Background: Null Tests

This section is probably not interpretable without some background. Both Texereau(1) and Berry(2) have good sections that introduce Foucault knife-edge testing of paraboloids. If the following discussion makes no sense, read over one of these reference sections, then come back to this web page.

When using a knife-edge test to examine a paraboloid mirror, each concentric ring has a different radius of curvature. When the knife edge cuts the returning light at the radius of curvature for a zone, both sides of the ring go gray simultaneously. The knife edge is moved forward or back to find the radius of curvature for each zone, and the points are plotted to determine how close the surface is to a paraboloid.

Plotting data from knife-edge tests seems like a lot of bother. Isn't there a simpler method? There are a number of "null tests" that in theory are simpler to apply and interpret than a Foucault Knife-edge test. A sphere can be null tested at its radius of curvature. Now each concentric ring has the same radius of curvature, so the whole surface goes gray at the same time as the knife-edge cuts the retuning light beam. Any deviation from a sphere is immediately obvious because that section of the mirror is either brighter of darker than the rest of the mirror. There is nothing to plot, and with experience one know immediately whether sections of the mirror are too high or too low. Using the same setup, a Ronchi grating will return straight lines in a null test. Unfortunately, a sphere does not make a good Newtonian mirror.

The simplest null test for a paraboloid is a star test. In theory, just passing a knife-edge in front of the eyepiece holder when focused on a star will give the same uniform graying of the mirror surface. The problem is that atmospheric seeing is virtually never good enough to give a good null, and you need a good mount to track the star. Selecting Polaris as the star will let you get by without a tracking mount, but atmospheric turbulence is more of a problem. Star test using a Ronchi grating have become popular, because they are much less sensitive to atmospheric turbulence. The Ronchi star test is a very good for quick evaluation of the mirror (or telescope) quality, but it is not very sensitive. Still, if your telescope is not performing well, it is a good place to start. For mirror making, it leaves a lot to be desired.

Many different workers have developed bench null tests for paraboloids that get around the problems with a knife-edge star test. Each of these methods requires an additional optical component to introduce compensating spherical aberration in the light source, usually a pinhole, so that it behaves as a star at infinity. The Dall test uses a plano-convex lens in front of the pinhole(3). A Ross test uses a plano-convex lens in front of both the pinhole and the knife-edge tester.(4) The Waineo null test(5) uses a spherical mirror, and is closely related to the Jones test(6). In each of these tests, the mirror must be set at a fixed distance from the light source to add the correct amount a spherical aberration. An additional consideration is that not all null tests are perfect nulls. There is residual spherical aberration with any particular setup, that can be evaluated using ray tracing software or the more specialized software included below(7,8). A null test is convenient in that there is nothing to measure, but remember each setup is limited by the quality of the compensatory optical element and the inherent quality of the null.

Waineo Null Tests Equipment

I prepared an 8" F5 sphere to use in the Waineo null test. It has a 1" hole in the center, and gives a very nice null with a knife-edge test. It is mounted in an adjustable cell on a home-made optics bench. The pinhole or slit is mounted on a block of oak and slides in an aluminum U-channel The critical distance from the light source to the reference mirror is set using the scale attached to the U-channel. The mirror is placed on the adjustable mirror mount, and everything is aligned. Align the light source and the paraboloid mirror to focus the light back to the reference mirror hole, and then align the reference mirror to put everything in line. There is a much more complete discussion of the alignment on the web(5). The entire light source and reference mirror assembly is mounted on drawer slides with a screw feed. The null is measured with a knife edge behind the reference mirror, and the null is achieved by moving the assembly back and forth using the screw feed. The null can be examined using either a knife-edge test or a Ronchi grating. The light source must be narrower than the Ronchi grating lines to be useful. Once is is set up and aligned, repeated test on the same mirror are quick and easy.

Here are some picture of the Waineo test setup.

References.

Note that references 7 and 8 include downloadable software for Macintosh computers.

(1) J. Texereau, How to Make a Telescope, Second Edition, 1984, Willmann-Bell, pp. 59-85.

(2) R. Berry, Build Your Own Telescope, Second Edition, 1994, Willmann-Bell, Chapter 11.

(3) a) H. Dall, "Null Test for Paraboloids," in Amateur Telescope Making Volume 1,"A. G. Ingalls Ed., 1996, Willmann-Bell, pp. 315-319. b) R. E. Cox and R. W. Sinnott, "Extensions of the Dall Null Test," Sky and Telescope, September, 1976, 210-216.

(4) D. E. Stoltzmann and P. Ceravolo, "Ross Null Test for Conic Mirrors," Applied Optics, 1993, 32, 1189-1199.

(5) The Waineo test is described on the Mel Bartel's web site. The Waineo null test information can be found here.

(6) R. W. Sinnott (and E. Jones), "The Reflective Null Test for Mirrors," Sky and Telescope, July, 1992, 85-90.

(7) A description of the Waineo test including software can be found at Mel Bartel's web site. I have adapted the program for calculating mirror distances, written by Bob Bridges, for a Macintosh computers. Download Waineo98.mac here.

(8) The article describing the Jones test included a basic program to calculate distances. You can download a chipmunk basic version of the Jones_program here.