Phase extraction from two randomly phase shifted interferograms by combining advanced principal component analysis and Lissajous ellipse fitting

In order to achieve the high accuracy and high speed in phase shifting interferometry, a phase extraction approach by combining advanced principal component analysis and Lissajous ellipse fitting (APCA-LEF) is proposed. It can obtain accurate phase distribution with only two no pre-filtering phase shifted interferograms, and it costs less time simultaneously. It removes the restriction that PCA needs more than three interferograms with well distributed phase shifts to subtract relatively accurate mean. Moreover, adjacent pixels taken part in the APCA process increases the accuracy by suppressing the effect of noise, also, it is suitable for different levels of noises. Last but not least, if the high accuracy is required, the phase shift would be best to far away from 0 rad and π rad. The simulations and experiments verify the correctness and feasibility of APCA-LEF.