Surface-roughness dependence of the intensity correlation function under speckle-pattern illumination

The surface-roughness dependence of the intensity correlation function of the speckle pattern, produced in the Fresnel region with fully developed speckle-pattern illumination, has been theoretically investigated and has been discussed as follows. This correlation function is represented by two correlation functions of scattered and unscattered components. As the diffuse object becomes rough, the speckle size varies from the speckle size of the illumination light to that obtained with the condition, so that the object is a deep phase screen. The speckle contrast, however, is always one.