Abstract
The competition between resolution and the imaging field of view is a long-standing problem in traditional imaging systems — they can produce either an image of a small area with fine details or an image of a large area with coarse details. Fourier ptychography (FP) is an approach for tackling this intrinsic trade-off in imaging systems. It takes the challenge of high-throughput and high-resolution imaging from the domain of improving the physical limitations of optics to the domain of computation. It also enables post-measurement computational correction of optical aberrations. We present the basic concept of FP, compare it to related imaging modalities and then discuss experimental implementations, such as aperture-scanning FP, macroscopic camera-scanning FP, reflection mode, single-shot set-up, X-ray FP, speckle-scanning scheme and deep-learning-related implementations. Various applications of FP are discussed, including quantitative phase imaging in 2D and 3D, digital pathology, high-throughput cytometry, aberration metrology, long-range imaging and coherent X-ray nanoscopy. A collection of datasets and reconstruction codes is provided for readers interested in implementing FP themselves.
Key points
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Fourier ptychography (FP) is a computational method for synthesizing raw data into a high-resolution and wide-field-of-view image through a combination of synthetic aperture and phase retrieval concepts. Unlike conventional techniques, which trade resolution against imaging field of view, FP can achieve both simultaneously.
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FP can computationally render both the intensity and the phase images of the sample from intensity-based measurements.
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FP has the intrinsic ability to computationally correct aberrations. As a result, in FP, the task of aberration correction is not a physical system design problem but, rather, a computational problem that can be resolved post-measurement.
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Defocus is a type of aberration and, thus, FP can computationally refocus images over a much extended range.
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Since the invention of FP, various innovations on the original method have been reported; this Technical Review discusses some of the most impactful ones, such as aperture-scanning and camera-scanning schemes, extensions for handling 3D specimens and X-ray FP, among others.
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A collection of FP datasets and reconstruction codes is provided to interested readers.
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Code availability
Example Fourier ptychography codes and datasets are available at https://github.com/SmartImagingLabUConn/Fourier-Ptychography
References
Lohmann, A. W., Dorsch, R. G., Mendlovic, D., Zalevsky, Z. & Ferreira, C. Space–bandwidth product of optical signals and systems. JOSA A 13, 470–473 (1996).
McConnell, G. et al. A novel optical microscope for imaging large embryos and tissue volumes with sub-cellular resolution throughout. eLife 5, e18659 (2016).
Fan, J. et al. Video-rate imaging of biological dynamics at centimetre scale and micrometre resolution. Nat. Photonics 13, 809–816 (2019).
Zheng, G., Horstmeyer, R. & Yang, C. Wide-field, high-resolution Fourier ptychographic microscopy. Nat. Photonics 7, 739–745 (2013).
Zheng, G., Kolner, C. & Yang, C. Microscopy refocusing and dark-field imaging by using a simple LED array. Opt. Lett. 36, 3987–3989 (2011).
Zheng, G., Ou, X., Horstmeyer, R., Chung, J. & Yang, C. Fourier ptychographic microscopy: A gigapixel superscope for biomedicine. Opt. Photonics News 25, 26–33 (2014).
Dong, S. et al. Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging. Opt. Express 22, 13586–13599 (2014).
Holloway, J., Wu, Y., Sharma, M. K., Cossairt, O. & Veeraraghavan, A. SAVI: Synthetic apertures for long-range, subdiffraction-limited visible imaging using Fourier ptychography. Sci. Adv. 3, e1602564 (2017).
Wakonig, K. et al. X-ray Fourier ptychography. Sci. Adv. 5, eaav0282 (2019).
Horstmeyer, R., Chung, J., Ou, X., Zheng, G. & Yang, C. Diffraction tomography with Fourier ptychography. Optica 3, 827–835 (2016).
Zuo, C., Sun, J., Li, J., Asundi, A. & Chen, Q. Wide-field high-resolution 3D microscopy with Fourier ptychographic diffraction tomography. Opt. Lasers Eng. 128, 106003 (2020).
Ryle, M. & Hewish, A. The synthesis of large radio telescopes. Mon. Not. R. Astron. Soc. 120, 220–230 (1960).
