ONE of the most outstanding inventions in optics of modern times is to be credited to Bernhard Schmidt, late optician of the Hamburg Observatory in Bergedorf. The first Schmidt camera saw the light of day one sultry afternoon in the late summer of 1930. Using the camera as a telescope, Schmidt and a friend amused themselves that afternoon by reading the epitaphs on the tombstones of a nearby cemetery, and by looking at various buildings in the distance. Among other objects was a windmill about two kilometers away; in Figure 1 the reader will see the reproduction of a photograph of this windmill, made by Schmidt with the first Schmidt camera. This photograph was made on a moonless night with an exposure of two hours. On the original print one can actually count the twigs on some of the distant trees.

As in most great inventions, Schmidt's method of eliminating coma and aberrations from reflecting telescopes is simplicity itself and, as one looks back, it seems incredible that no one appears to have thought of this simple solution long ago.

Several articles have been written about the Schmidt camera since the inventor set forth its principles in 1931, but little that is new has been included in these discussions. Since there are many ramifications of the Schmidt principle it has seemed worthwhile to discuss this remarkable camera and its applications fairly completely, for it will be found that there are but few fields in optics where this invention can't be applied to some advantage.

The outstanding defects in the images formed by lenses and mirrors are spherical aberration, coma, astigmatism, curvature of the field, distortion, and for lenses we have, in addition, chromatism. Of these defects, only one is distributed uniformly over the whole field; this defect is spherical aberration; all other defects are proportional to their distances from the axis.

Now a spherical mirror has no axis and, furthermore, a mirror is perfectly achromatic, so, could we but find a method of eliminating spherical aberration from the images produced by a spherical concave mirror, such as system should prove ideal.

Spherical aberration is caused by rays from various zones failing to come to the same focus: the more distant the zone is from the central ray the closer its focal plane is to the mirror. This defect, for spherical concave mirrors, is shown diagrammatically in Figure 2, at A. Suppose, now, we place a very small aperture in a screen at the center of curvature of a spherical concave mirror. as shown at B: this aperture will limit the size of the incident beam so that the center and outer zones will come practically to the same focus, for it can he shown that, for small apertures and focal ratios less than f/10 the Raleigh limit of /4 is not exceeded. If the incident beam be swung about the point o all parts of the mirror will be illuminated in turn and the focus will trace on the spherical curve, ff, which has its center at o. It will be seen that each point source of light toward which an optical arrangement might he turned would form its image on the focal curve ff. On increasing the size of the aperture the focus is no longer sharp: spherical aberration is now appreciable, but we can eliminate this defect by introducing equal and opposite aberrations into the incident beam, as shown in C. These opposite correcting spherical aberrations may be produced by a suitably shaped lens, or mirror, placed anywhere in the parallel beam for one particular point source of light, but when we are dealing with more than one source it becomes imperative to place the correcting plate in a position common to all rays; that is, with the optical center at the center of curvature of the mirror. For many purposes a large field is not required and it becomes more convenient to move the correcting plate away from this position and perhaps incorporate it with some other optical surface, such, for example, as the face of a prism or the collimator of a spectrograph. The corrections, of course are not identical for all positions of the correcting plate.

On introducing the correcting plate into the incident beam of light we also introduce chromatic aberrations. For moderate apertures this defect is negligible, but when we attempt to make a camera with an aperture greater than its focal length we run into difficulties: how these may be partially surmounted will be discussed later. Of course it is possible to design an achromatic correcting plate by using to plates, of different indices of refraction. It is also possible-and practical-to distribute the required corrections between several surfaces when it is desirable to avoid deep or steep curvatures.

The curvature of the field may he removed {approximately) by means of a simple plano-convex lens placed immediately in front of, or in contact with, the photographic plate, the plane side facing the emulsion. The radius of this lens is f/3 for glass with an index of refraction of 1.50. This is satisfactory for cameras having an f ratio of f/5 or less.

