Abstract

Traditional imaging systems exhibit a well-known trade-off between the resolution and the field of view of their captured images. Typical cameras and microscopes can either “zoom in” and image at high-resolution, or they can “zoom out” to see a larger area at lower resolution, but can rarely achieve both effects simultaneously. In this review, we present details about a relatively new procedure termed Fourier ptychography (FP), which addresses the above trade-off to produce gigapixel-scale images without requiring any moving parts. To accomplish this, FP captures multiple low-resolution, large field-of-view images and computationally combines them in the Fourier domain into a high-resolution, large field-of-view result. Here, we present details about the various implementations of FP and highlight its demonstrated advantages to date, such as aberration recovery, phase imaging, and 3D tomographic reconstruction, to name a few. After providing some basics about FP, we list important details for successful experimental implementation, discuss its relationship with other computational imaging techniques, and point to the latest advances in the field while highlighting persisting challenges.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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A. C. Chan, J. Kim, A. Pan, H. Xu, D. Nojima, C. Hale, S. Wang, and C. Yang, “Parallel fourier ptychographic microscopy for high-throughput screening with 96 cameras (96 eyes),” Sci. Rep. 9(1), 11114 (2019).
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J. Chung, G. W. Martinez, K. C. Lencioni, S. R. Sadda, and C. Yang, “Computational aberration compensation by coded-aperture-based correction of aberration obtained from optical Fourier coding and blur estimation,” Optica 6(5), 647 (2019).
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T. Aidukas, R. Eckert, A. R. Harvey, L. Waller, and P. C. Konda, “Low-cost, sub-micron resolution, wide-field computational microscopy using opensource hardware,” Sci. Rep. 9(1), 7457 (2019).
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F. Ströhl, I. S. Opstad, J.-C. Tinguely, F. T. Dullo, I. Mela, J. W. Osterrieth, B. S. Ahluwalia, and C. F. Kaminski, “Super-condenser enables labelfree nanoscopy,” Opt. Express 27(18), 25280–25292 (2019).
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A. Matlock and L. Tian, “High-throughput, volumetric quantitative phase imaging with multiplexed intensity diffraction tomography,” Biomed. Opt. Express 10(12), 6432 (2019).
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S. Chowdhury, M. Chen, R. Eckert, D. Ren, F. Wu, N. Repina, and L. Waller, “High-resolution 3D refractive index microscopy of multiple-scattering samples from intensity images,” Optica 6(9), 1211 (2019).
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A. Pan, C. Zuo, Y. Xie, M. Lei, and B. Yao, “Vignetting effect in fourier ptychographic microscopy,” Opt. Lasers Eng. 120, 40–48 (2019).
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C. Shen, A. C. S. Chan, J. Chung, D. E. Williams, A. Hajimiri, and C. Yang, “Computational aberration correction of vis-nir multispectral imaging microscopy based on fourier ptychography,” Opt. Express 27(18), 24923–24937 (2019).
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K. Wakonig, A. Diaz, A. Bonnin, M. Stampanoni, A. Bergamaschi, J. Ihli, M. Guizar-Sicairos, and A. Menzel, “X-ray Fourier ptychography,” Sci. Adv. 5(2), eaav0282 (2019).
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H. Zhang, S. Jiang, J. Liao, J. Deng, J. Liu, Y. Zhang, and G. Zheng, “Near-field fourier ptychography: super-resolution phase retrieval via speckle illumination,” Opt. Express 27(5), 7498–7512 (2019).
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L.-H. Yeh, S. Chowdhury, and L. Waller, “Computational structured illumination for high-content fluorescence and phase microscopy,” Biomed. Opt. Express 10(4), 1978–1998 (2019).
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C. Pang, J. Li, M. Tang, J. Wang, I. Mela, F. Ströhl, L. Hecker, W. Shen, Q. Liu, X. Liu, Y. Wang, H. Zhang, M. Xu, X. Zhang, X. Liu, Q. Yang, and C. F. Kaminski, “On-chip super-resolution imaging with fluorescent polymer films,” Adv. Funct. Mater. 29, 1900126 (2019).
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P. Song, S. Jiang, H. Zhang, X. Huang, Y. Zhang, and G. Zheng, “Full-field fourier ptychography (ffp): Spatially varying pupil modeling and its application for rapid field-dependent aberration metrology,” APL Photonics 4(5), 050802 (2019).
[Crossref]

M. R. Kellman, E. Bostan, N. A. Repina, and L. Waller, “Physics-Based Learned Design: Optimized Coded-Illumination for Quantitative Phase Imaging,” IEEE Trans. Comput. Imag. 5(3), 344–353 (2019).
[Crossref]

Y. Xue, S. Cheng, Y. Li, and L. Tian, “Reliable deep-learning-based phase imaging with uncertainty quantification,” Optica 6(5), 618 (2019).
[Crossref]

Y. F. Cheng, M. Strachan, Z. Weiss, M. Deb, D. Carone, and V. Ganapati, “Illumination pattern design with deep learning for single-shot Fourier ptychographic microscopy,” Opt. Express 27(2), 644 (2019).
[Crossref]

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light Sci. Appl. 8(1), 82 (2019).
[Crossref]

G. Ding, Y. Liu, R. Zhang, and H. L. Xin, “A joint deep learning model to recover information and reduce artifacts in missing-wedge sinograms for electron tomography and beyond,” Sci. Rep. 9(1), 12803 (2019).
[Crossref]

