Infrared and Laser Engineering, Volume. 51, Issue 11, 20220402(2022)
Phase retrieval algorithms: principles, developments and applications (invited)
[1] M Lax, W H Louisell, W B Mcknight. From Maxwell to paraxial wave optics. Phys Rev A, 11, 1365-1370(1975).
[2] [2] Cowley J M. Diffraction Physics[M]. Amsterdam: Elsevier, 1995.
[3] [3] Stratton J A. Electromagic They [M]. New Jersey: John Wiley & Sons, 2007.
[4] [4] Hecht E. Optics [M]. 4th ed. San Francisco: Addison Wesley, 2001.
[5] [5] Oppenhein A V, Lim J S. The imptance of phase in signals [C]Proceedings of IEEE, 1981, 69(5): 529541.
[6] H Giloh, J W Sedat. Fluorescence microscopy: Reduced photobleaching of rhodamine and fluorescein protein conjugates by
[7] D J Stephens, V J Allan. Light microscopy techniques for live cell imaging. Science, 300, 82-86(2003).
[8] F Zernike. Phase contrast, a new method for the microscopic observation of transparent objects part II. Physica, 9, 974-986(1942).
[9] G Nomarski. Differential microinterferometer with polarized waves. J Phys Radium, 16, 9-13(1955).
[10] Y Park, C Depeursinge, G Popescu. Quantitative phase imaging in biomedicine. Nat Photonics, 12, 578-589(2018).
[11] Y Jo, H Cho, S Y Lee, et al. Quantitative phase imaging and artificial intelligence: A review. IEEE J Sel Top Quantum Electron, 25, 1-14(2018).
[12] E Cuche, F Bevilacqua, C Depeursinge. Digital holography for quantitative phase-contrast imaging. Opt Lett, 24, 291-293(1999).
[13] U Schnars, W P O Jptner. Digital recording and numerical reconstruction of holograms. Meas Sci Technol, 13, R85(2002).
[14] T Tahara, X Quan, R Otani, et al. Digital holography and its multidimensional imaging applications: A review. Microscopy, 67, 55-67(2018).
[15] J Hartmann. Bemerkungen uber den bau und die justirung von spektrographen. Zt Instrumentenkd, 20, 17-27(1990).
[16] R V Shack, B C Platt. Production and use of a lecticular hartmann screen. J Opt Soc Am, 61, 656-661(1971).
[17] B C Platt, R V Shack. History and principles of shack-hartmann wavefront sensing. J Cataract Refr Surg, 17, S573-577(2001).
[18] S Esposito, A Riccardi. Pyramid wavefront sensor behavior in partial correction adaptive optic systems. Astron Astrophys, 369, L9-L12(2001).
[19] R Ragazzoni, E Diolaiti, E Vernet. A pyramid wavefront sensor with no dynamic modulation. Opt Commun, 208, 51-60(2002).
[20] M A A Neil, M J Booth, T Wilson. New modal wave-front sensor: A theoretical analysis. J Opt Soc Am A, 17, 1098-1107(2000).
[21] M J Booth. Wave front sensor-less adaptive optics: A model-based approach using sphere packings. Opt Express, 14, 1339-1352(2006).
[22] M J Booth. Adaptive optics in microscopy. Phil Trans R Soc A, 365, 2829-2843(2007).
[23] J W Cha, J Ballesta, P T C So. Shack-hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy. J Biomed Opt, 15, 046022(2010).
[24] D Dayton, J Gonglewski, B Pierson, et al. Atmospheric structure function measurements with a Shack-Hartmann wave-front sensor. Opt Lett, 17, 1737-1739(1992).
[25] J C Ricklin, F M Davidson. Atmospheric turbulence effects on a partially coherent Gaussian beam: Implications for free-space laser communication. J Opt Soc Am A, 19, 1794-1802(2002).
[26] J Liang, B Grimm, S Goelz, et al. Objective measurement of wave aberrations of the human eye with the use of a hartmann-shack wave-front sensor. J Opt Soc Am A, 11, 1949-1957(1994).
[27] E Moreno-Barriuso, R Navarro. Laser ray tracing versus hartmann-shack sensor for measuring optical aberrations in the human eye. J Opt Soc Am A, 17, 974-985(2000).
