The amateur who studies this paper will follow the tests exactly as the professional sees and makes them-and will discover no mysteries but mainly the same things he does on smaller mirrors, and some of the same old headaches Perusal should flatter his vanity, also confirming him in his methods.

One professional astronomer, director of a new observatory, asked this department to suggest the names of men qualified to make the acceptance tests on a very large mirror. Dr. Plaskett was of course named, as were others; and then A. W. Everest and other advanced amateurs were suggested. The astronomer had had the same thought-for many amateurs do more mirror testing than any professional, and in this way become highly expert in the eye-detection and interpretation of shadow subtleties. It turned out that the chief practical problem was not about the amateurs per se, but the university's trustees: "What would they say if I nominated amateurs! They'd never understand. I'd never live it down." We suspect he was right. The word "amateur" has two connotations.

Dr. Plaskett's article, which will require close study, follows:

The Warner and Swasey Company, who have designed and constructed the mechanical parts of the Lick, Yerkes, Victoria, and other large telescopes, have never undertaken, until the contract for the McDonald Observatory was signed in l9SS, to supply the optical parts for their instruments. The deaths of Dr. Brashear and Mr. McDowell, who had in recent years provided the optical parts required, and the desire to make the complete telescope, were probably the main reasons inducing this famous firm of telescope-builders to include an optical department in their organization. This was established in 193S under the direction of Mr. C. A. R. Lundin, who had previously acted as chief optician for the well-known firm of Alvan Clark and Sons.

The optical shop was fitted with a grinding and polishing machine for the 82" mirror and with a smaller machine for a 57 1/2" flat to be used in testing the 82". Work on the latter and on some smaller jobs occupied the time until the arrival of the 82" disk from Corning in October, 1934. Grinding was commenced on October 19, l9S4; and nearly four years later the mirror was completed, on October 14, 1938. The figuring was not, however, continuous throughout the period, as in the hope of early completion the figuring with the full-sized tool was unfortunately continued so far that, early in l9SY, the focal length became too short. Even though the parabolizing was nearly completed and the reduced focal length was within the range of adjustment provided in the mounting, neither the firm nor Mr. Lundin was willing to allow such a departure from the specifications. It required several months' work with the large tool to flatten the curve sufficiently, so that the final figuring-for the earlier close approach to the paraboloid was wiped out in the flattening process-- did not begin until October, 1937. Two months can hardly be considered an unduly long time to figure an optical surface of this size in a newly established shop.

Early in 1936 I was asked by Warner & Swasey Company to act as consultant in optical and other science

matters connected with their instrument work, and in 1937 I visited Cleveland twice-once in May during the flattening process and later, in October, after commencement of the refiguring. I was summoned again in March, 1938 when it seemed desirable to make a change in methods and remained, with two intermissions, consulting with Mr. Lundin until the mirror was completed on October 14. During a visit, late in March, of Dr. Struve, the director of the new observatory, and two associates-Dr. Van Biesbroeck and Dr. Kuiper-a different method of testing was proposed, depending on measurements at the center curvature from which a "curve of shape" was developed, the purpose of which was to give the true form of the surface with exact numerical values of the deviations from the paraboloid. The results from this method, which was extensively, used and which will be more fully discussed later, were, however, at first disappointing, and early in May the 57 1/2" flat, which had been given a very fine figure by Mr. Lundin a year earlier, was silvered and thereafter was used as principal means of testing the surface of the 82" mirror.

It may safely be said that, after the flat was set up and the shadow pattern at the focus could be observed--the method which Mr. Lundin had always hitherto used in figuring mirrors--the progress toward the final result was steady, if not quite continuous. As is probably the case with all optical work, especially large surfaces, various difficulties and occasional setbacks were encountered. It may be sufficient to mention first a sharply turned-up edge-much preferable, however, to one turned down-which required considerable handwork with small tools to reduce, at which Mr. Lundin is remarkably expert. A second difficulty was irregularity and lack of general smoothness over the surface, a problem completely solved by substituting for the full-sized tool a half-sized tool, with a long sweeping stroke

The final figure came quite rapidly at the last, as can be seen in the graphs in Figure 9, where the units are millionths of an inch and where the curves of shape of September 24, when the half-sized tool had barely come into use, and those of the final week of figuring are given. Dr. Struve and Mr. Fred Pearson, of the University of Chicago, paid a visit of inspection on October 6, when, under the knife-edge test at the focus, the figure looked so smooth and uniform that they adjudged it as nearly finished. However, tests at the center of curvature next morning and formation of the curve of shape showed it as still under-corrected to the extent of 20 millionths of an inch, a whole wave, and work was continued. Progress on one day enabled an estimate of the required time of polishing to be accurately made, and on this basis the paraboloid was considered completed on October 12, when the curve of shape showed deviations only slightly larger than a millionth of an inch, an eighteenth of a wave. Tests at the focus showed a high central zone, which Mr. Lundin reduced to practical invisibility in four short hand workings on October 12 and 13. The mirror was inspected and accepted by Dr. Struve on October 1S and was then made ready for aluminizing, necessary to make the Hartmann test and to figure the secondaries. The mirror was taken out of the vacuum chamber on October 24 and set up in the optical shop, where the visual and photographic tests were completed.

