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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 |12nλ| will give rise to n well-defined fringes.
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Gascoigne et al. (1944) studied this question.
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