Extraction of height–height correlation function of random surfaces from the average intensity of image speckles

Abstract

We present a method for the extraction of the height–height correlation function of random surfaces from the average intensity of image speckles. The setup of a Fourier transforming and imaging system with a variable aperture is used for both the theoretical analysis and experimental performances. Based on the analytical expression of the image intensity, an algorithm is developed to formulate numerically the intensity data versus the aperture radius into the pair of Bessel–Fourier transform and the inversion, from which the height–height correlation function is reconstructed. Three samples of Gaussian correlation are used for the experimental demonstration. The extracted height–height correlation function and the random surface parameters obtained thereby conform with those obtained by atomic force microscopy.