A derivative method of phase retrieval based on two interferograms with an unknown phase shift

Phase retrieval is one of the important study fields in the optical metrology of phase objects. In this paper, a rapid derivative method of phase retrieval is proposed that can both extract phase and determine an unknown phase shift based on two-step phase-shifting interferometry (PSI). By numerically calculating the first-order derivatives of two PSI images with the random phase distribution, one can directly obtain the quantitative phase image, without the need for dealing with the background term and reference intensity. We give the method with the theory, and illustrate it using the simulations of a ball and a red blood cell (RBC) and an optical experiment of a polystyrene sphere. From which, the effectiveness and accuracy of this method is verified, but the error of the experimental result is larger than that of the simulated result.