Abstract

High spatial resolution is the goal of many imaging systems. While designing a high-resolution lens with diffraction-limited performance over a large field of view remains a difficult task, creating a complex speckle pattern with wavelength-limited spatial features is easily accomplished with a simple random diffuser. With this observation and the concept of near-field ptychography, we report a new imaging modality, termed near-field Fourier ptychography, to address high-resolution imaging challenges in both microscopic and macroscopic imaging settings. ‘Near-field’ refers to placing the object at a short defocus distance with a large Fresnel number. We project a speckle pattern with fine spatial features on the object instead of directly resolving the spatial features via a high-resolution lens. We then translate the object (or speckle) to different positions and acquire the corresponding images by using a low-resolution lens. A ptychographic phase retrieval process is used to recover the complex object, the unknown speckle pattern, and the coherent transfer function at the same time. In a microscopic imaging setup, we use a 0.12 numerical aperture (NA) lens to achieve an NA of 0.85 in the reconstruction process. In a macroscale photographic imaging setup, we achieve ~7-fold resolution gain by using a photographic lens. The collection optics do not determine the final achievable resolution; rather, the speckle pattern’s feature size does. This is similar to our recent demonstration in fluorescence imaging settings (Guo et al., Biomed. Opt. Express, 9(1), 2018). The reported imaging modality can be employed in light, coherent X-ray, and transmission electron imaging systems to increase resolution and provide quantitative absorption and object phase contrast.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

2017 (5)

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] [PubMed]

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] [PubMed]

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
[Crossref] [PubMed]

L.-H. Yeh, L. Tian, and L. Waller, “Structured illumination microscopy with unknown patterns and a statistical prior,” Biomed. Opt. Express 8(2), 695–711 (2017).
[Crossref] [PubMed]

A. Maiden, D. Johnson, and P. Li, “Further improvements to the ptychographical iterative engine,” Optica 4(7), 736–745 (2017).
[Crossref]

2016 (3)

2015 (8)

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

S. Dong, P. Nanda, K. Guo, J. Liao, and G. Zheng, “Incoherent Fourier ptychographic photography using structured light,” Photon. Res. 3(1), 19–23 (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] [PubMed]

H. Yilmaz, E. G. van Putten, J. Bertolotti, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Speckle correlation resolution enhancement of wide-field fluorescence imaging,” Optica 2(5), 424–429 (2015).
[Crossref]

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
[Crossref] [PubMed]

C. Kuang, Y. Ma, R. Zhou, J. Lee, G. Barbastathis, R. R. Dasari, Z. Yaqoob, and P. T. So, “Digital micromirror device-based laser-illumination Fourier ptychographic microscopy,” Opt. Express 23(21), 26999–27010 (2015).
[Crossref] [PubMed]

S. Dong, K. Guo, S. Jiang, and G. Zheng, “Recovering higher dimensional image data using multiplexed structured illumination,” Opt. Express 23(23), 30393–30398 (2015).
[Crossref] [PubMed]

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), 33214–33240 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (4)

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3(1), 1927 (2013).
[Crossref] [PubMed]

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3(1), 2075 (2013).
[Crossref] [PubMed]

A. Jost and R. Heintzmann, “Superresolution Multidimensional Imaging with Structured Illumination Microscopy,” Annu. Rev. Mater. Res. 43(1), 261–282 (2013).
[Crossref]

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

2012 (3)

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J.-C. Olivo-Marin, “Bayesian estimation for optimized structured illumination microscopy,” IEEE Trans. Image Process. 21(2), 601–614 (2012).
[Crossref] [PubMed]

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

2011 (1)

2009 (2)

Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17(15), 12285–12292 (2009).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

2006 (1)

2004 (1)

2001 (1)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

1988 (1)

Allain, M.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Almoro, P.

Badizadegan, K.

Baird, M. A.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Barbastathis, G.

Beach, J. R.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Belkebir, K.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Bertolotti, J.

