On the interpretation of the Foucault test

The diffraction theory of the Foucault test is applied to discuss the intrinsic errors of the test when the Foucault shadows are interpreted by means of the ‘ grazing light ’ fiction in the usual manner. In § 2, formulae are obtained for the effects on the Foucault shadows of an arbitrary small change in the figure of the mirror under test. In § 3 the case of a weak, narrow local zone on an otherwise nearly true mirror is discussed and expressions are obtained in terms of the zone-profile for the changes in the Foucault shadows caused by the presence of the zone. The relationship between the zone-profile inferred by means of the ‘grazing light’ interpretation of the shadows and that actually present on the mirror is analyzed in § 4, and it is shown that the analysis suggests some modifications in the practical technique of figuring mirrors under the Foucault test. Lastly, the general formulae established for weak, narrow zonal errors are compared with the results of computation in four selected special cases and it is shown that they may be expected to remain useful approximations in cases of interest to the practical mirror-maker.