FAMILIAR OPTICAL DEVICES SUCH as eye glasses and binoculars form an image by refracting light with glass lenses. Yet when an amateur makes a telescope its main optical element is almost always a mirror. Why? Primarily because in making the mirror of a reflecting telescope the amateur need grind and polish only one optical surface. If a refracting telescope is to bring images in various colors to even roughly the same focus, its objective lens must ordinarily consist of two pieces of glass. Thus the maker of a refractor objective must grind and polish four surfaces. To make matters worse, the edges of both lens elements must be ground and fitted to a precisely machined cell so that their curves are centered on the optical axis of the telescope.

J. H. Rush of Boulder, Col., suggests an easier way to make a refractor: a remarkable design which, although it is completely corrected for color, has an objective lens consisting of only one piece of glass!

Rush writes: "Chromatic aberration has plagued the designers of refracting telescopes from the time of Galileo down to the present. This defect causes images to be blurred by overlapping colors and to be surrounded by colored halos. Yet a truly achromatic (color-free) refractor design has been available since 1899. In that year a German optical worker named L. Schupmann published a small book on what he called 'medial' telescopes. His work was curiously neglect ed. Lately it has been rediscovered and adapted to modern telescope designs by James G. Baker of the Harvard College Observatory, to whom I am indebted for much of my information on the Schupmann system.

"A brief review of the evolution of refractors may focus some light on the advantages and disadvantages of the Schupmann telescope. Isaac Newton decided (on the basis of inadequate experiments) that 'all refracting substances diverge the prismatic colors in a constant proportion to their mean refraction'; that is, the focal lengths of a lens for two particular wavelengths of light must always be in the same ratio, regardless of what kind of glass the lens is made of. This conclusion was in error, but it led Newton to decide that a color-compensating lens was impossible because any two pieces of glass that could cancel the dispersion of colors would also cancel the desired refracting power. He turned his attention to reflectors, and his great reputation discouraged others from challenging his conclusions.

"About 1730 Chester M. Hall of England disputed Newton's authority and produced the first achromatic lenses. It is interesting to note that Hall was encouraged in this undertaking by his observation that the various 'humours' in the eye produce an achromatic image. He concluded that a combination of different glasses should also do so. His observation was just as erroneous as Newton's (the eye is not achromatic), but Hall's error was optimistic and led to a notable advance in optics.

"Hall did not do much with his invention, but a few years later John Dollond independently invented the achromat and promoted it so energetically that it revolutionized telescope design. Achromatic lenses take advantage of the differing optical properties of various kinds of glass. A converging (positive) lens, usually of crown glass, is combined with a diverging (negative) lens, usually of flint glass. Because the dispersion of the flint glass ( its power to bend light of one color more than another) is greater than that of the crown glass, the flint element can be designed to reverse and cancel the color dispersion of the crown element without entirely canceling its mean refractive power [see drawing in Figure 3]. The resulting 'achromatic doublet' is commonly used as a telescope objective, and the same principle is of course applied in more complex lens systems.

"Unfortunately the doublet does not give perfect color correction. Color dispersion by glass or other substances is irrational. That is, the refraction for different colors is not proportional to their wavelength. Hence when refraction is plotted against wavelength, the resulting curves for different glasses do not have the same shape. A doublet can be designed to bring two chosen wavelengths to a focus at exactly the same distance from the lens; intermediate wavelengths fall a bit short, and those beyond the corrected region deviate seriously from the common focus. This 'secondary spectrum' is quite troublesome in a large instrument. The 40-inch achromat at the Yerkes Observatory, for example, focuses the yellow-green about a centimeter nearer the lens than the red and blue for which it is corrected. If three different kinds of glass are combined, three wavelengths can be brought to a common focus. Such a lens is called an apochromat. It gives a much better color correction than does the achromat, but is costly and suffers from other disadvantages.

"In complex lens systems an additional defect called lateral color usually appears. Such a system may focus all wavelengths of interest at practically the same distance from the last lens element. Yet the images in different colors may be of different sizes, so that they do not coincide except on the optical axis of the telescope. The result is an overlapping color effect similar to that produced by the more familiar longitudinal color just discussed.

"At this point one may ask: Why bother with refractors at all? Mirrors are entirely free of chromatic aberration, since the simple law of reflection holds for all wavelengths. The answer is mainly that a mirror system usually wastes more light than a good achromatic objective (a minor objection), and that, usually having only one figured surface, the mirror does not permit adequate control of other aberrations.

"The ideal mirror shape for focusing parallel rays, with which we are concerned in an astronomical objective, is the paraboloid. Its spherical aberration is zero. All light coming into such a mirror parallel to its axis is reflected (within the limitations due to the wave properties of light) to a single focal point on the axis. So far, so good. But parallel rays coming in at an angle to the axis, such as the light from a star that is not centered in the field, do not converge to a common focus-as any telescope-making enthusiast is painfully aware. The image is distorted by two types of aberration: astigmatism and coma. In the case of astigmatism, an object point off the optical axis is imaged as two lines at different focal distances and perpendicular to each other. The effects of coma, on the other hand, resemble those of spherical aberration. But instead of a point-source coming to focus as a circular patch of light in the plane of the image, as in spherical aberration, coma results in a comet-shaped patch. Moreover, the image field is a curved surface.

