the first-order spectrum will have the greatest intensity when

\[ a=b=\frac{g}{2}. \]

This is easy to understand from the drawing. If \(a\) is made smaller than \(\frac{g}{2}\), then the reflecting surface decreases, and with it the intensity. If it is made larger than \(\frac{g}{2}\), then elementary waves appear which have a path difference \(\frac{\lambda}{2}\) with the originally reflected waves and thereby lead to a decrease in intensity. Thus, for \(a=b=\frac{g}{2}\) the grating is the most luminous and at the same time suitable to an equal degree for all wavelengths. It is very valuable that in this type of grating the second-order spectrum disappears, because a single unit strip of width \(\frac{g}{2}\) does not turn the radiation in the direction in which the second-order spectrum could appear. Likewise all further spectra of even order are absent. It should be noted that the intensity in the first-order spectrum is equal to

\[ \frac{4}{\pi^2} \simeq \frac{4}{10} \]

of the intensity of the zero-order spectrum. The wire gratings in use belong to the type described and possess the indicated properties.

Fig. 27. Formation of the first-order spectrum in a plane grating

Laminar gratings \(^{75,76}\) are arrived at by the following consideration. It has already been said that the surface \(b\) must be blackened, since from \(b\), in the direction of the first-order spectrum, there proceed elementary waves having a path difference \(\frac{\lambda}{2}\) with respect to the waves reflected from \(a\), which leads to a decrease in intensity. The blackened surface \(b\) can be replaced by a reflecting surface if this new surface is raised by an amount \(h\) of the order of approximately \(\frac{\lambda}{4}\) (Fig. 28). From \(b\) the incident wave will be reflected earlier; the interfering path difference \(\frac{\lambda}{2}\) is removed. The waves reflected from \(b\) now travel in the same phase as those reflected from \(a\). In this case one obtains double the amplitude and quadruple the intensity in the spectrum. This is the advantage of the laminar grating over the wire grating. The property of not giving spectra of even order is preserved, since the strips \(a\) and \(b\) may still be regarded as independent unit slits. The disadvantage of the laminar grating is that the intensity in the first-order spectrum is no longer independent of the wavelength, since the ratio of the wavelength to the step height \(h\) begins to play a role. The calculated distribution of intensities is shown in Fig. 29. Since technically אויס

pletion of the grating does not always exactly correspond to the theoretical form, the actual distribution of intensities does not always exactly correspond to the calculated one. The theory of the laminar grating is considered in detail in Hölberg’s work^77.

We arrive at stepped gratings, also called echelettes^78, if, on an initially flat grating, we make

Fig. 28. Origin of the first-order spectrum in a laminar grating

Fig. 29. Approximate course of the intensity curve \(I\) in the first-order spectrum for a laminar grating \((h = 5\,\mu)\) — and for a wire grating ------
(In the figure: “laminar grating”; “wire grating.”)

oblique reflecting surface elements at such angles that the incident wave is geometrically reflected in the direction of the first-order spectrum (Fig. 30). Then in the first-order spectrum we obtain the intensity which usually appears in the zero-order spectrum. In addition, in comparison with the types of gratings described above, here the width of the reflecting surfaces is doubled. The intensity for a stepped grating is then

\[ \frac{4\pi^2}{4} \sim 10 \]

times greater than the intensities for the first types of gratings. These great advantages are opposed by the following drawbacks: a second-order spectrum appears. Further, there is only one intense first-order spectrum. The other first-order spectrum is very weak. This is a drawback, since checking both first-order spectra is very important for accurate measurement of wavelengths and for control purposes. Only for one wavelength \(\lambda_m\) are the geometrical conditions fulfilled which give the highest intensity in the first-order spectrum. For all other wavelengths the intensity is lower. Thus, as with the laminar grating, there is a nonuniform distribution of intensities in the first-order spectrum. Since the wave \(\lambda_m\) is thrown into the direction of the first-order spectrum by means of “geometrical reflection,” and every other wave by means of “diffraction,” one might expect a very rapid decrease in the intensity of the spectrum when moving away from \(\lambda_m\). This, however, is not the case. Calculation shows that the fall of intensity in a stepped grating occurs approximately as rapidly on both sides of the position of the maximum as in a laminar

Fig. 30. Origin of the first-order spectrum in a stepped grating

of the grating. It further turns out that the decrease of intensity for both types of gratings depends only slightly on the grating constant. Qualitatively, these circumstances can be illustrated as follows: a step grating recently used for one work\(^{51,b}\) has a constant of \(22.2\,\mu\), a blaze angle \(\varepsilon = 24^\circ\), and an intensity maximum at \(\lambda_m = 18\,\mu\) \(^{1}\).

With such a small width of an individual reflecting strip, diffraction for a wave of \(18\,\mu\) is so large that one may speak less of geometrical reflection in the proper sense of the word than of approximately uniform scattering into a half-space. This circumstance is the reason why the dependence of intensity on wavelength in the first-order spectrum remains within narrow limits. If a larger grating constant is chosen, then with a change of angle the intensity will decrease more rapidly in both directions; this will not occur with a change of wavelength, since the waves shift more closely together as the grating constant decreases.

In the most favorable case the intensities of wire, laminar, and step gratings are in the ratio \(1:4:10\).

On spectral investigations with the aid of gratings in the long-wave infrared region, a report by Randall\(^{51,b}\) has recently appeared, to which it is necessary to refer here.

LITERATURE

The list of literature does not claim to be complete; it includes only the papers mentioned in our review.

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\(^{1}\) The grating is set so that the reflected radiation travels in a direction close to that of the incident radiation. For the first-order spectrum in this case \(\lambda = 2g\sin(\alpha + \varepsilon)\). Owing to the presence of the factor \(2g\), the first-order spectrum appears, with oblique setting of the grating, approximately around \(24^\circ\). For a wavelength of \(18\,\mu\) the intensity has a maximum; for \(25\,\mu\), according to an approximate calculation, it falls to about \(75\%\).

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1. The generally correct course of the reflectivity can already be found in the work of O. Reinkober and M. Blüth.[^63] ↩↩↩↩

2. Die “durchsichtige Klappe.” The method is known under the name of the “transparent screen” method and was first developed by Rubens (Verh. d. D. Phys. Ges., 15, 109, 1896). The substance used as the screen absorbs the radiation under investigation while transmitting the rest. The difference between the deflections of the receiver obtained when measuring the radiation with the screen and without it gives the magnitude of the radiation under investigation (see also Schäfer and Matossi, Infrared Spectra, pp. 67–68, ONTI, 1935). Translator’s note. ↩↩↩