[28] D Sayre. Some implications of a theorem due to Shannon. Acta Crystallogr, 5, 843-843(1952).
[29] R W Gerchberg. A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik, 35, 237-246(1972).
[30] R W Gerchberg. Phase determination for image and diffraction plane pictures in the electron microscope. Optik, 34, 275-284(1971).
[31] J Miao, P Charalambous, J Kirz, et al. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature, 400, 342-344(1999).
[32] J Miao, D Sayre, H N Chapman, et al. Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects. J Opt Soc Am A, 15, 1662(1998).
[33] M R Howells, T Beetz, H N Chapman, et al. An assessment of the resolution limitation due to radiation-damage in X-ray diffraction microscopy. J Electron Spectrosc Relat Phenom, 170, 4-12(2009).
[34] E J Candès, S Thomas, V Vladislav. PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming. Commun Pure Appl Math, 66, 1241-1274(2013).
[35] I Waldspurger, A D’aspremont, S Mallat. Phase recovery, max-cut and complex semidefinite programming. Math Program, 149, 47-81(2015).
[36] E J Candès, X Li, M Soltanolkotabi. Phase retrieval via wirtinger flow: Theory and algorithms. IEEE Trans Inf Theory, 61, 1985-2007(2015).
[37] Y Chen, E J Candès. Solving random quadratic systems of equations is nearly as easy as solving linear systems. Commun Pure Appl Math, 70, 822-883(2017).
[38] G Wang, G B Giannakis, Y C Eldar. Solving systems of random quadratic equations via truncated amplitude flow. IEEE Trans Inf Theory, 64, 773-794(2018).
[39] [39] Eldar Y C, Kutyniok G. Compressed Sensing: They Applications [M]. Cambridge: Cambridge University Press, 2012.
[40] J L C Sanz. Mathematical considerations for the problem of Fourier transform phase retrieval from magnitude. SIAM J Appl Math, 45, 651-664(1985).
[41] A Fannjiang. Absolute uniqueness of phase retrieval with random illumination. Inverse Probl, 28, 075008(2012).
[42] E Hofstetter. Construction of time-limited functions with specified auto-correlation functions. IEEE Trans Inf Theory, 10, 119-126(1964).
[43] Y M Bruck, L Sodin. On the ambiguity of the image reconstruction problem. Opt Commun, 30, 304-308(1979).
[44] M Hayes. The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform. IEEE Trans Acoust, Speech, Signal Process, 30, 140-154(1982).
[45] R H T Bates. Fourier phase problems are uniquely solvable in more than one dimension. I: Underlying theory. Optik, 61, 247-262(1982).
[46] H Van, M Hayes, J Lim, et al. Signal reconstruction from signed fourier transform magnitude. IEEE Trans Acoust, Speech, Signal Process, 31, 1286-1293(1983).
[47] R Beinert. Non-negativity constraints in the one-dimensional discrete-time phase retrieval problem. Information and Inference: A Journal of the IMA, 6, 213-224(2017).
[48] R Beinert, G Plonka. Ambiguities in one-dimensional discrete phase retrieval from Fourier magnitudes. J Fourier Anal Appl, 21, 1169-1198(2015).
[49] [49] Elad M. Sparse Redundant Representations: From They To Applications In Signal Image Processing [M]. New Yk: SpringerVerlag, 2010.
[50] [50] Ranieri J, Chebira A, Lu Y M, et al. Phase retrieval f sparse signals: Uniqueness conditions [EBOL]. (20130814) [20221011]. https:arxiv.gabs1308.3058.
[51] [51] Ohlsson H, Eldar Y C. On conditions f uniqueness in sparse phase retrieval [C]2014 IEEE International Conference on Acoustics, Speech Signal Processing (ICASSP), 2014: 18411845.
[52] K Jaganathan, S Oymak, B Hassibi. Sparse phase retrieval: Uniqueness guarantees and recovery algorithms. IEEE Trans Signal Process, 65, 2402-2410(2017).
[53] E J Candès, J Romberg, T Tao. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory, 52, 489-509(2006).
[54] J R Fienup. Phase retrieval algorithms: A comparison. Appl Optics, 21, 2758-2769(1982).
[55] M R Teague. Irradiance moments: Their propagation and use for unique retrieval of phase. J Opt Soc Am, 72, 1199-1209(1982).