"There is nothing you can do about these defects. You have already determined the shape of the mirror, making it a paraboloid to eliminate spherical aberration; and you have determined its scale, to obtain the desired focal length. You can do nothing more with a single surface. Of course, in the case of compound reflecting telescopes, the experts do some tricks with secondary mirror surfaces and sometimes with special correcting lenses, but most amateurs leave these strictly alone.

"In a simple lens the index of refraction of the glass and the difference in the curvature of the two surfaces determine the focal length. By 'bending' the lens- keeping this difference constant while changing both radii of curvature-the designer can eliminate all coma and nearly all spherical aberration. Of course the designer still has to live with astigmatism, chromatic aberration and curvature of the field. In designing a doublet, he computes powers for the two elements that will give the desired focal length and color correction. Then, by suitably bending both elements independently, he eliminates both coma and spherical aberration. The perfection of these corrections depends very much on some subtle wisdom in the choice of glasses, which the designer usually attains by surviving his previous efforts.

"Here, then, is the principal advantage of the refractor. A doublet or triplet lens affords the designer degrees of freedom enough to correct the most troublesome aberrations independently. However, astigmatism remains a problem. It is an obstacle to good definition over wide fields, and usually limits an astronomical refractor to a very small area of the sky. But a reflector is even more sharply limited by astigmatism and coma.

"About 1930 Bernhard Schmidt of Germany came up with an excellent solution to these limitations with his now-famous lens-and-mirror combination. His instrument is especially advantageous for fast photography of wide angular fields at low magnification. Its peculiarly curved lens, or 'correcting plate,' is an obstacle to any but the most skilled opticians, but modified designs using spherical lens-surfaces have eliminated even that difficulty for some purposes. Yet the Schmidt is not a substitute for the long-focus refractor, so useful for astronomical observations that require a relatively large image. A Schmidt telescope is twice as long as a simple reflector or refractor of the same focal length.

"Schupmann described two types of unconventional telescopes: the brachymedial (or brachyt) and the medial. The brachyt is not capable of correcting chromatic aberration completely. For that reason I have not investigated its possibilities in detail. It has the great advantage of compactness and might be capable of acceptable performance over a limited field and spectral range, if carefully designed. The optical path of the brachyt is depicted in the accompanying drawing [Figure 1].

"Schupmann's other design, the medial, is something else again. It is capable of practically perfect correction of chromatic aberration over the full photographic spectral range. The medial, like the Schmidt system, uses both lenses and a mirror, but it is mainly a lens instrument and even in its simplest form it need not be much longer than the equivalent simple refractor. The objective is a simple lens of a good telescopic-quality crown glass, such as borosilicate crown No. 2 (BSC-2) or Schott boronkron No. 7 (BK-7). It is designed to have the desired focal length for some intermediate wavelength and is bent for zero coma.

"The mirror of the Schupmann telescope is called a Mangin mirror. It is simply a negative lens whose convex back surface is

aluminized [see Figure 4]. It is made of the same glass—preferably the same melt as the objective.

"The secret of the medial's performance is found in the field lens. Its function is to image the objective onto the Mangin mirror. Optically the effect is to superimpose the objective and the Mangin so that their combined dispersive power is that of a flat plate. The Mangin is bent so that its surface contributes enough positive power to form the final image.

"You can easily see how the medial tends to correct chromatic aberration. Since the lens power of the Mangin is negative, the focal length of the Mangin is greater for blue than for red light. But the primary image formed by the objective in blue light is nearer the objective and thus farther from the Mangin than the red image. Consequently the final image in both wavelengths will tend to fall at or near the same distance from the Mangin, because the difference in object distance is offset by the difference in focal lengths of the Mangin for blue and for red light. Detailed calculation shows, however, that this correction cannot be exact for more than two wavelengths unless a field lens is used to I image the objective onto the Mangin.

"If the field lens were perfectly achromatic, the Mangin could be designed to form4final images of the same size and at the same distance from the Mangin in all wavelengths. Practically, the field lens cannot be perfectly achromatic, and its secondary spectrum produces a slight amount of lateral color in the final image. Even a simple,. single-element field lens will reduce the secondary spectrum in the final image to a small fraction of that produced by an achromatic doublet objective of equivalent power. A good crown-flint field lens, designed for the image and object distances at which it is to be used, contributes an entirely negligible residue of chromatic aberration over the spectral range and image fields ordinarily used.

