07-22U

The theory of diffraction grating image forming according to the Talbot effect is described on the basis of the vector as well as scalar diffraction theories. In the frame of the vector theory we use the coupled-wave method and obtain a set of differential equations describing diffraction of TE and TM-polarized waves. We show that the symmetry of the dielectric permittivity function allows to rewrite the differential equations set of $2N+1$ dimensionality as two equation sets of $N+1$ and $N$ dimensions. Using Rayleigh-Sommerfeld integral we obtain analitic solutions for diffracted and surface waves. Numerical calculation of the grating self-images in the three Talbot-planes using these two methods are given. The obtained results give identical self-images intensity distribution of local maximums and minimums.