Fresnel Diffraction of the Plane Phase Grating

Abstract

Multibeam scalar theory is developed for the Fresnel patterns of the finite grating. An analytic expression is obtained for the intensity distribution of the distant pattern. This predicts the image formation which is found experimentally. For nearer patterns, a computing machine code has been programmed. The intensity distributions of patterns in which two orders interfere have been calculated. These are compared with the predictions of the Rayleigh–Voigt theory in the scalar form, and are shown to differ only by the expected edge effects. The results of the electromagnetic form of the Rayleigh–Voigt theory are obtained. Interesting differences between scalar and electromagnetic forms of the theory are pointed out and discussed. These may be used as the basis for a significant experimental test of the theory.