F. A. Korolev. High-Resolution Spectroscopy. Gostekhizdat, Moscow, 1953, 278 pp., price 8 rubles 25 kopecks.

F. A. Korolev’s monograph sets out the theory and practice of high-resolution spectroscopy. The theory of the echelon, the Lummer–Gehrcke plate, and the Fabry–Perot etalon is presented by the author with allowance for diffraction phenomena. At the end the questions of the width of spectral lines are discussed, as well as problems connected with monochromatic light sources. In the present review we shall touch only on the theory of spectral instruments as expounded by the author. It should be noted that, since the good book by S. E. Frish, Technique of Spectroscopy, published as far back as 1936, no books devoted to the theory of high-resolution spectral instruments have appeared. This fact in many respects obliged the author of the book under review, and it must be acknowledged that his monograph is a significant step forward in the theory of spectroscopy.

Chapter 1 gives a detailed theory of the echelon, suitable for the general case in which the angle of incidence of the light differs from zero. Such a complete exposition is, beyond doubt, the first. The fundamental difference between an echelon and plane-parallel plates is explained, warning other investigators against reducing instruments of both these types to a single optical scheme.

With an equally detailed exposition of the theory of the Lummer–Gehrcke plate, in Chapter 2 the author convincingly shows that neglect of diffraction phenomena in the plate leads to the paradoxical conclusion that the law of conservation of energy is violated. The development of the theory of this instrument is undoubtedly a great merit of the author.

Chapter 3 is devoted to the principal instrument of interference spectroscopy—the Fabry–Perot etalon. The author considers the dependence of the intensity of light in the interference pattern of the etalon on the optical characteristics of its mirrors and of the transparent medium between them. The author indicates that a diaphragm placed behind the etalon, cutting off multiply reflected beams, diminishes the resolving power of the etalon; the dependence of the effective reflection coefficient of the mirrors of the etalon on the diameter and thickness of the etalon and on the direction of the incident rays is given; the reduction of resolving power can be avoided by additional diaphragming of the entrance aperture of the etalon. The author calculates the influence of the accuracy of manufacture of the etalon mirrors on its resolving power. It is shown how, in the case of a multiplex, one should calculate the ratio of the thicknesses of the individual etalons.

In his monograph the author has approached the fundamental questions of spectroscopy in a new way and has given a number of new and interesting conclusions. Unfortunately, F. A. Korolev’s monograph is not free from certain substantial shortcomings, which should be corrected in the next edition.

First of all, the author may be reproached for inconsistency. In the preface he contrasts ordinary photometric concepts with the “unclear term intensity.” However, he uses this “unclear term” throughout the entire exposition of the theory of spectral

devices. Instead of the “usual photometric concepts,” which he promised to use, he introduces (without making any reservation anywhere) his own concept—“light force,” which is a characteristic not of the light source, as is generally accepted, but of the light beam that has passed through the device. The expediency of introducing such a concept is doubtful. This “light force” is not invariant with respect to the refractive index of the medium: when a light beam passes without losses from one optical medium into another, this light force changes in proportion to the ratio of the squares of the refractive indices of the two media, although the energy of the light beam does not change. It seems to us more logical to use the already existing physical concept—the reduced brightness of a light beam; for brevity one may assign to this quantity the old term “intensity of light.”

In striving to relate wave and photometric quantities to one another, F. A. Korolev introduces the concept of the “amplitude of a light oscillation incident on \(1\ \text{cm}^2\) of an opening.” In introducing such a concept he proceeds from the fact that the resultant oscillation in the focal plane of a lens placed behind a diaphragm opening is composed of elementary oscillations arriving from elements of the surface of the light wave incident on this opening; in the case when the path difference from each of these elements is equal to zero, the amplitude of the resultant oscillation in the focal plane of the lens is proportional to the width of the opening or, taking into account a second dimension, proportional to the area of this opening.

