Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Technical Review
  • Published:

Concept, implementations and applications of Fourier ptychography

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

  • 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.

  • FP can computationally render both the intensity and the phase images of the sample from intensity-based measurements.

  • 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.

  • Defocus is a type of aberration and, thus, FP can computationally refocus images over a much extended range.

  • 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.

  • A collection of FP datasets and reconstruction codes is provided to interested readers.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Comparison between Fourier ptychography and real-space ptychography.
Fig. 2: Implementations of Fourier ptychography.
Fig. 3: Quantitative phase imaging in 2D and 3D.
Fig. 4: Digital pathology and high-throughput cytometry via Fourier ptychography.
Fig. 5: Aberration metrology, surface inspection, long-range imaging and X-ray nanoscopy via Fourier ptychography.

Similar content being viewed by others

Code availability

Example Fourier ptychography codes and datasets are available at https://github.com/SmartImagingLabUConn/Fourier-Ptychography

References

  1. 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).

    Article  ADS  Google Scholar 

  2. McConnell, G. et al. A novel optical microscope for imaging large embryos and tissue volumes with sub-cellular resolution throughout. eLife 5, e18659 (2016).

    Article  Google Scholar 

  3. Fan, J. et al. Video-rate imaging of biological dynamics at centimetre scale and micrometre resolution. Nat. Photonics 13, 809–816 (2019).

    Article  ADS  Google Scholar 

  4. Zheng, G., Horstmeyer, R. & Yang, C. Wide-field, high-resolution Fourier ptychographic microscopy. Nat. Photonics 7, 739–745 (2013).

    Article  ADS  Google Scholar 

  5. Zheng, G., Kolner, C. & Yang, C. Microscopy refocusing and dark-field imaging by using a simple LED array. Opt. Lett. 36, 3987–3989 (2011).

    Article  ADS  Google Scholar 

  6. 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).

    Article  Google Scholar 

  7. Dong, S. et al. Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging. Opt. Express 22, 13586–13599 (2014).

    Article  ADS  Google Scholar 

  8. 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).

    Article  ADS  Google Scholar 

  9. Wakonig, K. et al. X-ray Fourier ptychography. Sci. Adv. 5, eaav0282 (2019).

    Article  ADS  Google Scholar 

  10. Horstmeyer, R., Chung, J., Ou, X., Zheng, G. & Yang, C. Diffraction tomography with Fourier ptychography. Optica 3, 827–835 (2016).

    Article  ADS  Google Scholar 

  11. 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).

    Article  Google Scholar 

  12. Ryle, M. & Hewish, A. The synthesis of large radio telescopes. Mon. Not. R. Astron. Soc. 120, 220–230 (1960).

    Article  ADS  Google Scholar 

  13. Gerchberg, R. W. A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik 35, 237–246 (1972).

    Google Scholar 

  14. Fienup, J. R. Phase retrieval algorithms: a comparison. Appl. Opt. 21, 2758–2769 (1982).

    Article  ADS  Google Scholar 

  15. 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).

    Article  Google Scholar 

  16. 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).

    Article  ADS  Google Scholar 

  17. Faulkner, H. M. L. & Rodenburg, J. Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. Phys. Rev. Lett. 93, 023903 (2004).

    Article  ADS  Google Scholar 

  18. Guizar-Sicairos, M. & Fienup, J. R. Phase retrieval with transverse translation diversity: a nonlinear optimization approach. Opt. Express 16, 7264–7278 (2008).

    Article  ADS  Google Scholar 

  19. Thibault, P., Dierolf, M., Bunk, O., Menzel, A. & Pfeiffer, F. Probe retrieval in ptychographic coherent diffractive imaging. Ultramicroscopy 109, 338–343 (2009).