"To sum up: The medial telescope uses a negative lens to cancel the dispersion of a positive objective of the same glass, and then interposes a concave mirror to intercept the light that has been so treated and focus it as the final image. Why bother? Why not forget the lenses and just use a mirror in the first place? The complication is justified by the superior optical corrections that can be made in the medial telescope. The medial telescope has several advantages, in addition to freedom from color, over the ordinary refractor. Its spectral range is not limited by the absorption in flint glass because other materials can be substituted-even in the field lens. The surfaces of the objective are less sharply curved than those of the equivalent achromat, so that residual aberrations are reduced and the mechanical strength of the lens is improved. The positive and negative powers of the objective and Mangin result in a nearly flat image-field.

"A unique advantage of the Schupmann medial is its adaptability to the Lyot solar coronagraph. The essential features of this instrument are: a simple objective to minimize scattering of white light into the system, a metal disk to eclipse the bright solar disk at the primary image, and a field lens and diaphragms to eliminate white light introduced by diffraction and reflection at the objective. To meet these conditions most coronagraphs have suffered the disadvantages of chromatic images; the medial offers an ideal way to get a colorfree image without interfering with the essential optics of the coronagraph.

"Coma causes no trouble, because it is eliminated in the objective by a suitable choice of radii, and in the Mangin by making the image and object distances equal for a mean wavelength. Two difficulties arise, however. Since the shape of the Mangin is totally determined by the twin requirements of color correction and mirror power, it is not possible with spherical surfaces to meet these conditions and at the same time shape the Mangin to cancel the spherical aberration of the objective. Probably the best way out of this difficulty is to figure an aspheric surface on the front of the Mangin, departing just enough from a sphere to bring the spherical aberration of the entire system to zero as determined by knife-edge or other test at the final image. This chore is comparable to parabolizing a mirror objective, but is tricky because of the relatively small size of the Mangin. It is possible, of course, to make the corrections on the primary, which is somewhat easier to work because of its size. Or, if you insist on spherical surfaces, you might make the Mangin lens and mirror elements separately, and bend the lens to cancel the spherical aberration (though I have not checked this possibility in detail).

"The Mangin must be tilted so that the reflected beam will clear the field lens and give access to the final image. This tilt introduces additional astigmatism into the image. Hence the tilt angle should be held to the absolute minimum. In a large instrument, astigmatism introduced by the tilt is eliminated by figuring a toroidal surface on the back of the Mangin, but it is more practical in a small telescope to cancel the astigmatism by the stratagem of tilting the objective on an axis perpendicular to the tilt axis of the Mangin.

"Two medial systems have been built on modernized plans developed by Dr. Baker at the Harvard College Observatory. Chester Cook of the Boston Amateur Telescope Makers has built an eight-inch; and Richard Dunn and James Gagan have developed a 16-inch. Both of these instruments have given fine results and have confirmed the theory of the color-free medial.

"To indicate what can be done, I have computed the objective and Mangin for a system of aperture f/18 at the wavelength of the hydrogen alpha line of the spectrum (6,563 angstrom units). This system is suitable for amateur use. The plans are based on an objective aperture of four inches. They can, of course, be scaled to a larger size, if the proportions among all dimensions are maintained. Data for the objective and the Mangin are given in the accompanying table [above].

"I have not specified the elements of the field lens because the procedure for designing a doublet is simple. A recommended procedure is given in the paper 'Computation of Achromatic Objectives,' by Robert E. Stephens. This paper is National Bureau of Standards Circular 549 (1954), and may be obtained for 10 cents from the Superintendent of Documents, Washington 25, D. C.

"In the design presented here the final image will be about 33.4 inches from the back of the Mangin. A diagonal eyepiece will be necessary to keep the observer's head out of the optical path. The system will be about 9.5 feet long-awkward, but not impractical, since the elements are light and little more than self-support is required of the tube. The telescope can of course be shortened by folding the optical path with a double mirror or reflecting prism behind the field lens. In addition to compactness, this arrangement has the advantage of locating the eyepiece in the usual position at the rear of the telescope.

"The Schupmann medial principle offers an opportunity to make a telescope of exceptionally fine definition, and making the telescope is not particularly difficult for the advanced amateur. Only one unconventional element is used, and it requires only one aspheric surface-a job no worse than parabolizing an ordinary mirror I shall be interested in hearing from anyone who decides to try a medial."

Nelson M. Griggs of R. D. No. 2, Old Baltimore Road, Boyds, Md., has announced the formation of a global network of amateur radio stations to provide fast communication without cost between scientific groups both in the U. S. and abroad. Although the network began operating only a month ago, participating stations already span the U. S. Some 30 astronomical groups are now using the facilities. More amateur stations are needed, particularly in Europe, Asia, Latin America and the South Pacific. The network clears routine traffic Monday through Friday on 7,125 kilocycles at 9 p.m. Eastern standard time and on 14,085 kilocycles at 9:30 p.m. E.S.T. Scientific groups may arrange to use the new facility by communicating directly with Griggs, whose amateur call is W3UCT.

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