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.