Definitive correction for nonlinear and random phase-step detuning using the universal phase-shifting algorithm (UPSA)

Nonlinear or random phase-steps detuning, induced by environmental and instrumental instabilities, remains a pervasive challenge in phase-shifting interferometry. This detuning error undermines the accuracy of standard linear phase-shifting algorithms (PSAs) and compromises the reliability of optical surface metrology. This work introduces a definitive solution: the Universal Phase-Shifting Algorithm (UPSA) as a universal post-processing corrector. We demonstrate that a single application of the UPSA transforms the erroneous, detuned output of any linear PSA into a perfect quadrature signal, recovering phase accuracy comparable to an ideal, well-tuned measurement. The UPSA operates blindly, requiring no estimation of the nonuniform phase-steps, and is uniquely effective at correcting linear PSAs with just three interferograms—a significant advantage over methods requiring extensive data sets. Crucially, we validate its robustness against noise and strong fringe amplitude variations using an unmodified commercial interferometer under standard optical-shop conditions. Therefore, the UPSA is not merely a theoretical improvement but an essential practical advancement, finally enabling trustworthy, high-precision phase measurements in both research and production environments.