Betzig, E.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Bian, Z.

Birri, M.

Borca, C.

Cederquist, J. N.

Chakrova, N.

Chen, B.-C.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Chen, M.

Chen, Q.

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] [PubMed]

Choi, C.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3(1), 2075 (2013).
[Crossref] [PubMed]

Choi, W.

Chung, J.

Clare, R. M.

Cloetens, P.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3(1), 1927 (2013).
[Crossref] [PubMed]

Coskun, A. F.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Cossairt, O.

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] [PubMed]

Dasari, R.

Dasari, R. R.

David, C.

Davidson, M. W.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Dierolf, M.

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3(1), 1927 (2013).
[Crossref] [PubMed]

Dong, J.

Dong, S.

Dubertret, B.

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J.-C. Olivo-Marin, “Bayesian estimation for optimized structured illumination microscopy,” IEEE Trans. Image Process. 21(2), 601–614 (2012).
[Crossref] [PubMed]

Eldar, Y. C.

Enders, B.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3(1), 1927 (2013).
[Crossref] [PubMed]

Falkenberg, G.

Feld, M. S.

Fienup, J. R.

Girard, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Göröcs, Z.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Greenbaum, A.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Grolimund, D.

Guizar-Sicairos, M.

Günaydin, H.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Science &Amp. Applications 7(2), 17141 (2018).
[Crossref]

Guo, K.

K. Guo, Z. Zhang, S. Jiang, J. Liao, J. Zhong, Y. C. Eldar, and G. Zheng, “13-fold resolution gain through turbid layer via translated unknown speckle illumination,” Biomed. Opt. Express 9(1), 260–275 (2018).
[Crossref] [PubMed]

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 (2016).
[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] [PubMed]

S. Dong, P. Nanda, K. Guo, J. Liao, and G. Zheng, “Incoherent Fourier ptychographic photography using structured light,” Photon. Res. 3(1), 19–23 (2015).
[Crossref]

S. Dong, K. Guo, S. Jiang, and G. Zheng, “Recovering higher dimensional image data using multiplexed structured illumination,” Opt. Express 23(23), 30393–30398 (2015).
[Crossref] [PubMed]

S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856–20870 (2014).
[Crossref] [PubMed]

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), 3305–3310 (2014).
[Crossref] [PubMed]

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), 13586–13599 (2014).
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Gustafsson, M. G.

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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Hammer, J. A.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Heintzmann, R.

A. Jost and R. Heintzmann, “Superresolution Multidimensional Imaging with Structured Illumination Microscopy,” Annu. Rev. Mater. Res. 43(1), 261–282 (2013).
[Crossref]

Holloway, J.

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] [PubMed]

Horstmeyer, R.

Humphry, M. J.

Ishikawa, T.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
[Crossref] [PubMed]

Isikman, S. O.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Jang, J.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3(1), 2075 (2013).
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Jeong, K.-H.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3(1), 2075 (2013).
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W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[Crossref] [PubMed]

Jiang, S.

Johnson, D.

Jost, A.

A. Jost and R. Heintzmann, “Superresolution Multidimensional Imaging with Structured Illumination Microscopy,” Annu. Rev. Mater. Res. 43(1), 261–282 (2013).
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Keum, D.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3(1), 2075 (2013).
[Crossref] [PubMed]

Kirchhausen, T.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Kohmura, Y.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
[Crossref] [PubMed]

Kreuzer, H. J.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[Crossref] [PubMed]

Kuang, C.

Lagendijk, A.

Le Moal, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Lee, J.

Li, D.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Li, P.

Li, X.

Liao, J.

Loriette, V.

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J.-C. Olivo-Marin, “Bayesian estimation for optimized structured illumination microscopy,” IEEE Trans. Image Process. 21(2), 601–614 (2012).
[Crossref] [PubMed]

Lu, H.

Luo, W.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Ma, Y.

Maiden, A.

Maiden, A. M.

A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28(4), 604–612 (2011).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

Marron, J. C.

