Solutions and analyses of fractional-Talbot array illuminations

摘要

Gratings with different opening ratios (1/M) will have different fractional-Talbot distances with pure-phase distributions. We describe a simple step-by-step numerical method, which can be used to calculate the positions of the fractional-Talbot pure-phase distribufons and their corresponding phases. It is observed that the pure-phase distributions will only be at p(1/2M)Z_(T) distances (where Z_(T) is the Talbot distance, p and M are integers and have no common divisor), and that there are specific symmetries of the phase distributions at the different fractional-Talbot distances. It is also found that the neighbouring-phase differences of the pure-phase distributions are regularly rearranged, depending on the different fractional-Talbot distances. So we can obtain the pure-phase distributions from the regularly-rearranged neighbouring-phase-difference distributions at the different fractional-Talbot distances, without using a step-by-step numerical method.