TWO MONTHS AGO, in this department in the October number, Norbert J. Schell, 1019 Third Avenue, Beaver Falls, Pa., presented the fundamentals of the new type of telescope invented by D. D. Maksutov of the State Optical Institute, Moscow. In the following article, he concludes that discussion for the immediate present. In the meantime 13 advanced amateurs, whom we have dubbed "The Mak Club," though there really is no formal organization other than a common interest and consciousness of a common, parallel aim, have ordered 8.2" disks (slightly larger and more finished-molded roughly to curve-than was mentioned two months ago) of optical glass of suitable specifications from Corning Glass Works, with which to make the thick meniscus lens which, with a spherical primary mirror, is the basic part of the Maksutov telescope. "The Mak Club" is open to all martyrs to science who wish to be pioneers, and more glass is said to be available, the disks alone at $32.50 or with a grinding tool of similar deep-curved shape and non-optical glass, at $40. Schell's discussion follows:

In the first article on the new Maksutov type of telescope, in the October number, which was necessarily of a general nature, it was possible to mention only certain of this telescope's features. Since Maksutov has offered his design as a solution of the problem of producing a telescope having a wide field of good definition, free from chromatic aberration and at the same time possessing the important advantages of simplicity and ease of construction-features not found in any previous type-it is felt that a further and more detailed analysis of its operating principles should be made in this second article. It is hoped that by this means, and as a supplement to the first article, the working principles will be covered, and that the two articles will serve as a foundation for later discussions.

CORRECTING ACTION-As stated in the first article, in the Maksutov telescope the negative spherical aberration of the spherical mirror is compensated by the positive spherical aberration of the meniscus lens. This is accomplished as a part of the overall diverging action of the lens. In the example given, of an 8" aperture, f/4 system, the radius of the mirror was stated to be 65.856". If this mirror were reflecting incident parallel light, the rays from a very small area at its center would come to a focus at a distance of half its radius, or 32.928", while the rays from a zone of 8" diameter would have a focus of .122" shorter, or 32.806". (This is in accordance with our familiar formula of , where r is radius of zone and R radius of mirror.) In the Maksutov, however, the distance S from mirror to focal plane comes out as 33.6". From this it can be seen that the meniscus acts as a negative lens, diverging the rays and lengthening the distance from mirror to focal plane for all zones including the center. The action gradually increases from the center toward the periphery, so that the rays from all zones are brought to (practically) the same focal plane. In this case, within tolerances mentioned below, we can consider the minimum amount of lengthening to be .672" at center, and the maximum .794", at outer zone, indicating the effect of the longest and shortest negative focal lengths, respectively, of the lens; in other words, its spherical aberration. (I am indebted to J. H. King for the information that designers usually refer to a weak lens of this kind as a lens of "zero power"-a point well taken and worth remembering.)

RESIDUAL ABERRATION-In the Maksutov system, with spherical surfaces on both the meniscus lens and mirror an overall correction is attained in the above manner, but it is not possible to secure an exact theoretical correction for all zones, nor for all wavelengths of light, and thus residual aberrations, both spherical and chromatic, remain. The extent of these residual aberrations determines the upper limits of aperture-focal ratios and aperture dimensions possible without deterioration of image quality.

In determining the effect of theoretical (or actual) aberrations on image quality, we must take into consideration the maximum resolving power of any given aperture as associated with the wavelength of light. Briefly, it has been shown by mathematical methods that, in a theoretically "perfect" optical system, the image of a point source does not conform strictly to geometric proportions, but consists of an interference pattern having a central concentration or disk, of finite size, surrounded by so-called diffraction rings, with most of the light in the disk; and that the diameter of the disk is inversely proportional to aperture diameter with a given wavelength of light. This disk is also known as the "Airy" disk. It has also been shown that if any aberrations in an optical system do not result in optical path differences between source and image greater than plus or minus 1/4 wavelength of light, they will cause neither a noticeable change in the size of this disk nor in its relative intensity. In aiming for unimpaired image quality, aberrations within the above limits may therefore be considered as allowable tolerances.

SPHERICAL ABERRATION-The control of residual aberrations consists of such adjustment of the design factors as to bring about a balanced correction with respect to a plane of "best focus," which may be referred to as the "focal plane," having as nearly as possible a minimum variation for different wavelengths of light and a minimum tendency to produce coma. It is obvious that, where there are differences, the "focal plane" will fall somewhere between the shortest and longest focal lengths. The differences may be termed displacements, either plus or minus, relative to the "focal plane." While spherical aberration concerns theoretical focal lengths of different wavelengths for the various zones of the aperture, a satisfactory balance can be found by adjustment for a single intermediate wavelength, provided chromatic dispersion is also balanced as will be described. By calculating the theoretical longitudinal displacements of focus for different zones in terms of angular dimensions, the "focal plane" is established as the plane in which equality of angular aberration is found for the extremes of such aberrations both plus and minus. The aim of the adjustment is to reduce the angular aberration at the "focal plane" to a minimum.

