Bibliography

M. Berek, Fundamentals of Practical Optics, translated from the German under the editorship of Acad. S. I. Vavilov, GTTI, 1933.

Berek’s small book (136 pp.) contains a very concise exposition of the foundations of geometrical optics as applied to the theory of optical instruments, and moreover from a special point of view, which the author calls “practical,” meaning by this the application of theory to the calculation of optical systems. In setting forth the basic concepts of the general theory of optical systems and in particular the results of Seidel’s third-order aberration theory, the author has in mind above all to illuminate the significance of theory for the calculation of optical systems and to enable the reader to enter into the range of theoretical questions before proceeding to the practice of computational optics; he does not deal with methods of calculation in the proper sense of the word, i.e. with the construction of equations, methods of finding their solutions, and methods of establishing the constructive elements of optical systems. Therefore the book cannot serve as a manual of computational optics.

The exposition presupposes a reader already familiar with the elements of geometrical optics; all the material is presented in an extremely compressed form, in most cases without derivations; reading the book requires great attention and effort. After a brief introduction, which gives a characterization of the errors of real optical systems, there follows a chapter setting forth the optics of an ideal system (in the paraxial region), and then a chapter containing formulas for the trigonometric calculation of ray paths in optical systems and for obtaining thereby the magnitudes of aberrations, followed by a description of methods of graphical representation of aberrations.

Next comes the central part of the book, presenting Seidel’s theory of aberrations, with special attention paid to the geometrical interpretation of the individual coefficients of Seidel’s expansion; for calculating these coefficients, formulas are given, whose use is illustrated by a large number of examples, chiefly from the field of photographic objectives. In these examples the author shows how the quality of a system can be evaluated without resorting to exact trigonometric calculations of ray paths, and how the system can be improved by following the changes in Seidel’s coefficients and their individual terms when the constructive elements of the system are changed; the analysis of the individual examples gives the author occasion to make many observations and indications of great value to one beginning work in the field of computational optics.

The book has a somewhat polemical character; it is directed against that school of opticians which traces its origin, probably, to Steinheil and which almost does not use theory in its calculations. Having usually had great experience and a stock of ready-made systems of every kind, the computational opticians of this school seek out their systems exclusively by trials with the aid of exact trigonometric calculations of ray paths, with subsequent interpolation or extrapolation of the system elements in order to improve it. Berek attempts to convince the reader that, in many cases, Seidel’s theory provides substantially more effective paths to the improvement of a system and guards against trials with hopelessly poor systems. Since the application and use of the theory in solving prac-

tical problems requires good training, mathematical development, and command of a rather complex system of relations among quantities, the beginning optician easily takes the path of trial and error—especially easily if he has at his disposal the labor of several calculators. Bereck’s book can help the beginning opticians of our young optical industry to resist the temptation to proceed along the line of least resistance, and can persuade them to think when calculating, and not merely to try things out.

Because Russian terminology in geometrical optics has not been developed, and the author’s terminology has its own peculiarities, the translation of the book encountered difficulties; therefore objections could be raised against some of the terms. Two unfortunate distortions of proper names are conspicuous: “Scheidingel” instead of “Steinheil” and “Kerbers” instead of “Kerber.”

The appearance of the translation of Bereck’s book is timely and undoubtedly useful; but, of course, the book cannot have a large circle of readers. All the greater is the merit of the State Technical-Theoretical Publishing House, which has issued a useful book that cannot count on great commercial success.

A. Tudorovskii