Fresnel diffraction due to phase gradient singularity

In this Letter, a singularity in the phase gradient is introduced as a new origin of the diffraction from phase objects. The continuity in the amplitude and phase of the wave and the singularity in the phase gradient are assumed to describe this phenomenon. Fresnel diffraction of Fresnel double mirror and biprism are studied as practical examples, and the diffracted intensity distribution is calculated. We show that the intensity of the diffracted field varies with an almost constant period along the average propagation direction. Using this value and the fringe spacing of the interference pattern on a plane normal to the average propagation direction, the angle between two interfering beams and the wavelength of the incident light could be simultaneously derived. The diffraction pattern of the Fresnel double mirror and Fresnel biprism were obtained experimentally, which were in good agreement with the theoretical results.