Other Tests

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The 1930s were boom years for amateur telescope making in the United States, primarily through the popularization efforts of individuals such as Russell Porter and Albert Ingalls. Estimates have been made that up to 250,000 telescopes were begun during the years before World War II. In a way, it was the only option. The Great Depression was raging, and established optical shops specialized in making expensive refractors or contracting for professional instruments. If you wanted a reasonably priced telescope in those times, you had to make it yourself.

Soon, a few amateurs turned "pro," making instruments of the type other amateurs wanted and could afford to buy. Slowly, as number of such manufacturers increased, the character of amateur astronomy changed. No longer was grinding glass a rite of passage for entrance into the astronomical world. The advent of commercial Schmidt-Cassegrain catadioptric telescopes around 1970 completed the transformation. Telescopes are now consumer items.

In the old days, nearly everyone had some familiarity (if not expertise) with the knife-edge test and a general acquaintance with the concepts behind testing during fabrication. Few modern amateur astronomers have been directly involved in making their own instruments. Amateurs have heard about shop tests but have only looked through testers at a convention display. Most amateur telescope makers today deal with the mechanical design and construction of their telescopes, not the optics.

Thus, much of the material below will be new to many people. It may seem that I deal curtly and summarily with the various optical shop tests appearing here. This abruptness is not my intention. The tests below can be entertaining and give new insights into optical quality. Each one is so different from the rest that it offers a fresh perspective into the aberrations on the wavefront. Most of my criticisms are not about the tests themselves, but their improper use.

However, I do want to point out that these tests are not recommended if all you want to know is whether or not your telescope is a good one. They are all interesting, and some are phenomenally sensitive, but they aren't the most direct path to knowing if your telescope can work well. The star test is that path.

For the purpose of completeness, these tests are described below, along with brief lists of difficulties for novices or unanticipated expenses. These reasons for not recommending them are varied, but most of them boil down to the following:

1. Most of these tests are useful during optical fabrication of individual optical pieces, not evaluation of finished telescopes.

2. Many of these tests involve the purchase or manufacture of accessory hardware, some of which can be very expensive.

3. Often, they require complicated data reduction or difficult theoretical knowledge.

4. Most are oriented toward one type of surface and require multiple tests or additional optics if they are to be applied to the whole instrument.

Readers are encouraged to find out more about one or more of the following testing techniques. Each one of them could fill (and perhaps deserves) its own book, just as this one has been devoted to the star test. You can spend a lifetime discovering the details concerning any of them.

A.1 The Foucault Test

Jean Bernard Leon Foucault was an all-purpose scientist. He is best known for demonstrating the rotation of the earth by precession of the axis of a pendulum and measuring the speed of light. He also took the first daguerrotype photograph of sunspots, thus initiating astrophotography. Foucault made an early metal-on-glass telescope mirror. Finally, he invented a sensitive test of optics at their center of curvature.

Imagine a reflective sphere 6 meters in diameter. Clearly, light radiating from a point at the center of that sphere and diverging outward would strike every portion of the sphere at the same time, ft would then reflect and converge to be perfectly imaged as a point on the source that emitted it originally.

Although it would be a beautiful thing to behold, a reflective sphere 6 meters in diameter has few uses. If only one tiny portion of that sphere were silvered, the reflective part would be a weakly concave area. The non-reflective portions could then be trimmed off. Let's say the remainder is a 10-inch (250-mm) f/6 (1500-mm) mirror that we wish to test.

Some method of reading the optical quality must be devised before it can be said that a true test is being done. The first problem is that a source of light at the center of the sphere, an illuminated pinhole for example, is imaged back on top of itself. The imaged light is unavailable to the optician. Foucault solved this problem by offsetting the source slightly. The image point in this case is found across the center of curvature at a distance about equal to the offset. As long as the distance between the pinhole and image is kept small, the test only is slightly affected by astigmatism.

The second problem is coming up with a method of probing the image point for incorrect focusing. One could inspect it with an eyepiece and thus have a variant of the star test, but this method was already known at the time of Foucault. The pinhole inspection procedure does not readily yield numbers useful to plan the next polishing step. Inspection with an eyepiece also demands an extremely small source; in the 250-mm mirror above, the pinhole should be less than 16^m (0.0006 inches) across. This restriction was especially severe in Foucault's time because portable light sources were based on flame and were hence quite weak, diffuse, and difficult to focus on a pinhole.

Foucault's clever solution was to introduce an occluding edge into the beam near the imaging point. This test goes by the popular name "Foucault's knife-edge test" although the method does not depend on the sharpness of the blade. The knife is slowly introduced near focus. In the simplest configuration, the tester's eye is placed close to the knife and peers past it at the mirror. If the knife is between the mirror and the image point, the dark shadow of the knife appears to darken from the same side of the mirror as the knife. Outside focus, the darkness appears to cross the mirror from the reverse side.

One need not use a pinhole source at all. A short slit can serve equally well as long as the knife is parallel to its image. This way, the illumination can be increased hundreds of times.

The knife is moved toward and away from the mirror until focus is located. If the focused point is struck precisely, the shadow on the mirror does not exhibit the direction of knife motion. A knife setting for which non-directional behavior is found proves the mirror must be part of a sphere. It dims evenly before darkening entirely. The Foucault test of a spherical minor is a true null test—the reflection blanks out. See Fig. A-l.

If any high or low places on the mirror exist, no mirror-knife separation can be found at which the mirror darkens uniformly. The test superficially resembles the shadows cast from a lamp shining from the side of the mirror

Fig. A-1. Two Foucault test setups, one is perfect and the other shows a slight hill in the mirror's profile (the aberration is exaggerated).

opposite the knife. The hill acts as a protrusion on the apparently flat surface. One side is very bright, and the other side is very dark. The elevated region is shown perched on a neutral-gray plane. Of course, this side-lighting concept should be viewed as a convenient delusion. The "hills" cast no shadows, and the entire appearance of the display can be changed merely by moving the knife along the axis of the mirror. In the figure, you can pull the knife back until the center bump is uniformly gray and appears to be sitting in a huge cupped depression.

Foucault's genius was that he did not rest once he found this sensitive test for spherical mirrors. He modified his new test to figure paraboloids used as the primary optical element of Newtonian telescopes. The problem with testing paraboloids at their "center of curvature" is that a parabola is not a circle and a single center of curvature is not defined on its surface. You can squint your eyes and convince yourself that the shallow dish is a sphere to first order, but a perfect paraboloid shouldn't null.

The behavior of light rays near the center of curvature of a paraboloid can be straightforwardly calculated, however. They converge along the horn-shaped caustic defined by an overcorrected surface. The caustic is a region in which ray optics strictly breaks down, but for the purpose of the purely geometric Foucault test, one pretends that it does not.

Jean Texereau drew a very informative diagram of this behavior, which is reprinted in Fig. A-2 (Texereau 1984). The caustic appears best in the ray diagram at the bottom left, where part of it is blocked by the knife. The appearance of the Foucault test at various knife positions is depicted on the right side by stippled drawings. The length of this ray-crossing region (which appears as a black bar at the tip of the knife) is related to the correction of the mirror. For a sphere at its center of curvature the length, of course, is zero. For a paraboloid it is

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