The effects of many phase errors that are distributed in any manner over the aperture of the objective are evaluated in terms of a coefficient <i>B</i> that governs contrast in the image of an unresolvably small object. The object and its surround are assumed self-radiant. The corresponding formulation for the contrast coefficient is solved for <i>n</i> zones that have different, stepped phase errors and for <i>n</i> zones within which the phase error has parabolic dependence on radial distance from the center of the zone. The resulting formulas for <i>B</i> are so simple and the significance of <i>B</i> sufficiently broad that the method is advantageous for estimating the effects of phase errors which are too complex to be treated in a practical manner by other methods.
HAROLD OSTERBERG and LUTHER W. SMITH, "Effects of Arbitrarily Located Phase Errors upon Contrast in the Image," J. Opt. Soc. Am. 54, 525-525 (1964)