Abstract

This paper presents a technique to image the complex index of refraction of a sample across three dimensions. The only required hardware is a standard microscope and an array of LEDs. The method, termed Fourier ptychographic tomography (FPT), first captures a sequence of intensity-only images of a sample under angularly varying illumination. Then, using principles from ptychography and diffraction tomography, it computationally solves for the sample structure in three dimensions. The experimental microscope demonstrates a lateral spatial resolution of 0.39 μm and an axial resolution of 3.7 μm at the Nyquist–Shannon sampling limit (0.54 and 5.0 μm at the Sparrow limit, respectively) across a total imaging depth of 110 μm. Unlike competing methods, this technique quantitatively measures the volumetric refractive index of primarily transparent and contiguous sample features without the need for interferometry or any moving parts. Wide field-of-view reconstructions of thick biological specimens suggest potential applications in pathology and developmental biology.

© 2016 Optical Society of America

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2015 (8)

2014 (6)

2013 (4)

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

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

K. Chung and K. Deisseroth, “CLARITY for mapping the nervous system,” Nat. Methods 10, 508–513 (2013).
[Crossref]

M. Broxton, L. Grosenick, S. Yang, N. Cohen, A. Andalman, K. Deisseroth, and M. Levoy, “Wave optics theory and 3D deconvolution for the light field microscope,” Opt. Express 21, 25418–25439 (2013).
[Crossref]

2012 (2)

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
[Crossref]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

2011 (1)

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

2010 (6)

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics 10, 1–6 (2010).

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

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7, 603–614 (2010).
[Crossref]

K. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[Crossref]

G. Hamanaka, M. Matsumoto, M. Imoto, and H. Kaneko, “Mesenchyme cells can function to induce epithelial cell proliferation in starfish embryos,” Dev. Dyn. 239, 818–827 (2010).
[Crossref]

C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, H. M. Quiney, B. Abbey, K. A. Nugent, and I. McNulty, “Fresnel coherent diffraction tomography,” Opt. Express 18, 11746–11753 (2010).
[Crossref]

2009 (1)

2008 (4)

M. D’Urso, K. Belkebir, L. Crocco, T. Isernia, and A. Liftman, “Phaseless imaging with experimental data: facts and challenges,” J. Opt. Soc. Am. A 25, 271–281 (2008).
[Crossref]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
[Crossref]

2007 (2)

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

Y. Huang and M. A. Anastasio, “Statistically principled use of in-line measurements in intensity diffraction tomography,” J. Opt. Soc. Am. A 24, 626–642 (2007).
[Crossref]

2006 (1)

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
[Crossref]

2005 (1)

2004 (1)

2002 (4)

2000 (1)

G. A. Tsihrintzis and A. J. Devaney, “Higher-order diffraction tomography: reconstruction algorithms and computer simulation,” IEEE Trans. Image Process. 9, 1560–1572 (2000).
[Crossref]

1998 (1)

1997 (1)

T. Takenaka, D. J. N. Wall, H. Harada, and M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
[Crossref]

1995 (1)

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

1993 (1)

1992 (1)

1989 (2)

Y. M. Wang and W. C. Chew, “An iterative solution of the two-dimensional electromagnetic inverse scattering problem,” Int. J. Imaging Syst. Technol. 1, 100–108 (1989).
[Crossref]

A. J. Devaney, “Structure determination from intensity measurements in scattering experiments,” Phys. Rev. Lett. 62, 2385–2388 (1989).
[Crossref]

1985 (1)

1984 (1)

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[Crossref]

1981 (2)

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[Crossref]

Abbey, B.

Adie, S. G.

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

Agard, D. A.

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[Crossref]

Agassiz, A.

A. Agassiz, Embryologic of the Starfish, in Vol. 5 of L. Agassiz Contributions to the Natural History of the United States (Cambridge, 1864), 76 p.

Ahmad, A.

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

Ames, B.

R. Horstmeyer, R. C. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New. J. Phys. 17, 053044 (2015).
[Crossref]

Anastasio, M. A.

Andalman, A.

Babacan, S. D.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White light diffraction tomography of unlabeled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Badizadegan, K.

Batey, D. J.

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

Beaurepaire, E.

Belkebir, K.

Bian, L.

Bishara, W.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Boccara, A. C.

Boppart, S. A.

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Boyden, E. S.

