Copyright 2001 By
Mark Christensen, Ph.D.
Last month we discussed the personal history of Bernhard Schmidt and introduced the architecture of the astro-photographic camera named for him. The key concept behind the Schmidt Camera is the use of a spherical mirror (the easiest shape to make), arranged symmetrically so as to avoid off axis aberrations, together with an aspheric (that is, non-spherical) corrector plate, whose function is to eliminate the residual spherical aberration of the mirror. The spherical aberration of the mirror is caused by the fact that the rays from the outer zones of a spherical mirror focus closer to the mirror than do the rays from the inner zones of the same mirror. Schmidt's solution was to introduce a plate (called variously a Schmidt corrector or a Schmidt plate) in front of the mirror. This plate has a gentle curve ground into it designed expressly to bend the rays precisely the amount needed to bring the rays from the various (radial) zones of the mirror to a single focus.
One of the design decisions that must be made is exactly what point shall be used as the common focus. For example, the outermost rays may be deflected outward (from the center of the mirror) by the plate. This pushes their focus point farther from the mirror. Depending on how much the outer rays are deflected the focus of the rays near the center of the mirror can be left unchanged, or moved inward (which means they must be bent inward by the plate) toward the mirror, to meet the rays from the outer zones at an intermediate common point. So there are an infinite number of such plates possible; all of which will correct the spherical aberration of the same spherical mirror.
Figures 1a, b and c show three possibilities in exaggerated scale. In the first example (1a) the corrector is flat near the center and is more strongly curved near the edge.
This means that the rays entering near the center will not be deflected at all so they will focus where they would have without the corrector, while those near the edge will be strongly deflected, bringing their rays to a focus further out from the mirror than they would have were the corrector not present. In Figure 1b, the rays from the outermost zone are moved outward to an intermediate point, while the rays from the innermost zones are moved inward to the same point.
Thus, at some intermediate radial zone of the plate there is no deflection applied. Finally, in Figure 1c, the innermost zones are fully corrected, while the outermost zones are not corrected at all, with their rays brought to a focus at the same place as they would be without a corrector.
The equation for the depth of all of these curves is given by the equation:
Depth = ( x4 – kr2x2 ) / ( 4(n – 1)R3 ),
where R is the radius of curvature of the mirror, r is one-half the diameter of the corrector and n is the index of refraction of the glass from which the corrector is to be made. The parameter 'k' determines the exact shape of the curve. The case with the least chromatic aberration is that of k = 1.5, which places the neutral (flat) zone at a radius of 0.866 times r, the full radius of the corrector. For k=1 the neutral zone is located at 0.707 times r. Figure 1b approximates these two cases. Figure 1a represents k=0, while 1c shows k=2.
Schmidt designed his first camera incorporating this device in 1929 and built it the following year. His article describing it was published shortly thereafter. His innovation was a classic example of an idea that the world was ready for, resulting in a whole range of creative efforts by the astronomical optics community.
First of these efforts was, of course, the manufacture of cameras along the lines of Schmidt's original design, including some built by amateurs in the USA. In 1932 Dr. H. Paige Bailey of Riverside, California built and used an 8" f/2.375 camera. Over the next year the Lower brothers of San Diego built and employed an 8" f/1.0 device, and immediately thereafter C.H. Nicholson of The Chicago Astronomical Society built two 92 mm f/2.0 cameras for the Yerkes and McDonald observatories. Shortly thereafter the first of several large Schmidt cameras was constructed for the Mt. Palomar observatories.
The optical designers of the world, professional and amateur, knew a good thing (the concept of a corrector plate in front of a mirror) when they saw it and immediately went to work designing variations. Thus in 1935 Franklin Wright of Berkley California described what he modestly called the "Short" camera, consisting of a corrector plate similar to that of Schmidt but combined with a non-spherical mirror (a so-called oblate ellipsoid). This system, while not as optically perfect as the Schmidt camera, will produce images that are very adequate for photography. It avoids the two most serious problems of the Schmidt camera, having a flat field, and is only half as long. For focal ratios of f/3 and above the Wright camera, shown in Figure 2 (Next Page), as it has come to be called, is very attractive.