[56] C Shen, M Liang, A Pan, et al. Non-iterative complex wave-field reconstruction based on Kramers–Kronig relations. Photonics Res, 9, 1003-1012(2021).
[57] [57] Mukherjee S, Seelamantula C S. An iterative algithm f phase retrieval with sparsity constraints: Application to frequency domain optical coherence tomography [C]2012 IEEE International Conference on Acoustics, Speech Signal Processing Processing (ICASSP), 2012: 553556.
[58] Y Shechtman, A Beck, Y C Eldar. GESPAR: Efficient phase retrieval of sparse signals. IEEE Trans Signal Process, 62, 928-938(2014).
[59] Y Rivenson, Y Zhang, H Günaydın, et al. Phase recovery and holographic image reconstruction using deep learning in neural networks. Light: Sci Appl, 7, 17141(2017).
[60] A Sinha, J Lee, S Li, et al. Lensless computational imaging through deep learning. Optica, 4, 1117(2017).
[61] T Nguyen, Y Xue, Y Li, et al. Deep learning approach for Fourier ptychography microscopy. Opt Express, 26, 26470-26484(2018).
[62] [62] Metzler C, Schniter P, Veeraraghavan A, et al. prDeep: Robust phase retrieval with a flexible deep wk [C]Proceedings of the 35th International Conference on Machine Learning, 2018, 80: 35013510.
[63] R Balan, P Casazza, D Edidin. On signal reconstruction without phase. Appl Comput Harmon Anal, 20, 345-356(2006).
[64] A Conca, D Edidin, M Hering, et al. An algebraic characterization of injectivity in phase retrieval. Appl Comput Harmon Anal, 38, 346-356(2015).
[65] Y C Eldar, S Mendelson. Phase retrieval: Stability and recovery guarantees. Appl Comput Harmon Anal, 36, 473-494(2014).
[66] Y Shechtman, Y C Eldar, O Cohen, et al. Phase retrieval with application to optical imaging: A contemporary overview. IEEE Signal Proc Mag, 32, 87-109(2015).
[67] C C Wackerman, A E Yagle. Use of fourier domain real-plane zeros to overcome a phase retrieval stagnation. J Opt Soc Am A, 8, 1898-1904(1991).
[68] G Lu, Z Zhang, F T S Yu, et al. Pendulum iterative algorithm for phase retrieval from modulus data. Opt Eng, 33, 548-555(1994).
[69] H Takajo, T Takahashi, H Kawanami, et al. Numerical investigation of the iterative phase-retrieval stagnation problem: Territories of convergence objects and holes in their boundaries. J Opt Soc Am A, 14, 3175-3187(1997).
[70] [70] Soifer V A, Kotlar V, Doskolovich L. Iteractive Methods F Diffractive Optical Elements Computation [M]. London: Tayl & Francis Group, 1997.
[71] J R Fienup. Reconstruction of an object from the modulus of its Fourier transform. Opt Letters, 3, 27-29(1978).
[72] J R Fienup, T Crimmins, W Holsztynski. Reconstruction of the support of an object from the support of its autocorrelation. J Opt Soc Am A, 72, 610-624(1982).
[73] [73] Fienup J R. Phase retrieval with continuous version of hybrid inputoutput [C]Frontiers in Optics, OSA Technical Digest (CD), 2003: ThI3.
[74] V Elser. Phase retrieval by iterated projections. J Opt Soc Am A, 20, 40-55(2003).
[75] D R Luke. Relaxed averaged alternating reflections for diffraction imaging. Inverse Probl, 21, 37(2004).
[76] J R Fienup, C C Wackerman. Phase-retrieval stagnation problems and solutions. J Opt Soc Am A, 3, 1897-1907(1986).
[77] G J Williams, M A Pfeifer, I A Vartanyants, et al. Three-dimensional imaging of microstructure in Au nanocrystals. Phys Rev Lett, 90, 175501(2003).
[78] I K Robinson, I A Vartanysnts, G J Williams, et al. Recon-struction of the shapes of gold nanocrystals using coherent X-Ray diffraction. Phys Rev Lett, 87, 195505(2001).
[79] N T D Loh, S Eisebitt, S Flewett, et al. Recovering magne-tization distributions from their noisy diffraction data. Phys Rev E, 82, 061128(2010).