Starting from these correct propositions, F. A. Korolev unlawfully applies concepts characterizing the diffraction field in the focal plane of the lens to the surface of the light wave incident on the lens. Thus, since the intensity of the incident light is proportional to the square of the amplitude, F. A. Korolev arrives at the erroneous conclusion that the intensity of the light incident on the aperture of the diffraction grating in the direction normal to it is proportional to the square of the width of the grating aperture (p. 19), whence it follows (taking into account the second dimension of the grating) that the intensity of the incident light is proportional to the square of the area of the aperture. From elementary physical considerations it follows that the “intensity of light” incident on a grating is proportional to the width of the latter. As for the intensity in the diffraction maximum, it is indeed proportional to the square of the width of the grating, and since in this case the width of the maximum is inversely proportional to the width of the grating, the total amount of diffracted light will be proportional to the width of the grating, i.e. to the magnitude of the incident luminous flux. The conclusion reached by F. A. Korolev, in passing from wave quantities to photometric ones, contradicts the law of conservation of energy: according to his formulas, the intensity of light in the diffraction maximum may be equal to the intensity of the incident light; where, then, is the light energy taken that goes into forming the diffraction pattern in other directions?

It should be noted that not only is the interpretation of certain quantities given by F. A. Korolev incorrect; the calculations themselves are also completely wrong. It is surprising that the conclusion obtained by the author on p. 254 concerning proportionality between the magnitude of the luminous flux and the area of the aperture did not seem to him to contradict his own assertion on p. 19 that the intensity of the incident light is proportional to the square of the width of the aperture of a diffraction grating.

In considering the distribution of light intensity in the interference pattern of a Fabry–Perot etalon when a plane wave is incident on it, F. A. Korolev takes into account diffraction only at the entrance aperture, i.e. he considers the special case in which a diaphragm is placed in front of the etalon

a diaphragm of such a size that the beam is not cut off by the etalon mirrors during multiple reflections; this latter circumstance is nowhere mentioned, although the monograph repeatedly points out that a complete accounting of all diffraction phenomena is being carried out. In practice it often happens that the entrance and exit apertures of the etalon are the same; then the introduction of a “diffraction factor” only at the entry of the beam into the etalon makes no sense. If many plane waves are incident on the etalon (which occurs with a broad light source), then considering the diffraction from the diaphragm in front of the etalon is altogether meaningless. It should be indicated that the intensity at any point of the etalon interference pattern is proportional to the intensity that would exist for the given etalon arrangement but in the absence of mirrors in it; in other words, if the diaphragm arrangement in front of the etalon forms a diffraction pattern, then the interference rings will be visible against the background of this pattern.

On pp. 106–107 it is incorrectly stated that the transmission of the entire etalon depends on the value $\vartheta$ (mirror transmission). From this the author draws the erroneous conclusion that “it is exceptionally important that, for large $\mathcal{R}$, the value $\vartheta$ retain a relatively high value.” In reality, however, the intensity of the etalon interference pattern depends only on the ratio of $\vartheta$ to $\varkappa$ (absorption in the mirrors), and therefore it is important that the value $\vartheta/\varkappa$ be sufficiently large; as for the values of $\vartheta$ and $\varkappa$ themselves, each of them separately may have very small significance.

Further, on p. 111, the author arrives at the conclusion that it is inexpedient to work with a glass etalon because of absorption in the glass; it should have been stipulated that this conclusion applies only to thick plates (20 mm and more), and that applying it to thin plates of the order of 3 mm would be incorrect, since absorption of 0.3% or less has little effect on the resolving power of the etalon and on the intensity of its rings.

In presenting the theory of the multiplex (pp. 122–129), the author does not give formulas for the intensity distribution in the interference pattern of this instrument; we note that the formulas usually given do not take into account the effect of multiple reflections between the two etalons of the multiplex.

In Appendix 5, pp. 271–272, the author asserts that interference films of cryolite and zinc sulfide (on a glass substrate) make it possible to obtain a reflection coefficient above 0.95, while absorption in such films is allegedly “much less than in metallic ones.” This assertion remains wholly on the conscience of the author, who uncritically copied the corresponding passage from the review article by G. V. Rozenberg cited by him (UFN, vol. 47, pp. 1–50, 1952), although the experimental material presented in the latter refutes this assertion. In multilayer interference reflectors obtained by evaporating dielectrics onto a glass substrate, which possess a reflection coefficient above 0.95, absorption in the visible region of the spectrum is greater than in silver mirrors. Improved reflectors are obtained by depositing 2–4 dielectric films on a silver substrate.

Despite all these shortcomings, which can easily be corrected in a subsequent edition, F. A. Korolev’s monograph is of great interest to persons engaged in spectroscopy or coming into contact in their work with this field of physics, and the appearance of this book should be warmly welcomed.

K. I. Tarasov