Showing papers on "Zernike polynomials published in 1969"

General Diffraction Theory of Optical Aberration Tests, from the Point of View of Spatial Filtering

Abstract: A general theory of optical-aberration tests, encompassing many well-known practical tests, is presented, utilizing the formalism of spatial filtering, employing coherent illumination. The basic diffraction integrals of the Ronchi-grating test, Foucault knife-edge test, phase Foucault knife-edge test, and the Zernike phase-contrast test are derived. Typical situations have been analyzed and numerical results are shown and discussed.

Orthonormal Expansion of the Aberration Difference Function and Its Application to Image Evaluation

Abstract: Method of orthonormal expansion of aberration function is applied to the evaluation of the normalized image contrast M introduced by H. H. Hopkins, the decrease of which is proportional to the variance of the wave aberration difference function V over the domain S common to the two pupils displaced relative to each other. The difference function V is expanded in terms of Zernike's circle polynomials, the domain S being approximated by an ellipse fitted to S. The orthogonal coefficients of V are derived from a linear transformation of the orthogonal coefficients of wave aberration expanded over the pupil domain. A general formula of this transformation matrix is presented. A method of calculating the normalized image contrast M is described in terms of orthonormalized aberrations together with some numerical examples.