[80] D L Misell. A method for the solution of the phase problem in electron microscopy. J Phys D: Appl Phys, 6, L6(1973).
[81] P Bao, F Zhang, G Pedrini, et al. Phase retrieval using multiple illumination wavelengths. Opt Lett, 33, 309-311(2008).
[82] L J Allen, M P Oxley. Phase retrieval from series of images obtained by defocus variation. Opt Commun, 1999, 65-75(2001).
[83] Y Zhang, G Pedrini, W Osten, et al. Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm. Opt Express, 11, 3234-3241(2003).
[84] P Almoro, G Pedrini, W Osten. Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field. Appl Optics, 45, 8596-8605(2006).
[85] P Gao, G Pedrini, C Zuo, et al. Phase retrieval using spatially modulated illumination. Opt Lett, 39, 3615(2014).
[86] F Zhang, G Pedrini, W Osten. Phase retrieval of arbitrary complex-valued fields through aperture- plane modulation. Phys Rev A, 75, 043805(2007).
[87] D Morris. Simulated annealing applied to the Misell algorithm for phase retrieval. Microwaves, Antennas and Propagation, 143, 298-303(1996).
[88] Y Xu, Q Ye, G Meng. Hybrid phase retrieval algorithm based on modified very fast simulated annealing. Int J Microw Wirel Technol, 10, 1072-1080(2018).
[89] H M L Faulkner, J M Rodenburg. Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm. Phys Rev Lett, 93, 023903(2004).
[90] J M Rodenburg, H M L Faulkner. A phase retrieval algorithm for shifting illumination. Appl Phys Lett, 85, 4795-4797(2004).
[91] A M Maiden, J M Rodenburg. An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy, 109, 1256-1262(2009).
[92] A M Maiden, M J Humphry, J Rodenburg. Ptychographic transmission microscopy in three dimensions using a multi-slice approach. J Opt Soc Am A, 29, 1606-1614(2012).
[93] A Maiden, D Johnson, P Li. Further improvements to the ptychographical iterative engine. Optica, 4, 736-745(2017).
[94] G Zheng, R Horstmeyer, C Yang. Wide-field, high-resolution Fourier ptychographic microscopy. Nat Photonics, 7, 739-745(2013).
[95] X Ou, R Horstmeyer, C Yang, et al. Quantitative phase imaging via Fourier ptychographic microscopy. Opt Lett, 38, 4845(2013).
[96] A Pan, Y Zhang, T Zhao, et al. System calibration method for Fourier ptychographic microscopy. J Biomed Optics, 22, 096005(2017).
[97] Y Zhang, A Pan, M Lei, et al. Data preprocessing methods for robust Fourier ptychographic microscopy. Opt Eng, 56, 123107(2017).
[98] A Pan, C Zuo, Y Xie, et al. Vignetting effect in Fourier ptychographic microscopy. Opt Laser Eng, 120, 40-48(2019).
[99] [99] Pan A, Shen C, Yao B, et al. Singleshot Fourier ptychographic microscopy via annular monochrome LED array [C]Frontiers in Optics + Laser Science APSDLS, 2019: FTh3 F.4.
[100] A Pan, Y Zhang, K Wen, et al. Subwavelength resolution Fourier ptychography with hemispherical digital condensers. Opt Express, 26, 23119-23131(2018).
[101] A Pan, B Yao. Three-dimensional space optimization for near-field ptychography. Opt Express, 27, 5433-5446(2019).
[102] A Chan, J Kim, A Pan, et al. Parallel Fourier ptychographic microscopy for high-throughput screening with 96 cameras (96 Eyes). Sci Rep, 9, 11114(2019).
[103] A Pan, K Wen, B Yao. Linear space-variant optical cryptosystem via Fourier ptychography. Opt Lett, 44, 2032-2035(2019).
[104] M Xiang, A Pan, Y Zhao, et al. Coherent synthetic aperture imaging for visible remote sensing via reflective Fourier ptychography. Opt Lett, 46, 29-32(2021).
[105] Y Gao, J Chen, A Wang, et al. High-throughput fast full-color digital pathology based on Fourier ptychographic microscopy via color transfer. Sci China-Phys Mech, 64, 114211(2021).
[106] A Wang, Z Zhang, S Wang, et al. Fourier ptychographic microscopy via alternating direction method of multipliers. Cells, 11, 1512(2022).
