High-Stability Algorithm in White-Light Phase-Shifting Interferometry for Disturbance Suppression

A hybrid algorithm, combining a "Gauss-type" envelope algorithm with the Carré algorithm, is proposed for disturbance suppression. For white-light phase-shifting interferometry (WLPSI), this novel algorithm provides suitable performance in suppressing noise caused by external conditions, such as mechanical vibrations, low-reflectivity surfaces, and poor-contrast interferograms. The algorithm is mathematically derived, and simulation testing is performed at the micro level to demonstrate that the algorithm can position the coherence peak correctly under challenging conditions. At the macro level, the algorithm is further verified on standard samples, with the repeatability of the step height being less than 0.32% in a favorable environment and 0.59% in a noisy environment. The repeatability of the roughness was 0.23% in a favorable environment and 0.65% in a noisy environment. Note that "repeatability" = "standard deviation"/"dean value", reflecting the stability as a percentage. The simulated and experimental results prove that the proposed algorithm is highly precise and robust. This algorithm reduces the environmental dependence of the performance of WLPSI instrumentation and expands its range of application.