    Article  Google Scholar 

  20. Maiden, A. M. & Rodenburg, J. M. An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109, 1256–1262 (2009).

    Article  Google Scholar 

  21. Dierolf, M. et al. Ptychographic X-ray computed tomography at the nanoscale. Nature 467, 436–439 (2010).

    Article  ADS  Google Scholar 

  22. Maiden, A. M., Humphry, M. J., Zhang, F. & Rodenburg, J. M. Superresolution imaging via ptychography. JOSA A 28, 604–612 (2011).

    Article  ADS  Google Scholar 

  23. Thibault, P. & Menzel, A. Reconstructing state mixtures from diffraction measurements. Nature 494, 68–71 (2013).

    Article  ADS  Google Scholar 

  24. Batey, D. J., Claus, D. & Rodenburg, J. M. Information multiplexing in ptychography. Ultramicroscopy 138, 13–21 (2014).

    Article  Google Scholar 

  25. Rodenburg, J. & Maiden, A. in Springer Handbook of Microscopy Ch. 17 (eds Hawkes, P. W. & Spence, J. C. H.) 819–904 (Springer, 2019).

  26. Horstmeyer, R. & Yang, C. A phase space model of Fourier ptychographic microscopy. Opt. Express 22, 338–358 (2014).

    Article  ADS  Google Scholar 

  27. Li, P. & Maiden, A. Lensless LED matrix ptychographic microscope: problems and solutions. Appl. Opt. 57, 1800–1806 (2018).

    Article  ADS  Google Scholar 

  28. 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).

    Article  ADS  Google Scholar 

  29. Zhang, F. et al. Translation position determination in ptychographic coherent diffraction imaging. Opt. Express 21, 13592–13606 (2013).

    Article  ADS  Google Scholar 

  30. Sun, J., Zuo, C., Zhang, L. & Chen, Q. Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations. Sci. Rep. 7, 1187 (2017).

    Article  ADS  Google Scholar 

  31. Song, P. et al. Super-resolved multispectral lensless microscopy via angle-tilted, wavelength-multiplexed ptychographic modulation. Opt. Lett. 45, 3486–3489 (2020).

    Article  ADS  Google Scholar 

  32. 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).

    Article  Google Scholar 

  33. 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).

    Article  ADS  Google Scholar 

  34. Horstmeyer, R., Heintzmann, R., Popescu, G., Waller, L. & Yang, C. Standardizing the resolution claims for coherent microscopy. Nat. Photonics 10, 68–71 (2016).

    Article  ADS  Google Scholar 

  35. Ou, X., Horstmeyer, R., Zheng, G. & Yang, C. High numerical aperture Fourier ptychography: principle, implementation and characterization. Opt. Express 23, 3472–3491 (2015).

    Article  ADS  Google Scholar 

  36. 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).

    Article  ADS  Google Scholar 

  37. Pan, A. et al. Subwavelength resolution Fourier ptychography with hemispherical digital condensers. Opt. Express 26, 23119–23131 (2018).

    Article  ADS  Google Scholar 

  38. Phillips, Z. F., Eckert, R. & Waller, L. in Imaging Systems and Applications IW4E.5 (Optical Society of America, 2017).

  39. Bian, L. et al. Content adaptive illumination for Fourier ptychography. Opt. Lett. 39, 6648–6651 (2014).

    Article  ADS  Google Scholar 

  40. Zhang, Y., Jiang, W., Tian, L., Waller, L. & Dai, Q. Self-learning based Fourier ptychographic microscopy. Opt. Express 23, 18471–18486 (2015).

    Article  ADS  Google Scholar 

  41. Li, S., Wang, Y., Wu, W. & Liang, Y. Predictive searching algorithm for Fourier ptychography. J. Opt. 19, 125605 (2017).

    Article  ADS  Google Scholar 

  42. 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).

    Article  ADS  Google Scholar 

  43. 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).

    Article  ADS  Google Scholar 

  44. 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).

    Article  Google Scholar 

  45. 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).

