Abstract

Generally, methods of three-dimensional imaging such as confocal microscopy and computed tomography rely on two essentials: multiple measurements (at a range of focus positions or rotations) and a weakly scattering specimen (to avoid distortion of the focal spot in the confocal microscope or to satisfy the projection approximation in tomography). Here we show that an alternative form of multi-measurement imaging, ptychography, can be extended to three dimensions and can successfully recover images in the presence of multiple scattering and when the projection approximation is not applicable. We demonstrate our technique experimentally using visible light, where it has applications in imaging thick samples such as biological tissues; however the results also have important implications for x ray and electron imaging.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Hoppe, “Diffraction in inhomogeneous primary wave fields: 1. Principle of phase determination from electron diffraction interference,” Acta Crystallogr. Sec. A 25, 495–501 (1969).
  2. K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
    [CrossRef]
  3. P. Thibault and V. Elser, “X-ray diffraction microscopy,” Annual Review Condensed Matter Physics 1, 237–255 (2010).
    [CrossRef]
  4. A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
    [CrossRef]
  5. K. Giewekemeyer, M. Beckers, T. Gorniak, M. Grunze, T. Salditt, and A. Rosenhahn, “Ptychographic coherent x-ray diffractive imaging in the water window,” Opt. Express 19, 1037–1050 (2011).
    [CrossRef]
  6. S. Hönig, R. Hoppe, J. Patommel, A. Schropp, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Full optical characterization of coherent x-ray nanobeams by ptychographic imaging,” Opt. Express 19, 16324–16329 (2011).
    [CrossRef]
  7. F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
    [CrossRef]
  8. C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).
  9. M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
    [CrossRef]
  10. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008).
    [CrossRef]
  11. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
    [CrossRef]
  12. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
    [CrossRef]
  13. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
    [CrossRef]
  14. 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]
  15. M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. Wepf, and O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express 19, 21345–21357 (2011).
    [CrossRef]
  16. T. Plamann and J. M. Rodenburg, “Double resolution imaging with infinite depth of focus in single lens scanning microscopy,” Optik 96, 31–36 (1994).
  17. J. M. Rodenburg, “Can Ronchigrams provide a route to sub-angstrom tomographic reconstruction?” Inst. Phys. Conf. Ser. 179, 185–190 (2004).
  18. P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
    [CrossRef]
  19. R. McIntosh, D. Nicastro, and D. Mastronarde, “New views of cells in 3D: an introduction to electron tomography,” Trends Cell Biol. 15, 43–51 (2005).
    [CrossRef]
  20. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
    [CrossRef]
  21. J. M. Schmitt, A. Knüttel, and M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11, 2226–2235(1994).
    [CrossRef]
  22. J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. Jürgen Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
    [CrossRef]
  23. L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt. 44, 3977–3984 (2005).
    [CrossRef]
  24. J. M. Rodenburg, A. M. Maiden, and M. J. Humphry, “Improvements in three dimensional imaging,” International Patent Application Number WO2012/038749 (2011).
  25. J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. 1. a new theoretical approach,” Acta Crystallogr. Sec. A 10, 609–619 (1957).
    [CrossRef]
  26. E. J. Kirkland, Advanced Computing in Electron Microscopy2nd ed. (Springer, 2010), Chap. 6.
  27. A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: A practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010).
    [CrossRef]
  28. A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28, 604–612 (2011).
    [CrossRef]

2012

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

2011

2010

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: A practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef]

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]

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

P. Thibault and V. Elser, “X-ray diffraction microscopy,” Annual Review Condensed Matter Physics 1, 237–255 (2010).
[CrossRef]

2009

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

2008

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef]

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

2006

2005

L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt. 44, 3977–3984 (2005).
[CrossRef]

R. McIntosh, D. Nicastro, and D. Mastronarde, “New views of cells in 3D: an introduction to electron tomography,” Trends Cell Biol. 15, 43–51 (2005).
[CrossRef]

2004

J. M. Rodenburg, “Can Ronchigrams provide a route to sub-angstrom tomographic reconstruction?” Inst. Phys. Conf. Ser. 179, 185–190 (2004).

