The Foucault (pronounced FOO-COH) test is an optical bench test for evaluating astronomical mirrors. It is named for its inventor, Leon Foucault. It is a null test for a sphere (in other words, it is most accurate and simple in measuring spherical mirrors), but is also commonly used to test parabolic mirrors.

To test the mirror, either a narrow slit or pinhole is placed at the center of curvature of the mirror to be tested, and illuminated from behind, so that light passes through the hole or slit and hits the mirror. A straightedge (typically a razor blade) is placed as close to the light source as possible, and the observer looks past the edge of the straightedge, with the eye as close as possible to it.

If the mirror is a perfect sphere, the source will be imaged back to itself (but upside down and backwards). If the straightedge is moved slightly to cover the image, it will cover it with a very slight movement (since the image is very small).

Because the observer's eye is so close to the image, it can't be focused on the retina. Instead, the eye focuses on the mirror's surface, which appears brightly illuminated. As the image is covered by the straightedge, if the mirror is a perfect sphere, it will appear to darken all at once, because every part of the mirror is reflecting light to the same point in space.

If there is any deviation from a perfect sphere, that part of the mirror will be reflecting light outside of the point, and that part of the mirror will appear either darker (if it was reflecting light to a point already covered by the straightedge) or lighter (if it was reflecting light to a point not yet covered by the straightedge) than the rest of the mirror.

If we're testing a parabolic mirror, for example, we consider the parabola to be made up of many concentric rings, each of which approximates a ring cut from a sphere. Of course, these rings will have different centers of curvature (if they had the same center, the mirror would be spherical).

A mask (it can be cut from cardboard) is placed in front of the mirror, so we can examine one ring at a time. The difference in center of curvatures of the various rings are measured, and from this, the deviation of the surface from a sphere can be computed. Rather than a mask, some people prefer to place a stick with pins in it in front of the mirror, and examine the area around pairs of pins equidistant from the center of the mirror.

Jean Texereau, in his book How to Make a Telescope says he has measured errors on a mirror's surface that are 1/300th of a wavelength of light high (that's 72 billionths of an inch high)!

The average amateur can't do so well, as such accuracy requires a trained eye, excellent conditions, and very accurate measuring equipment. However, it is quite possible to measure accurately errors on a parabolic mirror on the order of 1/10th of a wavelength of light or better, using very simple equipment.

You'll need a stand to hold the mirror being tested. You'll also need the tester itself, which consists of a platform to hold the light source and knife edge, which can be moved small distances accurately.

To perform the test, you need either a table at least twice as long as the mirror's approximate focal length, or two smaller tables set up some distance apart. The room in which the test is performed should be as vibration-free as possible, and be at a stable temperature and not too drafty (as all of these factors will be visible in the test, and make it difficult to get readings). A basement is usually ideal, if you have one. A comfortable chair is a plus, as well as dim lighting (which is easier than darkness or bright room light for performing the test).