    Article  Google Scholar 

  46. Zhou, Y. et al. Fourier ptychographic microscopy using wavelength multiplexing. J. Biomed. Opt. 22, 066006 (2017).

    Article  ADS  Google Scholar 

  47. Tian, L. et al. Computational illumination for high-speed in vitro Fourier ptychographic microscopy. Optica 2, 904–911 (2015).

    Article  ADS  Google Scholar 

  48. Tian, L. & Waller, L. Quantitative differential phase contrast imaging in an LED array microscope. Opt. Express 23, 11394–11403 (2015).

    Article  ADS  Google Scholar 

  49. Kuang, C. et al. Digital micromirror device-based laser-illumination Fourier ptychographic microscopy. Opt. Express 23, 26999–27010 (2015).

    Article  ADS  Google Scholar 

  50. 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).

    Article  Google Scholar 

  51. Tao, X. et al. Tunable-illumination for laser Fourier ptychographic microscopy based on a background noise-reducing system. Opt. Commun. 468, 125764 (2020).

    Article  Google Scholar 

  52. 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).

    Article  ADS  Google Scholar 

  53. 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).

    Article  Google Scholar 

  54. 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).

    Article  ADS  Google Scholar 

  55. 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).

    Article  ADS  Google Scholar 

  56. 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).

    Article  ADS  Google Scholar 

  57. Bian, Z., Dong, S. & Zheng, G. Adaptive system correction for robust Fourier ptychographic imaging. Opt. Express 21, 32400–32410 (2013).

    Article  ADS  Google Scholar 

  58. Pan, A. et al. System calibration method for Fourier ptychographic microscopy. J. Biomed. Opt. 22, 096005 (2017).

    Article  ADS  Google Scholar 

  59. Sun, J., Chen, Q., Zhang, Y. & Zuo, C. Efficient positional misalignment correction method for Fourier ptychographic microscopy. Biomed. Opt. Express 7, 1336–1350 (2016).

    Article  Google Scholar 

  60. Eckert, R., Phillips, Z. F. & Waller, L. Efficient illumination angle self-calibration in Fourier ptychography. Appl. Opt. 57, 5434–5442 (2018).

    Article  ADS  Google Scholar 

  61. 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).

    Article  ADS  Google Scholar 

  62. Yeh, L.-H. et al. Experimental robustness of Fourier ptychography phase retrieval algorithms. Opt. Express 23, 33214–33240 (2015).

    Article  ADS  Google Scholar 

  63. Liu, J. et al. Stable and robust frequency domain position compensation strategy for Fourier ptychographic microscopy. Opt. Express 25, 28053–28067 (2017).

    Article  ADS  Google Scholar 

  64. 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).

    Article  ADS  Google Scholar 

  65. Ou, X., Zheng, G. & Yang, C. Embedded pupil function recovery for Fourier ptychographic microscopy. Opt. Express 22, 4960–4972 (2014).

    Article  ADS  Google Scholar 

  66. 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).

    Article  ADS  Google Scholar 

  67. 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).

  68. Nguyen, T., Xue, Y., Li, Y., Tian, L. & Nehmetallah, G. Deep learning approach for Fourier ptychography microscopy. Opt. Express 26, 26470–26484 (2018).

    Article  ADS  Google Scholar 

  69. 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).

  70. Kappeler, A., Ghosh, S., Holloway, J., Cossairt, O. & Katsaggelos, A. in 2017 IEEE International Conference on Image Processing (ICIP) 1712–1716 (IEEE, 2017).

  71. Xue, Y., Cheng, S., Li, Y. & Tian, L. Reliable deep-learning-based phase imaging with uncertainty quantification. Optica 6, 618–629 (2019).

    Article  ADS  Google Scholar 

  72. Shamshad, F., Abbas, F. & Ahmed, A. in 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2019) 7720–7724 (IEEE, 2019).

  73. 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).

    Article  ADS  Google Scholar 

  74. Cheng, Y. F. et al. Illumination pattern design with deep learning for single-shot Fourier ptychographic microscopy. Opt. Express 27, 644–656 (2019).