1994

J. M. Schmitt, A. Knüttel, and M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11, 2226–2235(1994).
[CrossRef]

T. Plamann and J. M. Rodenburg, “Double resolution imaging with infinite depth of focus in single lens scanning microscopy,” Optik 96, 31–36 (1994).

1969

W. Hoppe, “Diffraction in inhomogeneous primary wave fields: 1. Principle of phase determination from electron diffraction interference,” Acta Crystallogr. Sec. A 25, 495–501 (1969).

1957

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. 1. a new theoretical approach,” Acta Crystallogr. Sec. A 10, 609–619 (1957).
[CrossRef]

Allain, M.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

Allen, L. J.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Barty, A.

Beckers, M.

Beerlink, A.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Beetz, T.

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef]

Bourgeois, L.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Boye, P.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Bunk, O.

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. Wepf, and O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express 19, 21345–21357 (2011).
[CrossRef]

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]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef]

Burghammer, M.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

S. Hönig, R. Hoppe, J. Patommel, A. Schropp, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Full optical characterization of coherent x-ray nanobeams by ptychographic imaging,” Opt. Express 19, 16324–16329 (2011).
[CrossRef]

Capello, L.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

Carbone, G.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

Chamard, V.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

Chapman, H. N.

Chen, G.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

Cowley, J. M.

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. 1. a new theoretical approach,” Acta Crystallogr. Sec. A 10, 609–619 (1957).
[CrossRef]

Cui, C.

D’Alfonso, A. J.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef]

Diaz, A.

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. Wepf, and O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express 19, 21345–21357 (2011).
[CrossRef]

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[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]

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef]

Dwyer, C.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Elser, V.

P. Thibault and V. Elser, “X-ray diffraction microscopy,” Annual Review Condensed Matter Physics 1, 237–255 (2010).
[CrossRef]

Etheridge, J.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Fienup, J. R.

Fink, M.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef]

Garcia-Sucerquia, J.

Giewekemeyer, K.

K. Giewekemeyer, M. Beckers, T. Gorniak, M. Grunze, T. Salditt, and A. Rosenhahn, “Ptychographic coherent x-ray diffractive imaging in the water window,” Opt. Express 19, 1037–1050 (2011).
[CrossRef]

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Gigan, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef]

Godard, P.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

Goldschmidt, A.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Gorniak, T.

Grunze, M.

Guizar-Sicairos, M.

Hau-Riege, S. P.

He, H.

Holler, M.

Hönig, S.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

S. Hönig, R. Hoppe, J. Patommel, A. Schropp, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Full optical characterization of coherent x-ray nanobeams by ptychographic imaging,” Opt. Express 19, 16324–16329 (2011).
[CrossRef]

Hoppe, R.

S. Hönig, R. Hoppe, J. Patommel, A. Schropp, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Full optical characterization of coherent x-ray nanobeams by ptychographic imaging,” Opt. Express 19, 16324–16329 (2011).
[CrossRef]

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Hoppe, W.

W. Hoppe, “Diffraction in inhomogeneous primary wave fields: 1. Principle of phase determination from electron diffraction interference,” Acta Crystallogr. Sec. A 25, 495–501 (1969).

Howells, M. R.

Hüe, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

Humphry, M. J.

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

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

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: A practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010).
[CrossRef]

J. M. Rodenburg, A. M. Maiden, and M. J. Humphry, “Improvements in three dimensional imaging,” International Patent Application Number WO2012/038749 (2011).

Hurst, A. C.

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

Jacobsen, C.

Jericho, M. H.

Jericho, S. K.

Jürgen Kreuzer, H.

Kalbfleisch, S.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Kewish, C.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

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]

Kirkland, E. J.

E. J. Kirkland, Advanced Computing in Electron Microscopy2nd ed. (Springer, 2010), Chap. 6.

Klages, P.

Knüttel, A.

Kraus, B.

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

Lerosey, G.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef]

Lucas, M. S.

Maiden, A. M.

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

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

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: A practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010).
[CrossRef]

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

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

J. M. Rodenburg, A. M. Maiden, and M. J. Humphry, “Improvements in three dimensional imaging,” International Patent Application Number WO2012/038749 (2011).

Marchesini, S.

Martínez-León, L.