M. R. Kellman, E. Bostan, N. A. Repina, and L. Waller, “Physics-Based Learned Design: Optimized Coded-Illumination for Quantitative Phase Imaging,” IEEE Trans. Comput. Imag. 5(3), 344–353 (2019).
[Crossref]

A. Muthumbi, A. Chaware, K. Kim, K. C. Zhou, P. C. Konda, R. Chen, B. Judkewitz, A. Erdmann, B. Kappes, and R. Horstmeyer, “Learned sensing: jointly optimized microscope hardware for accurate image classification,” Biomed. Opt. Express 10(12), 6351–6369 (2019).
[Crossref]

H. W. L. Lee and H. E. E. K. Y. A. Hn, “Reflective Fourier ptychographic microscopy using a parabolic mirror,” Opt. Express 27(23), 34382–34391 (2019).
[Crossref]

T. Aidukas, P. C. Konda, A. R. Harvey, M. J. Padgett, and P.-A. Moreau, “Phase and amplitude imaging with quantum correlations through Fourier Ptychography,” Sci. Rep. 9(1), 10445 (2019).
[Crossref]

S. Heuke, K. Unger, S. Khadir, K. Belkebir, P. C. Chaumet, H. Rigneault, and A. Sentenac, “Coherent anti-Stokes Raman Fourier ptychography,” Opt. Express 27(16), 23497 (2019).
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2018 (20)

P. Ferrand, A. Baroni, M. Allain, and V. Chamard, “Quantitative imaging of anisotropic material properties with vectorial ptychography,” Opt. Lett. 43(4), 763–766 (2018).
[Crossref]

S. Jiang, K. Guo, J. Liao, and G. Zheng, “Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow,” Biomed. Opt. Express 9(7), 3306 (2018).
[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for Fourier ptychography microscopy,” Opt. Express 26(20), 26470 (2018).
[Crossref]

H.-Y. Liu, D. Liu, H. Mansour, P. T. Boufounos, L. Waller, and U. S. Kamilov, “SEAGLE: Sparsity-Driven Image Reconstruction Under Multiple Scattering,” IEEE Trans. Comput. Imag. 4(1), 73–86 (2018).
[Crossref]

A. Zhou, N. Chen, H. Wang, and G. Situ, “Analysis of fourier ptychographic microscopy with half of the captured images,” J. Opt. 20(9), 095701 (2018).
[Crossref]

X. He, C. Liu, and J. Zhu, “Single-shot aperture-scanning fourier ptychography,” Opt. Express 26(22), 28187–28196 (2018).
[Crossref]

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
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M. Schürmann, G. Cojoc, S. Girardo, E. Ulbricht, J. Guck, and P. Müller, “Three-dimensional correlative single-cell imaging utilizing fluorescence and refractive index tomography,” J. Biophotonics 11(3), e201700145 (2018).
[Crossref]

S. Shin, D. Kim, K. Kim, and Y. Park, “Super-resolution three-dimensional fluorescence and optical diffraction tomography of live cells using structured illumination generated by a digital micromirror device,” Sci. Rep. 8(1), 9183 (2018).
[Crossref]

P. Li and A. Maiden, “Lensless LED matrix ptychographic microscope: problems and solutions,” Appl. Opt. 57(8), 1800 (2018).
[Crossref]

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Opt. Express 26(3), 2749 (2018).
[Crossref]

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9(5), 2130–2141 (2018).
[Crossref]

T. Kamal, L. Yang, and W. M. Lee, “In situ retrieval and correction of aberrations in moldless lenses using fourier ptychography,” Opt. Express 26(3), 2708–2719 (2018).
[Crossref]

J. Sun, C. Zuo, J. Zhang, Y. Fan, and Q. Chen, “High-speed Fourier ptychographic microscopy based on programmable annular illuminations,” Sci. Rep. 8(1), 7669 (2018).
[Crossref]

X. He, C. Liu, and J. Zhu, “Single-shot Fourier ptychography based on diffractive beam splitting,” Opt. Lett. 43(2), 214 (2018).
[Crossref]

B. Lee, J.-y. Hong, D. Yoo, J. Cho, Y. Jeong, S. Moon, and B. Lee, “Single-shot phase retrieval via fourier ptychographic microscopy,” Optica 5(8), 976–983 (2018).
[Crossref]

R. Eckert, Z. F. Phillips, and L. Waller, “Efficient illumination angle self-calibration in fourier ptychography,” Appl. Opt. 57(19), 5434–5442 (2018).
[Crossref]

A. Pan, Y. Zhang, K. Wen, M. Zhou, J. Min, M. Lei, and B. Yao, “Subwavelength resolution fourier ptychography with hemispherical digital condensers,” Opt. Express 26(18), 23119–23131 (2018).
[Crossref]

G.-J. Choi, J. Lim, S. Jeon, J. Cho, G. Lim, N.-C. Park, and Y.-P. Park, “Dual-wavelength Fourier ptychography using a single LED,” Opt. Lett. 43(15), 3526 (2018).
[Crossref]

M. Odstrcil, A. Menzel, and M. Guizar-Sicairos, “Iterative least-squares solver for generalized maximum-likelihood ptychography,” Opt. Express 26(3), 3108 (2018).
[Crossref]

2017 (10)

J. Sun, C. Zuo, L. Zhang, and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Rep. 7(1), 1187 (2017).
[Crossref]

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 096005 (2017).
[Crossref]