The method of testing the surface was a modification of the well-known method o f determining the center of curvature of a number of zones spaced uniformly over the surface and comparing these measured positions with those computed from the properties of the parabola. A cardboard diaphragm was placed in front of the mirror, containing 28 circular 1.5" holes, spaced uniformly along a horizontal diameter at a separation of 2.5". The innermost zone, No. 14, has a radius of 7.75"; and the outermost, No. 1, of 40.25". A series of shutters before the openings, manipulated by a rod extending through a partition, enabled the zones to be opened at will without going near the mirror. The intersection of the converging pencils from a fixed artificial star was determined at first by an eyepiece and later, more accurately, by a knife-edge. Obviously, in this case, the departures of the intersections from the computed positions are double those of the radii of curvature and four times those at the principal focus.

The knife-edge is attached to a slide moved parallel to the optical axis by a screw, the positions of intersection being obtained by lines scribed against a straight-edge on a stationary aluminum plate, rigidly attached at right angles to the slide. The positions of the intersections were either directly compared with a standard series in the computed positions, or later, as the mirror approached completion, the separations of the scratches were accurately measured by dividers on a steel scale. A modification developed by Mr. Burrell consisted in plotting the positions of the zonal openings as abscissae and the distances of the corresponding intersections from that at the center of the mirror as ordinates. The method is illustrated in the upper part of Figure 1, containing the measures of October 6, plotted as a curve which can be directly compared with a normal parabolic curve drawn in a dotted line through the computed positions. Blueprints were made of the fixed parts of this diagram, and the observed curve could be rapidly laid down on one of these prints from the scratches on the plate, the positions of longer radius being above and of shorter radius below the standard curve. The curve was at first considered as indicating where glass should be removed instead of showing where the surface was too flat or too concave.

It was the purpose of the curve of shape proposed by Dr. Struve, Dr. Van Biesbroeck, and Dr. Kuiper to overcome this difficulty and to represent graphically the actual form of the surface and the exact deviations from the paraboloid. The method is simple, the tilt of the element of the surface 6" wide, centered on any zonal aperture, being determined from the deviation of the intersection of the corresponding pencils from the computed position. The departure of the ends of this element from the paraboloid is thus obtained; and joining these ends together-in other words, algebraically summing the departures consecutively across the surface-gives its true form, the factors being so chosen that the departures of the intersections from normal, hereinafter called R, in hundredths of an inch, correspond to millionths on the curve of shape and on the surface.

Unfortunately, this method is also subject to ambiguity, particularly at the edge of the mirror, as the curve only begins to give reliable information halfway between zones 1 and 2; furthermore, the general slope depends upon the choice of zero, or the starting-point of the measures. This latter point is illustrated in the central part of Figure 1 in the measures of October 5. The deviations of the intersections plotted at the top of the figure with respect to the parabolic curve are repeated directly below, but on a different scale, in the broken curve drawn with respect to a straight-line base. These deviations, in hundredths of an inch, are transformed into the smooth curve of shape immediately below, showing deviations from the paraboloid in millionths of an inch. In the lower pair of curves the broken curve is exactly the same as above, except that 0.05" is subtracted from each measure, or the base line is lowered by 0.05". The curve of shape, however, is quite different, as not only is the slope radically different, indicating an alternative method of reaching a parabola of slightly different focus by removing glass both at edge and center instead of the center only, but also the average curvature is changed. Notwithstanding these difficulties, which rapidly diminish as the paraboloid is approached, the method is of distinct value in representing the exact form of the surface and in giving numerical values of the departure from the theoretical curve.

As soon as shadow tests at the focus were available, early in May, they were used exclusively as a guide for the next working, as there was then chance of ambiguity in the readings and the high zones could be accurately located and marked. The knife-edge shadow tests were supplemented and confirmed by the use of a Ronchi plate, where the condition of the surface was shown by the straightness and parallelism of the resultant bands. Measures at the center of curvature were transformed into curves of shape for Dr. Struve about once a week as a numerical record of progress until toward the end of the parabolizing, when it was felt desirable to check the shadow readings by measures at the center of curvature and by the formation of the curve of shape. For the last ten days or so, this was done after every polishing, as, although the shadow test recognizes very minute departures from regularity of figure, it is perhaps not so sensitive to very gradual changes as those due to slight under- or over-correction.

This was especially true in this instance, where the flat was a little over two thirds the size of the 82", of which hence, only a little over half, or just beyond the central hole, could be seen, and consequently the exact position of the knife-edge, its exact focusing, was uncertain, with resultant effect on the shadow pattern. As a result, though the shadow test was essential throughout to insure smoothness and regularity of figure and to determine where polishing was required, the final check on complete parabolization depended upon careful measures at the center of curvature and the resultant curve of shape. These were of great value during the last week of figuring, where the proper length of time for the next polishing was determined solely from past changes in the curve of shape. Thus, on October 11 (see Figure 2) the time required to complete the parabolizing, 1 1/2 hours, was gauged correctly, as seen in the lowest curve, from the change produced by the previous workings. And here again, the shadow test was essential, for otherwise the high central zone, which had no effect on the measures at the center curvature, would have escaped notice.

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