Abstract

The statistical properties of the speckle phase in the diffraction region are theoretically and experimentally investigated. The statistical parameters describing the equiprobability density ellipse, by which the speckle field is characterized, are first derived for the general case. By using the equiprobability density ellipse, the statistical properties of the speckle phase are next investigated theoretically as a function of the observation point in space and the illumination condition. The speckle phases were experimentally measured by means of a heterodyne interferometer to verify the theoretical results. In particular, when the diffuse object is illuminated by a Gaussian beam around its waist region, the statistical properties of the speckle phase are revealed to be similar to those observed already in the optical imaging system with respect to the defocusing.

© 1986 Optical Society of America

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