Abstract
The surface roughness dependence of the first-order probability density function (PDF) of an integrated speckle pattern, produced in the condition of circular detection aperture and gaussian scattering spot, was theoretically investigated. The mutual intensity J A ( x 1, y 1; x 2, y 2) containing two roughness parameters, dispersion of surface height 〈ø 2〉 lateral correlation length x c , was calculated. The exact first-order probability density function was analytically derived and numerically calculated by means of the Karhunen-Loeve expansion and fast Fourier transform (FFT). As a diffuse object became smooth, the first order probability density function was changed from negative exponential to sharp peak gaussian centered around mean intensity.
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