Measurement of roughness based on the Talbot effect in reflection from rough surfaces.

In the present work, the Talbot effect of a square grating is analyzed when light is reflected from a rough surface. It is shown theoretically that the scattered light intensity in the Fresnel diffraction limit depends on statistical properties of the rough surface, the angle of incidence of the light, the grating period, and a geometric coefficient, related to the ratio of distance of the rough surface and the observation plane from the grating. At Talbot distances of the grating, the surface height difference function, in terms of multiplication of the Talbot number, the grating period, and the geometric coefficient is the modulation transfer function (MTF) of the scattering in reflection from the rough surface.