Roughness and correlation-length determination of rough-surface objects using the speckle contrast

A method using the speckle contrast for the determination of both the roughness and the correlation length of surface-height variations of a rough-surface object is proposed on the basis of the statistical properties of the Gaussian speckle field in the image region. The expression for the speckle contrast is first theoretically derived in the optical imaging system as a function of the defocus distance and the surface parameters of the object. By solving the equations expressing the speckle contrasts at the image and defocus planes, a unique solution is found to exist for the roughness and the correlation length. In particular, a useful approximate relation that the roughness depends only on the contrast ratio is derived for relatively small values of the roughness. The experiments were performed to confirm the validity of the proposed method. The present method has an advantage of the simplicity in a measuring procedure where the contrasts at only the two points are required to determine the surface parameters.