Gerchberg, R. W. A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik 35, 237–246 (1972).
Fienup, J. R. Phase retrieval algorithms: a comparison. Appl. Opt. 21, 2758–2769 (1982).
Li, P., Batey, D. J., Edo, T. B. & Rodenburg, J. M. Separation of three-dimensional scattering effects in tilt-series Fourier ptychography. Ultramicroscopy 158, 1–7 (2015).
Hoppe, W. & Strube, G. Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences. Acta Crystallogr. A 25, 502–507 (1969).
Faulkner, H. M. L. & Rodenburg, J. Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. Phys. Rev. Lett. 93, 023903 (2004).
Guizar-Sicairos, M. & Fienup, J. R. Phase retrieval with transverse translation diversity: a nonlinear optimization approach. Opt. Express 16, 7264–7278 (2008).
Thibault, P., Dierolf, M., Bunk, O., Menzel, A. & Pfeiffer, F. Probe retrieval in ptychographic coherent diffractive imaging. Ultramicroscopy 109, 338–343 (2009).
Maiden, A. M. & Rodenburg, J. M. An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109, 1256–1262 (2009).
Dierolf, M. et al. Ptychographic X-ray computed tomography at the nanoscale. Nature 467, 436–439 (2010).
Maiden, A. M., Humphry, M. J., Zhang, F. & Rodenburg, J. M. Superresolution imaging via ptychography. JOSA A 28, 604–612 (2011).
Thibault, P. & Menzel, A. Reconstructing state mixtures from diffraction measurements. Nature 494, 68–71 (2013).
Batey, D. J., Claus, D. & Rodenburg, J. M. Information multiplexing in ptychography. Ultramicroscopy 138, 13–21 (2014).
Rodenburg, J. & Maiden, A. in Springer Handbook of Microscopy Ch. 17 (eds Hawkes, P. W. & Spence, J. C. H.) 819–904 (Springer, 2019).
Horstmeyer, R. & Yang, C. A phase space model of Fourier ptychographic microscopy. Opt. Express 22, 338–358 (2014).
Li, P. & Maiden, A. Lensless LED matrix ptychographic microscope: problems and solutions. Appl. Opt. 57, 1800–1806 (2018).
Maiden, A. M., Humphry, M. J. & Rodenburg, J. Ptychographic transmission microscopy in three dimensions using a multi-slice approach. JOSA A 29, 1606–1614 (2012).
Zhang, F. et al. Translation position determination in ptychographic coherent diffraction imaging. Opt. Express 21, 13592–13606 (2013).
Sun, J., Zuo, C., Zhang, L. & Chen, Q. Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations. Sci. Rep. 7, 1187 (2017).
Song, P. et al. Super-resolved multispectral lensless microscopy via angle-tilted, wavelength-multiplexed ptychographic modulation. Opt. Lett. 45, 3486–3489 (2020).
Kirkland, A., Saxton, W., Chau, K.-L., Tsuno, K. & Kawasaki, M. Super-resolution by aperture synthesis: tilt series reconstruction in CTEM. Ultramicroscopy 57, 355–374 (1995).
Haigh, S. J., Sawada, H. & Kirkland, A. I. Atomic structure imaging beyond conventional resolution limits in the transmission electron microscope. Phys. Rev. Lett. 103, 126101 (2009).
Horstmeyer, R., Heintzmann, R., Popescu, G., Waller, L. & Yang, C. Standardizing the resolution claims for coherent microscopy. Nat. Photonics 10, 68–71 (2016).
Ou, X., Horstmeyer, R., Zheng, G. & Yang, C. High numerical aperture Fourier ptychography: principle, implementation and characterization. Opt. Express 23, 3472–3491 (2015).
Sen, S., Ahmed, I., Aljubran, B., Bernussi, A. A. & de Peralta, L. G. Fourier ptychographic microscopy using an infrared-emitting hemispherical digital condenser. Appl. Opt. 55, 6421–6427 (2016).
Pan, A. et al. Subwavelength resolution Fourier ptychography with hemispherical digital condensers. Opt. Express 26, 23119–23131 (2018).
