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

Nonlinear or random phase-step 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.