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Wide-field, high-resolution Fourier ptychographic microscopy

A Corrigendum to this article was published on 27 August 2015

This article has been updated


We report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and digitally extend a microscope's depth of focus beyond the physical limitations of its optics.As a demonstration, we built a microscope prototype with a half-pitch resolution of 0.78 µm, a field of view of 120 mm2 and a resolution-invariant depth of focus of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify successful FPM operation. The reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one that is coupled to the physical limitations of the system's optics to one that is solvable through computation.

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Figure 1: Iterative recovery procedure of FPM (five steps).
Figure 2: FPM prototype set-up.
Figure 3: Extending the depth of focus with digital wavefront correction.
Figure 4: Gigapixel colour imaging via FPM.

Change history

  • 30 July 2015

    In the version of this Article originally published, the reported resolution for the microscope was the half-pitch resolution. However, the authors believe that with either coherent or incoherent light, full-pitch resolution offers a better definition of the imaging system limit. Therefore, the reported resolutions should have been 0.78 μm and 1.56 μm for half-pitch and full-pitch resolution, respectively. The achieved space–bandwidth product (SBP), defined for a complex signal using full-pitch resolution, is then ~0.23 x 109 pixels and the complex signal's Nyquist pixel area is 0.782 μm2. These corrections have been made in the online versions of the Article and Supplementary Note 3.


  1. 1

    Lohmann, A. W., Dorsch, R. G., Mendlovic, D., Zalevsky, Z. & Ferreira, C. Space–bandwidth product of optical signals and systems. J. Opt. Soc. Am. A 13, 470–473 (1996).

    ADS  Article  Google Scholar 

  2. 2

    Denis, L., Lorenz, D., Thiébaut, E., Fournier, C. & Trede, D. Inline hologram reconstruction with sparsity constraints. Opt. Lett. 34, 3475–3477 (2009).

    ADS  Article  Google Scholar 

  3. 3

    Xu, W., Jericho, M., Meinertzhagen, I. & Kreuzer, H. Digital in-line holography for biological applications. Proc. Natl Acad. Sci. USA 98, 11301–11305 (2001).

    ADS  Article  Google Scholar 

  4. 4

    Greenbaum, A. et al. Increased space–bandwidth product in pixel super-resolved lensfree on-chip microscopy. Sci. Rep. 3, 1717 (2013).

    Article  Google Scholar 

  5. 5

    Zheng, G., Lee, S. A., Antebi, Y., Elowitz, M. B. & Yang, C. The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM). Proc. Natl Acad. Sci. USA 108, 16889–16894 (2011).

    ADS  Article  Google Scholar 

  6. 6

    Zheng, G., Lee, S. A., Yang, S. & Yang, C. Sub-pixel resolving optofluidic microscope for on-chip cell imaging. Lab Chip 10, 3125–3129 (2010).

    Article  Google Scholar 

  7. 7

    Turpin, T., Gesell, L., Lapides, J. & Price, C. Theory of the synthetic aperture microscope. Proc. SPIE 2566, 230–240 (1995).

    ADS  Article  Google Scholar 

  8. 8

    Di, J. et al. 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, 5654–5659 (2008).

    ADS  Article  Google Scholar 

  9. 9

    Hillman, T. R., Gutzler, T., Alexandrov, S. A. & Sampson, D. D. High-resolution, wide-field object reconstruction with synthetic aperture Fourier holographic optical microscopy. Opt. Express 17, 7873–7892 (2009).

    ADS  Article  Google Scholar 

  10. 10

    Granero, L., Micó, V., Zalevsky, Z. & García, J. Synthetic aperture superresolved microscopy in digital lensless Fourier holography by time and angular multiplexing of the object information. Appl. Opt. 49, 845–857 (2010).

    ADS  Article  Google Scholar 

  11. 11

    Kim, M. et al. High-speed synthetic aperture microscopy for live cell imaging. Opt. Lett. 36, 148–150 (2011).

    ADS  Article  Google Scholar 

  12. 12

    Schwarz, C. J., Kuznetsova, Y. & Brueck, S. Imaging interferometric microscopy. Opt. Lett. 28, 1424–1426 (2003).

    ADS  Article  Google Scholar 

  13. 13

    Feng, P., Wen, X. & Lu, R. Long-working-distance synthetic aperture Fresnel off-axis digital holography. Opt. Express 17, 5473–5480 (2009).

    ADS  Article  Google Scholar 

  14. 14

    Mico, V., Zalevsky, Z., García-Martínez, P. & García, J. Synthetic aperture superresolution with multiple off-axis holograms. J. Opt. Soc. Am. A 23, 3162–3170 (2006).

    ADS  Article  Google Scholar 

  15. 15

    Yuan, C., Zhai, H. & Liu, H. Angular multiplexing in pulsed digital holography for aperture synthesis. Opt. Lett. 33, 2356–2358 (2008).

    ADS  Article  Google Scholar 

  16. 16

    Mico, V., Zalevsky, Z. & García, J. Synthetic aperture microscopy using off-axis illumination and polarization coding. Opt. Commun. 276, 209–217 (2007).

    ADS  Article  Google Scholar 

  17. 17

    Alexandrov, S. & Sampson, D. Spatial information transmission beyond a system's diffraction limit using optical spectral encoding of the spatial frequency. J. Opt. 10, 025304 (2008).

    Google Scholar 

  18. 18

    Tippie, A. E., Kumar, A. & Fienup, J. R. High-resolution synthetic-aperture digital holography with digital phase and pupil correction. Opt. Express 19, 12027–12038 (2011).

