Full-description of integer Lau effect with arbitrary amplitude diffracting grating

A complete theoretical explanation of the integer Lau effect is presented for arbitrary transmission function of diffracting grating based on Fresnel diffraction theory and Fourier series representation of the grating function. It is shown that, in the case of amplitude diffracting grating, for some gratings separation distances which are equal to an even multiple of an elementary distance the intensity distribution function at output plane in Lau setup are similar to the squared modulus of the diffracting grating. For the gratings separation distances equal to an odd multiple of the elementary distance the output intensity functions are also similar to the squared modulus of the diffracting grating but with only its even frequencies. Binary gratings are treated as an important case. Performed simulations and experiments verify correctness of this theoretical analysis.