[107] Jiasong Sun, Yuzhen Zhang, Qian Chen, et al. Fourier ptychographic microscopy: Theory, advances, and applications. Acta Optica Sinica, 36, 1011005(2016).
[108] An Pan, Baoli Yao. High-throughput and fast-speed Fourier ptychographic microscopy. Infrared and Laser Engi-neering, 48, 0603012(2019).
[109] P C Konda, L Loetgering, K C Zhou, et al. Fourier ptycho-graphy: Current applications and future promises. Opt Express, 28, 9603-9630(2020).
[110] A Pan, C Zuo, B Yao. High-resolution and large field-of-view Fourier ptychographic microscopy and its applications in biomedicine. Rep Prog Phys, 83, 096101(2020).
[111] G Zheng, C Shen, S Jiang, et al. Concept, implementations and applications of Fourier ptychography. Nat Rev Phys, 3, 207-223(2021).
[112] Shaohui Zhang, Guocheng Zhou, Baiqi Cui, et al. Review of Fourier ptychographic microscopy: Models, algorithms, and systems. Laser & Optoelectronics Progress, 58, 1400001(2021).
[113] M R Teague. Deterministic phase retrieval: A green’s function solution. J Opt Soc Am A, 73, 1434-1441(1983).
[114] J P Guigay. Fourier transform analysis of fresnel diffraction patterns and in-line holograms. Optik, 49, 121-125(1977).
[115] D Paganin, K A Nugent. Noninterferometric phase imaging with partially coherent light. Phys Rev Lett, 80, 2586(1998).
[116] T E Gureyev, C Raven, A Snigirev, et al. Hard X-ray quantitative non-interferometric phase- contrast microscopy. J Phys Appl Phys, 32, 563(1999).
[117] S V Pinhasi, R Alimi, L Perelmutter, et al. Topography retrieval using different solutions of the transport intensity equation. J Opt Soc Am A, 27, 2285-2292(2010).
[118] B Xue, S Zheng. Phase retrieval using the transport of intensity equation solved by the FMG-CG method. Opt-Int J Light Electron Opt, 122, 2101-2106(2011).
[119] V V Voitsekhovich. Phase-retrieval problem and orthogonal expansions: Curvature sensing. J Opt Soc Am A, 12, 2194-2202(1995).
[120] S Ros, E Acosta, S Bar. Modal phase estimation from wavefront curvature sensing. Opt Commun, 123, 453-456(1996).
[121] V V Volkov, Y Zhu, Graef M De. A new symmetrized solution for phase retrieval using the transport of intensity equation. Micron, 33, 411-416(2002).
[122] J Frank, S Altmeyer, G Wernicke. Non-interferometric, non-iterative phase retrieval by green’s functions. J Opt Soc Am A, 27, 2244-2251(2010).
[123] C Zuo, Q Chen, A Asundi. Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform. Opt Express, 22, 9220(2014).
[124] C Zuo, Q Chen, H Li, et al. Boundary-artifact-free phase retrieval with the transport of intensity equation II: Applications to microlens characterization. Opt Express, 22, 18310(2014).
[125] L Huang, C Zuo, M Idir, et al. Phase retrieval with the transport-of-intensity equation in an arbitrarily shaped aperture by iterative discrete cosine transforms. Opt Lett, 40, 1976(2015).
[126] C Zuo, J Li, J Sun, et al. Transport of intensity equation: A tutorial. Opt Laser Eng, 152, 106187(2020).
[127] [127] Hall S H, Heck H L. Advanced Signal Integrity f Highspeed Digital Designs [M]. Hoboken, NJ, USA: Wiley, 2009.
[128] [128] Graf U. Introduction to Hyperfunctions Their Integral Transfms: An Applied Computational Approach [M]. Basel: Birkhauser, 2010.
[129] T Ikeda, G Popescu, R R Dasari, et al. Hilbert phase microscopy for investigating fast dynamics in transparent systems. Opt Lett, 30, 1165-1167(2005).
[130] Y Beak, K Lee, S Shin, et al. Kramers–Kronig holographic imaging for high-space-bandwidth product. Optica, 6, 45-51(2019).
[131] Z Huang, L Cao. High bandwidth-utilization digital holo-graphic multiplexing: An approach using Kramers-Kronig relations. Adv Photonics Res, 3, 2100273(2022).