F. Chen, P. W. Tillberg, and E. S. Boyden, “Expansion microscopy,” Science 347, 543–548 (2015).
[Crossref]

Bronnikov, A. V.

Brown, W. J.

Broxton, M.

Bunk, O.

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Carney, P. S.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White light diffraction tomography of unlabeled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

Chen, B.

Chen, F.

Chen, M.

Chen, R. C.

R. Horstmeyer, R. C. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New. J. Phys. 17, 053044 (2015).
[Crossref]

Chew, W. C.

Y. M. Wang and W. C. Chew, “An iterative solution of the two-dimensional electromagnetic inverse scattering problem,” Int. J. Imaging Syst. Technol. 1, 100–108 (1989).
[Crossref]

Choi, W.

Choi, Y.

Chung, K.

K. Chung and K. Deisseroth, “CLARITY for mapping the nervous system,” Nat. Methods 10, 508–513 (2013).
[Crossref]

Cohen, N.

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Crocco, L.

D’Urso, M.

Dai, Q.

Dasari, R. R.

Davis, T. J.

Debailleul, M.

M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
[Crossref]

Deisseroth, K.

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Devaney, A. J.

G. A. Tsihrintzis and A. J. Devaney, “Higher-order diffraction tomography: reconstruction algorithms and computer simulation,” IEEE Trans. Image Process. 9, 1560–1572 (2000).
[Crossref]

M. H. Maleki and A. J. Devaney, “Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993).
[Crossref]

M. H. Maleki, A. J. Devaney, and A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
[Crossref]

A. J. Devaney, “Structure determination from intensity measurements in scattering experiments,” Phys. Rev. Lett. 62, 2385–2388 (1989).
[Crossref]

Dierolf, M.

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Dong, J.

Donk, J. V.

Dubois, A.

Edo, T. B.

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

Eldar, Y. C.

K. Jaganathan, Y. C. Eldar, and B. Hassibi, “Phase retrieval: an overview of recent developments,” arXiv:1510.07713v1 (2015).

Fang-Yen, C.

Feld, M. S.

Feng, S.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
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Georges, V.

M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
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Gerke, T. D.

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics 10, 1–6 (2010).

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T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White light diffraction tomography of unlabeled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Godden, T. M.

Goy, A.

Graf, B. W.

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
[Crossref]

Grosenick, L.

Guo, K.

Gureyev, T. E.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
[Crossref]

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born and Rytov-type approximations,” Appl. Opt. 43, 2418–2430 (2004).
[Crossref]

Haeberle, O.

M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
[Crossref]

Hamanaka, G.

G. Hamanaka, M. Matsumoto, M. Imoto, and H. Kaneko, “Mesenchyme cells can function to induce epithelial cell proliferation in starfish embryos,” Dev. Dyn. 239, 818–827 (2010).
[Crossref]

Harada, H.

T. Takenaka, D. J. N. Wall, H. Harada, and M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
[Crossref]

Hassibi, B.

K. Jaganathan, Y. C. Eldar, and B. Hassibi, “Phase retrieval: an overview of recent developments,” arXiv:1510.07713v1 (2015).

Horstmeyer, R.

R. Horstmeyer, R. C. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New. J. Phys. 17, 053044 (2015).
[Crossref]

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

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

Hosseini, P.

Huang, Y.

Humphry, M. J.

Imoto, M.

G. Hamanaka, M. Matsumoto, M. Imoto, and H. Kaneko, “Mesenchyme cells can function to induce epithelial cell proliferation in starfish embryos,” Dev. Dyn. 239, 818–827 (2010).
[Crossref]

Isernia, T.

Isikman, S. O.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
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Jaganathan, K.

K. Jaganathan, Y. C. Eldar, and B. Hassibi, “Phase retrieval: an overview of recent developments,” arXiv:1510.07713v1 (2015).

Johnson, I.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Kamilov, U. S.

Kaneko, H.

G. Hamanaka, M. Matsumoto, M. Imoto, and H. Kaneko, “Mesenchyme cells can function to induce epithelial cell proliferation in starfish embryos,” Dev. Dyn. 239, 818–827 (2010).
[Crossref]

Kang, J. W.

Kewish, C. M.

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

Kim, K.

Kim, T.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White light diffraction tomography of unlabeled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Kynde, S.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Lagasse, P. E.

Lau, R.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Lauer, V.

M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
[Crossref]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
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Lee, K.

