THE REASON why an amateur telescope maker is willing to spend many hours polishing a concave mirror, enjoying what must appear to others a tedious task, can now be explained to the non-telescope maker with the aid of the unique series of "focograms" shown at the left. These photographs span the polishing and shaping of a typical mirror from its beginning to its successful completion. They show exactly what a telescope maker sees when he uses the famous Foucault test to ascertain the current shape of his mirror. When explained, they will show that the task is actually a suspenseful adventure.

The Foucault test exaggerates the relief of concave mirrors; approximately 100,000 times. Thus irregularities far too small to be otherwise visible or detectable, even by micrometers, stand out so clearly that the worker can decide which areas need more shaping. Focograms are made by placing photographic film where the eye is normally placed in the Foucault test. Since they are not essential, few are made, and then usually only at the end of the work. Thus a record of a common procedure is a most uncommon thing. So far as is known only one amateur telescope maker has ever made focograms throughout all the stages of his first mirror. This amateur is Dr. C. P. Custer, a Stockton, Calif., surgeon, whose focograms are shown on this page.

In the interpretation of all the shapes as they change during polishing, the worker assumes that the mirror is illuminated from the right. The light and dark areas then indicate the shape of the curves. By examining Dr. Custer's focograms and the records he made as he worked, it is possible to follow the trials and tribulations of a mirror maker.

Focogram 1 was made after the mirror, which has a six-inch diameter and a 48-inch focal length, had already been through its preliminary grinding with finer and finer abrasives, had been brought to a spherical curve as nearly as possible by that means, and had been charged with optician's rouge. In the Foucault test a truly spherical mirror appears shadowless and flat, as in focogram 6. Focogram 1 therefore shows that at the beginning the mirror was not yet spherical. Actually it is everywhere within about 1/50,000 inch of spherical. Its rough, scored appearance is due mainly to the immense magnification of the Foucault test in the one direction of depth.

In focogram 2 most of the circular scorings have been smoothed out. The apparent notch at the top is the hook that holds the mirror in edgewise position in the tests. The narrow cusp of light at the right tells the experienced worker that the mirror has a turned-down edge, a common affliction in which curvature increases rapidly toward the perimeter.

In focogram a raised central area, an "inverted soup plate," has replaced the "saucer" of focogram 2 as a result of the unusually hard pitch used on the lap. Pitch that is too soft usually leads to an excessive deepening of the mirror's central areas, giving a hyperboloidal shape, while pitch that is very hard leads to this oblate spheroidal shape. Long polishing strokes will usually offset the latter but at first Dr. Custer cautiously experimented only on the slight central depression, hoping to find out how mirror correcting operates. He shived away a thin layer of the surface of the pitch on the lap opposite the central depression, and found that, after further polishing of the whole mirror, the area rose. It even formed a little peak as shown in focogram 4, giving the mirror the overall appearance of a coolie's hat. Thus he had put into practice for the first time the basic method of correcting a mirror's surface: polishing certain parts more than others. This is accomplished by altering the lap or by changing the pattern of the strokes that push the mirror over the lap in ways that effectively alter it.

THE FACT THAT the Foucault test can measure millionths of an inch, and that precision optics ideally calls for accuracy within two-millionths of an inch, sometimes leads to apprehension concerning the skill needed for such work. However, the glass is removed by such small amounts, each stroke planing off no more than perhaps a hundred-millionths of an inch, that the actual control is not formidable. The difficulties of mirror making are not so much of this tactical kind as they are strategic—the constant planning of the next move in a prolonged campaign. In mirror making as in chess, strategy is happily more interesting than tactics. In mirror correction there are many procedures and an endless variety of strokes. No two mirrors go through the same phases; the sport is infinitely varied.