Matsuyama, S.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
[Crossref] [PubMed]

McDermott, S.

Meinertzhagen, I. A.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[Crossref] [PubMed]

Menzel, A.

Meyer, B.

Milkie, D. E.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Min, J.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3(1), 2075 (2013).
[Crossref] [PubMed]

Moses, B.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Mosk, A. P.

Mudanyali, O.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Mudry, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Nanda, P.

Nicoletti, C.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Okada, H.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
[Crossref] [PubMed]

Olivo-Marin, J.-C.

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J.-C. Olivo-Marin, “Bayesian estimation for optimized structured illumination microscopy,” IEEE Trans. Image Process. 21(2), 601–614 (2012).
[Crossref] [PubMed]

Orieux, F.

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J.-C. Olivo-Marin, “Bayesian estimation for optimized structured illumination microscopy,” IEEE Trans. Image Process. 21(2), 601–614 (2012).
[Crossref] [PubMed]

Osten, W.

Ou, X.

Ozcan, A.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Science &Amp. Applications 7(2), 17141 (2018).
[Crossref]

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Park, Y.

Pasham, M.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Patommel, J.

Paxman, R. G.

Pedrini, G.

Pfeiffer, F.

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3(1), 1927 (2013).
[Crossref] [PubMed]

Ramchandran, K.

Rieger, B.

Rivenson, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Science &Amp. Applications 7(2), 17141 (2018).
[Crossref]

Rodenburg, J. M.

A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28(4), 604–612 (2011).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

Ryu, S.-W.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3(1), 2075 (2013).
[Crossref] [PubMed]

Savatier, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Sentenac, A.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012).
[Crossref]

Sepulveda, E.

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J.-C. Olivo-Marin, “Bayesian estimation for optimized structured illumination microscopy,” IEEE Trans. Image Process. 21(2), 601–614 (2012).
[Crossref] [PubMed]

Shao, L.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Sharma, M. K.

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] [PubMed]

Sheppard, C. J.

Shiradkar, R.

So, P. T.

Soltanolkotabi, M.

Stallinga, S.

Stockmar, M.

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3(1), 1927 (2013).
[Crossref] [PubMed]

Su, T.-W.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Sun, J.

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] [PubMed]

Tang, G.

Teng, D.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Science &Amp. Applications 7(2), 17141 (2018).
[Crossref]

Thibault, P.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3(1), 1927 (2013).
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Tian, L.

van Putten, E. G.

Veeraraghavan, A.

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] [PubMed]

Vos, W. L.

Waller, L.

Wellenreuther, G.

Willimann, M.

Wu, Y.

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] [PubMed]

Xin, H.

Xu, P.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Xu, W.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[Crossref] [PubMed]

Xue, L.

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
[Crossref] [PubMed]

Yabashi, M.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
[Crossref] [PubMed]

Yamada, J.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
[Crossref] [PubMed]

Yamauchi, K.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
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Yang, C.

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), 4787–4802 (2016).
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G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
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Yaqoob, Z.

Yasuda, S.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
[Crossref] [PubMed]

Ye, J. C.

J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3(1), 2075 (2013).
[Crossref] [PubMed]

Yeh, L.-H.

Yilmaz, H.

Zanette, I.

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3(1), 1927 (2013).
[Crossref] [PubMed]

Zhang, F.

Zhang, L.

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] [PubMed]

Zhang, M.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Zhang, X.

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[Crossref] [PubMed]

Zhang, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Science &Amp. Applications 7(2), 17141 (2018).
[Crossref]

Zhang, Z.

Zheng, G.