In the design data given in the October article for the f/4 system, the minus extreme (corresponding to shortest focal length) is identified with the 85 percent zone of aperture, and two identical plus extremes with the 35 percent and 100 percent zones. The "focal plane" lies between the focus for the 85 percent zone and that for the 100 percent zone. (The focal lengths of the 35 percent and 100 percent zones are not identical, as angular aberration decreases with aperture.) Thus adjustment is the best possible for spherical surfaces, as given by Maksutov, and is perfectly logical, but a fuller treatment will have to be postponed until such time as a mathematical discussion can be prepared.

CHROMATIC ABERRATION-As the meniscus lens is a single lens, it is natural that the question of its chromatic dispersion should arise, even though it is understood that this lens has a very long focus and therefore causes little dispersion. It is obvious that considerable variation in chromatic aberration could be expected, in a system of this kind, among lenses having different design characteristics. Maksutov found that, if the lens was made of sufficient thickness and suitable radii, chromatic aberration could be eliminated at the focus of a certain chosen zone of the aperture and held to a negligible amount for other zones.

The action for this zone is shown in schematic form in the drawing. The usual spectral lines C (in the red) and F (in the blue) are shown since the brightest part of the visual spectrum falls between these lines. The F line is refracted more than the C line and consequently diverges more after passing through the lens, so that it reaches the mirror at a point where it is reflected at a greater angle than the C line and thus meets the C line on the axis. For zones outside of the zone indicated, the C and F lines cross before they arrive at the axis, and for the inner zones they do not meet before crossing the axis. In the design data given, this zone is near the zone of extreme minus spherical aberration for mid-wavelength, previously mentioned. Stated differently, the dispersion, relative to this zone, is over-corrected for outer zones and under-corrected for inner zones.

This (corrected) zone is chosen so that the dispersion on either side of it, at maximum, is approximately the same with respect to theoretical angular dimensions at the focal plane. Actually, the dispersion (within the above limits) represents the difference between the residual spherical aberrations for the C and F lines and when distributed as indicated, consists of only a fraction of the total aberration.

DESIGN LIMITS-If the aberrations are controlled and minimized in the above manner, the allowable tolerances first mentioned fix the upper limits for design with maximum resolving power. These limits are those given in the table with the first article, and it is felt pardonable to repeat that they apply to spherical surfaces only. It is well, however, to consider that these limits are theoretical and, as such, can be expected to be attained with unimpaired image quality only if the glass specifications as well as radii and thickness dimensions are exactly realized. It is obvious that a departure in any of these factors will have the effect of widening the aberrations to some extent. On the other hand, as may be inferred from the table, the aberrations quite rapidly become smaller than the tolerances for resolving power as the aperture-focal ratio is reduced below the indicated upper limit for a given aperture. By taking a somewhat smaller aperture-focal ratio than the upper limit, in an actual design, we secure the advantage of a certain amount of tolerance for glass characteristics as well as for radii and thickness, which is highly desirable from a practical standpoint.

It is hoped that the amount of freedom in this respect can be determined and made available as a guide within a reasonable time. The very attractive prospect of producing a telescope capable of superlative performance, requiring nothing more difficult than spherical surfaces of a reasonably accurate radius, would seem to dictate the logical choice of design.

COMA AND FIELD CURVATURE-It is not feasible to outline coma without a-more or less complete mathematical treatment, which present space does not permit, however, it can be understood in the Maksutov by comparison with the action in the Schmidt camera. It will be recalled that the correcting plate in the Schmidt is located at the center of curvature of the mirror, and for that reason light from any part of the field is reflected symmetrically; consequently coma is not produced. In the Maksutov, while the lens is not located as far from the mirror, the action is similar, and coma is reduced to a negligible quantity over a wide field. In the data previously given, for the f/4 system, a field diameter of upward of two degrees is indicated without noticeable coma.

This brings up the question of field curvature, which was not previously mentioned. In this respect the Maksutov is again similar to the Schmidt camera; while its field is curved, the curvature is convex toward the mirror. This is the opposite to that in ordinary telescopes and should be of advantage in visual instruments, especially for short focal lengths, as the field curvature, concave toward the eyepiece, will be in the same direction as that of usual eyepieces, providing a closer "match" between their fields.

APPLICATION-Pending further descriptions of more complex designs available with this system, a final word is added regarding the possible applications of the fundamental system so far mentioned. As it is a corrected system, it can be considered and used the same as a corrected mirror, in any of the following applications:

1: For direct photography, with convex sprung films.

2: As a Newtonian, with diagonal, and so on, in any of its forms, and should be an exceptionally good ''Richest Field" instrument; of course, with suitable eyepieces for this purpose.

3: As a primary for a Cassegrain- in which case the secondary would have to be corrected to hyperbolic form in the regular manner.

4: As a primary for a Gregorian- also with corrected secondary of usual elliptical form.

5: Off-axis forms. Since what is true of the whole is true of a part, a section of diameter representing somewhat less than half of the full aperture in the fundamental design, wholly on one side of the axis, will function without any obstruction in the light path. This achievement, with spherical surfaces, requires special constructional considerations, also reserved for future articles.

In both the Cass and Greg, as mentioned above, the secondary focal planes would not be free of coma over as wide a field as at the primary focus, but this should not be noticeable in the smaller fields usually available in such instruments.

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