[132] N Gillis, F Glineur. Low-rank matrix approximation with weights or missing data is NP-hard. SIAM J Matrix Anal Appl, 32, 1149-1165(2011).
[133] Y M Lu, G Li. Phase transitions of spectral initialization for high-dimensional non-convex estimation. Information and Inference: A Journal of the IMA, 9, 507-541(2017).
[134] P Netrapalli, P Jain, S Sanghavi. Phase retrieval using alternating minimization. IEEE Trans Signal Process, 63, 4814-4826(2015).
[135] T Cai, J Fan, T Jiang. Distributions of angles in random packingon spheres. J Mach Learn Res, 14, 1837-1864(2013).
[136] G Wang, G B Giannakis, Y Saad. Phase retrieval via reweighted amplitude flow. IEEE Trans Signal Process, 66, 2818-2833(2018).
[137] [137] Yuan Z, Wang H, Wang Q. Phase retrieval via sparse Wirtinger flow[J]. J Comput Appl Math, 2019, 355: 162173.
[138] [138] Kolte R, Özgür A. Phase retrieval via incremental d Wirtinger flow [EBOL]. (20160610) [20220803]. https:arxiv.gabs1606.03196.
[139] H Zhang, Y Chi, Y Liang. Median-truncated nonconvex approach for phase retrieval with outliers. IEEE Trans Inf Theory, 64, 7287-7310(2018).
[140] G Wang, G B Giannakis, Y Saad, et al. Scalable solvers of random quadratic equations via stochastic truncated amplitude flow. IEEE Trans Signal Process, 65, 1961-1974(2017).
[141] S Pinilla, J Bacca, H Arguello. Phase retrieval algorithm via nonconvex minimization using a smoothing function. IEEE Trans Signal Process, 66, 4574-4584(2018).
[142] Q Luo, H Wang, S Lin. Phase retrieval via smoothed amplitude flow. Signal Process, 177, 107719(2020).
[143] S Loock, G Plonka. Phase retrieval for Fresnel measurements using a Shearlet sparsity constraint. Inverse Probl, 30, 055005(2014).
[144] Zhenya Yang, Chujun Zheng. Phase retrieval of pure phase object based on compressed sensing. Acta Physica Sinica, 62, 104203(2013).
[145] Y Shechtman, Y C Eldar, A Szameit, et al. Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing. Opt Express, 19, 14807-14822(2011).
[146] H Ohlsson, A Y Yang, R Dong, et al. Compressive phase retrieval from squared output measurements via semidefinite programming. IFCA Proceedings Volumes, 45, 89-94(2012).
[147] Chao Zuo, Shijie Feng, Xiangyu Zhang, et al. Deep learning based computational imaging: Status, challenges, and future. Acta Optica Sinica, 40, 0111003(2020).
[148] Y Nishizaki, R Horisaki, K Kitaguchi, et al. Analysis of non-iterative phase retrieval based on machine learning. Opt Rev, 27, 136-141(2020).
[149] F Wang, Y Bian, H Wang, et al. Phase imaging with an untrained neural network. Light: Sci Appl, 9, 77(2020).
[150] [150] Naimipour N, Khobahi S, Soltanalian M. UPR: A modeldriven architecture f deep phase retrieval [C]54th Asilomar Conference on Signals, Systems, Computers, 2020: 205209.
[151] S Boutet, I K Robinson. Coherent X-ray diffractive imaging of protein crystals. J Synchrotron Radiat, 15, 576-583(2008).
[152] M W Parker. Protein structure from X-ray diffraction. Journal of Biological Physics, 29, 341-362(2003).
[153] J Miao, T Ohsuna, O Terasaki, et al. Atomic resolution three-dimensional electron diffraction microscopy. Phys Rev Lett, 89, 155502(2002).
[154] O Kamimuraet, K Kawahara, T Doi, et al. Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes. Appl Phys Lett, 92, 024106(2008).
[155] A M Maiden, M J Humphry, F Zhang, et al. Superresolution imaging via ptychography. J Opt Soc Am A, 28, 604-612(2011).
[156] A M Maiden, J M Rodenburg, M J Humphry. Optical ptychography: A practical implementation with useful resolu-tion. Opt Lett, 35, 2585-2587(2010).
