Talbot effect of grating with fractal rough edges

Since the random edges of practically manufactured grating can be described by the self-affine fractal model, this paper investigates theoretically Fresnel diffraction of grating with rough edges on the basis of the self-affine fractal theory and discusses the variation of the Talbot image of grating with the rough parameters of edges. The amplitude gratings with different rough edges are produced with the help of the correlation function of the random distribution. Then, simulations of the diffraction intensity distributions of rough gratings are performed, and the modulation effect of speckles on Talbot image are shown. In order to explain the variation of the Talbot image of grating with rough edges, the theoretical analysis of the Talbot effect of grating with rough edges is given according to the statistic optics theory. The presented approximate analytic expression of the average diffraction intensity indicates the relationship between the diffraction and rough parameters of grating edges. The conclusions of this paper are useful for evaluating the Talbot image of practical grating.