    Article  ADS  Google Scholar 

  75. 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).

    Article  Google Scholar 

  76. Muthumbi, A. et al. Learned sensing: jointly optimized microscope hardware for accurate image classification. Biomed. Opt. Express 10, 6351–6369 (2019).

    Article  Google Scholar 

  77. 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).

  78. Kellman, M., Bostan, E., Chen, M. & Waller, L. in 2019 IEEE International Conference on Computational Photography (ICCP) 1–8 (IEEE, 2017).

  79. 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).

    Article  Google Scholar 

  80. Sun, M. et al. Neural network model combined with pupil recovery for Fourier ptychographic microscopy. Opt. Express 27, 24161–24174 (2019).

    Article  ADS  Google Scholar 

  81. Zhang, Y. et al. PgNN: Physics-guided neural network for fourier ptychographic microscopy. Preprint at https://arxiv.org/abs/1909.08869 (2019).

  82. Zhang, J. et al. Forward imaging neural network with correction of positional misalignment for Fourier ptychographic microscopy. Opt. Express 28, 23164–23175 (2020).

    Article  ADS  Google Scholar 

  83. 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).

    MathSciNet  MATH  Google Scholar 

  84. Wang, R. et al. Virtual brightfield and fluorescence staining for Fourier ptychography via unsupervised deep learning. Opt. Lett. 45, 5405–5408 (2020).

    Article  ADS  Google Scholar 

  85. Ou, X., Chung, J., Horstmeyer, R. & Yang, C. Aperture scanning Fourier ptychographic microscopy. Biomed. Opt. Express 7, 3140–3150 (2016).

    Article  Google Scholar 

  86. He, X., Jiang, Z., Kong, Y., Wang, S. & Liu, C. Fourier ptychography via wavefront modulation with a diffuser. Opt. Commun. 459, 125057 (2020).

    Article  Google Scholar 

  87. Choi, G.-J. et al. Dual-wavelength Fourier ptychography using a single LED. Opt. Lett. 43, 3526–3529 (2018).

    Article  ADS  Google Scholar 

  88. He, X., Liu, C. & Zhu, J. Single-shot aperture-scanning Fourier ptychography. Opt. Express 26, 28187–28196 (2018).

    Article  ADS  Google Scholar 

  89. Holloway, J. et al. Toward long-distance subdiffraction imaging using coherent camera arrays. IEEE Trans. Comput. Imaging 2, 251–265 (2016).

    Article  MathSciNet  Google Scholar 

  90. 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).

    Article  ADS  Google Scholar 

  91. 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).

    Article  ADS  Google Scholar 

  92. Pacheco, S., Zheng, G. & Liang, R. Reflective Fourier ptychography. J. Biomed. Opt. 21, 026010 (2016).

    Article  ADS  Google Scholar 

  93. Lee, H., Chon, B. H. & Ahn, H. K. Reflective Fourier ptychographic microscopy using a parabolic mirror. Opt. Express 27, 34382–34391 (2019).

    Article  ADS  Google Scholar 

  94. Shen, C. et al. Computational aberration correction of VIS-NIR multispectral imaging microscopy based on Fourier ptychography. Opt. Express 27, 24923–24937 (2019).

    Article  ADS  Google Scholar 

  95. 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).

  96. Chan, A. C. et al. Parallel Fourier ptychographic microscopy for high-throughput screening with 96 cameras (96 eyes). Sci. Rep. 9, 11114 (2019).

    Article  ADS  Google Scholar 

  97. 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).

  98. Lee, B. et al. Single-shot phase retrieval via Fourier ptychographic microscopy. Optica 5, 976–983 (2018).

    Article  ADS  Google Scholar 

  99. He, X., Liu, C. & Zhu, J. Single-shot Fourier ptychography based on diffractive beam splitting. Opt. Lett. 43, 214–217 (2018).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  101. 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).