Y. Zhang, A. Pan, M. Lei, and B. Yao, “Data preprocessing methods for robust fourier ptychographic microscopy,” Opt. Eng. 56(12), 1 (2017).
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J. Holloway, Y. Wu, M. K. Sharma, O. Cossairt, and A. Veeraraghavan, “SAVI: Synthetic apertures for long-range, subdiffraction-limited visible imaging using Fourier ptychography,” Sci. Adv. 3(4), e1602564 (2017).
[Crossref]

S. Chowdhury, W. J. Eldridge, A. Wax, and J. A. Izatt, “Structured illumination microscopy for dual-modality 3D sub-diffraction resolution fluorescence and refractive-index reconstruction,” Biomed. Opt. Express 8(12), 5776 (2017).
[Crossref]

S. Chowdhury, W. J. Eldridge, A. Wax, and J. A. Izatt, “Structured illumination multimodal 3D-resolved quantitative phase and fluorescence sub-diffraction microscopy,” Biomed. Opt. Express 8(5), 2496 (2017).
[Crossref]

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Coherent superresolution imaging via grating-based illumination,” Appl. Opt. 56(1), A79–A88 (2017).
[Crossref]

S. Li, Y. Wang, W. Wu, and Y. Liang, “Predictive searching algorithm for fourier ptychography,” J. Opt. 19(12), 125605 (2017).
[Crossref]

Y. Zhou, J. Wu, Z. Bian, J. Suo, G. Zheng, and Q. Dai, “Fourier ptychographic microscopy using wavelength multiplexing,” J. Biomed. Opt. 22(6), 066006 (2017).
[Crossref]

I. Ahmed, M. Alotaibi, S. Skinner-Ramos, D. Dominguez, A. A. Bernussi, and L. G. de Peralta, “Fourier ptychographic microscopy at telecommunication wavelengths using a femtosecond laser,” Opt. Commun. 405, 363–367 (2017).
[Crossref]

2016 (14)

S. Pacheco, G. Zheng, and R. Liang, “Reflective Fourier ptychography,” J. Biomed. Opt. 21(2), 026010 (2016).
[Crossref]

K. Guo, S. Jiang, and G. Zheng, “Multilayer fluorescence imaging on a single-pixel detector,” Biomed. Opt. Express 7(7), 2425 (2016).
[Crossref]

G. McConnell, J. Trägårdh, R. Amor, J. Dempster, E. Reid, and W. B. Amos, “A novel optical microscope for imaging large embryos and tissue volumes with sub-cellular resolution throughout,” eLife 5, e18659 (2016).
[Crossref]

U. S. Kamilov, D. Liu, H. Mansour, and P. T. Boufounos, “A Recursive Born Approach to Nonlinear Inverse Scattering,” IEEE Signal Process. Lett. 23(8), 1052–1056 (2016).
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G. Osnabrugge, S. Leedumrongwatthanakun, and I. M. Vellekoop, “A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media,” J. Comput. Phys. 322, 113–124 (2016).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

W. Krauze, P. Makowski, M. Kujawińska, and A. Kuś, “Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography,” Opt. Express 24(5), 4924 (2016).
[Crossref]

R. Horstmeyer, J. Chung, X. Ou, G. Zheng, and C. Yang, “Diffraction tomography with Fourier ptychography,” Optica 3(8), 827 (2016).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7(4), 1336 (2016).
[Crossref]

J. Chung, J. Kim, X. Ou, R. Horstmeyer, and C. Yang, “Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography,” Biomed. Opt. Express 7(2), 352 (2016).
[Crossref]

K. Guo, S. Dong, and G. Zheng, “Fourier ptychography for brightfield, phase, darkfield, reflective, multi-slice, and fluorescence imaging,” IEEE J. Sel. Top. Quantum Electron. 22(4), 77–88 (2016).
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S. Sen, I. Ahmed, B. Aljubran, A. A. Bernussi, and L. Grave de Peralta, “Fourier ptychographic microscopy using an infrared-emitting hemispherical digital condenser,” Appl. Opt. 55(23), 6421 (2016).
[Crossref]

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” Biomed. Opt. Express 7(11), 4787 (2016).
[Crossref]

X. Ou, J. Chung, R. Horstmeyer, and C. Yang, “Aperture scanning Fourier ptychographic microscopy,” Biomed. Opt. Express 7(8), 3140 (2016).
[Crossref]

2015 (14)

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23(3), 3472 (2015).
[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2(10), 904 (2015).
[Crossref]

L.-H. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of Fourier ptychography phase retrieval algorithms,” Opt. Express 23(26), 33214 (2015).
[Crossref]

L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica 2(2), 104 (2015).
[Crossref]

P. Li, D. J. Batey, T. B. Edo, and J. M. Rodenburg, “Separation of three-dimensional scattering effects in tilt-series Fourier ptychography,” Ultramicroscopy 158, 1–7 (2015).
[Crossref]

J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. C. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Opt. Express 23(13), 16933 (2015).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517 (2015).
[Crossref]

Y. Zhang, W. Jiang, L. Tian, L. Waller, and Q. Dai, “Self-learning based fourier ptychographic microscopy,” Opt. Express 23(14), 18471–18486 (2015).
[Crossref]

Z. F. Phillips, M. V. D’Ambrosio, L. Tian, J. J. Rulison, H. S. Patel, N. Sadras, A. V. Gande, N. A. Switz, D. A. Fletcher, and L. Waller, “Multi-contrast imaging and digital refocusing on a mobile microscope with a domed led array,” PLoS One 10(5), e0124938 (2015).
[Crossref]