Phillips, Z. F., Eckert, R. & Waller, L. in Imaging Systems and Applications IW4E.5 (Optical Society of America, 2017).
Bian, L. et al. Content adaptive illumination for Fourier ptychography. Opt. Lett. 39, 6648–6651 (2014).
Zhang, Y., Jiang, W., Tian, L., Waller, L. & Dai, Q. Self-learning based Fourier ptychographic microscopy. Opt. Express 23, 18471–18486 (2015).
Li, S., Wang, Y., Wu, W. & Liang, Y. Predictive searching algorithm for Fourier ptychography. J. Opt. 19, 125605 (2017).
Guo, K., Dong, S., Nanda, P. & Zheng, G. Optimization of sampling pattern and the design of Fourier ptychographic illuminator. Opt. Express 23, 6171–6180 (2015).
Sun, J., Chen, Q., Zhang, J., Fan, Y. & Zuo, C. Single-shot quantitative phase microscopy based on color-multiplexed Fourier ptychography. Opt. Lett. 43, 3365–3368 (2018).
Tian, L., Li, X., Ramchandran, K. & Waller, L. Multiplexed coded illumination for Fourier Ptychography with an LED array microscope. Biomed. Opt. Express 5, 2376–2389 (2014).
Dong, S., Shiradkar, R., Nanda, P. & Zheng, G. Spectral multiplexing and coherent-state decomposition in Fourier ptychographic imaging. Biomed. Opt. Express 5, 1757–1767 (2014).
Zhou, Y. et al. Fourier ptychographic microscopy using wavelength multiplexing. J. Biomed. Opt. 22, 066006 (2017).
Tian, L. et al. Computational illumination for high-speed in vitro Fourier ptychographic microscopy. Optica 2, 904–911 (2015).
Tian, L. & Waller, L. Quantitative differential phase contrast imaging in an LED array microscope. Opt. Express 23, 11394–11403 (2015).
Kuang, C. et al. Digital micromirror device-based laser-illumination Fourier ptychographic microscopy. Opt. Express 23, 26999–27010 (2015).
Chung, J., Lu, H., Ou, X., Zhou, H. & Yang, C. Wide-field Fourier ptychographic microscopy using laser illumination source. Biomed. Opt. Express 7, 4787–4802 (2016).
Tao, X. et al. Tunable-illumination for laser Fourier ptychographic microscopy based on a background noise-reducing system. Opt. Commun. 468, 125764 (2020).
Aidukas, T., Konda, P. C., Harvey, A. R., Padgett, M. J. & Moreau, P.-A. Phase and amplitude imaging with quantum correlations through Fourier ptychography. Sci. Rep. 9, 10445 (2019).
Dong, S., Guo, K., Nanda, P., Shiradkar, R. & Zheng, G. FPscope: a field-portable high-resolution microscope using a cellphone lens. Biomed. Opt. Express 5, 3305–3310 (2014).
Aidukas, T., Eckert, R., Harvey, A. R., Waller, L. & Konda, P. C. Low-cost, sub-micron resolution, wide-field computational microscopy using opensource hardware. Sci. Rep. 9, 7457 (2019).
Guo, C. et al. OpenWSI: a low-cost, high-throughput whole slide imaging system via single-frame autofocusing and open-source hardware. Opt. Lett. 45, 260–263 (2020).
Sun, J., Zuo, C., Zhang, J., Fan, Y. & Chen, Q. High-speed Fourier ptychographic microscopy based on programmable annular illuminations. Sci. Rep. 8, 7669 (2018).
Bian, Z., Dong, S. & Zheng, G. Adaptive system correction for robust Fourier ptychographic imaging. Opt. Express 21, 32400–32410 (2013).
Pan, A. et al. System calibration method for Fourier ptychographic microscopy. J. Biomed. Opt. 22, 096005 (2017).
Sun, J., Chen, Q., Zhang, Y. & Zuo, C. Efficient positional misalignment correction method for Fourier ptychographic microscopy. Biomed. Opt. Express 7, 1336–1350 (2016).
Eckert, R., Phillips, Z. F. & Waller, L. Efficient illumination angle self-calibration in Fourier ptychography. Appl. Opt. 57, 5434–5442 (2018).
