How to test optics

Aspheric (non-spherical) optical surfaces are used to produce images free of aberrations. For example, a concave spherical mirror produces perfect images of a point at its center of curvature, but suffers from spherical aberration when imaging light from infinity at its focal point. A parabolic mirror with the same focal length is aberration free for light incident parallel to its axis. The problem of manufacturing aspheric mirrors is primarily one of testing them, and measuring their surfaces. The tragic error in figuring the mirror for the Hubble Space Telescope is an example of how difficult adequate testing is.

The first satisfactory test for non-spherical surfaces was invented by Louis Foucault (around 1850), and is known as the knife-edge test. In this experiment you will apply this test to a concave mirror that is not spherical. The development of this test made it possible to build the large astronomical telescopes that have totally altered our perception of distant parts of the universe.

The basis of the test is very simple. A light source is set up behind a narrow slit, and the beam is directed toward a concave mirror. If the mirror were spherical, the reflected light would return toward the source. When the source is exactly at the center of curvature of the sphere, its image is perfect. Under these conditions, a sharp edge parallel to the slit and exactly at the focus will precisely block all of the light from the mirror. If you were to place your eye immediately behind this edge and focus on the mirror itself, you would see the mirror darken uniformly as the edge is moved into the beam.

Figure 7.1: The tester has a small prism that directs light from a narrow slit to the concave mirror. Light returns from the mirror to focus on the sharp straight edge. By moving the the edge inside or outside of best focus, the observer can see details of the imperfections on the surface.

Notice too, that if the edge is closer to the mirror than the center of curvature and introduced from the left, it will block light from the left side of the mirror. You will see a dark region on the left. If the edge is farther from the mirror than the center of curvature, it will block light from the right. You will now see a dark region on the right. So when the mirror darkens uniformly the knife-edge is exactly on the center of curvature.

The eye sees the left side of the mirror darken when the knife-edge enters, inside the focus, from the left. Yet the light pattern leaving the focus is darkened on the opposite side. Remember that the image on the eye is inverted, and that the brain turns the image around again!