K. Guo, Z. Zhang, S. Jiang, J. Liao, J. Zhong, Y. C. Eldar, and G. Zheng, “13-fold resolution gain through turbid layer via translated unknown speckle illumination,” Biomed. Opt. Express 9(1), 260–275 (2018).
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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 (2016).
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S. Dong, P. Nanda, K. Guo, J. Liao, and G. Zheng, “Incoherent Fourier ptychographic photography using structured light,” Photon. Res. 3(1), 19–23 (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] [PubMed]

S. Dong, K. Guo, S. Jiang, and G. Zheng, “Recovering higher dimensional image data using multiplexed structured illumination,” Opt. Express 23(23), 30393–30398 (2015).
[Crossref] [PubMed]

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), 3305–3310 (2014).
[Crossref] [PubMed]

S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856–20870 (2014).
[Crossref] [PubMed]

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), 13586–13599 (2014).
[Crossref] [PubMed]

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

Zhong, J.

Zhou, H.

Zhou, R.

Zuo, C.

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] [PubMed]

Annu. Rev. Mater. Res. (1)

A. Jost and R. Heintzmann, “Superresolution Multidimensional Imaging with Structured Illumination Microscopy,” Annu. Rev. Mater. Res. 43(1), 261–282 (2013).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (5)

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 (2016).
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IEEE Trans. Image Process. (1)

F. Orieux, E. Sepulveda, V. Loriette, B. Dubertret, and J.-C. Olivo-Marin, “Bayesian estimation for optimized structured illumination microscopy,” IEEE Trans. Image Process. 21(2), 601–614 (2012).
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J. Microsc. (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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J. Opt. Soc. Am. A (3)

Light: Science &Amp. Applications (1)

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Science &Amp. Applications 7(2), 17141 (2018).
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Nat. Methods (1)

A. Greenbaum, W. Luo, T.-W. Su, Z. Göröcs, L. Xue, S. O. Isikman, A. F. Coskun, O. Mudanyali, and A. Ozcan, “Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy,” Nat. Methods 9(9), 889–895 (2012).
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Nat. Photonics (2)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
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Opt. Express (10)

S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856–20870 (2014).
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S. Dong, K. Guo, S. Jiang, and G. Zheng, “Recovering higher dimensional image data using multiplexed structured illumination,” Opt. Express 23(23), 30393–30398 (2015).
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Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17(15), 12285–12292 (2009).
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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), 13586–13599 (2014).
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R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
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S. McDermott and A. Maiden, “Near-field ptychographic microscope for quantitative phase imaging,” Opt. Express 26(19), 25471–25480 (2018).
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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), 33214–33240 (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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Opt. Lett. (1)

Optica (2)

Photon. Res. (1)

Proc. Natl. Acad. Sci. U.S.A. (1)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
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Sci. Adv. (1)

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).
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Sci. Rep. (4)

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).
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J. Min, J. Jang, D. Keum, S.-W. Ryu, C. Choi, K.-H. Jeong, and J. C. Ye, “Fluorescent microscopy beyond diffraction limits using speckle illumination and joint support recovery,” Sci. Rep. 3(1), 2075 (2013).
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M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3(1), 1927 (2013).
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S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field X-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
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Science (1)

D. Li, L. Shao, B.-C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
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Ultramicroscopy (1)

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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Other (1)

K. Wakonig, A. Diaz, A. Bonnin, M. Stampanoni, A. Bergamaschi, J. Ihli, M. Guizar-Sicairos, and A. Menzel, “X-ray Fourier ptychography,” Science Advances 5, eaav0282 (2019).

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Figures (14)

