Abstract
In two previous papers the second-order statistics of time-averaged speckle were investigated for speckle patterns formed through moving apertures, in one case for speckle patterns produced in the far-field and in the other case for speckle patterns produced in an image plane. In the present paper attention is devoted to the first-order statistics, with two forms of solution being obtained for the probability density function of intensity, one an exact solution and the other an approximate solution. Both forms of solution are shown to apply equally to either the far-field scheme or the image-plane scheme. With the image-plane scheme it is found that, just as for the second-order statistics, the result is not influenced either by the aberrations of the lens or by the object having non-uniform brightness, subject to the previously obtained condition that the brightness fluctuations are slow in comparison to the size of the point spread function of the lens. As in the two previous papers, the theory only applies when there is a large number of independent scattering points contributing to any given point in the speckle pattern.
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