Application of the Schmidt Principle: In the accompanying diagrams, Figure 3, we have portrayed some of the numerous adaptations which may be made of the Schmidt principle. Unfortunately, Schmidt left no account of the various ramifications of his camera of which he must have thought, and we do not know, in most cases, who originated the various arrangements we present; most of them have been devised here, but we do not claim priority. In a few cases, where the originator is known, we have appended his name to the diagram although it is probable that others interested in fast cameras may have independently thought of them.

In the central column of the diagram we have arranged illustrations of the fundamental types of Schmidt cameras and, to the right and left some adaptations of these types, most of which need no explanation. No. VI, which shows the diaphragm replaced by a correcting mirror, is shown, as are most of these diagrams, in an exaggerated form; in practice it is necessary to reduce the angle between the incident and reflected beams to a minimum in order to reduce the foreshortening effect. A perfect correcting mirror should be figured in an elliptical form but, since such a figure is very difficult to produce, we must be satisfied with an approximation in the form of a circular correcting mirror. If the aperture ratio of a camera using a correcting mirror is small, the foreshortening will be negligible, and here we have a perfectly achromatic arrangement which should be exceedingly useful in working at the extreme limits of the spectrum.

When a Schmidt camera is constructed with an aperture greater than its focal length, the curves in the correcting plate becomes steep enough to introduce appreciable chromatic aberration. If, however, we use a thick mirror, R/2 in thickness, silvered on the back surface, as shown at IX, we increase the speed of a Schmidt camera a factor of 2-1/2 to 3 times, depending upon the kind of glass used, because, on passing from one medium to another, the energy-density of a cone of rays is changed by a factor equal to the square of the inverse ratio of the indices of refraction of the two media. To put this in other words: since the rays, after passing through the surface of the mirror, are refracted toward the normal, they appear, as seen from the surface of the mirror, to emanate from a point closer to the axis; hence the angle subtended by an object is reduced, and the image formed by the mirror is correspondingly diminished in size. The geometrical focal length, however, has been changed but little, and thus we can obtain the speed of an f/0.66 camera with a field and correction plate curvature of an f/l.0 camera. This is shown clearly in Figure 4, where an ordinary Schmidt camera is compared with one of the thick mirror type.

In such a camera the correcting plate is placed at a distance of R/2n from the front surface of the mirror, where R is the radius of the mirror and n the index of refraction of the glass. This position is the apparent center of curvature of the mirror as seen from the mirror surface. (In all cases where the focal curve lies at the surface of the glass the photographic emulsion should have a film of oil between it and the glass, in order to make optical contact. Coal-oil will be found quite suitable for this purpose.)

In XII, Figure 3, we have the extreme form of solid type-one in which there is no medium other than glass between the correcting surface and the focus. This was first suggested to us by the late Sinclair Smith. We do not know of such a camera having been made and there are some practical optical difficulties to be surmounted in constructing a solid Schmidt; furthermore, the increased absorption of the thick glass becomes important, and, since it must be sufficiently homogeneous for its purpose, such large blocks are very expensive. The two parts, separated by the dotted line in the diagram, should be figured separately but when cemented together they must be accurately co- axial. The photographic plate could be introduced into the focal curve through a hole in the half containing the correcting surface, either from the side or along the axis as shown.

The difficulties of the extreme thick mirror types may be overcome by a variation of Wright's ("Amateur Telescope Making- Advanced") system; that is, by placing the correcting surface at the focus as shown in XV; but here we are confronted with two non-spherical surfaces, extremely difficult to figure in conjunction with each other. An experimental camera of this type, with an aperture ratio of f/1, was constructed here, but it was not a success because the higher order aberrations rendered the images unsatisfactory. It is possible that a camera, geometrically f/4, or with an equivalent focal ratio of f/3, would be entirely satisfactory.