Levinson, H.

Levoy, M.

Li, P.

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

Li, X.

Liftman, A.

Magistretti, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Maher, J. R.

Maiden, A. M.

Maleki, M. H.

Marchesini, S.

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

Marquet, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Marti, O.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Matsumoto, M.

G. Hamanaka, M. Matsumoto, M. Imoto, and H. Kaneko, “Mesenchyme cells can function to induce epithelial cell proliferation in starfish embryos,” Dev. Dyn. 239, 818–827 (2010).
[Crossref]

Matthews, T. E.

Mavandadi, S.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
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McNulty, I.

Medina, M.

Menzel, A.

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

Mir, M.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White light diffraction tomography of unlabeled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

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T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
[Crossref]

Nesterets, Y. I.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
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V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7, 603–614 (2010).
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K. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[Crossref]

Nugent, K. A.

Ou, X.

Ozcan, A.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Paganin, D. M.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
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D. M. Paganin, Coherent X-Ray Optics (Oxford University, 2006).

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Park, Y.

Pavani, S. R. P.

Pavillon, N.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

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Perezmendez, V.

Pfeifer, M. A.

Pfeiffer, F.

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Piestun, R.

Pogany, A.

Popescu, G.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White light diffraction tomography of unlabeled live cells,” Nat. Photonics 8, 256–263 (2014).
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Putkunz, C. T.

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Schneider, P.

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

Shoreh, M. H.

Simon, B.

M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
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Suman, R.

Sung, Y.

Suo, J.

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T. Takenaka, D. J. N. Wall, H. Harada, and M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
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Tam, K. C.

Tanaka, M.

T. Takenaka, D. J. N. Wall, H. Harada, and M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
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Tang, G.

Thibault, P.

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

F. Chen, P. W. Tillberg, and E. S. Boyden, “Expansion microscopy,” Science 347, 543–548 (2015).
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Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Tropp, J. A.

R. Horstmeyer, R. C. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New. J. Phys. 17, 053044 (2015).
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G. A. Tsihrintzis and A. J. Devaney, “Higher-order diffraction tomography: reconstruction algorithms and computer simulation,” IEEE Trans. Image Process. 9, 1560–1572 (2000).
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T. Takenaka, D. J. N. Wall, H. Harada, and M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
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Y. M. Wang and W. C. Chew, “An iterative solution of the two-dimensional electromagnetic inverse scattering problem,” Int. J. Imaging Syst. Technol. 1, 100–108 (1989).
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T. C. Wedberg and J. J. Stamnes, “Comparison of phase retrieval methods for optical diffraction tomography,” Pure Appl. Opt. 4, 39–54 (1995).
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M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
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Wilkins, S. W.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
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T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born and Rytov-type approximations,” Appl. Opt. 43, 2418–2430 (2004).
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E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
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R. Horstmeyer, R. C. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New. J. Phys. 17, 053044 (2015).
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X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23, 3472–3491 (2015).
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X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960–4972 (2014).
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G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
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S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
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Biomed. Opt. Express (1)

Dev. Dyn. (1)

G. Hamanaka, M. Matsumoto, M. Imoto, and H. Kaneko, “Mesenchyme cells can function to induce epithelial cell proliferation in starfish embryos,” Dev. Dyn. 239, 818–827 (2010).
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T. Takenaka, D. J. N. Wall, H. Harada, and M. Tanaka, “Reconstruction algorithm of the refractive index of a cylindrical object from the intensity measurements of the total field,” Microwave Opt. Technol. Lett. 14, 182–188 (1997).
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V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7, 603–614 (2010).
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T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White light diffraction tomography of unlabeled live cells,” Nat. Photonics 8, 256–263 (2014).
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G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
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T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics 10, 1–6 (2010).

Nature (1)

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
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New. J. Phys. (1)

R. Horstmeyer, R. C. Chen, X. Ou, B. Ames, J. A. Tropp, and C. Yang, “Solving ptychography with a convex relaxation,” New. J. Phys. 17, 053044 (2015).
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S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
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S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. USA 109, 7175–7180 (2012).
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Ultramicroscopy (2)

P. Li, D. J. Batey, T. B. Edo, and J. M. Rodenburg, “Separation of three-dimensional scattering effects in tilt-series Fourier ptychography,” Ultramicroscopy 158, 1–7 (2015).
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O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
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Supplementary Material (3)

NameDescription
» Supplement 1: PDF (7846 KB)      Supplemental document.
» Visualization 1: MP4 (7134 KB)      Tomographic reconstruction of a Trichinella spiralis parasite.
» Visualization 2: MP4 (11279 KB)      3D reconstruction of a starfish embryo at larval stage.