Mastronarde, D.

R. McIntosh, D. Nicastro, and D. Mastronarde, “New views of cells in 3D: an introduction to electron tomography,” Trends Cell Biol. 15, 43–51 (2005).
[CrossRef]

Mastropietro, F.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

McIntosh, R.

R. McIntosh, D. Nicastro, and D. Mastronarde, “New views of cells in 3D: an introduction to electron tomography,” Trends Cell Biol. 15, 43–51 (2005).
[CrossRef]

Menzel, A.

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. Wepf, and O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express 19, 21345–21357 (2011).
[CrossRef]

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]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef]

Metzger, T. H.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

Midgley, P. A.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

Moodie, A. F.

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. 1. a new theoretical approach,” Acta Crystallogr. Sec. A 10, 609–619 (1957).
[CrossRef]

Morgan, A. J.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Nicastro, D.

R. McIntosh, D. Nicastro, and D. Mastronarde, “New views of cells in 3D: an introduction to electron tomography,” Trends Cell Biol. 15, 43–51 (2005).
[CrossRef]

Noy, A.

Nugent, K. A.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Osten, W.

Patommel, J.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

S. Hönig, R. Hoppe, J. Patommel, A. Schropp, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Full optical characterization of coherent x-ray nanobeams by ptychographic imaging,” Opt. Express 19, 16324–16329 (2011).
[CrossRef]

Pedrini, G.

Pfeiffer, F.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

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]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef]

Plamann, T.

T. Plamann and J. M. Rodenburg, “Double resolution imaging with infinite depth of focus in single lens scanning microscopy,” Optik 96, 31–36 (1994).

Popoff, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef]

Putkunz, C. T.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Rakete, C.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Roberts, A.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Rodenburg, J. M.

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

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

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: A practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010).
[CrossRef]

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

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

J. M. Rodenburg, “Can Ronchigrams provide a route to sub-angstrom tomographic reconstruction?” Inst. Phys. Conf. Ser. 179, 185–190 (2004).

T. Plamann and J. M. Rodenburg, “Double resolution imaging with infinite depth of focus in single lens scanning microscopy,” Optik 96, 31–36 (1994).

J. M. Rodenburg, A. M. Maiden, and M. J. Humphry, “Improvements in three dimensional imaging,” International Patent Application Number WO2012/038749 (2011).

Rosen, R.

Rosenhahn, A.

Salditt, T.

K. Giewekemeyer, M. Beckers, T. Gorniak, M. Grunze, T. Salditt, and A. Rosenhahn, “Ptychographic coherent x-ray diffractive imaging in the water window,” Opt. Express 19, 1037–1050 (2011).
[CrossRef]

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Samberg, D.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Schmitt, J. M.

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).
[CrossRef]

Schöder, S.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

S. Hönig, R. Hoppe, J. Patommel, A. Schropp, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Full optical characterization of coherent x-ray nanobeams by ptychographic imaging,” Opt. Express 19, 16324–16329 (2011).
[CrossRef]

Scholten, R. E.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Schroer, C. G.

S. Hönig, R. Hoppe, J. Patommel, A. Schropp, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Full optical characterization of coherent x-ray nanobeams by ptychographic imaging,” Opt. Express 19, 16324–16329 (2011).
[CrossRef]

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Schropp, A.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

S. Hönig, R. Hoppe, J. Patommel, A. Schropp, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Full optical characterization of coherent x-ray nanobeams by ptychographic imaging,” Opt. Express 19, 16324–16329 (2011).
[CrossRef]

Shapiro, D.

Spence, J. C.

Stangl, J.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

Stephan, S.

S. Hönig, R. Hoppe, J. Patommel, A. Schropp, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Full optical characterization of coherent x-ray nanobeams by ptychographic imaging,” Opt. Express 19, 16324–16329 (2011).
[CrossRef]

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

Sweeney, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

Thibault, P.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

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]

P. Thibault and V. Elser, “X-ray diffraction microscopy,” Annual Review Condensed Matter Physics 1, 237–255 (2010).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef]

Weierstall, U.

Wepf, R.

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. Wepf, and O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express 19, 21345–21357 (2011).
[CrossRef]

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]

Weyland, M.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

Xu, W.