Dr. Custer next writes, "I now found what my spherical stroke was"—the stroke that would avoid hyperbolas and oblate spheroids and attain the sphere. Each worker and each lap has an individual stroke, discovered by experiment. Written guides teach general principles but cannot impart particulars for each worker. This is why the art appeals to those who enjoy hobbies that cannot be reduced to cut and dried routine. Dr. Custer found that his hard pitch called for very long strokes; it later proved that six-and-one-half-inch strokes would approximately hold a sphere.

These very long strokes reduced the big bulge of focogram 4 to the near sphere of focogram 5; in focogram 6 it became a true sphere, or would have appeared so (except for the turned-down edge) in the visual Foucault test. Focograms tend to exaggerate all evil appearances, perhaps because the film stores light. At this point the sphere could have been converted to the desired paraboloid by deepening the surface toward the center. Unfortunately at this early stage in polishing many pits still remain from grinding. When these pits have been removed by polishing the entire surface to a level below their bottoms, the spherical shape will almost surely have been replaced by some other, since no shape can be held long. The curves drift constantly. The attempts to perfect the shape of the mirror before removing the pits are made to gain practice, learn stratagems, and simply because it is fun.

"Focogram 7 was made," Dr. Custer writes, "after alternating between a sphere and an oblate spheroid. At this point I sent the mirror to the Tinsley Laboratories for an interim check-up." It was returned with the report: excellently spherical except for a turned-down edge and a small central hill.

"When I received the mirror back," Dr. Custer continues, "I poured hot pitch on its back to reattach the handle. Lo and behold! I had a deep hyperbola that persisted indefinitely until I knocked the handle off. Instantly the mirror returned to its original shape. Next time, in attaching the handle, I heated the mirror also and cold-pressed it on the lap overnight. The true figure returned. These procedures occupied a week during which I did quite a little thinking."

WHETHER THE WORKER is a novice or an old hand, he almost inevitably finds himself in perplexing situations that sometimes drive him to wit's end. He may carry these problems around with him for days. An average mirror is good for about five such scrapes. Should the mirror maker happen somehow to proceed to an uneventful finish he should reward himself as unluckily slighted, for he has not yet really lived. While dwelling profoundly on a problem such as Dr. Custer's, one worker was hit by a truck and his arm was broken. Ultimately a solution (or a truck) arrives, sometimes by "trying -anything once" but more often by analytic thought.

"In focogram 8, made only three minutes after the mirror was off the lap, I finally had an optical surface," Dr. Custer rejoices. By this he means a surface smooth in texture, unlike the "dog-biscuit" surface in focogram 5 caused by too rapid strokes which heat the glass and expand it unevenly. Nearly an hour later, after some of the heat of friction created even by deliberate strokes had been dissipated, focogram 9 was made. The central area had risen. Change of shape during cooling is an additional phenomenon to complicate mirror making, though the worker learns to predict its amount to some extent. In the later, more crucial stages of his work he prefers to let the mirror cool a full hour before testing, or even work an hour or less at a time and leave the mirror overnight to cool fully.

Focogram 10, made one hour after removing the mirror from the lap, and focogram 11, made two hours after removal, show well the effects of expansion due to the frictional heat even of slow strokes made perhaps once every three seconds. "See how the spherical figure rose during the second hour," Dr. Custer exclaims. The rise, which resembles a goose egg on a bumped head, may have totaled several millionths of an inch. "This convinced me that most of the disturbance of figure was coming from flexure of the glass due to the handle cemented to it with pitch. So I knocked the handle off and have been polishing without a handle ever since, and the figure now becomes permanent after 45 minutes of cooling. No more handles for me! The base of the handle was only four inches in width and the pitch protruded a quarter of an inch beyond its edge." This handle was much too large.

"From here on I got into plenty of trouble from other sources," Dr. Custer, remarks. "In hope of attaining a sphere, I tried to eliminate the central hill of focogram 11 by overhung strokes an inch from the edge of the mirror. All of a sudden the hill disappeared and an astonishing depression appeared in its place." Old hands at mirror making, recalling their own similar mistakes, both past and present, will enjoy all these candid confessions. The stroke chosen threw multiplied pressure on one small central area, and excavated rapidly to and below the sphere. It is perhaps best to have made as many of the standard mistakes as possible; this confers the feeling of belonging."

