Talbot image of two-dimensional fractal grating

Talbot effect of two-dimensional fractal grating built by square aperture arrays is studied theoretically and experimentally in this paper. The amplitude fractal gratings are produced by use of the spatial light modulator, and the diffraction intensity distributions of fractal gratings with different fractal level in Fresnel diffraction field are measured with the help of the two-dimensional CCD. Talbot images of fractal gratings with 1-level and 2-level fractal are obtained in practical experiment. The analytic expression of Fresnel diffraction intensity of the fractal gratings is derived through decomposing fractal gratings into the sum of many periodic gratings. Theoretic results predict the self-image of fractal grating reappears at some certain distance. The numerical calculations also show the Talbot image and the fractional Talbot image of fractal grating. These results may extend the application of fractal grating in the optical processing of information and laser measurement.