Talbot effect of curved grating

Fresnel diffraction of curved grating with the parabolic cylinder, the cylindrical surface or the elliptic cylinder profile, is studied theoretically and experimentally. The transmittance function of grating with the smaller curvature is expressed by Fourier series and the mathematic expression of the diffraction intensity in Fresnel region is deduced. The influence of the curvature of grating on the diffraction distribution is analysed theoretically. The simulation results show the longitudinal intensity distribution of curved grating takes on the divergence structure, and this structure gets clearer with increase of the curvature degree. The transverse distribution at Talbot distance deviates from the grating structure and the magnified image of grating appears at modified Talbot distance. One practical experiment is conducted and the experimental results verify these theoretic predictions. The work of this paper will be helpful for understanding the diffraction of curved grating and prompting the application of Talbot effect of grating in wave-front sense and optical encode.