Fresnel diffraction of cylindrical and spherical wavefronts from a phase plate

TL;DR

This paper formulates and experimentally verifies the Fresnel diffraction of cylindrical and spherical wavefronts from a phase plate, demonstrating its potential for optical metrology and wavefront characterization.

Contribution

It introduces a new formulation for Fresnel diffraction of curved wavefronts from a phase plate and demonstrates its application in measuring wavefront curvature and displacement.

Findings

Diffraction intensity is periodic along lines parallel to the plate edge.

Phase distribution varies linearly with the square of the position.

Experimental verification confirms the theoretical model.

Abstract

In the last two decades, Fresnel diffraction (FD) of a plane wave from phase steps has been systematically studied and applied for precise measurements of light wavelength, and height and refractive index of the step. In this study we formulate FD of cylindrical and spherical wavefronts from a transparent step in transmission mode. It is shown that, the 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 depends on the light wavelength, the plate thickness and refractive index, and the radius of wavefront curvature (RWC) on the observation plane. Therefore, it has significant potential in optical metrology, by a single-shot recording. 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.