Using higher steps phase-shifting algorithms and linear least-squares fitting in white-light scanning interferometry

•New PSAs were derived based on the local linear conditions.•Center wavelength of the light source was calculated by using linear least squares fitting.•Simulated noises were mixed into regular WLSI signal to discuss the robustness of the proposed method.•Higher steps PSAs give better linearity and stability in WLSI.

White-light scanning interferometry (WLSI) has been a well-established tool for measuring the profile of objects. Since the white-light source is continuous in spectrum, the phase ambiguity problem can be avoided. Specimens with discontinuous profile can therefore be possibly measured by WLSI. In this paper, using higher steps, i.e. nine and eleven steps, phase-shifting algorithms (PSAs) based on local linear conditions of envelope function were proposed. The actual zero optical path difference position was retrieved by extracting the phase value and phase compensation. Maximum intensity peak positions at five points were used to calculate the center wavelength of the light source by both phase unwrapping and linear least-squares fitting. Both simulated and experimental results showed that the proposed nine- and eleven-step PSAs have good linearity and robustness to accurately measure the profile and center wavelength of the light source.