Yadlowsky, M.

Zhang, F.

Acta Crystallogr. Sec. A

W. Hoppe, “Diffraction in inhomogeneous primary wave fields: 1. Principle of phase determination from electron diffraction interference,” Acta Crystallogr. Sec. A 25, 495–501 (1969).

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. 1. a new theoretical approach,” Acta Crystallogr. Sec. A 10, 609–619 (1957).
[CrossRef]

Annual Review Condensed Matter Physics

P. Thibault and V. Elser, “X-ray diffraction microscopy,” Annual Review Condensed Matter Physics 1, 237–255 (2010).
[CrossRef]

Appl. Opt.

Inst. Phys. Conf. Ser.

J. M. Rodenburg, “Can Ronchigrams provide a route to sub-angstrom tomographic reconstruction?” Inst. Phys. Conf. Ser. 179, 185–190 (2004).

J. Microsc.

A. Schropp, P. Boye, A. Goldschmidt, S. Hönig, R. Hoppe, J. Patommel, C. Rakete, D. Samberg, S. Stephan, S. Schöder, M. Burghammer, and C. G. Schroer, “Non-destructive and quantitative imaging of a nano-structured microchip by ptychographic hard X-ray scanning microscopy,” J. Microsc. 241, 9–12 (2011).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Commun.

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

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, and V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Commun. 2, 568 (2011).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef]

Nature

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]

Opt. Express

Opt. Lett.

Optik

T. Plamann and J. M. Rodenburg, “Double resolution imaging with infinite depth of focus in single lens scanning microscopy,” Optik 96, 31–36 (1994).

Phys. Rev. B

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Science

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef]

Trends Cell Biol.

R. McIntosh, D. Nicastro, and D. Mastronarde, “New views of cells in 3D: an introduction to electron tomography,” Trends Cell Biol. 15, 43–51 (2005).
[CrossRef]

Ultramicroscopy

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

Other

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett. (in press).

J. M. Rodenburg, A. M. Maiden, and M. J. Humphry, “Improvements in three dimensional imaging,” International Patent Application Number WO2012/038749 (2011).

E. J. Kirkland, Advanced Computing in Electron Microscopy2nd ed. (Springer, 2010), Chap. 6.

Supplementary Material (2)

» Media 1: MOV (1605 KB)     
» Media 2: MOV (2905 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

Schematic detailing the nomenclature used to describe the 3PIE method. (a) The algorithm performs a multi-slice calculation to arrive at an approximation to the wavefront incident upon the detector; (b) This wavefront is modified to match the recorded data and the result used to update each of the slices used in the forward multi-slice calculation.

Fig. 2.
Fig. 2.

Experimental setup for collection of ptychographic data. The optional diffuser consisted of a thin piece of plastic film covering the 100 μm mounted pinhole. Lens L1 was an antireflection coated doublet with fL1=3cm. Lens L2 was a matching doublet during the experiments resulting in Figures 3, 5 and 8, but was replaced by a 10× Olympus microscope objective (fL2=18mm) for the experiment resulting in Figs. 6 and 7. The distance d was accurately measured before each experiment. A typical diffraction pattern from the system is shown to the right on a logarithmic scale. The lower inset shows the modulus and phase of a typical probe function reconstructed by the 3PIE. The upper inset shows the arrangement of the two microscope slides used as specimens for Fig. 3 (left) and Fig. 8 (right), together with the planes used for the 3PIE reconstructions.

Fig. 3.
Fig. 3.

Final reconstructions of a butterfly wing and capsella embryo. The progress of this reconstruction is shown in (Media 1). The specimens were placed coverslip to coverslip and ptychographic data collected. The conventional ePIE reconstruction yielded the modulus and phase shown in (a) and (b). The 3PIE reconstruction was carried out at two planes coincident with the two specimens (see upper inset of Fig. 2) and produced the moduli and phases of (c) and (d) at the first plane and (e) and (f) at the second plane. Scale bar is 100 μm.

Fig. 4.
Fig. 4.

