High-throughput and fast-speed Fourier ptychographic microscopy: A review

Pan An; Yao Baoli

doi:10.3788/irla201948.0603012

[1] Thorn K. A quick guide to light microscopy in cell biology [J]. Molecular Biology of the Cell, 2016, 27(2): 219-222.

[2] Murphy D B, Davidson M W. Fundamentals of Light Microscopy and Electronic Imaging [M]. Hoboken: John Wiley & Sons, 2012.

[3] Turpin T, Gesell L, Lapides J, et al. Theory of the synthetic aperture microscope [C]//SPIE, 1995, 2566: 230-240.

[4] Holloway J, Wu Y, Sharma M K, et al. SAVI: Synthetic apertures for long-range, subdiffraction-limited visible imaging using Fourier ptychography [J]. Science Advances, 2017, 3(4): e1602564.

[5] Fischer R S, Wu Y, Kanchanawong P, et al. Microscopy in 3D: a biologist′s toolbox [J]. Trends in Cell Biology, 2011, 21(12): 682-691.

[6] Day R N, Davidson M W. The fluorescent protein palette: tools for cellular imaging [J]. Chemical Society Reviews, 2011, 40(12): 5923.

[7] Dean K M, Palmer A E. Advances in fluorescence labeling strategies for dynamic cellular imaging [J]. Nature Chemical Biology, 2014, 10(7): 512-523.

[8] Pawley J B. Handbook of Biological Confocal Microscopy [M]. Madison: Springer, 2006.

[9] Minsky M. Memoir on inventing the confocal scanning microscope [J]. Scanning, 1988, 10(4): 128-138.

[10] Sekar R B, Periasamy A. Fluorescence resonance energy transfer(FRET) microscopy imaging of live cell protein localizations [J]. The Journal of Cell Biology, 2003, 160(5): 629-633.

[11] Heim R, Tsien R Y. Engineering green fluorescent protein for improved brightness, longer wavelengths and fluorescence resonance energy transfer [J]. Current Biology, 1996, 6(2): 178-182.

[12] Selvin P R. The renaissance of fluorescence resonance energy transfer [J]. Nature Structural & Molecular Biology, 2000, 7(9): 730-734.

[13] Bastiaens P I, Squire A. Fluorescence lifetime imaging microscopy: spatial resolution of biochemical processes in the cell [J]. Trends in Cell Biology, 1999, 9(2): 48-52.

[14] Digman M A, Caiolfa V R, Zamai M, et al. The phasor approach to fluorescence lifetime imaging analysis [J]. Biophysical Journal, 2008, 94(2): L14-L16.

[15] Axelrod D. Total internal reflection fluorescence microscopy in cell biology[J]. Traffic, 2011, 2(11): 764-774.

[16] Maire G, Giovannini H, Talneau A, et al. Phase imaging and synthetic aperture super-resolution via total internal reflection microscopy[J]. Optics Letters, 2018, 43(9): 2173-2176.

[17] Gustafsson M G. Surpassing the lateral resolution limit by a factor of two using structed illumination microscopy [J]. Journal of Microscopy, 2000, 198(Pt2): 82-87.

[19] York A G, Parekh S H, Dalle Nogare D, et al. Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy[J]. Nature Methods, 2012, 9(7): 749-754.

[20] Mudry E, Belkebir K, Girard J, et al. Structuredillumination microscopy using unknown speckle patterns[J]. Nature Photonics, 2012, 6: 312-315.

[21] Gao P, Pedrini G, Osten W. Phase retrieval with resolution enhancement by using structured illumination[J]. Optics Letters, 2013, 38(24): 5204-5207.

[22] Gao P, Pedrini G, Osten W. Structured illumination for resolution enhancement and autofocusing in digital holographic microscopy[J]. Optics Letters, 2013, 38(8): 1328-1330.

[23] Qian J, Lei M, Dan D, et al. Full-color structured illumination optical sectioning microscopy[J]. Scientific Reports, 2015, 5: 14513.

[24] Dan D, Lei M, Yao B, et al. DMD-based LED-illumination super-resolution and optical sectioning microscopy[J]. Scientific Reports, 2013, 3: 1116.

[25] Zhou X, Lei M, Dan D, et al. Image recombination transform algorithm for superresolution structured illumination microscopy [J]. Journal of Biomedical Optics, 2016, 21(9): 096009.