K. Guo, S. Dong, P. Nanda, and G. Zheng, “Optimization of sampling pattern and the design of fourier ptychographic illuminator,” Opt. Express 23(5), 6171–6180 (2015).
[Crossref]

C. Kuang, Y. Ma, R. Zhou, J. Lee, G. Barbastathis, R. R. Dasari, Z. Yaqoob, and P. T. C. So, “Digital micromirror device-based laser-illumination Fourier ptychographic microscopy,” Opt. Express 23(21), 26999 (2015).
[Crossref]

S. Dong, P. Nanda, K. Guo, J. Liao, and G. Zheng, “Incoherent fourier ptychographic photography using structured light,” Photonics Res. 3(1), 19–23 (2015).
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R. Horstmeyer, X. Ou, G. Zheng, P. Willems, and C. Yang, “Digital pathology with Fourier ptychography,” Comput. Med. Imaging. Graph. 42, 38–43 (2015).
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S. Pacheco, B. Salahieh, T. Milster, J. J. Rodriguez, and R. Liang, “Transfer function analysis in epi-illumination Fourier ptychography,” Opt. Lett. 40(22), 5343 (2015).
[Crossref]

2014 (17)

A. J. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. J. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
[Crossref]

R. Horstmeyer and C. Yang, “A phase space model of Fourier ptychographic microscopy,” Opt. Express 22(1), 338–358 (2014).
[Crossref]

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8(5), 342–344 (2014).
[Crossref]

S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856 (2014).
[Crossref]

L. Tian, J. Wang, and L. Waller, “3D differential phase-contrast microscopy with computational illumination using an LED array,” Opt. Lett. 39(5), 1326 (2014).
[Crossref]

L. Bian, J. Suo, G. Situ, G. Zheng, F. Chen, and Q. Dai, “Content adaptive illumination for fourier ptychography,” Opt. Lett. 39(23), 6648–6651 (2014).
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G. Zheng, X. Ou, R. Horstmeyer, J. Chung, and C. Yang, “Fourier Ptychographic Microscopy: A Gigapixel Superscope for Biomedicine,” Opt. Photonics News 25(4), 26 (2014).
[Crossref]

S. Dong, K. Guo, P. Nanda, R. Shiradkar, and G. Zheng, “FPscope: a field-portable high-resolution microscope using a cellphone lens,” Biomed. Opt. Express 5(10), 3305 (2014).
[Crossref]

G. Zheng, X. Ou, and C. Yang, “0.5 gigapixel microscopy using a flatbed scanner,” Biomed. Opt. Express 5(1), 1–8 (2014).
[Crossref]

R. Horstmeyer, X. Ou, J. Chung, G. Zheng, and C. Yang, “Overlapped fourier coding for optical aberration removal,” Opt. Express 22(20), 24062–24080 (2014).
[Crossref]

S. Dong, R. Shiradkar, P. Nanda, and G. Zheng, “Spectral multiplexing and coherent-state decomposition in Fourier ptychographic imaging,” Biomed. Opt. Express 5(6), 1757 (2014).
[Crossref]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
[Crossref]

S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22(11), 13586 (2014).
[Crossref]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960 (2014).
[Crossref]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376 (2014).
[Crossref]

M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, “Tabletop nanometer extreme ultraviolet imaging in an extended reflection mode using coherent fresnel ptychography,” Optica 1(1), 39–44 (2014).
[Crossref]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

2013 (8)

D. Claus, D. Robinson, D. Chetwynd, Y. Shuo, W. Pike, J. D. J. José, and J. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15(3), 035702 (2013).
[Crossref]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845 (2013).
[Crossref]

Z. Bian, S. Dong, and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express 21(26), 32400 (2013).
[Crossref]

J. R. Fienup, “Phase retrieval algorithms: a personal tour,” Appl. Opt. 52(1), 45–56 (2013).
[Crossref]

S. Chowdhury and J. Izatt, “Structured illumination quantitative phase microscopy for enhanced resolution amplitude and phase imaging,” Biomed. Opt. Express 4(10), 1795–1805 (2013).
[Crossref]

P. G. Pitrone, J. Schindelin, L. Stuyvenberg, S. Preibisch, M. Weber, K. W. Eliceiri, J. Huisken, and P. Tomancak, “Openspim: an open-access light-sheet microscopy platform,” Nat. Methods 10(7), 598–599 (2013).
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2012 (5)

B. Goris, W. Van den Broek, K. J. Batenburg, H. Heidari Mezerji, and S. Bals, “Electron tomography based on a total variation minimization reconstruction technique,” Ultramicroscopy 113, 120–130 (2012).
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Y. Sung, W. Choi, N. Lue, R. R. Dasari, and Z. Yaqoob, “Stain-Free Quantification of Chromosomes in Live Cells Using Regularized Tomographic Phase Microscopy,” PLoS One 7(11), e49502 (2012).
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C. A. Schneider, W. S. Rasband, and K. W. Eliceiri, “Nih image to imagej: 25 years of image analysis,” Nat. Methods 9(7), 671–675 (2012).
[Crossref]

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref]

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14(6), 063004 (2012).
[Crossref]

2011 (2)

2010 (1)

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
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2009 (4)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
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Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
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P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
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T. R. Hillman, T. Gutzler, S. A. Alexandrov, and D. D. Sampson, “High-resolution, wide-field object reconstruction with synthetic aperture fourier holographic optical microscopy,” Opt. Express 17(10), 7873–7892 (2009).
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2008 (5)

