Abstract

The general theoretical consideration for evaluating the statistics of the image illuminance of the uniform diffuse object under any illumination mode is described. The basis is the diffraction theory of an optical image given by Hopkins and the mathematical model of Enloe. With the help of the concept of the effective source, the frequency distribution of the spatial power spectral density of the speckle noise can be evaluated for any stage of partial coherence. In this paper, four cases are examined in which the effective source consists of (i) a single point source (coherent), (ii) multiple point sources, (iii) an extended plane source, and (iv) two small separate plane sources. One of the conclusions is that a ring source having the same extension as the aperture of an optical system serves to reduce the noise power to one-half of that, produced by a coherent (point) source. According to the general formula derived, the statistics of the coherent image-forming system can be described as a special case of the general treatment. This formula is useful in the evaluation of optical noise in various problems of optical image formation.

© 1974 Optical Society of America

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Equations (63)

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