A contribution to the theory of the Foucault test

Abstract

A diffraction theory of the Foucault test is developed which covers the practically important case of a circular mirror with errors of figure of arbitrary form, tested with a knife-edge whose lateral adjustment is variable. The theory is first applied to discuss the changes in appearance of a true mirror as the knife-edge is advanced across the axis. Next, corresponding formulae are obtained for the case of a mirror possessing a small amount of primary spherical aberration, tested near mean focus. Lastly, the theory is applied to obtain an estimate of the sensitiveness of the test, first as a means of determining focal position, and secondly as a means of detecting primary spherical aberration.