J. Di, J. Zhao, H. Jiang, P. Zhang, Q. Fan, and W. Sun, “High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear ccd scanning,” Appl. Opt. 47(30), 5654–5659 (2008).
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J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

M. D’Urso, K. Belkebir, L. Crocco, T. Isernia, and A. Litman, “Phaseless imaging with experimental data: facts and challenges,” J. Opt. Soc. Am. A 25(1), 271 (2008).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
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O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
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2007 (5)

S. Marchesini, “Invited Article : A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78(1), 011301 (2007).
[Crossref]

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107(2-3), 227–231 (2007).
[Crossref]

Y. Huang and M. A. Anastasio, “Statistically principled use of in-line measurements in intensity diffraction tomography,” J. Opt. Soc. Am. A 24(3), 626 (2007).
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W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
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T. M. Kreis and K. Schluter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46(5), 055803 (2007).
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2006 (3)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
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V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Synthetic aperture superresolution with multiple off-axis holograms,” J. Opt. Soc. Am. A 23(12), 3162–3170 (2006).
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J. A. Jensen, S. I. Nikolov, K. L. Gammelmark, and M. H. Pedersen, “Synthetic aperture ultrasound imaging,” Ultrasonics 44, e5–e15 (2006).
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2005 (1)

2004 (3)

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born- and Rytov-type approximations,” Appl. Opt. 43(12), 2418–2430 (2004).
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D. R. Luke, “Relaxed Averaged Alternating Reflections for Diffraction Imaging,” Inverse Problems 37, 13 (2004).
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J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
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2003 (2)

2002 (2)

G. Gbur and E. Wolf, “Diffraction tomography without phase information,” Opt. Lett. 27(21), 1890 (2002).
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V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205(2), 165–176 (2002).
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2000 (1)

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
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1998 (1)

A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography,” IEEE Trans. Image Process. 7(2), 204–221 (1998).
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1997 (2)

T. Takenaka, D. J. Wall, H. Harada, and M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microw. Opt. Technol. Lett. 14(3), 182–188 (1997).
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I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
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1996 (2)

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H. N. Chapman, “Phase-retrieval x-ray microscopy by wigner-distribution deconvolution,” Ultramicroscopy 66(3-4), 153–172 (1996).
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1995 (1)

T. C. Wedberg and J. J. Stamnes, “Comparison of phase retrieval methods for optical diffraction tomography,” Pure Appl. Opt. 4(1), 39–54 (1995).
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1993 (2)

M. H. Maleki and A. J. Devaney, “Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 10(5), 1086 (1993).
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J. Rodenburg, B. McCallum, and P. Nellist, “Experimental tests on double-resolution coherent imaging via stem,” Ultramicroscopy 48(3), 304–314 (1993).
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1992 (2)

B. McCallum and J. Rodenburg, “Two-dimensional demonstration of wigner phase-retrieval microscopy in the stem configuration,” Ultramicroscopy 45(3-4), 371–380 (1992).
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M. H. Maleki, A. J. Devaney, and A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9(8), 1356 (1992).
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1989 (2)

A. J. Devaney, “Structure determination from intensity measurements in scattering experiments,” Phys. Rev. Lett. 62(20), 2385–2388 (1989).
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R. Bates and J. Rodenburg, “Sub-ångström transmission microscopy: a fourier transform algorithm for microdiffraction plane intensity information,” Ultramicroscopy 31(3), 303–307 (1989).
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1986 (1)

1982 (1)

1981 (2)

1978 (2)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35(2), 237 (1972).

1970 (1)

R. Hegerl and W. Hoppe, “Dynamische Theorie der Kristallstrukturanalyse durch Elektronenbeugung im inhomogenen Primärstrahlwellenfeld,” Berichte der Bunsengesellschaft für physikalische Chemie 74(11), 1148–1154 (1970).
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1957 (1)

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. i. a new theoretical approach,” Acta Crystallogr. 10(10), 609–619 (1957).
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Berichte der Bunsengesellschaft für physikalische Chemie (1)

R. Hegerl and W. Hoppe, “Dynamische Theorie der Kristallstrukturanalyse durch Elektronenbeugung im inhomogenen Primärstrahlwellenfeld,” Berichte der Bunsengesellschaft für physikalische Chemie 74(11), 1148–1154 (1970).
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Biomed. Opt. Express (18)

