The Theory of the Foucault Test

A diffraction theory for the Foucault knife-edge test is given, a closed expression being obtained for the variation of light-intensity over a mirror with arbitrary error when it is tested with a knife-edge. The geometrical explanation of the test is derived as the limit when λ → 0, and examples are given of several commonly occurring errors. In particular, it is shown that an edge turned by $$\frac12n\lambda$$ will give rise to n well-defined fringes.