Research On The Phase Retrieval Algorithms In The Lateral Shearing Phase-shifting Interferometry

With the continuous improvement of the accuracy of optical measurement system,phase-shifting interferometry has been developed rapidly.Phase retrieval plays an important role in system measurement accuracy as the primary link in phase-shift interferometry.Phase retrival is subdivided into two steps: phase extraction and phase unwrapping.Although the existing phase extraction algorithm can correct random phase-shift error,the accuracy of phase extraction would decrease in the harsh conditions of background intensity and modulation amplitude disturbance,and non-complete period interference fringes.This dissertation focuses on multi-step random phase extraction,two-step random phase extraction,fast unwrapping and so on.For different interference environment,a corresponding phase extraction algorithm or fast unwrapping algorithm is proposed.In the multi-step phase-shift interferometry,two improved algorithms are proposed to solve the problems of background intensity and modulation amplitude disturbances and the non-complete period interference fringes.The first improved algorithm combines the difference method and the elliptic fitting of the Lissajous figure technology to extract the phase from three interferograms.It is unnecesary to construct the sine and cosine two components.The background intensity could be removed by differential operation between the three interferograms.Then the phase could be extracted after ellipse fitting.The second algorithm is based on Schmidt orthogonal and minimum Phase extraction algorithm of two times elliptic fitting.Firstly,the DC term of the background intensity could be eliminated by the differential operation between the interferograms,And then the random phase-shifting error is eliminated by the Schmidt orthogonalization.Finally,the least-squares ellipse fitting technique is used to further correct the background intensity error,and extract the phase.The experiments and numerical simulations of different interference conditions are carried out.The accuracy and feasibility of the two proposed algorithms are analyzed.Aiming at the problem of limited phase extraction of non-complete period interference fringes in two-step phase-shift interferometry,the phase extraction algorithm based on Schmidt orthogonalization and least squares ellipse fitting from three interferograms is modified,then a phase extraction algorithm for two interferograms is obtained.The background intensity is removed by high-pass filtering,and then the phase could be extracted by the Schmidt orthogonalization and least-squares ellipse fitting techniques.In addition,an improved algorithm based on normalization and nonlinear error minimization is proposed to solve the tilt phase-shift problem in two-phase interferometry.The algorithm normalizes the interference after filtering out the background intensity,which could eliminate the modulation amplitude.Then the tilt phase-shift and the phase could be calculated by minimizing the nonlinear error.It is easy to introduce enormous undersampling introduced from industrial cameras.To solve this problem,an improved phase unwrapping algorithm is proposed by combining the K value rounding and the two-directional shearing technique.Firstly,the anti-undersampling performance of the algorithm is improved significantly by the two-directional shearing technique.Then the noise immune performance of the algorithm is enhanced by the K value rounding method.The anti-undersampling and noise immune performance of the improved algorithm are analyzed by numerical simulations and experiments.In addition,an optical measurement system which can measure small size objects is constructed by combining lateral shearing phase shift interferometry and fringe projection technology.The experimental results verify the feasibility of the proposed improved phase extraction algorithm.