Measurement of surface parameters from autocorrelation function of speckles in deep Fresnel region with microscopic...

The derived two-dimensional autocorrelation function of speckles in the deep Fresnel region shows that it is related to the scattering of rough surface with the scattered intensity profile acting as the aperture function. We propose the method that is convenient for measuring surface parameters from the normalized autocorrelation function of speckles acquired with a microscopic imaging system. In experiment, a multi-scale behavior of the speckles has been identified, which is compatible with fractal character. With the speckle intensity data, we calculate the normalized autocorrelation function of the speckles and extract the roughness, the lateral correlation length and the roughness exponent of the random surface samples by fitting the expression to the autocorrelation function data. Comparison of the results with an atomic force microscopic measurements shows that our method has a satisfying accuracy.