Phase Diversity Wavefront Sensing And Its Application In Image Restoration

Phase diversity (PD) can be used not only as a wavefront sensor but also a post-detectionimageprocessingtechnology. Ithas greatpotentialinthefiled ofhighresolutionimaging.Inthispaper, the key technique of PD is studied according theory and experiment centering on the twomajorapplicationdomain:wavefrontsensingandimagerestoration.At first,the fundamental principle of an imaging system is analysed, and the intensitydistribution formula in the image plan is derived.It's proved that the intensitydistribution in theimage plan is the same whether coherent or incoherent imaging in the case of point source,whichlayatheoretical foundation forthelatersimulationandexperiment.An objectivefunctionis given by using maximum-likelihood estimation and least square estimation, and necessity ofcollecting more than one image is analysed. The stabilization of the inverse problem is studied,andsomeregularizationstrategies are given. Inordertoacquiremultipleimagessimultaneously,a new PD wavefront sensor (WFS) based on grating is designed. Compared with previousmethods such as moving the camera, this kind of PDWFS can better satisfy the requirements ofPD.Theanalyticexpressionsoftheobjectivefunction'sgradient arederived accordingtoprincipleof PD. Various optimization methods such as steepest descent method, conjugate gradientmethod and quasi-Newton method for solving the PD problem are compared in numericalsimulations. The result shows that, when the wavefront is described by pixels, the L-BFGSmethod performs much better than the others in both computing time and accuracy. It's anappropriate choice for PD algorithm.However, when the aberration to be measured is large, thenonlinearity of the objective function is aggravated, and it's easy falling into a local extremumusingthe traditional algorithm. In order to solve this problem, a hybrid algorithm ispresented inthis paper. This algorithm can improve the accuracy in measurement of heavy aberrationconsumedly. In order to validatethe simulation, anexperimental testbed is built based on pointsource to study the performance of PDWFS for static aberrations in different types andmagnitudes. The wavefront sensing errors which caused by various factors are detailedresearched, and approaches of eliminating or reducing these errors are given. These approachescould improve thesensingaccuracygreatly.Theroot meansquare(RMS) ofthe residual errorisreducedtoaboutλ/100.Next, a remote sensing imaging system based on PD is designed and its performance issimulated. A novel color PD remote sensing imaging system is designed based on Bayer filter for the fist time. Simulation shows that the remote sensing imaging system based on PD canreduce the influence of the factors such as atmospheric turbulence and system aberrations, andcan improve the resolution of the remote sensing imaging system effectively. The color systemcan not only reduce the influence of wavefront aberrations but also obtain color image whichcontainsmore visualinformation,andcanbettermeethuman's perception.Finally,PD wavefront sensingand PDpost-detection image processing is combined to form ahybrid method. The performance of this method is simulated for point source and extendedsource. A closed-loop adaptive optics (AO) experimental setup using PDWFS and LC-SLM isbuilt based on a point source, and the hybrid method is examined at different atmosphericturbulence levels for the first time. The simulation and experimental results both demonstratethat the hybrid method can conquer the influence of residual aberrations left by AO partiallycorrected,andimprovetheresolutionoftheimagingsystemfurther.