A systematic analysis has been performed that predicts the existence of 36 cases in which 100% modulated, square-wave irradiance distributions can be generated in the Fresnel regime by simple binary-phase gratings. These types of distributions, referred to here as Lohmann images, have been previously predicted by researchers studying phase gratings known as Talbot array illuminators. Twenty of the cases are reported, to the best of my knowledge, for the first time. Sixteen of these new cases result in Lohmann images with twice the spatial frequency of the original grating. Experimental verifications of the theoretical predictions are presented.
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