"I then decided to widen this depression into a paraboloid," says Dr. Custer, "but the deeper hyperboloid developed instead. So with reduced (six-inch) strokes I let the oblate spheroid come back, eliminated this with 3/4-inch of side overhang, and took focogram 12, showing I had a sphere." The faint pucker at the right is a dab of dried rouge water.

"Further maneuvers, too varied to describe here, produced the surface shown in focogram 13, a sphere with an outside zone that has fooled all who have seen it. This apparently raised outer zone is actually a depressed zone with a high outer rim. Further maneuvers smoothed the mirror, and 25 strokes were then given to reach the paraboloid. Here I was amazed," Dr. Custer laments, "to find that the mirror had gone 50 per cent deeper than the paraboloid."

Three weary hours of two-thirds strokes repaired the damage. Two rounds of elliptical strokes with lap on top of mirror left the zone barely perceptible, showing that it had consisted mainly of turned-up edge, but also left scratches. Alas, a third round changed the turned-up edge to a turned-down edge. "This disturbed me no end," Dr. Custer sighs. "So I rushed in where angels fear to tread and ground off a zone 3/32-inch wide with Carborundum." The result is shown in focogram 14. It proved later that only half the width of the turned-down zone had been ground off.

At this point the mirror was again tested by the Tinsley Laboratories, who pronounced the surface a paraboloid with 72 per cent correction and suggested masking off the remaining part of the turned-down zone with a diaphragm. Focogram 15 was therefore made with a diaphragm, and reveals a 5 5/8-inch paraboloidal mirror of excellent quality.

Since the Custer telescope has twice the diameter and twice the length of the Porter design, it has approximately eight times the latter's weight—350 pounds. Theoretically, therefore, its mounting is eight times overloaded. Yet it has proved satisfactory. Several factors account for this. First, there are ball bearings on both axes. On the declination axis there are 205 balls in a race at the edge eight inches in diameter. "Without these," says Dr. Custer, "the tube would be hardly movable by hand, let alone by the vernier adjustment screw. With them, I can move the tube with my little finger." Second, the pier, pedestal, mounting itself, tube and counterweight are all rock-solid. The parts are well designed and accurately assembled without looseness. Third, partly because of this careful assembly the axes remain effectively a full eight inches in diameter. Their connecting casting is rigid. For a less painstaking builder, loading this- mounting with a 850-pound telescope would be to push luck to the limit or past it. Dr. Custer's correspondence and his photographs show that he was meticulous with every detail of it.

"I could hang my full weight on the counterweight arm and not bend it a millimeter," Dr. Custer answers to a pointed question. "Its cone is fastened by multiple screws to a curved sheet of boiler iron that covers the entire end of the inside of the tube and is welded to it. Thus the cone is not merely screwed to the thin tube."

The observing chair may be quickly moved up or down the pedestal and reattached at any of the holes in angle irons welded to the pier. Its own seat and back are also adjustable for height and distance from the tube.

The mirror cell has a three-point support and is housed within an outer "basket" having screen-covered ventilating openings, two hasps and two padlocks. Without removing the-basket the mirror may be covered when not in use with a cap inserted through a slot in its side and manipulated through one of five large ventilating holes along the tube. The tube is swung to the pier and a flashlight bulb beneath the mirror is plugged into the wiring for the lights that illuminate the setting circles. This prevents dewing. Snap switches for these lights and for the drive motor are placed within quick reach on the south side of the gearbox base for the mounting.

Suppliers and Organizations

The Society for Amateur Scientists
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East Greenwich, RI 02818
Phone: 1-877-527-0382 voice/fax

Internet: http://www.sas.org/

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