[26] Yeh L H, Tian L, Waller L. Structured illumination microscopy with unknown patterns and a statistical prior [J]. Biomedical Optics Express, 2017, 8(2): 695-711.

[27] Qian J, Dang S, Wang Z, et al. Large-scale 3D imaging of insects with nature color [J]. Optics Express, 2019, 27(4): 4845-4857.

[28] Betzig E, Patterson G H, Sougrat R, et al. Imaging intracellular fluorescent proteins at nanometer resolution [J].Science, 2006, 313(5793): 1642-1645.

[29] Hess S T, Girirajan T P, Mason M D. Ultra-high resolution imaging by fluorescence photoactivation localization microscopy[J]. Biophysical Journal, 2006, 91(11): 4258-4272.

[30] Rust M J, Bates M, Zhuang X. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy(STORM) [J].Nature Methods, 2005, 3(10): 793-795.

[31] Huang B, Babcock H, Zhuang X. Breaking the diffraction barrier: super-resolution imaging of cells [J]. Cell, 2010, 143(7): 1047-1058.

[32] Sigal Y M, Zhou R, Zhuang X. Visualizing and discovering cellular structures with super-resolution microscopy [J]. Science, 2018, 361(6405): 880-887.

[33] Hell S W, Wichmann J. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy [J]. Optics Letters, 1994, 19(11): 780-782.

[34] Gao P, Prunsche B, Zhou L, et al. Background suppression in fluorescence nanoscopy with stimulated emission doubledepletion [J]. Nature Photonics, 2017, 11: 163-169.

[35] Denk W, Strickler J H, Webb W W. Two-photon laser scanning fluorescence microscopy[J]. Science, 1990, 348(4951): 73-76.

[36] Helmchen F, Denk W. Deep tissue two-photon microscopy [J]. Nature Method, 2005, 2(12): 932-940.

[37] Keller P J, Schmidt A D, Wittbrodt J, et al. Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy[J]. Science, 2008, 322(5904): 1065-1069.

[38] Chen B C, Legant W R, Wang K, et al. Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution[J]. Science, 2014, 346(6208): 1257998.

[39] Keller P J, Ahrens M B. Visualizing whole-brain activity and development at the single-cell level using light-sheet microscopy [J]. Neuron, 2015, 85(3): 462-483.

[40] Hoebe R A, Van Oven C H, Gadella T W Jr, et al. Controlled light-exposure microscopy reduces photobleaching and phototoxicity in fluorescence live-cell imaging [J]. Nature Biotechnology, 2007, 25(2): 249-253.

[41] Gordeon M P, Ha T, Selvin P R. Single-molecule high-resolution imaging with photobleaching [J]. Proceedings of the National Academy of Sciences, 2004, 101(17): 6462-6465.

[42] Ferrara M A, Di Caprio G, Managò S, et al. Label-free imaging and biochemical characterization of bovine sperm cells [J]. Biosensors, 2015, 5(2): 141-157.

[43] Zernike F. Phase contrast, a new method for the microscopic observation of transparent objects[J]. Physica, 1942, 9(7): 686-698.

[44] Nomarski G. Differential microinterferometer with polarized waves[J]. Journal de Physique et le Radium, 1955, 16: 9-13.

[45] Gao P, Yao B, Min J, et al. Parallel two-step phase-shifting point-diffraction interferometry for microscopy based on a pair of cubebeamsplitters [J]. Optics Express, 2011, 19(3): 1930-1935.

[46] Gao P, Yao B, Lindlein N, et al. Phase-shift extraction for generalized phase-shifting interferometry [J]. Optics Letters,2009, 34(22): 3553-3555.

[47] Gao P, Harder I, Nercissian V, et al. Phase-shifting point-diffraction interferometry with common-path and in-line configuration formicroscopy [J]. Optics Letters, 2010, 35(5): 712-714.

[48] Guo R, Yao B, Gao P, et al. Off-axis digital holographic microscopy with LED illumination based on polarization filtering[J]. Applied Optics, 2013, 52(34): 8233-8238.

[49] Zheng J, Gao P, Shao X, et al. Refractive index measurement of suspended cells using opposed-view digital holographic microscopy [J]. Applied Optics, 2017, 56(32): 9000-9005.