Zhou, A. et al. Fast and robust misalignment correction of Fourier ptychographic microscopy for full field of view reconstruction. Opt. Express 26, 23661–23674 (2018).
Yeh, L.-H. et al. Experimental robustness of Fourier ptychography phase retrieval algorithms. Opt. Express 23, 33214–33240 (2015).
Liu, J. et al. Stable and robust frequency domain position compensation strategy for Fourier ptychographic microscopy. Opt. Express 25, 28053–28067 (2017).
Zheng, G., Ou, X., Horstmeyer, R. & Yang, C. Characterization of spatially varying aberrations for wide field-of-view microscopy. Opt. Express 21, 15131–15143 (2013).
Ou, X., Zheng, G. & Yang, C. Embedded pupil function recovery for Fourier ptychographic microscopy. Opt. Express 22, 4960–4972 (2014).
Song, P. et al. Full-field Fourier ptychography (FFP): Spatially varying pupil modeling and its application for rapid field-dependent aberration metrology. APL Photonics 4, 050802 (2019).
Yang, C., Qian, J., Schirotzek, A., Maia, F. & Marchesini, S. Iterative algorithms for ptychographic phase retrieval. Preprint at https://arxiv.org/abs/1105.5628 (2011).
Nguyen, T., Xue, Y., Li, Y., Tian, L. & Nehmetallah, G. Deep learning approach for Fourier ptychography microscopy. Opt. Express 26, 26470–26484 (2018).
Boominathan, L., Maniparambil, M., Gupta, H., Baburajan, R. & Mitra, K. Phase retrieval for Fourier Ptychography under varying amount of measurements. Preprint at https://arxiv.org/abs/1805.03593 (2018).
Kappeler, A., Ghosh, S., Holloway, J., Cossairt, O. & Katsaggelos, A. in 2017 IEEE International Conference on Image Processing (ICIP) 1712–1716 (IEEE, 2017).
Xue, Y., Cheng, S., Li, Y. & Tian, L. Reliable deep-learning-based phase imaging with uncertainty quantification. Optica 6, 618–629 (2019).
Shamshad, F., Abbas, F. & Ahmed, A. in 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2019) 7720–7724 (IEEE, 2019).
Zhang, J., Xu, T., Shen, Z., Qiao, Y. & Zhang, Y. Fourier ptychographic microscopy reconstruction with multiscale deep residual network. Opt. Express 27, 8612–8625 (2019).
Cheng, Y. F. et al. Illumination pattern design with deep learning for single-shot Fourier ptychographic microscopy. Opt. Express 27, 644–656 (2019).
Kellman, M. R., Bostan, E., Repina, N. A. & Waller, L. Physics-based learned design: optimized coded-illumination for quantitative phase imaging. IEEE Trans. Comput. Imaging 5, 344–353 (2019).
Muthumbi, A. et al. Learned sensing: jointly optimized microscope hardware for accurate image classification. Biomed. Opt. Express 10, 6351–6369 (2019).
Horstmeyer, R., Chen, R. Y., Kappes, B. & Judkewitz, B. Convolutional neural networks that teach microscopes how to image. Preprint at https://arxiv.org/abs/1709.07223 (2017).
Kellman, M., Bostan, E., Chen, M. & Waller, L. in 2019 IEEE International Conference on Computational Photography (ICCP) 1–8 (IEEE, 2017).
Jiang, S., Guo, K., Liao, J. & Zheng, G. Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow. Biomed. Opt. Express 9, 3306–3319 (2018).
Sun, M. et al. Neural network model combined with pupil recovery for Fourier ptychographic microscopy. Opt. Express 27, 24161–24174 (2019).
Zhang, Y. et al. PgNN: Physics-guided neural network for fourier ptychographic microscopy. Preprint at https://arxiv.org/abs/1909.08869 (2019).
Zhang, J. et al. Forward imaging neural network with correction of positional misalignment for Fourier ptychographic microscopy. Opt. Express 28, 23164–23175 (2020).