Other designers followed Wright's example. James Baker, in Amateur Telescope Making Book 3 (ATM3, 1949) described a hybrid camera, having the considerable advantages of using a spherical mirror, along with a corrector plate, while its focal point lies in front of the corrector, along with a short tube. These advantages come at the cost of introducing a doublet lens near the focal point. This camera, known as the Baker camera, has only been built in small numbers. Many other alternatives of the basic Schmidt design were invented, as exemplified by the no less than 22 (!) variations presented in the article by Hendrix and Christie, first published in 1939 in Scientific American, and reprinted in ATM3.
In addition to these efforts, the science behind the corrector plate attracted some of the best minds in mathematics and optics. For example, in 1940 Constintine Caratheodory, a Greek mathematician who is famous for establishing the foundations of modern abstract integration (measure) theory, published the definitive discussion of the off-axis aberrations of the Schmidt camera, proving that they were symmetrical.
In 1954 E.H. Linfoot of Cambridge Observatory published his seminal book Recent Advances in Optics. In this book he collected and systematically discussed the work of the optical design community on optical systems based on the 'Schmidt Principle', along with other topics, such as the first complete theory of the Foucault Test. Included were not only the Schmidt and Wright cameras but also the theory behind Schmidt Cassegrain telescopes. In these instruments there are three elements: the corrector plate, a large primary concave mirror, and a smaller convex mirror. The first mass produced examples of this class of instrument were produced in the 1970's under the DynaMax brand. Shortly thereafter Celestron entered the market, followed by the Meade company. However, virtually all of these systems have focal ratios of either f/6 or f/10, and all have virtually the same optical layout, seen in Figure 3.
In addition to these designs Linfoot also described a number of higher speed Schmidt-Cassegrain camera designs created by Baker. One of these cameras, with an aperture of 33 inches and a focal ratio of f/3.6, was built for Boyden Observatory in South Africa. This camera has a useful file of more than 10 inches in diameter. All of these designs require some degree of aspheric figuring of one or both of the mirrors if good off-axis performance is to be achieved. In the same book Linfoot also presented a new design for a high speed (f/3) camera, using only spherical mirrors, and possessing a flat field behind the primary mirror. The sole disadvantage to this system is the fact that the corrector plate is spaced slightly further from the primary mirror than in the standard Schmidt camera. To the knowledge of this author only one of these cameras has been built; a pilot model with 15 inches of aperture located at St. Andrews Observatory in Scotland. It entered service shortly before Linfoot's book was published.
While Linfoot presented an excellent summary of the work up to that time and systematically developed the analytical tools needed to derive further variations based on what he called 'the Schmidt Principle', the creativity of the optical and astronomical communities continued to produce new variations. So over time a number of new designs have been introduced. The first of these was that of D.D Maksutov and A. Bouwers, who were, respectively, working in Russia and Holland during WWII. They realized that the aspheric corrector plate could be replaced with a double meniscus lens with very steep curves. Figure 4 shows an example of a camera based on this principle.
Progress has not stopped at this. Maksutov-Cassegrain telescopes were almost immediately developed and new applications of the corrector principle continue to appear. Houghton suggested that the single (and difficult to make because of its steep curves) corrector of the Maksutov type be replaced by a doublet lens. From this idea several designs were developed in the 1970's and 80's by Lurie and Buchroeder. The general layout of Lurie's design is similar to Wright's, except that the single aspheric corrector is replaced by an air spaced doublet that is located about 20% inside the focus of the primary mirror. This produces a tube length even shorter than that of a similar Wright design, as well as yielding images that are nearly diffraction limited over a 35 mm film frame for an 8" f/4 camera.
All of these systems have a disadvantage. They require large correctors in front of the primary mirror. Next month we will discuss one last variation: Systems using only small correctors, located between the primary mirror and the focal plane.
References:
Amateur Telescope Making, Book 3. A. G Ingallis, Editor. Scientific American, Kingsford Press. 1953.
Amateur Telescope Making, Book 2. A. G Ingallis, Editor. Scientific American, Kingsford Press. 1946.
Recent Advances In Optics. E.H. Linfoot. Oxford University Press, London, United Kingdom, 1955.
Telescope Optics: Evaluation and Design. H.G.J Rutten & M.A.M. van Venrooij, William-Bell, Inc., 1988.
Tools of the Astronomer. G.R. Miczaika & W.M. Sinton, Harvard University Press, Cambridge, MA., 1961.