Our analysis is based on the pure phase distribution equations of the Fresnel diffraction of an amplitude grating. Suppose P and M are positive integers which have no common divisor and 1/M is the opening ratio of the amplitude grating. Characteristics of the pure distributions are analysed. For instance at the fractional P/2M Talbot distance and (1-P/2M) Talbot distance, the amplitudes of the Fresnel diffraction field of the grating are the same while the phases are opposite. As an example we design two Talbot illuminators which phase distributions occur respectively at the fractional P/2M and (1-P/2M ) Talbot distance. Both phase distribution can carry out illumination behind them. Array illumination has important application in information optics
Statistical characteristics and variation of speckle intensity in deep fresnel diffraction region
