Fringe-Order Determination Method in White-Light Phase-Shifting Interferometry for the Compensation of the Phase Delay and the Suppression of Excessive Phase Unwrapping

White-light phase-shifting interferometry (WLPSI) is widely recognized as a standard method to measure shapes with high resolution over a long distance. In practical applications, WLPSI, however, is associated with some degree of ambiguity of its phase, which occurs due to a phase delay, which is the offset between the phase of the fringes and the fringe envelope peak position. In this paper, a new algorithm is proposed for the determination of a fringe order suitable for samples in which the phase delay mainly occurs due to noise, diffraction and a steep angle. The concepts of the decouple factor and the connectivity are introduced and a method for calculating the decouple factor and the connectivity is developed. With the phase-unwrapping procedure which considers these values, it is demonstrated that our algorithm determines the correct fringe order. To verify the performance of the algorithm, a simulation was performed with the virtual step height under noise. Some specimens such as step height standard and a column spacer with a steep angle are also measured with a Mirau interference microscope, after which the algorithm is shown to be effective and robust.