Phase Extraction Algorithm Based on the Spatial Carrier-Frequency Phase-Shifting Gradient

For improving the accuracy and processing speed of phase extraction, a new phase extraction algorithm based on the spatial carrier-frequency phase-shifting gradient (SCFPS-G) is proposed. First, three-frame sub-interferograms along the direction of spatial carrier-frequency phase-shifting gradient (SCFPS-G), which can be constructed by the differential method from only one-frame spatial carrier-frequency interferogram (SCFI). And then, the measured phase will be extracted by unknown phase-shifting algorithms. Compared with the existing spatial carrier-frequency phase-shifting (SCFPS) algorithms, the proposed SCFPS-G algorithm not only can improve the efficiency of constructing sub-interferograms, but also decrease one-frame sub-interferogram requirement for phase extraction, so the data redundancy of interferogram and the influence of noise will be reduced. Specially, it is found even if the carrier frequency becomes very small, corresponding to the large spatial bandwidth utilization of image sensor, the proposed SCFPS-G algorithm still can work well. And the obvious advantages of the SCFPS-G algorithm in accuracy, processing time and feasibility of phase extraction can be demonstrated by the numerical simulations and the experimental results.