A52 The Point Diffraction Interferometer

An interferometric test generally requires extra equipment of the highest quality. However, an elegant solution was invented by R.N. Smartt and John Strong (1972) and announced by them at an Optical Society of America conference. This method requires the manufacture of a sophisticated mask, but presumably an isolated worker may still attempt the test because of its low cost. Telescope testing was reported by Smartt and W.H. Steel (1975), and the evaluation of unknown wavefronts has been mentioned by others (Alfred and Mills 1989; Mallick 1978). This technique has also appeared in popular literature (Delvo 1985).

The aberrated beam of a telescope is imaged into a blurry spot bigger than the diffraction disk of a perfect aperture but still small enough to be close to the proper size. The aberration is preserved through the focus but only if the whole wavefront is allowed to contribute. If an opaque mask with a tiny hole is placed somewhere near the focus, the transmitted beam passing through that hole diverges spherically, no matter where the hole is located. That perfect wavefront occurs because individual portions of the wavefront are each behaving perfectly. The sum of all these spots at the plane of focus behaves imperfectly because they are mutually out of phase. Another way of thinking about it is to use a filtration argument. So much spatial information has been filtered out of the image passing through the tiny hole that the emerging signal can't help but be clean.

As this tiny hole is increased in size, the wavefront produced by it remains approximately spherical until the hole is about the size of a perfect diffraction disk. Then, sensibly, it begins to degrade into the actual wave-front.

This process is very interesting but is still of no help because nothing interferes with this perfect wavefront. If the mask is taken away, the original wavefront is present but no perfect wavefront exists with which it can interfere. If, however, the opaque mask is made slightly transparent, it is possible to cause the perfect wavefront escaping through the hole to interfere with the greatly diminished original wavefront.

A point-diffraction interferometer is sketched in Fig. A-13. The original

dimmed complete wovefroni

Fig. A-13. The point-diffraction interferometer.

wavefront and the wavefront escaping through the hole differ by the lined region. If a few visible fringes are desired, the hole must be offset until the sphere is tilted with respect to the darkened, complete wavefront by a few wavelengths. The hole is moved to the outer parts of the image, and the perfectly spherical wavefront emerging from this decentered hole becomes very dark. Transmission of the mask must be set low in order to obtain high-contrast fringes.

The first disadvantage of this test is that most of the light is cut off. This problem can be overcome by darkening the room and allowing your eyes to adapt or by using long-exposure photography. The second difficulty involves mask making. The maximum radius of the hole is a fixed function of the focal ratio, d = 1.22XF, so that number is no problem. But the transmission of the mask must vary from 0.005 to 0.05 depending on the severity of the aberration and how much tilt is desired.

Most users prefer to avoid cutting the hole. Instead, they make it part of the filtering operation. The filter can be made from a mostly exposed piece of finegrained photographic film. The holes are made by shading the film with tiny microspheres during the exposure step, as in Delvo's article, or these spheres can shade a glass slide during partial aluminizing. Smartt and Steel also describe an adjustable transmission mask comprised of two polarizing layers, one of which is punctured. To tune such a mask, they turn the unpierced polarizer until high-contrast fringes are seen. This polarizer is immersed in a liquid having the same index of refraction as the mounting plastic of polarizing material.

Although this test typically uses a laser and is performed in a bench-test autocollimation mode, the common-path arrangement does not demand the use of monochromatic light. Autocollimation is also not required. Smartt and Steel describe a test conducted at the focus of a large telescope on the image of a star. The test required excellent seeing, a stable mounting, and probably (although they didn't say) extraordinary patience.

In Delvo's article, the difficulty of making these masks has been reduced. Drops of liquid mercury are smashed into a high-resolution photographic plate, covering it with tiny mercury spheres.5 Unfortunately, such clever fabrication methods can't cure the test's most severe problem, which is pinhole alignment. The mask must be placed to within a few dozen micrometers from the center of the pattern. A kinematic stage is required if the user wants to avoid excruciating effort, preferably a stage with three axes.

To review, the difficulties of the point-diffraction interferometer test are as follows:

1. This test image is very dim.

2. The number of visible fringes and the contrast of the interference pattern are coupled together because the brightness of the spot drops away as it is decentered.

3. Convenient operation requires an expensive kinematic stage.

4. At the center of curvature, non-spherical mirror testing is difficult because the fringes are no longer straight. Test-reduction software is available, but its profitable use still demands great care and effort.

5. The most convenient configuration requires a full-diameter autocollimation flat.

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