Efficient phase-shift error compensation algorithm based on probability density function

Abstract

In non-digital projection systems, the inaccuracy of phase shifts is one of the most important nonlinear errors. In this paper, an efficient and universal compensation algorithm is proposed, which does not need to find the exact phase shift amounts, but to compensate the periodical errors by a universal two-coefficient error model. With this model, only two error coefficients should to be searched for any multi-step phase shift algorithm. To find the error coefficients, a correlation process and a tool known as the probability density function (PDF) are used. First, a set of pre-simulated PDF curves are generated with the different error coefficients. Second, a practical PDF curve from captured fringes is calculated. Finally, the correlation process is carried out to locate the most similar simulated PDF curve, whose error coefficients are the practical ones. In this paper, we demonstrate the compensation for three, four and five-step phase-shifting algorithms separately. Experimental results show that this method has high universality, and can meet the requirements of rapid and high accuracy measurement.