Robust three-frame coefficient-tuning iterative algorithm for accurate phase retrieval with random phase shifts

• A three-frame random phase retrieval method based on the coefficient-tuning iterative algorithm is proposed. • The method is computationally efficient with high phase retrieval accuracy. • The accuracy is not constrained by the shape or number of fringes. • The method has lower sensitivity to fluctuations in the background intensity and modulation. Random phase-shifting algorithm is widely used in phase-shifting interferometry (PSI) to recover phase distributions under unknown phase shifts. However, the applicability of existing algorithms is constrained by various preconditions such as ideal background illumination, sufficient image acquisition volume, and adequate fringes in interferograms. This paper proposes a three-frame random phase retrieval method based on the coefficient-tuning iterative algorithm (CTIA), which is fast, stable and easy to implement. Compared to other existing high-precision phase-shifting algorithms, this method can achieve the accurate phase extraction from interferograms with background intensity and modulation fluctuations, and its accuracy is not constrained by the shape or number of fringes. Simulations and experiments both verify that the proposed algorithm provides an accurate and robust phase reconstruction tool for random three-frame PSI used in laser interferometric topography and roughness measurements.