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Figures (7)

Fig. 1.
Fig. 1. Setup for Fourier ptychographic tomography (FPT). (a) Labeled diagram of the FPT microscope, including optical functions of interest. (b) FPT captures multiple images under varied LED illumination. (c) A ptychography-inspired algorithm combines these images in a 3D k-space representation of the complex sample. (d) FPT outputs a 3D tomographic map of the complex index of refraction of the sample. Included images are experimental measurements from a starfish embryo (real index component, threshold applied; see Fig. 7).

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Fig. 2.
Fig. 2. Mathematical summary of FPT. (a) The field from the jth LED scatters through the sample and exits its top surface as Uj(x′) (in 2D). This field forms U^j(kx) at the microscope back focal plane, where it is bandlimited by the microscope aperture a(kx) before propagating to the image plane to form the jth sampled intensity image. (b) Under the first Born approximation, each detected image is the squared magnitude of the Fourier transform of one colored “shell” in (kx,kz) space. (c) By filling in this space with a ptychographic phase-retrieval algorithm, FPT reconstructs the complex values within the finite bandpass volume V^e(kx,kz) (color indicates expected bowl overlap for this example). The Fourier transform of this reconstruction yields our complex refractive index map with resolutions Δx and Δz along x and z.

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Fig. 3.
Fig. 3. Improved lateral resolution with FPT. (a) Single raw image of 0.8 μm microspheres. Beads within each cluster are not resolved. (b) Refractive index (real) from Δz=0 slice (1 of 30) of the FPT reconstruction, resolving each microsphere.

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Fig. 4.
Fig. 4. FPT quantitatively measures refractive index in 3D. (a) Tomographic reconstruction of 12 μm microspheres in oil with lateral (Δz=0) slice on left, axial (Δy=25  μm) slice on right, and one-dimensional plots of index shift along both x and z. (b) Digitally propagated FP reconstruction (middle) and refocused light field (right) created from the same data. FPT (left) best matches the expected spherical bead profile.

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Fig. 5.
Fig. 5. Testing the axial resolution of FPT. (a) The sample contains two layers of microspheres separated by a thin layer of oil. Raw images (b) focused at the center of the two layers and (c) on the top layer do not clearly resolve overlapping microspheres. (d)–(f) Slices of the FPT tomographic reconstruction, showing |Δn|, clearly resolve each sphere within the two individual sphere layers.

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Fig. 6.
Fig. 6. Tomographic reconstruction of a Trichinella spiralis parasite. (a) The worm’s curved trajectory resolved within various z planes. (b) Refocusing the same distance to each respective plane does not clearly distinguish each in-focus worm segment (marked by white arrows). Since the worm is primarily transparent, in-focus worm sections exhibit minimal intensity contrast, presenting significant challenges for segmentation (see intensity along each black dash in inset plots, where black dash location is in-focus in left image). FPT, on the other hand, exhibits maximum contrast at each worm voxel. See Visualization 1.

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Fig. 7.
Fig. 7. 3D reconstruction of a starfish embryo at larval stage. (a) Three different axial planes of the FPT tomogram show significant feature variation (e.g., protocol is completely missing from Δz=−3.7  μm plane, expected developing mesenchyme cells are only visible in Δz=−3.7  μm plane). (b) Such axial information, and even certain structures (e.g., mesenchyme cells and various epithelia cells, marked in (a)) are completely missing from standard microscope images after manual refocusing. (c) A high-resolution DIC confocal scan of the Δz=−3.7  μm plane confirms presence of structures of interest. See Visualization 2.

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Equations (6)

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V(r)=k4π(n2(r)−nb2).
Us(r′)=∫G(|r′−r|)V(r)U(r)dr.
Ui(j)(r)=exp(1ikj·r),
kj=(kjx,kjy,kjz)=k(sin θjx,sin θjy,1−sin2 θjx−sin2 θjy).
U^s(j)(k)=V^(k−kj).
g(x,y,j)=|F[V^(k2D−kj2D,kz−kjz)·a(k2D)]|2.

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