[50] Guo R, Wang F. Compact and stable real-time dual-wavelength digital holographic microscopy with a long-working distance objective [J]. Optics Express, 2017, 25(20): 24512-24520.

[51] Mico V, Ferreira C, Garcia J. Surpassing digital holography limits bylensless object scanning holography [J]. Optics Express, 2012, 20(9): 9382-9395.

[52] Creath K. Phase-shifting speckle interferometry [J]. Applied Optics, 1985, 24(18): 3053-3058.

[53] Rao C, Jiang W, Ling N. Measuring the power-law exponent of an atmospheric turbulence phase power spectrum with a Shack-Hartmann wave-front sensor[J]. Optics Letters, 1999, 24(15): 1008-1010.

[54] Klibanov M V, Sacks P E, Tikhonravov A V. The phase retrieval problem [J]. Inverse Problems, 1995, 11(1): 1-28.

[55] Teague M R. Deterministic phase retrieval: A Green′s function solution[J]. Journal of the Optical Society of America, 1983, 73(11): 1434-1441.

[56] Fienup J R. Phase retrieval algorithms: a comparison[J]. Applied Optics, 1982, 21(15): 2758-2769.

[57] Fienup J R. Reconstruction of an object from the modulus of its Fourier transform[J]. Optics Letters, 1978, 3(1): 27-29.

[58] Zuo C, Chen Q, Asundi A. Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform [J]. Optics Express, 2014, 22(8): 9220-9244.

[59] Zuo C, Chen Q, Huang L, et al. Phase discrepancy analysis and compensation for fast Fourier transform based solution of the transport of intensity equation [J]. Optics Express, 2014, 22(14): 17172-17186.

[60] Huang L, Zuo C, Idir M, et al. Phase retrieval with the transport-of-intensity equation in an arbitrarily shaped aperture by iterative discrete cosine transforms[J]. Optics Letters, 2015, 40(9): 1976-1979.

[61] Li J, Chen Q, Sun J, et al. Optimal illumination pattern for transport-of-intensity quantitative phase microscopy[J]. Optics Express, 2018, 26(21): 27599-27614.

[62] Zuo C, Chen Q, Qu W, et al. High-speed transport-of-intensity phase microscopy with an electrically tunable lens [J]. Optics Express, 2013, 21(20): 24060-24075.

[63] Zuo J, Vartanyants I, Gao M, et al. Atomic resolution imaging of a carbon nanotube from diffraction intensities [J]. Science, 2003, 300(5624): 1419-1421.

[64] Faulkner H M L, Rodenburg J M. Movable aperture lenless transmission microscopy: a novel phase retrieval algorithm[J]. Physical Review Letters, 2004, 93(2): 023903.

[65] Rodenburg J M, Faulkner H M L. A phase retrieval algorithm for shifting illumination[J]. Applied Physics Letters, 2004, 85(20): 4795-4797.

[66] Maiden A M, Rodenburg J M. An improved ptychographical phase retrieval algorithm for diffractive imaging[J]. Ultramicroscopy, 2009, 109(10): 1256-1262.

[67] Thibault P, Dierolf M, Bunk O, et al. Probe retrieval in ptychographic coherent diffractive imaging[J]. Ultramicroscopy, 2009, 109(4): 338-343.

[68] Maiden M, Humphry J, Rodenburg J. Ptychographic transmission microscopy in three dimensions using a multi-slice approach[J]. Journal of the Optical Society of America A, 2012, 29(8): 1606-1614.

[69] Li P, Batey D, Edo T, et al. Separation of three-dimensional scattering effects in tilt-series Fourier ptychography[J]. Ultramicroscopy, 2015, 158:1-7.

[70] Maiden A, Johnson D, Li P. Further improvements to the ptychographical iterative engine[J]. Optica, 2017, 4(7): 736-745.

[71] Pfeifer M, Williams G, Vartanyants I, et al. Three-dimensional mapping of a deformation field inside a nanocrystal [J]. Nature, 2006, 442: 63-66.

[72] Thibault P, Dierolf M, Menzel A, et al. High-resolution scanning x-ray diffraction microscopy[J]. Science, 2008, 321(5887): 379-382.

[73] Humphry M J, Kraus B, Hurst A C, et al. Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging[J]. Nature Communications, 2012, 3: 730.

