Application Research Of Phase Diversity Image Reconstruction Technology In Liquid Crystal Adaptive Optical System

In order to reduce the influence from atmospheric turbulence in the imaging of telescopes,the international large-scale ground-based telescopes above several meters are all equipped with adaptive optics(AO)system.AO can eliminate the wavefront distortion caused by turbulence on the imaging beam in real time,and restore the imaging resolution of the telescope to the diffraction limit.However,the time delay of AO system from the wavefront detection to the correction always leaves some wavefront residuals,especially in the case of strong winds and strong atmospheric turbulence,resulting in the corrected image far from reaching the system diffraction limit.At this point,post-digital image processing is needed.The phase diversity(PD)technique is to solve the distortion residual wavefront and reconstruct the highresolution image by using the focus image and the image with the known aberration.PD technology is one of the most effective methods to further improve the imaging resolution after AO correction,and is more suitable for liquid crystal adaptive optics system(LC AOS).In LCAOS,the imaging beam is first divided into a P-polarized beam and an S-polarized beam.Two liquid crystal wavefront correctors are used in parallel on the two optical paths to correct the wavefront distortion respectively,then two polarization imaging images can be obtained or they can be combined to get a high energy image.In this study,one of the polarized images is added with fixed aberrations to realize PD image processing,which makes the imaging quality of LC AOS with the advantage of matching large aperture telescopes of more than 8 meters to a higher level.The PD technique still has the following problems: First,the particle swarm optimization algorithm for solving the objective function can achieve global optimization,but the calculation time is too long.The second,different diversity function results in different accuracy of the reconstructed wavefront by PD.Third,the reconstructed image obtained by the conventional Tikhonov regularization still has some blur.In view of the above problems of PD,this paper improves the PD from three aspects: acceleration of the optimization algorithm,selection of diversity function and modification of regularization method.Firstly,the optimization algorithm in PD is studied.The traditional gradient-based algorithm can only achieve local convergence.Although the particle swarm optimization algorithm based on biological population behavior can achieve global optimization,the number of iterations and the number of particles required for convergence is at least 120×120.Combined with the chaotic initialization of 200 particles,the total number of objective function calculations is 14600,and the calculation time is about 13 minutes.According to the characteristics that the aim of PD is the Zernike coefficient,the iterative algorithm for independent optimization of Zernike coefficients is proposed.That is,only one Zernike coefficient is optimized at a time,and other coefficients are fixed,so that the correct coefficients can be obtained after multiple rounds of iteration.When the algorithm optimizes the coefficients of each dimension,the golden section search is applied,where about 11 iterations are needed.When solving 12 Zernike coefficients,the overall iteration can reach convergence in 17 rounds.At this time,the total number of calculations is 11×12×17=2244.Compared to the particle swarm algorithm,the number of calculations is reduced to about 1/6 of the original,and the corresponding calculation time is reduced from 13 minutes to about 2 minutes,and its convergence was comparable to the particle swarm optimization algorithm.The optimization of the diversity function is studied.It is found that a point spread function(PSF)can solve two wavefronts that are oddly symmetric with each other,that is,the wavefront solution is not unique.Further combined with the PD model,it is deduced that the use of odd-order Zernike aberrations as a diversity function will result in the non-unique of the wavefront.The wavefront reconstruction accuracy of different diversity function is further evaluated by Cramer-Rao lower bound(CRLB).The simulation results show that the average CRLB corresponding to the defocus is the smallest i.e.the wave with higher accuracy can be recovered.Finally,the defocusing PSF obtained by the combination of the aberration and the defocus function is deduced,and the quantitative relationship between the optimal defocus amount and main spatial frequency of the aberration is obtained based on the image contrast.It shows the optimal defocus amount is proportional to the main frequency component of the aberration spectrum,that is,the higher the frequency of the aberration,the larger the corresponding optimal defocus amount,which provides a quantitative basis for optimal defocus setting.A regularization method for improving the quality of reconstructed images was studied.The traditional Tikhonov regularization based on the prior is that the simplest image total energy is minimized,which is low-pass filtering in the Fourier spectral domain and unable to separate the high-frequency information of the image from the noise,so that the reconstructed image is too smooth.In the field of image deblurring and denoising,the best effect at present is the nonlocal localized sparse representation(NCSR)regularization method.The regularization method is based on image non-local self-similarity and sparse representation characteristics.Based on the non-local selfsimilarity feature,the whole image can be split into a series of small image block processing,and the similarity between the image blocks can be used to recover the repeated details in the image.The sparse representation can represent the effective information of the image with fewer coefficients.Compared with the Fourier spectrum,the noise and image information can be divided more open,so that the noise can be removed more thoroughly.The image reconstruction of the PD is image deconvolution by a PSF obtained from the recovered wavefront.Therefore,it is considered to add the NCSR to the image reconstruction process of the PD to improve the quality of the reconstructed image.The simulation results show that the peak signal-to-noise ratio of the reconstructed image with NCSR regularization is improved by 5-10 dB compared with that of the traditional PD reconstruction image,and the structural similarity is also improved.Simple experiment was built in the experimental room,and the image quality reconstructed by the NCSR regularized PD was significantly improved.After adding the NCSR regularization,the calculation time has increased,and the overall time is enlarged from 2 minutes to about 3.5 minutes.Based on the Zernike coefficient independent optimization algorithm,the selection of the optimal defocus amount and the NCSR regularization method,the PD technique is applied to the liquid crystal adaptive optics system.The number of image pixels processed in the experiment is 200×200,and 12 Zernike modes are used to reconstruct the wavefront.The results show that the highest spatial resolutions that can be clearly distinguished are 1.59× diffraction limitation with AO on,and 1.26× diffraction limitation by the PD with NCSR.Finally,the LC AOS was applied to the 2-meter telescope in our institute for space object observation.The observation results of the star show that the angular resolution of the AO corrected image is 0.47?,and it is improved to 0.18? by the PD.The results of the satellite show that the edge of the satellite is significantly sharper,and the signalto-noise ratio of the image is increased from 19.91 dB to 47.22 dB.The conclusions obtained in this thesis prove that,through the modification of the optimization algorithm of PD technique,the research of diversity function,the sparse regularization method and its research on the application of liquid crystal adaptive system,the high-resolution imaging of the LC AOS combined with the PD technology is realized,which expands the use of liquid crystal adaptive optics in large telescopes.It has important research significance and application value for astronomical research,such observations of dark matter,quasars,and red-shifted galaxies,and for national space security such as the surveillance tracking of spy satellites.