Generalized 2-step phase-shifting algorithm for fringe projection

Fringe projection profilometry using the phase-shifting technique enables high-precision, high-speed and flexible measurements. Among them, the two-step phase-shifting method has become an important approach to coordinate the accuracy and measurement speed; methods especially based on the amount of phase-shift of π/2, π or 3π/2 can improve time efficiency by reducing steps in unique way. In this paper, a phase iterative technique is proposed and established for two-step phase-shifting with arbitrary phase shift. The general mathematical scheme and parameters linear and nonlinear optimization of the proposed method are described in detail. The simulational and experimental results show that the proposed technique is an effective and precise phase detection method for two-step phase-shifting profilometry.