Baydin, A. G., Pearlmutter, B. A., Radul, A. A. & Siskind, J. M. Automatic differentiation in machine learning: a survey. J. Mach. Learn. Res. 18, 5595–5637 (2017).
Wang, R. et al. Virtual brightfield and fluorescence staining for Fourier ptychography via unsupervised deep learning. Opt. Lett. 45, 5405–5408 (2020).
Ou, X., Chung, J., Horstmeyer, R. & Yang, C. Aperture scanning Fourier ptychographic microscopy. Biomed. Opt. Express 7, 3140–3150 (2016).
He, X., Jiang, Z., Kong, Y., Wang, S. & Liu, C. Fourier ptychography via wavefront modulation with a diffuser. Opt. Commun. 459, 125057 (2020).
Choi, G.-J. et al. Dual-wavelength Fourier ptychography using a single LED. Opt. Lett. 43, 3526–3529 (2018).
He, X., Liu, C. & Zhu, J. Single-shot aperture-scanning Fourier ptychography. Opt. Express 26, 28187–28196 (2018).
Holloway, J. et al. Toward long-distance subdiffraction imaging using coherent camera arrays. IEEE Trans. Comput. Imaging 2, 251–265 (2016).
Guo, K., Dong, S. & Zheng, G. Fourier ptychography for brightfield, phase, darkfield, reflective, multi-slice, and fluorescence imaging. IEEE J. Sel. Top. Quantum Electron. 22, 77–88 (2015).
Pacheco, S., Salahieh, B., Milster, T., Rodriguez, J. J. & Liang, R. Transfer function analysis in epi-illumination Fourier ptychography. Opt. Lett. 40, 5343–5346 (2015).
Pacheco, S., Zheng, G. & Liang, R. Reflective Fourier ptychography. J. Biomed. Opt. 21, 026010 (2016).
Lee, H., Chon, B. H. & Ahn, H. K. Reflective Fourier ptychographic microscopy using a parabolic mirror. Opt. Express 27, 34382–34391 (2019).
Shen, C. et al. Computational aberration correction of VIS-NIR multispectral imaging microscopy based on Fourier ptychography. Opt. Express 27, 24923–24937 (2019).
Wojdyla, A., Benk, M. P., Naulleau, P. P. & Goldberg, K. A. in Image Sensing Technologies: Materials, Devices, Systems, and Applications Vol. 106560W (International Society for Optics and Photonics, 2018).
Chan, A. C. et al. Parallel Fourier ptychographic microscopy for high-throughput screening with 96 cameras (96 eyes). Sci. Rep. 9, 11114 (2019).
Konda, P. C., Taylor, J. M. & Harvey, A. R. Parallelized aperture synthesis using multi-aperture Fourier ptychographic microscopy. Preprint at https://arxiv.org/abs/1806.02317 (2018).
Lee, B. et al. Single-shot phase retrieval via Fourier ptychographic microscopy. Optica 5, 976–983 (2018).
He, X., Liu, C. & Zhu, J. Single-shot Fourier ptychography based on diffractive beam splitting. Opt. Lett. 43, 214–217 (2018).
Gustafsson, M. G. Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy. J. Microsc. 198, 82–87 (2000).
Dong, S., Nanda, P., Shiradkar, R., Guo, K. & Zheng, G. High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography. Opt. Express 22, 20856–20870 (2014).
Guo, K. et al. 13-fold resolution gain through turbid layer via translated unknown speckle illumination. Biomed. Opt. Express 9, 260–275 (2018).
Zhang, H. et al. Near-field Fourier ptychography: super-resolution phase retrieval via speckle illumination. Opt. Express 27, 7498–7512 (2019).
Yeh, L.-H., Chowdhury, S. & Waller, L. Computational structured illumination for high-content fluorescence and phase microscopy. Biomed. Opt. Express 10, 1978–1998 (2019).
Dong, S., Nanda, P., Guo, K., Liao, J. & Zheng, G. Incoherent Fourier ptychographic photography using structured light. Photonics Res. 3, 19–23 (2015).
Simons, H., Poulsen, H. F., Guigay, J. & Detlefs, C. X-ray Fourier ptychographic microscopy. Preprint at https://arxiv.org/abs/1609.07513 (2016).
