Spatial mismatch calibration using circular carrier technique in the simultaneous phase shifting interferometry

In most simultaneous phase shifting interferometry (SPSI) systems, a group of phase shifting interferograms are captured simultaneously at the different physical locations to retrieve the phase. The data of different interferograms should be spatially matched correctly, which is hard to realize by existing methods or this spatial mismatch will lead to phase retrieving error. In this paper, a spatial mismatch calibration method is proposed, where the circular carrier is introduced in the interferograms of the SPSI system, and the modulating phases of any two interferograms can be retrieved by the demodulation technique of circular carrier interferogram. The slope of the difference between these two phases is proportional to the mismatch value, so this error can be extracted and the experiment setup calibrated. The main error sources of the proposed method are analyzed with the conclusion that its match precision can be achieved up to 0.5 pixel. In addition, the simulated interferograms and actual interferograms captured in a SPSI system are processed to validate our proposed method.