Improvement realized by moving from a projection-based propagation model to a multi-slice model; (a) The evolution of the error metric given by Eq. (4) of the main text as the ePIE and 3PIE reconstructions shown in Fig. 3 progress; (b) The error between one of the measured diffraction patterns and the corresponding pattern as generated by the ePIE reconstruction and its multiplicative model; (c) The same error measure calculated using the 3PIE reconstruction and its multi-slice model. Parts (b) and (c) are plotted on identical grey scales.

Fig. 5.
Fig. 5.

Ptychographic data were collected from a piece of tissue paper in this experiment. 3PIE separated the fibers of the tissue at two planes; (a) and (b) modulus and phase of the downstream plane, (c) and (d) modulus and phase of the upstream plane. (e) and (f) the reconstructed probe.

Fig. 6.
Fig. 6.

Reconstruction of a spirogyra. A higher illumination NA (formed using a 10× microscope objective) and a shorter camera length (d=32mm) were used in the setup from which these reconstructions were generated. (a) and (b) white light brightfield images focusing on (a) the top and (b) the bottom of the spiragyra; (c) modulus and (d) phase of the first slice of the 3PIE reconstruction, focused at the bottom of the spiragyra; (e) modulus and (f) phase of the second slice, focused at the top. Scale bar is 25 μm.

Fig. 7.
Fig. 7.

Second three-plane reconstruction from the spirogyra data used in Fig. 6. Here the 3PIE was combined with a ptychographic super-resolution method to both increase the resolution of the reconstruction and to allow a third slice, between the previous two, to be introduced. The spacing between the slices in this reconstruction is 11 μm.

Fig. 8.
Fig. 8.

3PIE reconstruction using five object planes. In this example two slides were placed back to back and the reconstruction carried out over the five planes labelled in the upper inset of Fig. 2. The progress of a similar reconstruction is shown in (Media 2); (a) and (b) modulus and phase of the first slice, coincident with dust on a coverslip; (c) and (d) modulus and phase of the second slice, 180 μm downstream and coincident with a butterfly wing sample; (e) and (f) third slice, 1.1 mm downstream, coincident with the two touching faces of the microscope slides; (g) and (h) fourth slice, 1.2 mm downstream, coincident with an insect sample, showing mainly its eye. (i) and (j) fifth slice, 160 μm downstream, coincident with the second coverslip. The scale bars are 100 μm.

Fig. 9.
Fig. 9.

Evolution of the exit wave, ψe,n(r), as the forward calculation of the 3PIE passes through the five slices shown in Fig. 8. Top row: the modulus of ψe,n(r) for (left) n=1 through to (right) n=5. Bottom row: the reconstructed probe wavefront propagated to the same five reconstruction planes without the specimen present. The comparison shows the significant effect of the specimen on the illuminating probe as it propagates through the layers of the two microscope slides.

Fig. 10.
Fig. 10.

Simple ray-optic schematic illustrating how 3D information is encoded in a ptychographic scan. The circle and square represent the 3D specimen. At a first probe position (a) the detector records a projection of the circle and square—without diffraction effects there is no 3D information encoded in this recording. However when the probe is moved to a second position (b), and a second recording made, parallax has caused the projections of the circle and square to move by different amounts—this relative movement can be used to deduce their position along the optical axis.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

Ψj(u)=F[P(rRj).O(r)],
Ψj(u)=F[O3(r).PΔz2[O2(r).PΔz1[P(rRj).O1(r)]]],
Ψc(u)=Ic(u)Ψc(u)|Ψc(u)|.
ψe,N=F1[Ψc(u)].
U[f(r),g(r),Δψ(r)]=f(r)+αg*(r)|g(r)|max2Δψ(r).
ψi,N(r)=U[ψi,N(r),ON(r),Δψ(r)],ON(r)=U[ON(r),ψi,N(r),Δψ(r)].
ψe,N1(r)=PΔz(N1)[ψi,N(r)].
ψi,N1(r)=U[ψi,N1(r),ON1(r),Δψ(r)],ON1(r)=U[ON1(r),ψi,N1(r),Δψ(r)].
P(rRc)=U[P(rRc),O1(r),Δψ(r)],O1(r)=U[O1(r),P(rRc),Δψ(r)].
E(k)=j=1Ju(|Ψj,k(u)|Ij(u))2uIj(u),

Metrics