S. Chowdhury and J. Izatt, “Structured illumination quantitative phase microscopy for enhanced resolution amplitude and phase imaging,” Biomed. Opt. Express 4(10), 1795–1805 (2013).
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R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9(5), 2130–2141 (2018).
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S. Jiang, K. Guo, J. Liao, and G. Zheng, “Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow,” Biomed. Opt. Express 9(7), 3306 (2018).
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L.-H. Yeh, S. Chowdhury, and L. Waller, “Computational structured illumination for high-content fluorescence and phase microscopy,” Biomed. Opt. Express 10(4), 1978–1998 (2019).
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A. Muthumbi, A. Chaware, K. Kim, K. C. Zhou, P. C. Konda, R. Chen, B. Judkewitz, A. Erdmann, B. Kappes, and R. Horstmeyer, “Learned sensing: jointly optimized microscope hardware for accurate image classification,” Biomed. Opt. Express 10(12), 6351–6369 (2019).
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A. Matlock and L. Tian, “High-throughput, volumetric quantitative phase imaging with multiplexed intensity diffraction tomography,” Biomed. Opt. Express 10(12), 6432 (2019).
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S. Chowdhury, W. J. Eldridge, A. Wax, and J. A. Izatt, “Structured illumination multimodal 3D-resolved quantitative phase and fluorescence sub-diffraction microscopy,” Biomed. Opt. Express 8(5), 2496 (2017).
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S. Chowdhury, W. J. Eldridge, A. Wax, and J. A. Izatt, “Structured illumination microscopy for dual-modality 3D sub-diffraction resolution fluorescence and refractive-index reconstruction,” Biomed. Opt. Express 8(12), 5776 (2017).
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J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” Biomed. Opt. Express 7(11), 4787 (2016).
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X. Ou, J. Chung, R. Horstmeyer, and C. Yang, “Aperture scanning Fourier ptychographic microscopy,” Biomed. Opt. Express 7(8), 3140 (2016).
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J. Chung, J. Kim, X. Ou, R. Horstmeyer, and C. Yang, “Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography,” Biomed. Opt. Express 7(2), 352 (2016).
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J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7(4), 1336 (2016).
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K. Guo, S. Jiang, and G. Zheng, “Multilayer fluorescence imaging on a single-pixel detector,” Biomed. Opt. Express 7(7), 2425 (2016).
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G. Zheng, X. Ou, and C. Yang, “0.5 gigapixel microscopy using a flatbed scanner,” Biomed. Opt. Express 5(1), 1–8 (2014).
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S. Dong, R. Shiradkar, P. Nanda, and G. Zheng, “Spectral multiplexing and coherent-state decomposition in Fourier ptychographic imaging,” Biomed. Opt. Express 5(6), 1757 (2014).
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L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376 (2014).
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L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
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S. Dong, K. Guo, P. Nanda, R. Shiradkar, and G. Zheng, “FPscope: a field-portable high-resolution microscope using a cellphone lens,” Biomed. Opt. Express 5(10), 3305 (2014).
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Comput. Med. Imaging. Graph. (1)

R. Horstmeyer, X. Ou, G. Zheng, P. Willems, and C. Yang, “Digital pathology with Fourier ptychography,” Comput. Med. Imaging. Graph. 42, 38–43 (2015).
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eLife (1)

G. McConnell, J. Trägårdh, R. Amor, J. Dempster, E. Reid, and W. B. Amos, “A novel optical microscope for imaging large embryos and tissue volumes with sub-cellular resolution throughout,” eLife 5, e18659 (2016).
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IEEE J. Sel. Top. Quantum Electron. (1)

K. Guo, S. Dong, and G. Zheng, “Fourier ptychography for brightfield, phase, darkfield, reflective, multi-slice, and fluorescence imaging,” IEEE J. Sel. Top. Quantum Electron. 22(4), 77–88 (2016).
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IEEE Signal Process. Lett. (1)

U. S. Kamilov, D. Liu, H. Mansour, and P. T. Boufounos, “A Recursive Born Approach to Nonlinear Inverse Scattering,” IEEE Signal Process. Lett. 23(8), 1052–1056 (2016).
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IEEE Trans. Comput. Imag. (4)

H.-Y. Liu, D. Liu, H. Mansour, P. T. Boufounos, L. Waller, and U. S. Kamilov, “SEAGLE: Sparsity-Driven Image Reconstruction Under Multiple Scattering,” IEEE Trans. Comput. Imag. 4(1), 73–86 (2018).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
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M. R. Kellman, E. Bostan, N. A. Repina, and L. Waller, “Physics-Based Learned Design: Optimized Coded-Illumination for Quantitative Phase Imaging,” IEEE Trans. Comput. Imag. 5(3), 344–353 (2019).
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M. R. Kellman, E. Bostan, N. A. Repina, and L. Waller, “Physics-Based Learned Design: Optimized Coded-Illumination for Quantitative Phase Imaging,” IEEE Trans. Comput. Imag. 5(3), 344–353 (2019).
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IEEE Trans. Image Process. (1)

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Inverse Problems (1)

D. R. Luke, “Relaxed Averaged Alternating Reflections for Diffraction Imaging,” Inverse Problems 37, 13 (2004).
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J. Biomed. Opt. (4)

Y. Zhou, J. Wu, Z. Bian, J. Suo, G. Zheng, and Q. Dai, “Fourier ptychographic microscopy using wavelength multiplexing,” J. Biomed. Opt. 22(6), 066006 (2017).
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A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 096005 (2017).
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A. J. Williams, J. Chung, X. Ou, G. Zheng, S. Rawal, Z. Ao, R. Datar, C. Yang, and R. J. Cote, “Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis,” J. Biomed. Opt. 19(6), 066007 (2014).
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J. Biophotonics (1)

M. Schürmann, G. Cojoc, S. Girardo, E. Ulbricht, J. Guck, and P. Müller, “Three-dimensional correlative single-cell imaging utilizing fluorescence and refractive index tomography,” J. Biophotonics 11(3), e201700145 (2018).
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J. Comput. Phys. (1)

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J. Opt. (3)

A. Zhou, N. Chen, H. Wang, and G. Situ, “Analysis of fourier ptychographic microscopy with half of the captured images,” J. Opt. 20(9), 095701 (2018).
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S. Li, Y. Wang, W. Wu, and Y. Liang, “Predictive searching algorithm for fourier ptychography,” J. Opt. 19(12), 125605 (2017).
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J. Opt. Soc. Am. (2)

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Light Sci. Appl. (1)

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light Sci. Appl. 8(1), 82 (2019).
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Microw. Opt. Technol. Lett. (1)

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Nat. Methods (3)

