SURFACE-ROUGHNESS DEPENDENCE OF THE 1ST-ORDER PROBABILITY DENSITY-FUNCTION FOR INTEGRATED SPECKLE

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)(x1, y1; x2, y2) containing two roughness parameters, dispersion of surface height [phi2] and 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.