Copyright 2000 By
Mark Christensen, Ph.D.
All astronomers, professional or amateur, have seen splendid wide-angle deep sky photographs in magazines and books. The captions of many of these photographs state that they were obtained using a Schmidt Camera. Knowledgeable readers will know that this refers to some combination of a 'corrector plate' and one or more mirrors. How did this kind of telescope come about, and why are they collectively referred to by the rubric of 'Schmidt'?
Bernhard Schmidt was born at the Estonian island of Nargen in 1879 of a Swedish mother and a German father. He was interested in science and mathematics from an early age, with his interests not always rewarded as one might hope. At the age of 11, while dressed in his Sunday best, he lost his right hand and forearm while making an explosive device of his own design. This traumatic event did not put an end to his interest in science, however, as he later enrolled in the engineering school of the University of Gothenburg, Sweden, studying optics. Around the turn of the century he moved to Mittweida, Germany, in the Jena district. Jena is famous as the home of the Carl Zeiss optical workshops. Herr Schmidt rapidly established himself as a producer of high quality astronomical instruments for both the amateur and professional observers. He lived a simple bachelor's life, talking long walks in the surrounding woods, accepting and completing only a few orders a year. He did all his work by hand.
In 1926 he was enticed to join the staff of Hamburg Observatory by the director, Dr. Schorr. The arrangement was somewhat unstructured, in keeping with Herr Schmidt's general approach to life, with Dr. Schorr describing Schmidt as an "informal colleague".
While working at the observatory (again as the spirit moved him) he began to contemplate how the wide field performance of astronomical cameras could be improved. In those times, as now, a large astronomical camera meant a reflector system, not a photographic lens. In its simplest form such a system consisted of a parabolic mirror. Now a parabola is only symmetric about its primary axis. It gives geometrically perfect images on that axis, with rays from all radial zones converging to a single point. See Figure 1 below. For stars not on the primary axis the situation is different, with the rays cutting the image plane at various points, as shown in the close-up in Figure 2. This produces an imperfect image.
Figure 1: On Axis Rays of a Parabola
Figure 2: Off Axis Rays
The primary forms of this imperfection are called 'coma' and 'astigmatism'. Coma, which causes off axis images of stars to look like tiny comets, increases linearly with the distance from the center of the field, while astigmatism, which causes the star to look like a small cross, increases with the square of that distance. For moderate distances from the center coma is the dominant imperfection, or aberration. To be precise, the coma (in arc seconds) is given by:
Coma in arc seconds = 333 d/f2
where d = the distance in degrees from the center,
and f = the focal ratio, or focal length (F) divided by mirror diameter (M).
Thus a f/3 parabola will suffer from approximately 37 arc seconds of coma at 1 degree from its axis. A more useful way to express this is:
Coma in inches = 333 ( D / 3600 ) / f2 = 0.0925 * D / f2
where D is the distance from the center in inches.
If we desire to use our parabolic camera with a 35 mm camera then D = 0.7 at the corner of the field. Thus contribution to the size of a star image at the corner due to coma will be:
Coma in inches at corner = 0.06475 / f2
For a f/4 reflector this yields an image size of 0.06475/16 = 0.00405 inches, while for a f/3 the coma will produce an image 0.06475/9 = 0.0072 inches. The first number is tolerable (barely), while the second is marginal. For comparison purposes, the resolution of most films is of the order of 0.01 mm, or 0.004 inches, while at normal viewing distances the human eye can only discern images larger than about 0.04 mm (or 0.016 inches) on a 35 mm slide. Up to a point coma is the dominant aberration. For larger angles (or distances) from the center astigmatism is dominate. Examining the formula shows this:
Astigmatism in arc seconds = 405 d2 / f4
Or
Astigmatism in inches = 405 * 57.3 * ( D2 / 3600) / (F* f4) = 6.45 * D2 / ( F * f4)
Now Herr Schmidt was fully aware of all this. He thought long and deeply about how he might design and build an astronomical camera capable of working over large angles with low focal ratios and high image quality (that is, little coma or astigmatism). In the spring of 1929, while accompanying Walter Baade onboard a ship in the Indian Ocean during an eclipse expedition to the Philippines, he described his solution. The root cause of both coma and astigmatism is the fact that the parabola is only symmetric to rays arriving parallel to its axis. Schmidt's key insight was that a spherical mirror, with a circular stop located at its center of curvature, is symmetrical to rays coming from any direction. A spherical mirror is of course the easiest to make, which is a considerable advantage.
Figure 3: Spherical Mirror with Stop
At Center Of Curvature
There are two problems with a spherical mirror used by itself. First, the best image lies on a sphere of radius equal to the focal length of the mirror. This can be dealt with by curving the film on a spherical holder. Of course, this eliminates the possibility of using roll film cameras, although a field-flattening lens can be used. However, the use of roll film cameras also requires a very large diagonal mirror as the f/ ratio decreases. More fundamentally, however the image produced by a sphere is not in perfect focus, in the center or elsewhere. This effect, known as spherical aberration, is shown in Figure 4.
Figure 4: Imperfect Focus of
Spherical Mirror
This, of course, is why the parabola was introduced by Newton in the first place. Schmidt's solution to this problem was to introduce a thin lens, or plate, at the center of curvature of the mirror, that is, where the stop is shown in Figure 3. The purpose of the corrector plate is to introduce very small deflections in the rays shown in Figure 4 so that they all cross the axis at the same point. Placing the corrector at the radius of curvature of the mirror retains the symmetry of the system and thus coma and astigmatism are largely avoided. Of course, since the corrector plate functions as a prism, some false color is introduced into the image but the effect on the image is very minor because the corrector plate has very weak curvature. The greatest depth of the corrector plate for an 8" f/2 camera is, for example, only a few thousands of an inch.
Herr Schmidt built his first mirror-corrector telescopic camera in 1930, using a 17.3 inch mirror and a 14.2 inch corrector to achieve a focal ratio of f/1.7, producing a telescope of unheard of 'speed'. He completed the grinding and figuring of the corrector plate in a marathon work session lasting more than 48 hours. It produced spectacular image, ushering in a new area in astronomical photography and spawning a whole series of derivative applications of the 'Schmidt Principle'. Schmidt died December 1, 1935 while adjusting a larger camera but his ideas took root. Next month we'll examine some of the results, along with some more details of the corrector plate itself.
Reference: Amateur Telescope Making, Book 3, Albert G. Ingallis (Editor), Scientific American, Kingsport Press, 1953. Pages 365-375.
