Surface recovery method with phase error suppression in white light phase-shifting interferometry

White light phase-shifting interferometry is a well-established measurment method in precision manufacturing, widely applied to the surface measurement of complex micro- and nano-structures. In practical applications, background fluctuations caused by light source stability and intensity noise of the camera disturbs the interference signal, leading to inaccurate localization of zero optical path difference and reconstruction of surface topography. In this paper, an anti-noise recovery algorithm based on moving half-period difference and real-frequency domain combinatorial localization is proposed to suppress the random intensity error and background drift. Step height standard samples and an in-house etched step were tested to evaluate the proposed algorithm. Experimental results demonstrate that the absolute error and repeatability for the step height standard are 7.00 nm and 0.005% respectively, and the absolute error of the in-house etched step is 1.5 nm. The measurement comparisons with four widely utilized algorithms prove the effectiveness of the proposed algorithm.