Research On Iterative Phase Retrieval Algorithm For Quantitative Phase Detection

Quantitative phase detection is an important topic in the field of optics.The traditional interferometric method relies on the interference of light,and has a strict requirement on the coherence of the light source,the test equipment and the test environment.The iterative phase retrieval algorithm,as a typical non-interference phase measurement method,only requires the far-field intensity information of the light wave,then the phase information of the object light can be quantitatively retrieved without complicated interference devices.It plays an important role in biomedical microscopy,X-ray imaging,adaptive optics,geometric characterization of optical components and surface reconstruction of antennas.This paper systematically studies the main theory of the iterative phase retrieval algorithm,aiming to solve three key problems in its theory(the“selection and optimization of spatial modulation methods” problem,the “local optimal” problem and the “noise sensitivity” problem),so as to improve the comprehensive performance of phase retrieval algorithm,and provides the theoretical basis for quick and accurate quantitative phase detection.The main work of this paper includes the following aspects:(1)Research on the “selection and optimization of spatial modulation methods” problemThis section comparatively studies the advantages and disadvantages of two spatial modulation methods(the random mask modulation and the phase modulation)in terms of the algorithm accuracy and rate,and studies the impact of the number,range and distribution of phase modulation factors on the performance of iterative phase retrieval algorithms.A phase modulation factor optimization method based on Zernike polynomial is proposed.This method provides a theoretical guidance for the optimization of the phase modulation factor settings,and effectively improves the accuracy of the retrieved spatial phase when the number of the intensity measurements is limited.(2)Research on the “local optimal” problemFirstly,research on the “local optimal” problem from the perspective of initialization strategy.This section discusses the uniqueness of the phase retrieval solution in detail,that is,under what circumstances,there is a unique corresponding relationship between the spatial phase and the Fourier amplitude.The root of the “local optimal” problem of the iterative phase retrieval algorithm is explored in detail,and different types of initialization strategies to solve the “local optimal” problem(the spectral initialization,the null initialization and the global optimization preprocessing)are compared.Based on this,an iterative phase retrieval algorithm based on the covariance matrix adaptation evolution strategy(CMAES-AP)is proposed.The algorithm fully combines the global characteristic of the covariance matrix adaptation evolution strategy with the fast convergence rate of the iterative phase retrieval algorithm,which can ensure the convergence to the global optimum with a high probability under random spatial initial guesses.Secondly,research on the “local optimal” problem from the perspective of phase retrieval problem model.A Phase Cut algorithm based on low-rank matrix completion is studied in detail.By introducing a vector lifting method and a convex relaxation strategy,the original non-convex phase retrieval problem is transformed into a solvable positive semi-definite programming problem,thereby eliminating the ambiguity of the problem itself.Aiming at the problem that the algorithm time complexity is too large when the Phase Cut algorithm solves large-scale and high-resolution problems,a frequency-domain extrapolative iterative phase retrieval algorithm is proposed.By introducing the spatial-domain interpolation and frequency-domain extrapolation,the nearglobal initial solution solved by Phase Cut algorithm in low resolution is gradually increased to high-resolution global optimal solution in stages,which significantly improves the global characteristic of the iterative phase retrieval algorithm under random spatial initial guesses.(3)Research on the “noise sensitivity” problemA spatial autocorrelation filtering method based on the autocorrelation theorem is proposed,which realizes iterative filtering by setting the support domain constraints of the spatial autocorrelation.This method can effectively filter out the invalid data outside the support domain of the spatial autocorrelation and reduce the error of the Fourier amplitude caused by noise.Combining the spatial autocorrelation filtering and the frequency-domain Wiener filtering,an iterative phase retrieval algorithm based on dual-domain filtering is proposed.This algorithm fully considers the special corresponding relationship between the spatial domain and the frequency domain in the phase retrieval problem model,and by applying the deconvolution Wiener filter to the“blind deconvolution” phase retrieval problem,it effectively improves the accuracy of the retrieved spatial phase for iterative phase retrieval algorithms at low signal-to-noise ratio.(4)Experimental verification and application of the modified iterative phase retrieval algorithmsThrough the optical quantitative phase detection experiment,the effectiveness of the modified algorithms proposed in this thesis for the“selection and optimization of spatial modulation methods” problem,the “local optimal” problem and the “noise sensitivity” problem is verified,and different types of the modified algorithms are combined with each other.By comparing the advantages and disadvantages of the modified algorithms and their combined algorithms in algorithm accuracy and rate,it is found that the hybrid algorithm,which is combined by the phase factor optimization method,the CMAES-AP and the dual-domain filtering method,is the best choice with respect to the comprehensive performance of algorithm accuracy and rate.Finally,the modified iterative phase retrieval algorithms are applied to the surface reconstruction of the Shanghai TM-65 m reflector antenna,which realizes the high-precision measurement of the geometric surface of the large reflector antenna.