Normalized and orthogonal phase retrieval algorithm based on Lissajous ellipse fitting

• A normalized and orthogonal phase retrieval algorithm is proposed. • Parameters related to the phase are calculated by Lissajous ellipse fitting. • The method has a shorter calculation time and higher calculation accuracy. • The accuracy is not affected by the number of fringes and phase shifts. • The method maintains stable accuracy whether symmetrical or asymmetrical fringes. A normalized and orthogonal phase retrieval algorithm based on Lissajous ellipse fitting (NOLEF) is proposed in this study, which can extract phase distributions under random phase shifts with high accuracy. In this algorithm, the parameters related to the phase can be calculated via Lissajous ellipse fitting after the normalization and orthogonalization processes. Compared with other high-accuracy phase-shifting algorithms, the proposed method has a shorter calculation time and provides stable and accurate phase extraction with random phase-shifting interferograms, in which the accuracy is not affected by the number of fringes and phase shifts; it is also suitable for interferograms with different backgrounds and modulations. This method's feasibility and performance at different number of fringes and noise levels are verified via experimental and simulation analyses.