Residue-enhanced symmetrical decoupling iteration for robust high-precision tilt phase-shifting interferometry

Generalized phase-shifting interferometry is crucial for high-precision metrology, but it is hindered by vibration-induced tilt errors and optimization instabilities. To address limitations such as non-smooth convergence and sensitivity to outliers in existing iterative solvers, we propose the residue-enhanced symmetrical decoupling iteration (RSEDI) algorithm. RESDI features a residue-adaptive weighting mechanism to suppress systematic artifacts and a dynamic smoothing strategy to stabilize the optimization path. Furthermore, a symmetrical piston correction module is incorporated to enforce temporal continuity, effectively preventing phase wrapping failures under low signal-to-noise ratios. Numerical simulations and experiments confirm that the proposed method achieves robust, high-fidelity phase reconstruction, significantly outperforming state-of-the-art algorithms in vibration-prone environments.