[74] Holler M, Diaz A, Guizar-sicairos M, et al. X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution[J]. Scientific Reports, 2014, 4: 3857.

[75] Dierolf M, Menzel A, Thibault P, et al. Ptychographic X-ray computed tomography at the nanoscale[J]. Nature, 2010,467: 436-440.

[76] Wang H, Liu C, Pan X, et al. The application of ptychography in the field of high power laser[C]//SPIE, 2015, 9255: 925534.

[77] Thibault P, Menzel A. Reconstructing state mixtures from diffraction measurements[J]. Nature, 2013, 494(7435): 68-71.

[78] Liu C, Walther T, Rodenburg J M. Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination[J]. Ultramicroscopy, 2009, 109(10): 1263-1275.

[79] Yao Yudong, Liu Cheng, Pan Xingchen, et al. Research status and development trend of PIE imaging method[J]. Chinese Journal of Lasers, 2016, 43(6): 0609001. (in Chinese)

[80] Chen Wen, Jiang Zhilong, Liu Cheng, et al. Depth resolved imaging by 3PIE with dual-beam illumination[J]. Acta Optica Sinica, 2016, 36(8): 0811002. (in Chinese)

[81] Yu W, Wang S, Veetil S, et al. High-quality image reconstruction method for ptychography with partially coherent illumination[J]. Physical Review B, 2016, 93: 241105.

[82] Pan An, Wang Dong, Shi Yishi, et al. Incoherent ptychography in Fresnel domain with simultaneous multi-wavelength illumination[J]. Acta Physica Sinica, 2016, 65(12): 124201.(in Chinese)

[83] Pan An, Zhang Xiaofei, Wang Bin, et al. Experimental study on three-dimensional ptychography for thick sample[J]. Acta Physica Sinica, 2016, 65(1): 014204. (in Chinese)

[84] Pan A, Zhou M, Zhang Y, et al. Adaptive-window angular spectrum algorithm for near-field ptychography [J]. Optics Communications, 2019, 430: 73-82.

[85] Pan A, Yao B. Three-dimensional space optimization for near-field ptychography [J]. Optics Express, 2019, 27(4):5433-5446.

[86] Shi Y, Li T, Wang Y, et al. Optical image encryption via ptychography[J]. Optics Letters, 2013, 38(9): 1425-1427.

[87] Shi Y, Wang Y, Li T, et al. Ptychographical imaging algorithm with a single random phase encoding[J]. Chinese Physics Letters, 2013, 30(7): 074203.

[88] Gao Q, Wang Y, Li T, et al. Optical encryption of unlimited-size images based on ptychographic scanning digital holography [J]. Applied Optics, 2014, 53(21): 4700-4707.

[89] Li T, Shi Y. Security risk of diffractive-imaging-based optical cryptosystem[J]. Optics Express, 2015, 23(16): 21384-21391.

[90] Liu Zhenjun, Guo Chen, Tan Jiubin. Lensfree computational imaging based on multi-distance phase retrieval [J]. Infrared and Laser Engineering, 2018, 47(10): 1002002. (in Chinese)

[91] Zhou M, Min J, Gao P, et al. Single-beam phase retrieval with partially coherent light illumination [J]. Journal of Optics, 2016, 18(1): 015701.

[92] Redondo R, Bueno G, Valdiviezo J C, et al. Autofocus evaluation for brightfield microscopy pathology [J]. Journal of Biomedical Optics, 2012, 17(3): 036008.

[93] Wang Z, Lei M, Yao B, et al. Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing[J]. Biomedical Optics Express, 2015, 6(11): 4353-4364.

[94] Heng X, Erickson D, Baugh L R, et al. Optofluidic microscopy: a method for implementing high resolution optical microscope on a chip [J]. Lab on a Chip, 2006, 6(10): 1274-1276.

[95] Psaltis D, Quake S R, Yang C. Developing optofluidic technology through the fusion of microfluidics and optics [J].Nature, 2006, 442(7101): 381-386.

[96] Heng X, Hsiao E, Psaltis D, et al. An optical tweezer actuated, nanoaperture-grid based optofluidic microscope implementation[J]. Optics Express, 2007, 15(25): 16367-16375.

[97] Lew M, Cui X, Heng X, et al. Interference of a four-hole aperture for on-chip quantitative two-dimensional differential phase imaging [J]. Optics Letters, 2007, 32(20): 2963-2965.