    Article  ADS  Google Scholar 

  102. Guo, K. et al. 13-fold resolution gain through turbid layer via translated unknown speckle illumination. Biomed. Opt. Express 9, 260–275 (2018).

    Article  Google Scholar 

  103. Zhang, H. et al. Near-field Fourier ptychography: super-resolution phase retrieval via speckle illumination. Opt. Express 27, 7498–7512 (2019).

    Article  ADS  Google Scholar 

  104. Yeh, L.-H., Chowdhury, S. & Waller, L. Computational structured illumination for high-content fluorescence and phase microscopy. Biomed. Opt. Express 10, 1978–1998 (2019).

    Article  Google Scholar 

  105. Dong, S., Nanda, P., Guo, K., Liao, J. & Zheng, G. Incoherent Fourier ptychographic photography using structured light. Photonics Res. 3, 19–23 (2015).

    Article  Google Scholar 

  106. Simons, H., Poulsen, H. F., Guigay, J. & Detlefs, C. X-ray Fourier ptychographic microscopy. Preprint at https://arxiv.org/abs/1609.07513 (2016).

  107. 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).

    Article  Google Scholar 

  108. 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).

    Article  Google Scholar 

  109. 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).

    Article  Google Scholar 

  110. Godden, T., Suman, R., Humphry, M., Rodenburg, J. & Maiden, A. Ptychographic microscope for three-dimensional imaging. Opt. Express 22, 12513–12523 (2014).

    Article  ADS  Google Scholar 

  111. Tian, L. & Waller, L. 3D intensity and phase imaging from light field measurements in an LED array microscope. Optica 2, 104–111 (2015).

    Article  ADS  Google Scholar 

  112. Chowdhury, S. et al. High-resolution 3D refractive index microscopy of multiple-scattering samples from intensity images. Optica 6, 1211–1219 (2019).

    Article  ADS  Google Scholar 

  113. Song, P. et al. Super-resolution microscopy via ptychographic structured modulation of a diffuser. Opt. Lett. 44, 3645–3648 (2019).

    Article  ADS  Google Scholar 

  114. 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).

    Article  ADS  Google Scholar 

  115. Ou, X., Horstmeyer, R., Yang, C. & Zheng, G. Quantitative phase imaging via Fourier ptychographic microscopy. Opt. Lett. 38, 4845–4848 (2013).

    Article  ADS  Google Scholar 

  116. Zheng, G. Breakthroughs in photonics 2013: Fourier ptychographic imaging. IEEE Photonics J. 6, 0701207 (2014).

    Article  Google Scholar 

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

    Article  Google Scholar 

  118. Williams, A. J. et al. Fourier ptychographic microscopy for filtration-based circulating tumor cell enumeration and analysis. J. Biomed. Opt. 19, 066007 (2014).

    Article  ADS  Google Scholar 

  119. 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).

    Article  Google Scholar 

  120. 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).

    Article  ADS  Google Scholar 

  121. 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).

    Article  ADS  Google Scholar 

  122. 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).

    Article  Google Scholar 

  123. 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).

    Article  MathSciNet  MATH  Google Scholar 

  124. Horstmeyer, R. et al. Solving ptychography with a convex relaxation. New J. Phys. 17, 053044 (2015).

    Article  ADS  Google Scholar 

  125. Hesse, R., Luke, D. R. & Neumann, P. Alternating projections and Douglas-Rachford for sparse affine feasibility. IEEE Trans. Signal Process. 62, 4868–4881 (2014).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  126. Heuke, S. et al. Coherent anti-stokes Raman Fourier ptychography. Opt. Express 27, 23497–23514 (2019).

    Article  ADS  Google Scholar 

  127. Goodman, J. W. Introduction to Fourier Optics 4th edn (Macmillan Learning, 2017).

  128. Horstmeyer, R., Ou, X., Chung, J., Zheng, G. & Yang, C. Overlapped Fourier coding for optical aberration removal. Opt. Express 22, 24062–24080 (2014).