One of the neatest of all solid types is that shown in XVII-the folded solid Schmidt, designed by Hendrix. Here we have few practical optical difficulties, although there are four components. Of the seven plane surfaces only the hypotenuse of the large prism must be worked to a high degree of precision; the cemented surfaces are sufficiently accurate if worked to a wave because the cement, which should have an index of refraction equal to that of the glass, fills in the irregularities between the surfaces. Small errors in the thickness of the components may be rectified when adjusting the small prism during the final assembly.

The "off-axis" type, illustrated in XX, is exceedingly useful in practice because, with this arrangement, the photographic plate or film may be placed outside the light beam. This system also is adaptable for visual observations. Making a single off-axis correcting plate of large dimensions is, unfortunately, somewhat wasteful of time and material, because it is necessary to figure a correcting plate of more than twice the required diameter. If more than one camera of the same focal length is required, the waste is reduced, because several off-axis plates can be cut from the original one. This type seems to be the only practical one for mass production.

In XIX the Schmidt principle is used in the form of a microscope. Such an arrangement might prove useful for low power work where a large field is desired, such as in microphotometry; but perhaps the most ingenious arrangement is that of Hayward, XXI, in which he suggests a thick mirror with the focal curve ground out of the mirror face, and serving as a reservoir for small living organisms. An unsilvered portion of the spherical mirror serves to admit light for dark field illumination.

The Design and Construction of Correcting Plates: The deviation, , of the surface of a correcting plate from a plane is given by the biquadratic parabola formula

  (1)

 where x is the radius of the zone; k, a constant; r, the radius of the correcting plate; R, the radius of curvature of the spherical mirror; and n, the index of refraction of the glass.

Now, let Then (1) becomes (2) 

which is in a convenient form for computation. Giving k various values from-1.0 to +3.0, we obtain the series of curves shown in Figure 5. When k=0 we have a lens with a sharply turned up edge and flat in the center. This form is one of the most difficult to figure, yet the writers have seen it recommended for amateurs! As k is increased the center rises and the edge is depressed until, when k is unity, edge and center are equally high, and the depressed zone lies 0.707 r from the center. In this form the amount of glass to be abraded from the lens surface is a minimum and it is this figure which we have found most satisfactory for general purposes; it is also the easiest to construct. When k=l.5 we have a correcting plate in which the effect of chromatic aberration is at a minimum.

This is the type of correcting plate which we have used for our "thick-mirror Schmidt" cameras: several of which have been constructed here. When k=2 the neutral zone is at the edge of the plate and the figure becomes difficult to achieve in practice. In plates the edge gives some trouble while figuring, because of the flexible nature of the tools used in this work, hence it is best to make the plates at least 1" larger than the required diameter; the troublesome edge can then be masked out when the camera is assembled. It is estimated that the cost of labor in making a correcting plate is reduced at least 50 percent by making a generous allowance for the edge. Differentiating (2) and equating to zero,

(3) 

This gives the distance of the neutral zone from the center, and, by substituting this value for x, in (2), we obtain

(4)

the depth of the curve at this zone. With these two dimensions, (3) and (4), at our disposal the correcting plate may be rapidly roughed out to shape, the depth of the zone being measured with a suitable micrometer.

The angular field, , of a Schmidt camera is given by the equation

(5)

where d' is the diameter of the plate holder and f is the focal length of the mirror, and, in order to utilize all the light, the diameter, D, of the mirror must be

(6)

where d is the diameter of the correcting plate. For ordinary purposes d' should not greatly exceed

The correcting plate is made from planeparallel glass plates free from striae. It is very important that the plates be plane-parallel, especially for telescopes used for stellar photography. If the plates are not plane-parallel, ghost images, caused by the internal reflections in the lens, will be formed to one side of the brighter stars. (It has been suggested to us that these ghost images might prove useful in stellar photometry.) When the plates are plane-parallel these, spurious images fall on the image of the star causing them. For ordinary work a high-grade plate glass, such as Crystalex, may be used, but when high ultra-violet transmission is desired, glass such as Schott's U.B.K.5 or Vitaglass must be used. A satisfactory thickness for the correcting plate is of the order of 1/40 to 1/50 of its diameter.

