Fast and accurate tilt-shift-immune phase-shifting algorithm based on self-adaptive selection of interferogram subblocks and principal component analysis

To eliminate the effect of tilt-shift error on the accuracy of phase-shifting interferometry (PSI), a fast and accurate tilt-shift-immune phase-shifting algorithm based on the self-adaptive selection of interferogram subblocks and principal component analysis (SSPCA) is proposed. First, each interferogram is divided into several subblocks, and principal component analysis and the least-squares method (LSM) are applied to obtain the phase-shift value of each subblock. Next, according to the correlation coefficients between each phase-shift curve, valid and invalid subblocks can be distinguished. Finally, all phase-shift values of the valid subblocks are used to fit the tilt phaseshift plane, and phase results can be obtained using the LSM. Simulations indicate that the accuracy of SSPCA can reach 0.03 rad both for small (1 rad) and large (2π rad) tilt amplitudes, and it takes only one-tenth or less of the processing time of iterative algorithms. Experiments proved that SSPCA can be applied even without a precision phase shifter and thus provides a low-cost approach for PSI with both high precision and speed.