December 1998 Newsletter

Stockton Astronomical Society

Valley Skies

Valley Skies - December 1998 Issue

The Telescope Nut
by Jeff Baldwin

Parabolizing, Part II

here are at least three ways to compare a sphere to a paraboloid (see illustration). One is to match their edges. Another is to match a mid-zonal region, usually the 71% zone (0% being the center, 100% being the edge). Lastly, you can match their centers. Which way you compare them determines how you will correct the mirror to change it from a sphere to a paraboloid.

I usually allow the edge of the mirror to be considered perfect and alter the remaining glass to a paraboloid in reference to the edge. The sphere has the same radius of curvature throughout its surface, but the paraboloid has a shorter radius of curvature near the center, longer towards the edge, and a continuously smooth rate of change of curvature as you move from the center to the edge. To accomplish this on the glass, you must change your polishing techniques so that the center is worked more than the edge in this nice smooth continuous fashion. This will cause the center to deepen and become more concave, while the edge gets the least amount of work and will maintain a longer radius of curvature.

Radius of curvature, paraboloid, sphere, concave, zone: what do these terms mean in the context of making mirrors?

Imagine connecting a pencil to a string and connecting the other end of the string to the floor. Now tighten the string and draw the circle allowed by moving the pencil and keeping the string tight. The radius of curvature of the circle is the length of the string. A mirror has a radius of curvature, and if it is a spherical mirror, the radius of curvature is the same everywhere. If the mirror is a paraboloid, its radius of curvature changes from longer on the outer regions to shorter on the inner regions. We'll call these regions "zones". The center of the mirror is the 0% zone, the edge is the 100% zone, and the zones form circles around the center. Concave means that it is curved like a bowl, or a crater. Convex would be the other way, like a dome, or the top of your head (unless you're Frankenstein).

OK, back to it. We need to polish the mirror so that the center gets more work (correction) than the outer regions, rather than keeping it spherical. To do this, I like to use sub-diameter laps. Instead of using a pitch lap that is the same size as the mirror, I make a new pitch lap that is smaller than the mirror, usually around 25% to 33% of the size of the mirror. As I walk around the barrel, I stroke the sub-diameter pitch lap across and back so that the lap crosses the center of the mirror on odd strokes and slightly to the right of the center of the mirror on the even strokes. As you progress around the mirror, this will place corrective work on the center on EVERY stroke, while it only hits the outer zones on occasional strokes. Furthermore, as you move in towards the center zone the work increases, and as you move out towards the outer zones the work decreases, and this rate of change is smooth.

This will keep the outer zone the same as it was as a sphere, but reduce the inner zone's radius of curvature. The mirror will progress from a sphere to a prolate ellipsoid, then to a paraboloid, then to a hyperboloid, then to more severe hyperboloids. So as you can see, a paraboloid is only one of the things you could get. The biggest trick in the business is knowing when to stop. If you stop before you have a paraboloid, your mirror is under-corrected. Oblate ellipsoids, spheres and prolate ellipsoids are all under-corrected. A paraboloid is corrected. All the hyperboloids are over-corrected. Only one of them is what you want (with Newtonian optics), and that is the paraboloid.

We need to find out a way to determine when enough is enough, and that is the topic next time. We already know about how far to correct the glass. Those charts I had in last month's Telescope Nut show how much glass is to be removed to do the trick. However, knowing when you've gone that far will be determined by the Foucault test, Ronchi test, star test, caustic test, null test (either with stars or with autocollimation), interferometer test (either laser or birefringence), Ross or Dall null tests, and a variety of other tests that are available to opticians. We'll start out using the Foucault and Ronchi tests. Later we'll use the caustic test and star test.

Next month we will hit more vocabulary (prolate ellipsoid, oblate ellipsoid, paraboloid, hyperboloid), and we will discuss the Foucault test.

Clear Glass...Jeff Baldwin
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