The plates are best supported, during grinding and polishing, on a circular felt pad which should be shrunk before use; the pad should be a little smaller than the lens. For small lenses the glass is held in position by a metal ring slightly larger in diameter than the disk and projecting above the level of the turntable by an amount sufficient to hold it in place, but not high enough to interfere with the motions of the tool. During grinding and polishing the plate should be rotated frequently upon the felt base. In the case of large lenses the plate is best retained on the table by means of sets of vertical spring bronze "fingers" attached to the turntable; at least six such sets should be used.

It will be noted that a certain polishing action is going on, on the rear surface of the plate, during the polishing stage, due to the motion of the plate upon its supporting pad which is difficult to keep free from rouge at this stage. The effect of this is eliminated, after the required figure has been approximated on the front surface, by making the final corrections on the back. During grinding no abrasive should reach the back surface of the correcting plate because of the protective gap between the felt and the edge of the lens. (This is the reason for cutting the felt disk smaller than the plate.)

The best form of tool we have found for grinding out the zones is constructed as follows. Three triants (120-degree sectors of circles) are cut from moderately stiff spring-bronze sheet in such a manner that the grain of the metal-that is, the direction in which the sheet was rolled-is the same in each. These sectors are then cut into radial "fingers," to the underside of the extremities of which are cemented the grinding facets. These facets are cut from unglazed ceramic tile, such as the small size used for bathroom floors. The sectors are then attached to a suitable hub and, if necessary, the fingers may be bent downward and outward, keeping the outer ends parallel to the surface of the plate.

Polishing is done with facets of moderately soft pitch attached to a sponge rubber base, about 1/4'' thick, the rubber permitting the tool to conform to the zonal curvature of the correcting plate. Polishing tools with a sponge-rubber base will be found excellent for working on all optical surfaces where zonal curvature exists.

It will be realized, we think, that all but the smallest tools are of the ring form. For smoothing out irregularities in the curvature of the zones a small common tool, one quarter, or less of the diameter of the plate may be used. This should be given a long elliptical stroke in the direction of the zone.

Schmidt's method of polishing correcting plates was to place them concentrically on the lip of a shallow circular metal pan, the edge of which was ground so that an airtight seal could be made between the glass and the metal. The air was then pumped out of the pan, causing the center of the plate to be depressed; then, by the use of a spherical tool of the correct curvature, the zones were' automatically polished to shape. This method is not to be recommended, however, except for mass production, when it becomes the modus operandi.

The figure of the plate may be examined during the grinding stage by dipping it into a solution of ethyl cinnimate and Xylol, mixed in a proportion of 4:1. This forms a smooth coating which has approximately the same index of refraction as the glass. After a little experience it is surprising how readily one can detect small irregularities in the curvature, or the displacement of a zone, by direct visual inspection of the form, using a good straightedge held in contact with the plate as a guide for the eye.

The Chinese mirror effect is sometimes useful in correcting local irregularities, and even in polishing and figuring plates with small curvature. The lens is here supported on suitably shaped pads of secured rubber, such as that used for patching automobile inner tubes; the part of the lens thus supported is abraded more rapidly than the unsupported regions.

A number of methods have been worked out here for testing correcting plates, some of which will now be described. The figure of the correcting plate may be readily examined with a knife-edge if one has a telescope sufficiently large to take in the collimated beam from the assembled camera, as shown in Figure 6 at A. Using this method, a point source of light is placed at the focus of the camera, and the knife-edge at the focus of the telescope. The sensitivity of this test is proportional to the square of the ratio of the focal length of the telescope to that of the camera.

Where a large telescope is not available for testing we can make use of a small one, in conjunction with a pentaprism or an optical square, as shown at B. Here we have a small telescope rigidly set up at right angles to the axis of the camera. The optical square, consisting of two plane mirrors mounted at an angle of 45 degrees, or a pentaprism, is set up in front of the telescope on a base which may be moved across the collimated beam of light. The image of the light source is focused on the intersection of a pair of cross-wires in the focal plane of the telescope. As the pentaprism is moved across the collimated beam the image should remain on the vertical wire; any lateral motion is due to the poor figure of the optical system; vertical motions may be due to irregularities in the motion of the pentaprism.

