Figure-error determination from diffraction-based mathematical analysis of experimental Foucault-test data, compared with results of scatterplate interferometry

Abstract

Edward H. Linfoot developed an integral expression for the irradiance in the image of a lens or mirror under the Foucault knife-edge test as a function of figure error. Samuel Katzoff developed a convenient method of inverting the linearized form of Linfoot's equation to express figure error in terms of the irradiance distribution in the image (Foucault pattern). This paper presents the results of an experimental study on a 20-centimeter-diameter f/5 spherical mirror to complement the analytical work of Linfoot and Katzoff. The results clearly affirm the practicability of the Foucault test to quantitative evaluation of figure errors of near-diffraction-limited optical elements via the Linfoot/Katzoff formulation. The evaluation was based on a comparison of Foucault-test figure error data with parallel data from independent scatterplate interferometer measurements. The results are particaularly significant in that they reveal the fallacy of the widespread regard of the Foucault test as limited to qualications for the field of optical testing, since the test is basically simple, its implementation for quantitative figure error analysis is straightforward, and the associated experiemntal data processing is much simpler than that of interferometric testing methods. The question of potential use in figure error sensing in the planned large orbital telescope seems particularly pertinent.