Detlefs, C., Beltran, M. A., Guigay, J.-P. & Simons, H. Translative lens-based full-field coherent X-ray imaging. J. Synchrotron Rad. 27, 119–126 (2020).
Pedersen, A. et al. X-ray coherent diffraction imaging with an objective lens: Towards three-dimensional mapping of thick polycrystals. Phys. Rev. Res. 2, 033031 (2020).
Cowley, J. M. & Moodie, A. F. The scattering of electrons by atoms and crystals. I. A new theoretical approach. Acta Crystallogr. 10, 609–619 (1957).
Godden, T., Suman, R., Humphry, M., Rodenburg, J. & Maiden, A. Ptychographic microscope for three-dimensional imaging. Opt. Express 22, 12513–12523 (2014).
Tian, L. & Waller, L. 3D intensity and phase imaging from light field measurements in an LED array microscope. Optica 2, 104–111 (2015).
Chowdhury, S. et al. High-resolution 3D refractive index microscopy of multiple-scattering samples from intensity images. Optica 6, 1211–1219 (2019).
Song, P. et al. Super-resolution microscopy via ptychographic structured modulation of a diffuser. Opt. Lett. 44, 3645–3648 (2019).
Bian, Z. et al. Ptychographic modulation engine: a low-cost DIY microscope add-on for coherent super-resolution imaging. J. Phys. D Appl. Phys. 53, 014005 (2019).
Ou, X., Horstmeyer, R., Yang, C. & Zheng, G. Quantitative phase imaging via Fourier ptychographic microscopy. Opt. Lett. 38, 4845–4848 (2013).
Zheng, G. Breakthroughs in photonics 2013: Fourier ptychographic imaging. IEEE Photonics J. 6, 0701207 (2014).
Horstmeyer, R., Ou, X., Zheng, G., Willems, P. & Yang, C. Digital pathology with Fourier ptychography. Comput. Med. Imaging Graph. 42, 38–43 (2015).
Williams, A. J. et al. Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis. J. Biomed. Opt. 19, 066007 (2014).
Kim, J., Henley, B. M., Kim, C. H., Lester, H. A. & Yang, C. Incubator embedded cell culture imaging system (EmSight) based on Fourier ptychographic microscopy. Biomed. Opt. Express 7, 3097–3110 (2016).
Kamal, T., Yang, L. & Lee, W. M. In situ retrieval and correction of aberrations in moldless lenses using Fourier ptychography. Opt. Express 26, 2708–2719 (2018).
Chung, J., Martinez, G. W., Lencioni, K. C., Sadda, S. R. & Yang, C. Computational aberration compensation by coded-aperture-based correction of aberration obtained from optical Fourier coding and blur estimation. Optica 6, 647–661 (2019).
Chung, J., Kim, J., Ou, X., Horstmeyer, R. & Yang, C. Wide field-of-view fluorescence image deconvolution with aberration-estimation from Fourier ptychography. Biomed. Opt. Express 7, 352–368 (2016).
Candes, E. J., Strohmer, T. & Voroninski, V. Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming. Commun. Pure Appl. Math. 66, 1241–1274 (2013).
Horstmeyer, R. et al. Solving ptychography with a convex relaxation. New J. Phys. 17, 053044 (2015).
Hesse, R., Luke, D. R. & Neumann, P. Alternating projections and Douglas-Rachford for sparse affine feasibility. IEEE Trans. Signal Process. 62, 4868–4881 (2014).
Heuke, S. et al. Coherent anti-stokes Raman Fourier ptychography. Opt. Express 27, 23497–23514 (2019).
Goodman, J. W. Introduction to Fourier Optics 4th edn (Macmillan Learning, 2017).
Horstmeyer, R., Ou, X., Chung, J., Zheng, G. & Yang, C. Overlapped Fourier coding for optical aberration removal. Opt. Express 22, 24062–24080 (2014).
Zhang, M., Zhang, L., Yang, D., Liu, H. & Liang, Y. Symmetrical illumination based extending depth of field in Fourier ptychographic microscopy. Opt. Express 27, 3583–3597 (2019).
