Motion-induced error reduction for phase-shifting profilometry with phase probability equalization

Abstract

Phase-shifting algorithms have been widely used for three-dimensional (3D) shape measurement. However, when measuring moving objects, the object motion may distort the linear phase and lead to the phase error. This paper presents an effective phase probability equalization (PPE) method for motion-induced error reduction, which directly equalizes the distorted phase to estimate the linear phase. In general, adequate sampling pixels are needed to compute the accurate phase probability (PP). This paper further presents an improved shifted-phase probability equalization (SPE) method, which combines the original phase and its π-shifted phase to double the sampling pixels. Both simulations and experiments have been conducted to measure objects moving in z-direction, and their results validate that the proposed PPE and SPE methods could effectively compensate the motion-induced error.