[98] Cui X, Lee L M, Heng X, et al. Lensless high-resolution on-chip optofluidic microscopes for Caenorhabditis elegans and cell imaging [J]. Proceedings of the National Academy of Science, 2008, 105(31): 10670-10675.

[99] Wu J, Cui X, Lee L M, et al. The application of Fresnel zone plate based projection in optofluidic microscopy [J]. Optics Express, 2008, 16(20): 15595-15602.

[100] Pang S, Cui X, DeModena J, et al. Implementation of a color-capable optofluidic microscope on a RGB CMOS color sensor chip substrate [J]. Lab on a Chip, 2010, 10(4): 411-414.

[101] Zheng G, Lee S A, Yang S, et al. Sub-pixel resolving optofluidic microscope for on-chip cell imaging [J]. Lab on a Chip, 2010, 10(22): 3125-3129.

[102] Zheng G, Lee S A, Antebi Y, et al. The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM) [J]. Proceedings of the National Academy of Science, 2011, 108(41): 16889-16894.

[103] Bishara W, Su T W, Coskun A F, et al. Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution [J]. Optics Express, 2010, 18(11): 11181-11191.

[104] Greenbaum A, Luo W, Su T W, et al. Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy [J]. Nature Methods, 2012, 9(9): 889-895.

[105] Luo W, Greenbaum A, Zhang Y, et al. Synthetic aperture-based on-chip microscopy[J]. Light: Science & Applications, 2015, 4: e261.

[106] Zhang J, Sun J, Chen Q, et al. Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy [J]. Scientific Reports, 2017, 7(1): 11777.

[107] Zheng G, Horstmeyer R, Yang C. Wide-field, high-resolution Fourier ptychographic microscopy[J]. Nature Photonics, 2013, 7(9): 739-745.

[108] Ou X, Horstmeyer R, Yang C, et al. Quantitative phase imaging via Fourier ptychographic microscopy[J]. Optics Letters, 2013, 38(22): 4845-4848.

[109] Zheng G, Ou X, Horstmeyer R, et al. Characterization of spatially varying aberrations for wide field-of-view microscopy[J]. Optics Express, 2013, 21(13): 15131-15143.

[110] Ou X, Zheng G, Yang C. Embedded pupil function recovery for Fourier ptychographic microscopy[J]. Optics Express, 2014, 22(5): 4960-4972.

[111] Bian Z, Dong S, Zheng G. Adaptive system correction for robust Fourier ptychographic imaging [J]. Optics Express, 2013, 21(26): 32400-32410.

[112] Zheng G. Breakthroughs in photonics 2013: Fourier ptychographic imaging[J]. IEEE Photonics Journal, 2014, 6(2): 1-7.

[113] Dong S, Nanda P, Shiradkar R, et al. High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography [J]. Optics Express, 2014, 22(17): 20856-20870.

[114] Dong S, Shiradkar R, Nanda P, et al. Spectral multiplexing and coherent-state decomposition in Fourier ptychographic imaging[J]. Biomedical Optics Express, 2014, 5(6): 1757-1767.

[115] Horstmeyer R, Ou X, Zheng G, et al. Digital pathology with Fourier ptychography [J]. Computerized Medical Imaging and Graphics, 2015, 42: 38-43.

[116] Guo K, Liao J, Bian Z, et al. Instant scope: a low-cost whole slide imaging system with instant focal plane detection [J]. Biomedical Optics Express, 2015, 6(9): 3210-3216.

[117] Guo K, Dong S, Nanda P, et al. Optimization of sampling pattern and the design of Fourier ptychographic illuminator [J]. Optics Express, 2015, 23(5): 6171-6180.

[118] Horstmeyer R, Chung J, Ou X, et al. Diffraction tomography with Fourier ptychography [J]. Optica, 2016, 3(8): 827-835.

[119] Pacheco S, Zheng G, Liang R. Reflective Fourier ptychography [J]. Journal of Biomedical Optics, 2016, 21(2): 026010.

[120] Chung J, Kim J, Ou X, et al. Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography[J]. Biomedical Optics Express, 2016, 7(2): 352-368.

[121] Zheng G, Ou X, Yang C. 0.5 gigapixel microscopy using a flatbed scanner[J]. Biomedical Optics Express, 2013, 5(1): 1-8.