Guo, K. et al. Microscopy illumination engineering using a low-cost liquid crystal display. Biomed. Opt. Express 6, 574–579 (2015).
Dong, S., Bian, Z., Shiradkar, R. & Zheng, G. Sparsely sampled Fourier ptychography. Opt. Express 22, 5455–5464 (2014).
Bian, L. et al. Motion-corrected Fourier ptychography. Biomed. Opt. Express 7, 4543–4553 (2016).
Zhang, Y., Pan, A., Lei, M. & Yao, B. Data preprocessing methods for robust Fourier ptychographic microscopy. Optical Eng. 56, 123107 (2017).
Pan, A., Zuo, C., Xie, Y., Lei, M. & Yao, B. Vignetting effect in Fourier ptychographic microscopy. Opt. Lasers Eng. 120, 40–48 (2019).
Zuo, C., Sun, J. & Chen, Q. Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy. Opt. Express 24, 20724–20744 (2016).
Bian, L. et al. Fourier ptychographic reconstruction using Wirtinger flow optimization. Opt. Express 23, 4856–4866 (2015).
Bian, L. et al. Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient. Sci. Rep. 6, 27384 (2016).
Chen, S., Xu, T., Zhang, J., Wang, X. & Zhang, Y. Optimized denoising method for fourier ptychographic microscopy based on wirtinger flow. IEEE Photonics J. 11, 1–14 (2019).
Bostan, E., Soltanolkotabi, M., Ren, D. & Waller, L. in 2018 25th IEEE International Conference on Image Processing (ICIP) 3823–3827 (IEEE, 2018).
Liu, J., Li, Y., Wang, W., Tan, J. & Liu, C. Accelerated and high-quality Fourier ptychographic method using a double truncated Wirtinger criteria. Opt. Express 26, 26556–26565 (2018).
Zhang, Y., Song, P., Zhang, J. & Dai, Q. Fourier ptychographic microscopy with sparse representation. Sci. Rep. 7, 8664 (2017).
Zhang, Y., Cui, Z., Zhang, J., Song, P. & Dai, Q. Group-based sparse representation for Fourier ptychography microscopy. Opt. Commun. 404, 55–61 (2017).
Zhang, Y., Song, P. & Dai, Q. Fourier ptychographic microscopy using a generalized Anscombe transform approximation of the mixed Poisson-Gaussian likelihood. Opt. Express 25, 168–179 (2017).
Fan, Y., Sun, J., Chen, Q., Wang, M. & Zuo, C. Adaptive denoising method for Fourier ptychographic microscopy. Opt. Commun. 404, 23–31 (2017).
Sun, Y. et al. in 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2019) 7665–7669 (IEEE, 2019).
Jagatap, G., Chen, Z., Nayer, S., Hegde, C. & Vaswani, N. Sample efficient fourier ptychography for structured data. IEEE Trans. Comput. Imaging 6, 344–357 (2019).
Ling, R., Tahir, W., Lin, H.-Y., Lee, H. & Tian, L. High-throughput intensity diffraction tomography with a computational microscope. Biomed. Opt. Express 9, 2130–2141 (2018).
Li, J. et al. High-speed in vitro intensity diffraction tomography. Adv. Photonics 1, 066004 (2019).
Matlock, A. & Tian, L. High-throughput, volumetric quantitative phase imaging with multiplexed intensity diffraction tomography. Biomed. Opt. Express 10, 6432 (2019).
Pham, T.-A. et al. Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering. Opt. Express 26, 2749–2763 (2018).
Acknowledgements
G.Z. acknowledges the support of NSF 1510077, NSF 2012140 and the UConn SPARK grant. P.S. acknowledges the support of the Thermo Fisher Scientific Fellowship. C.Y. acknowledges the support of the Rosen Bioengineering Center Endowment Fund (9900050).
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Zheng, G., Shen, C., Jiang, S. et al. Concept, implementations and applications of Fourier ptychography. Nat Rev Phys 3, 207–223 (2021). https://doi.org/10.1038/s42254-021-00280-y
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DOI: https://doi.org/10.1038/s42254-021-00280-y