Friday, May 20, 2005

Foucault Test

If you are an historian or other academic, you may think that a "Foucault test" is one where you are asked to make sense of an incomprehensible block of deconstructionist text. But actually, there is another Foucault--one who came up with something useful.

Big Bertha, the 17.5" reflector I bought a while back (very cheap) has never performed as well at high magnification as it should. I've done enough experimentation now that I believe the problem is either a defective primary mirror, or the diagonal mirror is too large.

What makes a telescope mirror defective, and what is a Foucault test? You may recall (but more likely, you don't) that somewhere along the way, proponents of the New Math showed you a cone, slice about four different ways. My recollection of this was from fourth or fifth grade. I could not for the life of me see why I should care about the difference between a circle (cutting the cone parallel to the base), an ellipse (cutting the cone at a bit of angle), a parabola (cutting the cone parallel to the slope), or an hyperbola (cutting the cone at a sharper angle than the slope).

Here's a picture, to refresh your memory:

Associated with every figure sliced from the screaming flesh of the cone are two foci. The two foci are on top of each other for a circle, and some distance apart for an ellipse. Here's how you use those foci to draw an ellipse:

It turns out that all planetary orbits are ellipses.

The parabola has two foci also--one real close, the other at infinity. The hyperbolas far focus is beyond infinity (which makes only a little less sense than saying it is at infinity).

What does any of this have to do with telescopes and Foucault?

It turns out that the ideal telescope mirror is a parabola: one focus is up close--about where you put your eye. The other focus is at infinity. A parabola takes the image at infinity (and for practical purposes, all astronomical objects are at infinity) and focuses all the light and image where you put your eye.

Making parabolic mirrors isn't easy. You normally start by grinding a telescope mirror spherical, and then altering its shape with some rather empirical methods, into a parabola. I've done this before, long, long ago, when I made a telescope mirror. It isn't easy--and until the middle of the nineteenth century, no one really knew how to tell when a mirror had reached the perfection of a parabola. Just to make life really miserable for telescope makers, to make a really good telescope mirror, you have to make that parabola so accurately that it is accurate within 1/4 wavelength of light. Yes, you read that correctly. This means that the surface of the mirror has to be within tolerances of millionths of an inch.

Until Jean Foucault (who also invented the gyroscope, Foucault pendulum, and proved that light moved more slowly in water than in air) came up with the Foucault test, figuring out whether a mirror was a proper parabola was largely experimental. You took the telescope outside, aimed at a star, and then tried to see if it would focus correctly or not. If it was fuzzy--if you couldn't get a crisp focus--it probably wasn't a parabola.

The Foucault test is capable of measuring those millionths of an inch difference between a spherical mirror, and a parabolic mirror--and doing it with surprisingly simple mechanisms. Here's a detailed description of it. The essence of it, however, is that different parts of a parabolic mirror--different "zones"--will come to slightly different focal points than a spherical mirror. For a light source at the focal point, the spherical mirror will bring all the light back to the same point. The parabolic mirror will bring the light from different rings on the mirror to slightly different points--and a few millionths of an inch turn into fractions of inch of difference on the focal points.

Anyway, I used to have a Foucault tester. I don't know. I am going to try and find someone locally who has one that I can use on Big Bertha's mirror.

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