The characteristic of the fractional Talbot effect of a grating and a fractional Fourier transformation under spherical lightwave illumination

摘要

In this paper we study how to fulfil fractional Talbot effect by using of a grating and a fractional Fourier transformation in case of sphere lightwave illumination. Our analysis is based on the Guigay theory about the diffraction of a grating and the fractional optical Fourier transformation. First we turn the diffraction of a grating and a fractional Fourier transformation under spherical lightwave illumination into that of a single effective grating under parallel lightwave illumination. With the aid of fractional Talbot effect of a grating under parallel lightwave illumination, we give out the fractional Talbot effect condition of the system under spherical lightwave illumination. Calculations show that the fractional Talbot distances and period can be adjusted conveniently by the incite light wavelength, the period of the grating, the parameter of the fractional optical Fourier transformation and the distance of the spherical lightwave. The more parameters connected to fractional Talbot selfimaging, the more easily to carry out fractional Talbot effect. Our analysis will perfect fractional Talbot self-imaging theory and will be useful in applications of fractional Talbot effect.