Modified two-step phase-shifting algorithm: analysis, demonstration, and application

Abstract

As a powerful means of accurate phase measurements, phase-shifting interferometry (PSI) has been applied in many fields of optical non-contact and non-destructive testing. Conventional phase-shifting algorithms require a minimum of three fringe patterns shifted in phase with respect to one another [1, 2]. To simplify the computation process, Wizinowich developed a twoplus-one (2 + 1) phase-shifting algorithm, in which two fringe patterns with π/2 phase shift are captured, and a third flat image is collected which is the average of two patterns with a phase shift of π [3]. Recently Zhang et al. have modified 2 + 1 algorithm and applied for fringe projection system, in which the 3rd pattern is directly captured instead of indirectly averaging two π-phase-shifted images [4]. Recently, Yang et al utilized two deformed fringe patterns with a phase-shift increment of π/2 to measure the 3-D object shape [5]; Quan et al. proposed a method in which two πphase-shifted patterns are used in fringe projection system [6]. Independently, we have proposed a two-step algorithm in PSI [7, 8], however, the following two additional measurements are needed: (1) measuring the intensities of both object wave and reference wave [8], (2) measuring the reference wave intensity and then solving a related equation [7]. In this paper, we will address this issue by modifying and improving the two-step phase-shifting algorithm mentioned above, in which only two phase-shifted fringe patterns with removal of direct current (DC) component and an arbitrary phase shift δ (0 < δ < π) can be utilized.