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Nat. Photonics (3)

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8(5), 342–344 (2014).
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Nature (2)

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New J. Phys. (1)

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14(6), 063004 (2012).
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Opt. Commun. (1)

I. Ahmed, M. Alotaibi, S. Skinner-Ramos, D. Dominguez, A. A. Bernussi, and L. G. de Peralta, “Fourier ptychographic microscopy at telecommunication wavelengths using a femtosecond laser,” Opt. Commun. 405, 363–367 (2017).
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Opt. Eng. (2)

T. M. Kreis and K. Schluter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46(5), 055803 (2007).
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Y. Zhang, A. Pan, M. Lei, and B. Yao, “Data preprocessing methods for robust fourier ptychographic microscopy,” Opt. Eng. 56(12), 1 (2017).
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Opt. Express (28)

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
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T. R. Hillman, T. Gutzler, S. A. Alexandrov, and D. D. Sampson, “High-resolution, wide-field object reconstruction with synthetic aperture fourier holographic optical microscopy,” Opt. Express 17(10), 7873–7892 (2009).
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R. Horstmeyer, X. Ou, J. Chung, G. Zheng, and C. Yang, “Overlapped fourier coding for optical aberration removal,” Opt. Express 22(20), 24062–24080 (2014).
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J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. C. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Opt. Express 23(13), 16933 (2015).
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Y. Zhang, W. Jiang, L. Tian, L. Waller, and Q. Dai, “Self-learning based fourier ptychographic microscopy,” Opt. Express 23(14), 18471–18486 (2015).
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C. Kuang, Y. Ma, R. Zhou, J. Lee, G. Barbastathis, R. R. Dasari, Z. Yaqoob, and P. T. C. So, “Digital micromirror device-based laser-illumination Fourier ptychographic microscopy,” Opt. Express 23(21), 26999 (2015).
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S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22(11), 13586 (2014).
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Z. Bian, S. Dong, and G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express 21(26), 32400 (2013).
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R. Horstmeyer and C. Yang, “A phase space model of Fourier ptychographic microscopy,” Opt. Express 22(1), 338–358 (2014).
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X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960 (2014).
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W. Krauze, P. Makowski, M. Kujawińska, and A. Kuś, “Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography,” Opt. Express 24(5), 4924 (2016).
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X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23(3), 3472 (2015).
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K. Guo, S. Dong, P. Nanda, and G. Zheng, “Optimization of sampling pattern and the design of fourier ptychographic illuminator,” Opt. Express 23(5), 6171–6180 (2015).
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S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856 (2014).
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L.-H. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of Fourier ptychography phase retrieval algorithms,” Opt. Express 23(26), 33214 (2015).
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H. W. L. Lee and H. E. E. K. Y. A. Hn, “Reflective Fourier ptychographic microscopy using a parabolic mirror,” Opt. Express 27(23), 34382–34391 (2019).
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T. Kamal, L. Yang, and W. M. Lee, “In situ retrieval and correction of aberrations in moldless lenses using fourier ptychography,” Opt. Express 26(3), 2708–2719 (2018).
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T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Opt. Express 26(3), 2749 (2018).
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M. Odstrcil, A. Menzel, and M. Guizar-Sicairos, “Iterative least-squares solver for generalized maximum-likelihood ptychography,” Opt. Express 26(3), 3108 (2018).
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A. Pan, Y. Zhang, K. Wen, M. Zhou, J. Min, M. Lei, and B. Yao, “Subwavelength resolution fourier ptychography with hemispherical digital condensers,” Opt. Express 26(18), 23119–23131 (2018).
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T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for Fourier ptychography microscopy,” Opt. Express 26(20), 26470 (2018).
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X. He, C. Liu, and J. Zhu, “Single-shot aperture-scanning fourier ptychography,” Opt. Express 26(22), 28187–28196 (2018).
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Y. F. Cheng, M. Strachan, Z. Weiss, M. Deb, D. Carone, and V. Ganapati, “Illumination pattern design with deep learning for single-shot Fourier ptychographic microscopy,” Opt. Express 27(2), 644 (2019).
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H. Zhang, S. Jiang, J. Liao, J. Deng, J. Liu, Y. Zhang, and G. Zheng, “Near-field fourier ptychography: super-resolution phase retrieval via speckle illumination,” Opt. Express 27(5), 7498–7512 (2019).
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S. Heuke, K. Unger, S. Khadir, K. Belkebir, P. C. Chaumet, H. Rigneault, and A. Sentenac, “Coherent anti-Stokes Raman Fourier ptychography,” Opt. Express 27(16), 23497 (2019).
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C. Shen, A. C. S. Chan, J. Chung, D. E. Williams, A. Hajimiri, and C. Yang, “Computational aberration correction of vis-nir multispectral imaging microscopy based on fourier ptychography,” Opt. Express 27(18), 24923–24937 (2019).
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Opt. Photonics News (1)

G. Zheng, X. Ou, R. Horstmeyer, J. Chung, and C. Yang, “Fourier Ptychographic Microscopy: A Gigapixel Superscope for Biomedicine,” Opt. Photonics News 25(4), 26 (2014).
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Optica (9)

L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica 2(2), 104 (2015).
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Figures (13)

