Single-shot measurements by Fresnel diffraction of divergent waves from a phase plate

Recently, Fresnel diffraction (FD) of a plane wave from phase steps has been studied and applied for precise measurements of the light wavelength, and height and refractive index of the step, by changing the angle of incidence or step height to induce phase shifts. In this study, we formulate the FD of cylindrical and spherical wavefronts as 1D and 2D divergent waves from a phase plate. Since the phase difference of the divergent wave varies continuously along the edge of the phase plate, it can be applied for single-shot measurements. It is shown that the diffracted intensity distribution is a periodic function along the lines parallel to the plate edge. The phase distribution in this direction is a linearly varying function of the position squared, with a slope dependent on the light wavelength, plate thickness and refractive index, and the radius of wavefront curvature (RWC) on the observation plane. The diffraction patterns are simulated and experimentally verified. Also, the RWC and displacement are determined as examples of applications in the experimental part of the report.