[1] [1] Zhang Yixin, Chi Zeying. Propagation imaging of light waves in atmosphere[M]. Beijing: National Defense Industry Press, 1997.

[2] [2] Yang Lei. Researches of the Phase diversity wavefront reconstruction techniques its application in the high resolution image restation[D]. Yunnan: Yunnan Observaty, Graduate School of Chinese Academy of Sciences, 2007

[3] [3] Gonsalves R A, Chidlaw R. Wavefront sensing by phase retrieval[C]Applications of Digital Image Processing III, 1979: 3239.

[4] [4] Fusco T, Michau V, Mugnier L, et al. Comparative theetical experimental study of a ShackHartmann a phase diversity sens, f highprecision wavefront sensing dedicated to space active optics[C]International Conference on Space Optics, 2014.

[5] Gonsalves R A. Phase retrieval and diversity in adaptive optics[J]. Optical Engineering, 21, 829-832(1982).

[6] Zhang Peiguang, Yang Chengliang, Xu Zihao, et al. High-accuracy wavefront sensing by phase diversity technique with bisymmetric defocuses diversity phase[J]. Scientific Reports, 7, 15361(2017).

[7] Nesterov Y. Gradient methods for minimizing composite objective function[J]. Core Discussion Papers, 140, 125-161(2007).

[8] [8] Shewchuk J R. An introduction to the conjugate gradient method without the agonizing pain[M]. Pittsburgh (USA): Carnegie Mellon University, 1994.

[10] Li Donghui, Fukushima M. On the global convergence of the BFGS method for nonconvex unconstrained optimization problems[J]. SIAM Journal on Optimization, 11, 1054-1064(2001).

[11] Kirkpatrick S, Gelatt C D, VecchiM P. Optimization by simulated annealing[J]. Science, 220, 671-680(1983).

[12] [12] Holl J H. Adaptation in natural artificial systems: an introducty analysis with applications to biology, control, artificial intelligence[M]. Cambridge: MlT Press, 1992.

[13] [13] Eberhart R C, Kennedy J. A new optimizer using particle swarm they[C]Proceedings of the Sixth International Symposium on Micro Machine Human Science. 1995.

[14] Zhang Peiguang, Yang Chengliang, Xu Zihao, et al. Hybrid particle swarm global optimization algorithm for phase diversity phase retrieval[J]. Optics Express, 24, 25704(2016).

[15] [15] Xu Zihao. Research on highresolution liquid crystal adaptive optics technique with phase diversity[D]. Changchun: Changchun Institute of Optics, Fine Mechanics Physics, Chinese Academy of Sciences, 2018.

[16] Ge Yingjian, Wang Shengqian, Xian Hao. Phase diversity method based on an improved particle swarm algorithm used in co-phasing error detection[J]. Applied Optics, 59, 9735-9743(2020).

[17] Qi Xin, Ju Guohao, Zhang Chunyue, et al. Object-independent image-based wavefront sensing approach using phase diversity images and deep learning[J]. Optics Express, 27, 26102-26119(2019).

[18] Wu Yu, Guo Youming, Bao Hua, et al. Sub-millisecond phase retrieval for phase-diversity wavefront sensor[J]. Sensors, 20, 4877(2020).

[19] Wu Daosheng, Yang Chengliang, Zhang Peiguang, et al. Phase diversity technique with sparse regularization in liquid crystal adaptive optics system[J]. Journal of Astronomical Telescopes Instruments and Systems, 4(2018).

[22] Yu Hongli, Yang Chengliang, Xu Zihao, et al. Analysis and reduction of errors caused by Poisson noise for phase diversity technique[J]. Optics Express, 24, 22034-22042(2016).

[23] Li Dequan, Xu Shuyan, Wang Dong, et al. Phase diversity algorithm with high noise robust based on deep denoising convolutional neural network[J]. Optics Express, 27, 22846-22854(2019).

[24] Paxman R G, Fienup J R. Optical misalignment sensing and image reconstruction using phase diversity[J]. Journal of the Optical Society of America A, 5, 914-923(1988).

[25] Lofdahl M G, Duncan A L, Paxman R G, et al. Phase diversity experiment to measure piston misalignment on the segmented primary mirror of the Keck II Telescope[J]. Astronomical Telescopes & Instrumentation, 3356, 1190-1201(1998).

[26] Blanc A, Fusco T, Hartung M, et al. Calibration of NAOS and CONICA static aberrations. Application of the phase diversity technique[J]. Astronomy & Astrophysics, 399, 373-83(2003).

[27] [27] Geges J A, Drance P, Gleichman K, et al. Highspeed closedloop dual defmablemirr phasediversity testbed[C]. Proceedings of SPIE, 2007, 6711: 671105.

[28] [28] Lamb M, Creia C, Sauvage J F, et al. Expling the operational effects of phase diversity f the calibration of noncommon path errs on NFIRAOS[C]SPIE Astronomical Telescopes + Instrumentation, 2016.

[29] Carreras R A, Restaino S R. Field experimental results using phase diversity on a binary star[J]. NASA Technical Report, 97(1996).

[30] Hirzberger J, Feller A, Riethmüller T, et al. Performance validation of phase diversity image reconstruction techniques[J]. Astronomy & Astrophysics, 529, 1-5(2011).

[32] Wu Daosheng, Yang Chengliang, Li Hao, et al. Astronomical observation by 2-meter telescope based on liquid crystal adaptive optics with phase diversity[J]. Optics Communications, 439, 129-132(2019).