Fig. 1.
Fig. 1. Fourier ptychography explanation: (a) Diagram of a standard microscope, where a Köhler-type illumination, consisting of many mutually incoherent emitters, is provided by an extended light source. Only light emanating from a single such emitter is shown. Some of the light is absorbed and the remaining light is scattered (i.e., diffracted) by the object and the imaging system records only a part of this scattered light, resulting in a blurry image. Cameras can only detect intensity, so the phase information of the object is also lost. (b) In Fourier ptychography, a movable point source generates a plane wave of light to illuminate the object. FP uses an array of these point sources to generate a wide array of varying plane wave illumination angles. These point sources are turned on time-sequentially and one image is captured per illumination angle. When the object is illuminated with a plane wave at a higher angle, the scattered light that is normally missed by the imaging system now passes through the objective. Images that capture only the scattered light have a dark background (darkfield) and the images that capture both scattered and unscattered light have a bright background (brightfield). FP combines multiple images of both types using a reconstruction algorithm to form a high-resolution complex-valued result.
Fig. 2.
Fig. 2. Spatial-frequency sampling in FP: (a) In a standard imaging setup, the limited acceptance angle ($\theta$) of the lens defines a bandpass filter in the Fourier domain that limits the detected image resolution. (b) Tilting the illumination plane wave by an angle $\phi$ shifts the sample’s Fourier spectrum, which is equivalently described by a shifting lens bandpass filter. (c) Fourier ptychography uses an LED array to provide multi-angle illumination to capture information from many segments of the Fourier spectrum via a shifting bandpass filter.
Fig. 3.
Fig. 3. FP reconstruction algorithm follows an alternate projection type scheme. A $j^{th}$ low-resolution image estimate is generated from a high-resolution image guess. True amplitude of this low-resolution image is known, hence corrected and the phase is left unchanged. This updated low-resolution image is then used to update the high-resolution image guess. This process is repeated for all the LEDs several times to achieve a good reconstruction. There is an overlap between two adjacent illumination angles, which encourages the convergence of this algorithm.
Fig. 4.
Fig. 4. FP increases the space-bandwidth product (SBP) of microscopes. (a, b) FP can achieve the same resolution as a 20X 0.5-NA objective lens just by using a 2X 0.08-NA objective lens, but with multi-angle illumination extending to $NA_{\textrm {ill}}=0.42$. FP system has a wider FOV, therefore larger SBP, and extended DOF with longer working distance. (c) Example gigapixel-scale FP reconstruction using a low-NA objective. Similar high-resolution images can be obtained with higher-NA objectives, but over a much smaller FOV (marked as circles).
Fig. 5.
Fig. 5. Ptychography word is derived from convolution, hence the relationship between ptychography and FP is explained with the help of convolution. The object and its Fourier spectrum switch places between these two techniques. The object is shifted in ptychography and the object’s Fourier spectrum is shifted in FP accordingly.
Fig. 6.
Fig. 6. The cut-off frequency of an incoherent imaging system is twice that of a coherent system with the same imaging optics. Fourier ptychography can be considered as a coherent structured illumination technique under a broad definition of "structuring" the incident plane wave illumination angle.
Fig. 7.
Fig. 7. High-NA illumination systems for FP: (a) Three bowl shaped LED arrays that can achieve illumination NAs close to one in air. (b) Oil immersion condenser was also proposed to provide an illumination NA of 1.2. Such high angle illumination can lead to high-resolution, large SBP image reconstructions. Figures courtesy of [2123,36].
Fig. 8.
Fig. 8. Quantitative phase reconstruction results in FP. Figures courtesy of [2528].
Fig. 9.
Fig. 9. (a) FP can recover and correct for large aberrations within a low-cost imaging system using a mobile phone camera lens as the objective. The image above shows two small segments from the full FOV. (b) FP can also recover and subsequently apply system aberrations for deconvolving fluorescence images. Here, the FP reconstruction phase gradient is overlaid with the fluorescence image for better visualization. Figures courtesy of [24,33].
Fig. 10.
Fig. 10. Approaches for faster FP data acquisition. Figures courtesy of [26,44,45,138].
Fig. 11.
Fig. 11. Example 3D reconstructions of C. elegans using the first Born model (a) and the multi-slice model (b). Figures courtesy of [51,55].
Fig. 12.
Fig. 12. 3D space-bandwidth product (SBP) for various combinations of illumination and imaging NAs. (a) $k_xk_z$ cross-sections of the k-space coverage for various NAs, and the theoretical corresponding $xz$ cross-sections of a reconstructed 0.8-$\mu m$-diameter bead. For low imaging NAs, the illumination NA has a less of an effect than for high imaging NAs. (b) The theoretical 3D SBP for various NAs, calculated as the product of the 3D FOV (assuming arbitrarily a 20-$\mu m$ axial range) and the 3D k-space coverage volume. These calculations were based on specifications from [173]. Figure courtesy of [174]
Fig. 13.
Fig. 13. Comparison of various deep learning approaches in FP. (a) The conventional approach (top) and a gradient-descent-based approach, with the forward model written in an automatic differentiation library. (b) Approaches that train a CNN to learn a mapping between the data and the reconstruction, replacing the forward model. The bottom approach bypasses the reconstruction and optimizes a CNN for a particular task. These approaches may also incorporate optimization of the LED weights in order to design the hardware. (c) These approaches still use the forward model, but reparameterize the reconstruction with a CNN, which may be pretrained (top) or untrained (bottom).

Tables (1)

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Table 1. Summary of FP benefits.

Equations (2)

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I j = | F 1 [ s ^ ( f x s i n ( ϕ x j ) λ , f y s i n ( ϕ y j ) λ ) a ( f x , f y ) ] | 2 ,
R = λ N A obj + N A ill .