Fast spatial carrier phase-shifting algorithm based on a constructed reference-phase

A fast and straightforward spatial carrier phase-shifting (SPS) algorithm based on a constructed reference phase is presented. This reference phase is obtained from the interferogram carrier-frequency values, and the interesting phase can be directly extracted from a single interferogram without any carrier-removal operation. Numerical simulations show that the computation times when it is used the proposed method are approximately 4.5 times faster than the Fourier transform approach and about 2 orders of magnitude faster than the least-square SPS method. The proposed method can be applied to phase measurements for high-speed dynamic or moving objects.