Interferometric phase reconstruction by nonuniform shifting of the reference beam

A method for phase measurement in common-path interferometers, believed to be novel, is presented. We use the property of phase reconstruction algorithms, such as the Carré and Hariharan algorithms, that do not require uniform phase across the reference beam. Only the ratio of the phase steps must be the same at each pixel. We show phase measurement and reconstruction in a common-path interferometer by shifting either the tilt or the focus of the reference wave front. We present a theoretical explanation of phase measurement using this property. We also present results from a proof-ofprinciple experiment using a scatterplate interferometer, in conjunction with the tilt phase-shifting technique, to measure the reflected phase of a test optical element. Furthermore, we present a computer simulation to demonstrate the mathematical validity of this measurement technique using defocus shifting, rather than tilt shifting, in the reference wave front.