[157] H N Chapman, K A Nugent. Coherent lensless X-ray imaging. Nat Photonics, 4, 833-839(2010).
[158] J Wu, H Zhang, W Zhang, et al. Single-shot lensless imaging with fresnel zone aperture and incoherent illumination. Light: Sci Appl, 9, 53(2020).
[159] A Alfalou, C Brosseau. Optical image compression and encryption methods. Adv Opt Photonics, 1, 589(2009).
[160] R K Wang, I A Watson, C R Chatwin. Random phase encoding for optical security. Opt Eng, 35, 2464-2469(1996).
[161] Guohai Situ, Jingjuan Zhang, Yan Zhang, et al. A cascaded-phases retrieval algorithm for optical image encryption. Journal of Optoelectronics · Laser, 15, 341(2004).
[162] Y Shi, G Situ, J Zhang. Multiple-image hiding in the Fresnel domain. Opt Lett, 32, 1914-1916(2007).
[163] J J Huang, Hwang, E H, C Y Chen, et al. Lensless multiple-image optical encryption based on improved phase retrieval algorithm. Appl Opt, 51, 2388(2012).
[164] C Guo, S Liu, J T Sheridan. Iterative phase retrieval algorithms. Part I: Optimization. Appl Opt, 54, 4698-4708(2015).
[165] C Guo, S Liu, J T Sheridan. Iterative phase retrieval algorithms. Part II: Attacking optical encryption systems. Appl Opt, 54, 4709-4718(2015).
[166] C Guo, C Wei, J Tan, et al. A review of iterative phase retrieval for measurement and encryption. Opt Lasers Eng, 89, 2-12(2017).
[167] S Wang, X Meng, Y Wang, et al. Phase retrieval algorithm for optical information security. Chin Phys B, 28, 084203(2019).
[168] L Hu, C Liu, W Shen, et al. Advancement of adaptive optics in astronomical observation. Sci China-Phys Mech, 47, 084202(2017).
[169] D G Sandler, S Stahl, J R P Angel, et al. Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes. J Opt Soc Am A, 11, 925-945(1994).
[170] C Rao, L Zhu, X Rao, et al. 37-element solar adaptive optics for 26-cm solar fine structure telescope at Yunnan Astronomical Observatory. Chin Opt Lett, 8, 966-968(2010).
[171] N B Baranova, A V Mamaev, N F Pilipetsky, et al. Wave-front dislocations: Topological limitations for adaptive systems with phase conjugation. J Opt Soc Am, 73, 525-528(1983).
[172] Y Ping, A Ming, L Yuan, et al. Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients. Opt Express, 15, 17051(2007).
[173] S Zommer, E N Ribak, S G Lipson, et al. Simulated annealing in ocular adaptive optics. Opt Letters, 31, 939-941(2006).
[174] R El-Agmy, H Bulte, A H Greenaway, et al. Adaptive beam profile control using a simulated annealing algorithm. Opt Express, 13, 6085(2005).
[175] M S Zakynthinaki, Y G Saridakis. Stochastic optimization for adaptive real-time wavefront correction. Numerical Algorithms, 33, 509-520(2003).
[176] [176] Feng L, Zeng Z, Wu Y. Phase retrieval hybrid algithm f optical surface testing of the high dynamic range err [C]Proceedings of SPIE, 2014, 9282: 92822Y.
[177] J R Fienup, J C Marron, T J Schulz, et al. Hubble space telescope characterized by using phase retrieval algorithms. Appl Optics, 32, 1747-1767(1993).
[178] [178] Dean B H, Aronstein D L, Smith J S, et al. Phase retrieval algithm f JWST flight testbed telescope [C]Proceedings of SPIE, 2006, 6265: 626511.
[179] Shengyi Li, Xiaojun Hu, Yulie Wu. Phase retrieval on site testing for large mirrors. Acta Photonica Sinica, 38, 365(2009).
[180] Yulie Wu, Xiaojun Hu, Yifan Dai, et al. In-situ surface measurement for large aperture optical mirror based on phase retrieval technology. Journal of Mechanical Engineering, 45, 157-163(2009).
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Aiye Wang, An Pan, Caiwen Ma, Baoli Yao. Phase retrieval algorithms: principles, developments and applications (invited)[J]. Infrared and Laser Engineering, 2022, 51(11): 20220402
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