Power spectral distributions of dot arrays with gaussian random spatial fluctuations

The behaviors of power spectral distributions of randomized dot arrays are investigated to reveal a variety of their photographic patterns that depend strongly on the exposure condition. For this purpose a theoretical analysis is expanded on the basis of the Gaussian statistics for the fluctuations of the dots, by which an analytical result is obtained. The behaviors of power spectral distributions are quantitatively examiiied by using the generalized fluctuation parameter and discussed by taking into account the exposure condition for photographic recordings. It has been revealed experimentally and theoretically that the Airy-disk pattern resulting from the diffraction of a number of independent elementary dots is observed in the long exposure, while the line spectra resulting from the mean periodic structure of dot arrays are observed in the vicinity of the origin in the short exposure. In this process of exposure, moreover, the light-depletion phenomenon, which was first reported by Stark [J. Opt. Soc. Am. 67, 700 (1977); 68; 1785 (1978)] and later analyzed in some detail by Martin and Aime [J. Opt. Soc. Am. 69, 1315 (1979)], is interpreted from the novel standpoint involving the fluctuations and the exposure condition. As a result, it was found that this phenomenon is recognized in a certain restricted range of the fluctuation parameter of dots under the condition of an appropriate exposure.