Fig. 1
Fig. 1 The near-field Fourier ptychography approach for super-resolution phase retrieval. (a) - (b) The experimental setup, where the object is placed at a short defocus distance to convert complex amplitude into intensity variations. A translated spackle pattern is used for sample illumination and the captured images are used for super-resolution phase retrieval. The captured images of an amplitude (c1) and phase (c2) object under uniform illumination. The recovered intensity (d1) and phase (d2) of the amplitude and the phase object.
Fig. 2
Fig. 2 The flowchart of the recovery process.
Fig. 3
Fig. 3 The outline of the recovery algorithm.
Fig. 4
Fig. 4 Simulation of the near-field FP for super-resolution phase retrieval. (a) The ground-truth object. (b) The simulated raw image under speckle and uniform illumination. Near-field FP recoveries by placing the object at a 40-μm defocus distance (c) and in-focus position (d). (e) The recovered Fourier spectrum for (c), where the circle indicates the original CTF.
Fig. 5
Fig. 5 The imaging performance with different numbers of translated positions and different noise levels. (a)-(b) The recovered object with different numbers of translated positions. (c) The RMS errors are plotted as a function of iterations. (d)-(e) The recovered object with different noise levels; the performance is quantified via the RMS error in (f).
Fig. 6
Fig. 6 Near-field FP for microscopy imaging. The captured raw image under uniform illumination (a) and speckle illumination (b). (c) The recovered object using different numbers of translated positions, with an unknown speckle pattern. (d) The recovered object using different numbers of translated positions and with a pre-recovered speckle pattern.
Fig. 7
Fig. 7 Quantitative phase recovery via the near-field FP. The captured raw image under (a) uniform illumination and (b) speckle illumination. The recovered phase by placing the target at the 40-μm defocused distance (c) and the in-focus position (d). The phase profiles are plotted along the red and black dash arc in (c) and (d).
Fig. 8
Fig. 8 Experimental demonstration of a blood smear sample using the reported approach. (a) The captured image of blood smear under uniform illumination (a) and speckle illumination (b). (c) The recovered intensity and phase using the near-field FP.
Fig. 9
Fig. 9 Wide-field, high-resolution imaging via the near-field FP. (a) The recovered gigapixel intensity image of a blood smear section, with a field of view of 6.6 mm by 4.5 mm. (b1)-(b3) show three magnified view of (a). (c1)-(c3) The captured images under uniform illumination.
Fig. 10
Fig. 10 Near-field FP for macroscale photographic imaging. (a) The experimental setup, where we use a diffuser and a large plano-convex lens to project the laser speckles onto the object. We use the same image-plane defocus distance as the microscope setup in Fig. 1(a). (b) The captured image of the USAF resolution target under uniform illumination. (c) The captured raw near-field FP image under speckle illumination. (d1) The high-resolution recovered object using the reported approach. (d2) The magnified view of the resolution target.
Fig. 11
Fig. 11 The simulated high-resolution amplitude (a) and phase (b) of the input object.
Fig. 12
Fig. 12 The simulated CTF for low-resolution image generation. (a) The amplitude of simulated CTF. (b) The phase of simulated CTF with defocus aberration. The intensity of captured low-resolution image without aberration (c) and with the defocus aberration (d).
Fig. 13
Fig. 13 The simulated captured low-resolution image sequence. (a) The first generated low-resolution measurement. The initial guess of the high-resolution object (b) and speckle (c).
Fig. 14
Fig. 14 The recovered high-resolution amplitude (a), phase (b), and the speckle (c).

Equations (5)

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I j (x,y)= | (O(x x j ,y y j )P(x,y))PSF(x,y) | 2
Φ j ( k x , k y )= Φ j ( k x , k y )+ γ ϕ conj(CTF)( Ψ j ( k x , k y ) Ψ j ( k x , k y )) max( | CTF | 2 )
CTF=CTF+ γ CTF conj( Φ j ( k x , k y ))( Ψ j ( k x , k y ) Ψ j ( k x , k y )) max( | Φ j ( k x , k y ) | 2 )
O j (x x j ,y y j )= O j (x x j ,y y j )+ conj( P j (x,y))( φ j (x x j ,y y j ) φ j (x x j ,y y j )) (1 α obj ) | P j (x,y) | 2 + α obj max( | P j (x,y) | 2 )
P j (x,y)= P j (x,y)+ conj( O j (x x j ,y y j ))( φ j (x x j ,y y j ) φ j (x x j ,y y j )) (1 α P ) | O j (x x j ,y y j ) | 2 + α P max( | O j (x x j ,y y j ) | 2 )

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