A precise three-step phase retrieval algorithm suitable for the interferograms with less than one fringes numbers

In order to improve the accuracy and expand the range of the phase-shifting algorithm application, a precise three-step phase retrieval algorithm suitable for the interferograms with less than one fringes numbers is proposed. The proposed method improves the accuracy, on the one hand because normalization and subtraction are introduced to reduce background intensity fluctuation, on the other hand because Lissajous ellipse fitting (LEF) method is introduced to reconstruct phase maps from the normalized and Gram-Schmidt (GS) orthonormalized maps. Because the approximation operations for cumulative sum aren't used in the GS method, the proposed algorithm is suitable for not only interferograms that the fringes numbers are more than one but also interferograms that fringes numbers are less than one. Moreover, the proposed method can be applied to simple and complex patterns. Thus, the proposed algorithm has a wider range of applications. The proposed algorithm's reliability and performance are confirmed by simulations and experiments.