    Article  ADS  Google Scholar 

  129. 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).

    Article  ADS  Google Scholar 

  130. Guo, K. et al. Microscopy illumination engineering using a low-cost liquid crystal display. Biomed. Opt. Express 6, 574–579 (2015).

    Article  ADS  Google Scholar 

  131. Dong, S., Bian, Z., Shiradkar, R. & Zheng, G. Sparsely sampled Fourier ptychography. Opt. Express 22, 5455–5464 (2014).

    Article  ADS  Google Scholar 

  132. Bian, L. et al. Motion-corrected Fourier ptychography. Biomed. Opt. Express 7, 4543–4553 (2016).

    Article  Google Scholar 

  133. Zhang, Y., Pan, A., Lei, M. & Yao, B. Data preprocessing methods for robust Fourier ptychographic microscopy. Optical Eng. 56, 123107 (2017).

    Article  ADS  Google Scholar 

  134. Pan, A., Zuo, C., Xie, Y., Lei, M. & Yao, B. Vignetting effect in Fourier ptychographic microscopy. Opt. Lasers Eng. 120, 40–48 (2019).

    Article  Google Scholar 

  135. Zuo, C., Sun, J. & Chen, Q. Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy. Opt. Express 24, 20724–20744 (2016).

    Article  ADS  Google Scholar 

  136. Bian, L. et al. Fourier ptychographic reconstruction using Wirtinger flow optimization. Opt. Express 23, 4856–4866 (2015).

    Article  ADS  Google Scholar 

  137. Bian, L. et al. Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient. Sci. Rep. 6, 27384 (2016).

    Article  ADS  Google Scholar 

  138. 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).

    Google Scholar 

  139. Bostan, E., Soltanolkotabi, M., Ren, D. & Waller, L. in 2018 25th IEEE International Conference on Image Processing (ICIP) 3823–3827 (IEEE, 2018).

  140. 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).

    Article  ADS  Google Scholar 

  141. Zhang, Y., Song, P., Zhang, J. & Dai, Q. Fourier ptychographic microscopy with sparse representation. Sci. Rep. 7, 8664 (2017).

    Article  ADS  Google Scholar 

  142. Zhang, Y., Cui, Z., Zhang, J., Song, P. & Dai, Q. Group-based sparse representation for Fourier ptychography microscopy. Opt. Commun. 404, 55–61 (2017).

    Article  ADS  Google Scholar 

  143. 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).

    Article  ADS  Google Scholar 

  144. Fan, Y., Sun, J., Chen, Q., Wang, M. & Zuo, C. Adaptive denoising method for Fourier ptychographic microscopy. Opt. Commun. 404, 23–31 (2017).

    Article  ADS  Google Scholar 

  145. Sun, Y. et al. in 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2019) 7665–7669 (IEEE, 2019).

  146. 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).

    Article  MathSciNet  Google Scholar 

  147. 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).

    Article  Google Scholar 

  148. Li, J. et al. High-speed in vitro intensity diffraction tomography. Adv. Photonics 1, 066004 (2019).

    Article  ADS  Google Scholar 

  149. Matlock, A. & Tian, L. High-throughput, volumetric quantitative phase imaging with multiplexed intensity diffraction tomography. Biomed. Opt. Express 10, 6432 (2019).

    Article  Google Scholar 

  150. Pham, T.-A. et al. Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering. Opt. Express 26, 2749–2763 (2018).

    Article  ADS  Google Scholar 

Download references

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).

Author information

Authors and Affiliations

Authors

Contributions

G.Z. prepared the display items. S.J. prepared the initial draft of the Supplementary Note. All authors contributed to all aspects of manuscript preparation, revision and editing.

Corresponding authors

Correspondence to Guoan Zheng or Changhuei Yang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Physics thanks Ashok Veeraraghavan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s42254-021-00280-y

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing