Segmented phase unwrapping is an intractable problem in the phase-shifting technique. To solve the problem, this Letter presents an iterative pseudo-phase inpainting algorithm (IPPI). By means of image inpainting, the IPPI can be used to realize the pseudo-phases connecting each other among these phase islands. The error points in the pseudo-phases can be reduced by iterations of phase inpainting with the assistance of the reference pseudo-phase obtained by introducing the numerical carrier frequency and using the 2D Fourier transform. Compared with other methods, the proposed algorithm does not have to do any processing on the effective area of the wrapped phase, which ensures the authenticity of the result. The simulated and experimental verifications show that the proposed method not only possesses high precision, but also can be applied to a segmented phase with severe noise.

The polarization based phase shifting method is an effective way for dynamic measurements. However, when this technique is applied to the measurements of large optics, the interferometric results are easily limited by the birefringence of large optics. The birefringence changes the polarization states of reference light and test light, and brings constant polarization aberrations into the measurement results independent of the phase shifting procedure. In this article, the detailed theoretical analysis on the mechanism of polarization aberration is presented. Afterwards, we propose a new interferometric method to determine the birefringence effects by measuring the transmitted wavefronts of the large optics, which are considered as birefringent samples. Theoretical analysis shows that the polarization error in the linearly polarized system can be corrected by two independent measurements with orthogonal polarization states. The phase retardance can be obtained from the wavefront difference of the transmitted wavefronts when switching the polarization states of the incident lights. The birefringence distribution obtained is used to calibrate the polarization aberrations in the measurement result of a homemade large aperture measurement platform and the correction result is compared with the result via the wavelength tuning phase shifting method. The elimination of the polarization aberrations can be observed in the final results.