Foucault published this in 1859, in his memoir on the construction of silvered-glass telescopes, and it changed who was allowed to make a telescope. Before it, figuring a mirror was a guild skill passed by apprenticeship and judged by the finished star image. After it, the surface could be measured directly, zone by zone, by anyone with a dark room. The silvered-glass mirror itself — Foucault's other contribution, replacing brittle speculum metal — and this test together put large reflectors within reach of amateurs, where they have remained ever since.

Why it is so sensitive. Two amplifications stack. First, a bump of height x on the surface displaces the reflected wavefront by 2x, because the light travels the error twice. Second, the test converts a longitudinal displacement of the focus into a lateral sweep of a visible shadow across a disc many centimetres wide — an enormous lever arm. The eye is very good at spotting an asymmetric grey gradient, and that is all the skill the test asks of it. Surface defects far smaller than the wavelength of the light being used show up as plain shading.

The counter-intuitive part. A parabolic mirror — the shape you actually want — does not null at the centre of curvature. Only a sphere does. Tested this way a good paraboloid looks wrong: it shows the classic doughnut, like a sphere lit from one side. Beginners routinely polish that away and end up with a beautifully spherical, optically useless mirror. The doughnut is the target, not the fault.

What it cannot tell you. The knife-edge test measures rotationally symmetric zones extremely well and astigmatism poorly — a mirror that is slightly cylindrical can pass zone testing and still perform badly. That is why serious workers rotate the mirror between tests and cross-check with a star test on a real night sky. Foucault's method is a superb tool with a known blind spot, and pretending otherwise produces confident measurements of the wrong thing.

Optical

Blueprints (1)

Foucault Knife-Edge Test