    ADS  Article  Google Scholar 

  19. 19

    Gutzler, T., Hillman, T. R., Alexandrov, S. A. & Sampson, D. D. Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue. Opt. Lett. 35, 1136–1138 (2010).

    ADS  Article  Google Scholar 

  20. 20

    Alexandrov, S. A., Hillman, T. R., Gutzler, T. & Sampson, D. D. Synthetic aperture Fourier holographic optical microscopy. Phys. Rev. Lett. 97, 168102 (2006).

    ADS  Article  Google Scholar 

  21. 21

    Rodenburg, J. M. & Bates, R. H. T. The theory of super-resolution electron microscopy via Wigner-distribution deconvolution. Phil. Trans. R. Soc. Lond. A 339, 521–553 (1992).

    ADS  Article  Google Scholar 

  22. 22

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

    ADS  Article  Google Scholar 

  23. 23

    Rodenburg, J. M. et al. Hard-X-ray lensless imaging of extended objects. Phys. Rev. Lett. 98, 034801 (2007).

    ADS  Article  Google Scholar 

  24. 24

    Thibault, P. et al. High-resolution scanning X-ray diffraction microscopy. Science 321, 379–382 (2008).

    ADS  Article  Google Scholar 

  25. 25

    Dierolf, M. et al. Ptychographic coherent diffractive imaging of weakly scattering specimens. New J. Phys. 12, 035017 (2010).

    ADS  Article  Google Scholar 

  26. 26

    Maiden, A. M., Rodenburg, J. M. & Humphry, M. J. Optical ptychography: a practical implementation with useful resolution. Opt. Lett. 35, 2585–2587 (2010).

    ADS  Article  Google Scholar 

  27. 27

    Humphry, M., Kraus, B., Hurst, A., Maiden, A. & Rodenburg, J. Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging. Nat. Commun. 3, 730 (2012).

    ADS  Article  Google Scholar 

  28. 28

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

    ADS  Article  Google Scholar 

  29. 29

    Fienup, J. R. Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint. J. Opt. Soc. Am. A 4, 118–123 (1987).

    ADS  Article  Google Scholar 

  30. 30

    Fienup, J. R. Reconstruction of an object from the modulus of its Fourier transform. Opt. Lett. 3, 27–29 (1978).

    ADS  Article  Google Scholar 

  31. 31

    Fienup, J. R. Lensless coherent imaging by phase retrieval with an illumination pattern constraint. Opt. Express 14, 498–508 (2006).

    ADS  Article  Google Scholar 

  32. 32

    Levoy, M., Ng, R., Adams, A., Footer, M. & Horowitz, M. Light field microscopy. ACM Trans. Graphics 25, 924–934 (2006).

    Article  Google Scholar 

  33. 33

    Levoy, M., Zhang, Z. & McDowall, I. Recording and controlling the 4D light field in a microscope using microlens arrays. J. Microsc. 235, 144–162 (2009).

    MathSciNet  Article  Google Scholar 

  34. 34

    Arimoto, H. & Javidi, B. Integral three-dimensional imaging with digital reconstruction. Opt. Lett. 26, 157–159 (2001).

    ADS  Article  Google Scholar 

  35. 35

    Hong, S.-H., Jang, J.-S. & Javidi, B. Three-dimensional volumetric object reconstruction using computational integral imaging. Opt. Express 12, 483–491 (2004).

    ADS  Article  Google Scholar 

  36. 36

    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 

  37. 37

    Tyson, R. Principles of Adaptive Optics (CRC Press, 2010).

  38. 38

    Brady, D. et al. Multiscale gigapixel photography. Nature 486, 386–389 (2012).

    ADS  Article  Google Scholar 

  39. 39

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

    ADS  Article  Google Scholar 

  40. 40

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

    ADS  Article  Google Scholar 

  41. 41

    Colomb, T. et al. Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation. Appl. Opt. 45, 851–863 (2006).

    ADS  Article  Google Scholar 

  42. 42

    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).

    ADS  Article  Google Scholar 

  43. 43

    Wu, J. et al. Wide field-of-view microscope based on holographic focus grid illumination. Opt. Lett. 35, 2188–2190 (2010).

    ADS  Article  Google Scholar 

  44. 44

    Wu, J., Zheng, G., Li, Z. & Yang, C. Focal plane tuning in wide-field-of-view microscope with Talbot pattern illumination. Opt. Lett. 36, 2179–2181 (2011).

    ADS  Article  Google Scholar 

  45. 45

    Reinhard, E. et al. High Dynamic Range Imaging: Acquisition, Display, and Image-based Lighting (Morgan Kaufmann, 2010).

  46. 46

    Gunturk, B. K. & Li, X. Image Restoration: Fundamentals and Advances Vol. 7 (CRC Press, 2012).

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The authors thank Xiaoze Ou for discussions and help with experiments. The authors acknowledge funding support from the National Institutes of Health (grant no. 1DP2OD007307-01).

Author information




G.Z. initiated this line of investigation, designed and implemented the project. G.Z., R.H. and C.Y. contributed, developed, refined the concept and wrote the paper.

Corresponding author

Correspondence to Guoan Zheng.

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Competing interests

G.Z. and C.Y. are named inventors on a number of related patent applications. G.Z. and C.Y. also have a competing financial interest in Clearbridge Biophotonics and ePetri, Inc., which, however, did not support this work.

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

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