An excellent test for cameras having an aperture f/5, or less, is made by placing the correcting plate directly in contact with the mirror, as at C. The test is made on the axis of the lens, in a manner similar to that used for testing a parabolic mirror in the center of curvature; that is, by measuring the apparent radius of curvature of the various zones with a knife-edge at the focus. In this case the test is twice as sensitive as that for a parabolic mirror because the light passes twice through the lens. The formula now becomes ; this, when both knife-edge and light source move together.

A Ronchi screen placed inside the focus of a Schmidt camera will form a series of fringes on a screen placed at a suitable distance from the focal point, as shown at D. By using an opal or ground-glass screen these fringes may be examined readily. Each fringe should be straight with parallel boundaries, but the presence of zones in the correcting plate distorts these fringes which are interpreted in the usual manner. The familiar Ronchi screen method of testing is excellent, also, for lenses with large aperture ratios, or where the focus is too short for the eye to focus on the equivalent plane.

An illuminated, small, silvered glass serves as an excellent point source of light for testing purposes. The illuminating beam should be concentrated on the face of the bead facing the mirror or lens to be tested. Any stray light which passes the bead should be blocked off by a suitable diaphragm placed behind it-a totally reflecting prism is excellent.

To test a correcting plate made to work in the extreme regions of the spectrum (infra-red or ultra-violet) we can construct a testing mirror of radius R' so that, in equation (1) and, thus make the tests in visual light which gives an index of refraction of n'.

There are, of course, numerous other methods of testing correcting plates, but those given here are sufficient, we think, for the average reader. It must be remembered that the plates, to begin with must be plane-parallel, and they must be free from striae. In selecting plate glass for correcting plates sheets should be first tested with a micrometer for uniformity of thickness, and then tested for striae by holding the sheet between a small bright source of light, such as an arc, and a white screen. Shadowlike streaks on the screen show the presence of these defects, and their positions can then be marked on the glass with a wax pencil. Unless a large plate is required an area large enough for the purpose usually can be selected from relatively cheap glass.-Pasadena, California, March, 1939.

THIS completes the article by Hendrix and Christie. In reply to a request, the latter states that Schmidt died about four years ago. His only article appeared in Central-Zeitung für Optik und Mechanik, Bund 52, Heft 2, and in Mitteilungen Hamburg-Bergedorf, Bund 7 No. 36, under the title of 'Ein lichtstarkes komafries Spiegelsystem.'

Because of his full occupation with important optical work now in progress at Pasadena, the senior author sincerely regrets that he will not at present find it possible to answer requests for further information.

Crystalex: Pittsburgh Plate Glass Co., 2222 Grant Bldg., Pittsburgh. Pa.

Schott's glass: Fish-Schurman Corp., 250 E. 43rd St. New York. N. Y.

Vitaglass: The Vitaglass Corp., 220 Fifth Ave., New York, N. Y.

The Schmidt camera gives great promise in astronomy, professional and amateur, and there is lots of work for the amateur to do with it. Heretofore a heavy discouragement in undertaking a Schmidt has been the interminable job of excavating the very deep curve of the primary-about 1/2" deep on a 12-1/2", disk. It is hoped that plans under way as we go to press will make possible the purchase of pre-roughed-out 12-1/2" disks.

Last April this column stated that two off-axis mirrors had been made at the Mt. Wilson shops: we learn that two dozen is more nearly the correct number.

Stellafane convention, Sat., July 22.

Convention of amateur astronomers, including planetarium show and banquet, at Hayden Planetarium, New York, Aug. 19 and 20. Former day will also be Amateur Astronomers' Day at World's Fair; Professor Shapley will give a talk. A three-week exhibit of amateurs' work will be held at Hayden Planetarium July 30 to Aug. 20.

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.