Research On Fast And High Precision Phase Retrieval Algorithms

Phase-shifting interferometry(PSI)with non-contact and high precision is widely used in microscopic three-dimensional topography detection.In phase-shifting interferometry,the height information of the measured object is hidden in the phase.Therefore,it is necessary to use a phase extraction algorithm to extract the phase information from the light intensity information.There are two indicators for evaluating the performance of the phase extraction algorithm,one is the accuracy of the algorithm,and the other is the running time of the algorithm.The accuracy of phase extraction is mainly affected by factors such as disturbance,noise,the number of interference fringes,and phase shift errors.The running time of the phase extraction algorithm is affected by many factors,such as the number of interferograms.In order to reduce the time required for phase extraction,a non-iterative method is adopted while minimizing the number of interferograms required.Most phase extraction algorithms can correct the translation error,but when there are background light intensity disturbances,modulation amplitude disturbances,incomplete periodic interference fringes,and tilt phase shift errors,the accuracy of phase extraction will decrease.This thesis proposes corresponding phase extraction algorithms to solve these problems.The existing phase extraction algorithm based on three interferograms can correct the translation error,however,when there are disturbances in the background light intensity and modulation amplitude,the accuracy of the phase extraction will decrease.Aiming at the problems of background light intensity and modulation amplitude disturbance,a phase extraction algorithm based on vector normalization of three interferograms is proposed.The algorithm first uses normalization to filter out the background light intensity and modulation amplitude disturbances,and then performs differential operations to filter out the DC component.Finally,the phase information of the measured object is extracted from the normalized diamond vector.The effectiveness of the algorithm is verified by experimental simulation,and the phase information can be extracted with high precision even under the disturbance of background light intensity and modulation amplitude.Although the existing phase extraction algorithm based on two interferograms can extract phase information quickly and accurately,the accuracy of phase extraction will decrease if there are non-complete periodic interference fringes.Aiming at the limited phase extraction problem of the number of non-complete periodic interference fringes,a phase extraction algorithm based on vector normalized ellipse fitting is proposed.This algorithm first performs addition and subtraction operations,and then normalization operations to eliminate the impact of amplitude imbalance.Finally,the least squares ellipse is used to fit the ellipse coefficients,and the phase information is extracted.Experiments and simulations verify the effectiveness of the algorithm,and the phase information can be extracted quickly and accurately even when the number of interference fringes is less than one.Aiming at the problem of tilt phase shift error,a phase extraction algorithm based on ellipse fitting ellipse standardization is proposed.The algorithm first uses two interferograms to fit an oblique ellipse equation,then uses the least square method to solve the oblique ellipse equation coefficients,and solves the oblique ellipse parameters according to the solved oblique ellipse equation coefficients.Finally,the oblique ellipse parameters are converted into standard ellipse equations,and the phase information is extracted through the ellipse equations.In the process of ellipse standardization,the phase shift error caused by the unstable light source,the air disturbance and the unstable phase shifter is corrected,and the accuracy of the algorithm is improved.Experiments and simulations have verified the effectiveness of the algorithm,and the phase information can be extracted quickly and accurately even when tilted and shifted.