[122] Guo K, Bian Z, Dong S, et al. Microscopy illumination engineering using a low-cost liquid crystal display[J]. Biomedical Optics Express, 2015, 6(2): 574-579.

[123] Dong S, Horstmeyer R, Shiradkar R, et al. Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging[J]. Optics Express, 2014, 22(11): 13586-13599.

[124] Horstmeyer R, Chen R Y, Ou X, et al. Solving ptychography with a convex relaxation[J]. New Journal of Physics, 2015, 17(5): 053044.

[125] Horstmeyer R, Yang C. A phase space model of Fourier ptychographic microscopy[J]. Optics Express, 2014, 22(1): 338-358.

[126] Kim J, Henley B M, Kim C H, et al. Incubator embedded cell culture imaging system(emsight) based on fourier ptychographic microscopy [J]. Biomedical Optics Express, 2016, 7(8): 3097-3110.

[127] Ou X, Chuang J, Horstmeyer R, et al. Aperture scanning Fourier ptychographic microscopy[J]. Biomedical Optics Express, 2016, 7(8): 3140-3150.

[128] Mico V, Zheng J, Garcia J, et al. Resolution enhancement in quantitative phase microscopy [J]. Advances in Optics and Photonics, 2019, 11(1): 135-214.

[129] Tian L, Wang J, Waller L. 3D differential phase-contrast microscopy with computational illumination using an LED array[J]. Optics Letter, 2014, 39(5): 1326-1329.

[130] Liu Z, Tian L, Liu S, et al. Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope [J]. Journal of Biomedical Optics, 2014, 19(10): 106002.

[131] Tian L, Waller L. Quantitative differential phase contrast imaging in an LED array microscope [J]. Optics Express, 2015, 23(9): 11394-11403.

[132] Chen M, Tian L, Waller L. 3D differential phase contrast microscopy[J]. Biomedical Optics Express, 2016, 7(10): 3940-3950.

[133] Phillips Z F, Chen M, Waller L. Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC) [J]. PloS One, 2017, 12(2): e0171228.

[134] Yeh L H, Dong J, Zhong J, et al Experimental robustness of Fourier ptychography phase retrieval algorithms[J]. Optics Express, 2015, 23(26): 33214-33240.

[135] Tian L, Waller L. 3D intensity and phase imaging from light field measurements in an LED array microscope[J]. Optica, 2015, 2(2): 104-111.

[136] Tian L, Li X, Ramchandran K, et al. Multiplexed coded illumination for Fourier ptychography with an LED array microscope[J]. Biomedical Optics Express, 2014, 5(7): 2376-2389.

[137] Tian L, Liu Z, Yeh L H, et al. Computational illumination for high-speed in vitro fourier ptychographic microscopy [J].Optica, 2015, 2(10), 904-911.

[138] Guo K, Zhang Z, Jiang S, et al. 13-fold resolution gain through turbid layer via translated unknown speckle illumination [J]. Biomedical Optics Express, 2018, 9(1): 260-274.

[139] Yilmaz H, Putten E, Bertolotti J, et al. Speckle correlation resolutionenhancement of wide-field fluorescence imaging [J].Optica, 2015, 2(5): 424-429.

[140] Yeh L H, Chowdhury S, Waller L. Computational structured illumination forhigh-content fluorescence and phase microscopy [J]. Biomedical Optics Express, 2019, 10(4): 1978-1998.

[141] Zhang Y, Jiang W, Dai Q. Nonlinear optimization approach for Fourier ptychographic microscopy[J]. Optics Express, 2015, 23(26): 33822-33835.

[142] Bian L, Suo J, Zheng G, et al. Fourier ptychographic reconstruction using Wirtinger flow optimization[J]. Optics Express, 2015, 23(4): 4856-4866.

[143] Bian L, Zheng G, Guo K, et al. Motion-corrected Fourier ptychography [J]. Biomedical Optics Express, 2016, 7(11): 4543-4553.

[144] Sun J, Chen Q, Zhang Y, et al. Efficient positional misalignment correction method for fourier ptychographic microscopy[J]. Biomedical Optics Express, 2016, 7(3): 1336-1350.

[145] Zuo C, Sun J, Chen Q. Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy [J]. Optics Express, 2016, 24(18): 20724-20744.

