On the Theory of the Zonal Foucault Test

Abstract

The aim of the paper is to provide a theory of the zonal Foucault test which permits a discussion of its systematic errors and of its limiting accuracy. In Sections 2 and 3 it is shown that ray theory is inadequate for this purpose and that the analysis must be based on diffraction theory. In Sections 4 and 5 the diffraction theory of the test is developed and it is shown that, provided certain precautions are observed, the zonal readings for a true spherical mirror are not disturbed by the coherence-asymmetry which may be present in the illumination. In Section 6 it is shown that, in the zonal testing of astronomical paraboloids with f/300 f/300 zonal apertures and with a pinhole or slit of width not much exceeding 0.001 inch, the zonal readings are not sensibly disturbed by the diffraction phenomena and the Foucault shadows on the two members of a pair of zonal apertures show the same sequence of changes as the knife-edge is brought across. It follows that, used in this way, the test is free from appreciable systematic errors and its accuracy is in practice limited only by the observer's limited power of brightness-discrimination.