Yang Song

This Letter presents a simple radial shearing interferometery with circular gratings to measure the radial first-order derivative of arbitrary wavefront phase. Two spatial phase-shifted radial shearing interferograms can be simultaneously obtained by the system, and a two-step phase-shifting algorithm with arbitrary phase-shift value is proposed for phase retrieval. The measurement for spherical wave has shown the feasibility and validity, and the optical system is used to measure the radial first-order derivative of projection wavefront phase of a propane flame with plane incident wave.

A spatial phase-shifting shearing interferometry is presented in this paper. The whole optical configuration is simple and consists of three Ronchi gratings. Four phase-shifted shearing interferograms can be obtained simultaneously. The explicit intensity distributions of shearing interferograms are given and a corresponding four-step spatial phase-shifting algorithm is proposed to extract phase information from the new interferometry. This spatial phase-shifting configuration is applied to extract phase projection of a propane flame and a mathematical error analysis is presented.

Double grating interferometer is usually used to achieve phase information from distorted wave front by its temporal phase-shifting characteristic. In this paper, the spatial phase-shifting characteristic of double grating interferometer is presented. The explicit intensity distributions of interferograms produced by double gratings are derived with the scalar diffraction theory, and the stable phase shift is found between plus-first, zero and minus-first order interferograms. Results indicate that the phase shift only depends on the grating period and the distance between two gratings if no phase object exists. If phase object exists, it varies on the interferograms. But the phase shifts are equal at any special point of interferograms. In particular, the triple grating interferometer is presented to generate at least four phase shift interferograms simultaneously with the similar method.