[146] Fan Y, Sun J, Chen Q, et al. Adaptive denoising method for Fourier ptychographic microscopy[J]. Optics Communications, 2017, 404: 23-31.

[147] Sun J, Zuo C, Zhang L, et al. Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations [J]. Scientific Reports, 2017, 7(1): 1187.

[148] Sun J, Zuo C, Zhang J, et al. High-speed fourier ptychographic microscopy based on programmable annular illuminations [J].Scientific Reports, 2018, 8(1): 7669.

[149] Sun J, Chen Q, Zhang J, et al. Single-shot quantitative phase microscopy based on color-multiplexed Fourier ptychography [J]. Optics Letters, 2018, 43(14): 3365-3368.

[150] Pan A, Zhang Y, Zhao T, et al. System calibration method for Fourier ptychographic microscopy [J]. Journal of Biomedical Optics, 2017, 22(9): 096005.

[151] Zhang Y, Pan A, Lei M, et al. Data preprocessing methods for robust Fourier ptychographic microscopy [J]. Optics Engineering, 2017, 56(12): 123107.

[152] Pan A, Zhang Y, Wen K, et al. Subwavelength resolution Fourier ptychography with hemispherical digital condensers [J]. Optics Express, 2018, 26(18): 23119-23131.

[153] Pan A, Zuo C, Xie Y, et al. Vignetting effect in Fourier ptychographic microscopy [J]. Optics and Lasers in Engineering, 2019, 120: 40-48.

[154] Pan A, Wen K, Yao B. Linear space-variant optical cryptosystem via Fourier ptychography[J]. Optics Letters, 2019, 44(8): 2032-2035.

[155] Maiden A M, Humphry M J, Sarahan M C, et al. An annealing algorithm to correct positioning errors in ptychography [J]. Ultramicroscopy, 2012, 120: 64-72.

[156] Zhang F, Peterson I, Vila-Comamala J, et al. Translation position determination in ptychographic coherent diffraction imaging [J]. Optics Express, 2013, 21(11): 13592-13606.

[157] Horstmyer R, Ou X, Chuang J, et al. Overlapped Fourier coding for optical aberration removal [J]. Optics Express, 2014, 22(20): 24062-24080.

[158] Horstmeyer R, Heintzmann R, Popescu G, et al. Standardizing the resolution claims for coherent microscopy [J]. Nature Photonics, 2016, 10: 68-76.

[159] Gibbs J W. Fourier series [J]. Nature, 1898, 59: 200.

[160] Pan A, Zhang Y, Zhao T, et al. https://www.sites.google.com/site/dranpanblog/publications.

[161] Sun J, Chen Q, Zhang Y, et al. Sampling criteria for Fourier ptychographic microscopy in object space and frequency space [J]. Optics Express, 2016, 24(14): 15765-15781.

[162] Bian L, Suo J, Situ G, et al. Content adaptive illumination for Fourier ptychography [J]. Optics Letters, 2014, 39(23): 6648-6651.

[163] Zhang Y, Jiang W, Tian L, et al. Self-learning based Fourier ptychographic microscopy [J]. Optics Express, 2015, 23(14): 18471-18486.

[164] He X, Liu C, Zhu J. Single-shot fourier ptychography based on diffractive beam splitting [J]. Optics Letters, 2018, 43(2): 214-217.

[165] Lee B, Hong K, Yoo D, et al. Single-shot phase retrieval via Fourier ptychography [J]. Optica, 2018, 5(8): 976-983.

[166] Konda P, Taylor J M, Harvey A R. Scheimpflug multi-aperture Fourier ptychography: coherent computational microscope with gigapixels/s data acquisition rates using 3D printed components[C]//SPIE, 2017, 10076: 100760R.

[167] Konda P, Taylor J M, Harvey A R. Parallelized aperture synthesis using multi-aperture Fourier ptychographic microscopy [J]. arXiv preprint arXiv, 2018: 1806.02317.

[168] Thibault P, Guizar-Sicairos M. Maximum-likelihood refinement for coherent diffraction imaging [J]. New Journal of Physics, 2012, 14(6): 063004.

[169] Bian L, Suo J, Chung J, et al. Fourier ptychographic reconstruction using poisson maximum likelihood and truncated Wirtinger gradient [J]. Scientific Reports, 2016, 6: 27384.