Abstract

Ptychographic techniques are currently the subject of increasing scientific interest due to their capability to retrieve the complex transmission function of an object at very high resolution. However, they impose a substantial burden in terms of acquisition time and dimension of the scanned area, which limits the range of samples that can be studied. We have developed a new method that combines the ptychographic approach in one direction with Fresnel propagation in the other by employing a strongly asymmetric probe. This enables scanning the sample in one direction only, substantially reducing exposure times while covering a large field of view. This approach sacrifices ptychographic–related resolution in one direction, but removes any limitation on the probe dimension in the direction orthogonal to the scanning, enabling the scan of relatively large objects without compromising exposure times.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  2. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40–55 (2003).
    [CrossRef]
  3. B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
    [CrossRef]
  4. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
    [CrossRef] [PubMed]
  5. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm,” Ultramicroscopy 109, 1256–1262 (2009).
    [CrossRef] [PubMed]
  6. T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).
    [CrossRef]
  7. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
    [CrossRef] [PubMed]
  8. M. Krenkel, M. Bartels, and T. Salditt, “Transport of intensity phase reconstruction to solve the twin image problem in holographic x–ray imaging,” Opt. Express 21, 2220–2235 (2013).
    [CrossRef] [PubMed]
  9. J. Hagemann, A. L. Robisch, D. R. Luke, C. Homann, T. Hohage, P. Cloetens, H. Suhonen, and T. Salditt, “Reconstruction of wave front and object for inline holography from a set of detection planes,” Opt. Express 22, 11552–11569 (2014).
    [CrossRef]
  10. 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, 1927 (2013).
  11. R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick–Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
    [CrossRef]
  12. K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, “X–ray propagation microscopy of biological cells using waveguides as a quasipoint source,” Phys. Rev. A 83, 023804 (2011).
    [CrossRef]
  13. C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
    [CrossRef] [PubMed]
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, 1996).
  15. D. M. Paganin, Coherent X–Ray Optics (Oxford University Press, 2006).
    [CrossRef]
  16. J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE Press, 2010).
  17. M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103(R) (2012).
    [CrossRef]
  18. C. Rau, U. Wagner, Z. Pesic, and A. De Fanis, “Coherent imaging at the Diamond beamline I13,” Phys. Status Solidi A 208, 2522–2525 (2011).
    [CrossRef]
  19. N. Banterle, K. Huy Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super–resolution microscopy,” J. Struct. Biol. 183, 363–367 (2013).
    [CrossRef] [PubMed]

2014 (1)

2013 (3)

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, 1927 (2013).

N. Banterle, K. Huy Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super–resolution microscopy,” J. Struct. Biol. 183, 363–367 (2013).
[CrossRef] [PubMed]

M. Krenkel, M. Bartels, and T. Salditt, “Transport of intensity phase reconstruction to solve the twin image problem in holographic x–ray imaging,” Opt. Express 21, 2220–2235 (2013).
[CrossRef] [PubMed]

2012 (2)

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
[CrossRef] [PubMed]

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103(R) (2012).
[CrossRef]

2011 (2)

C. Rau, U. Wagner, Z. Pesic, and A. De Fanis, “Coherent imaging at the Diamond beamline I13,” Phys. Status Solidi A 208, 2522–2525 (2011).
[CrossRef]

K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, “X–ray propagation microscopy of biological cells using waveguides as a quasipoint source,” Phys. Rev. A 83, 023804 (2011).
[CrossRef]

2009 (2)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

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

2008 (1)

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

2007 (1)

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick–Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

2004 (1)

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).
[CrossRef]

2003 (1)

2002 (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef] [PubMed]

1982 (1)

Abbey, B.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

Banterle, N.

N. Banterle, K. Huy Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super–resolution microscopy,” J. Struct. Biol. 183, 363–367 (2013).
[CrossRef] [PubMed]

Bartels, M.

M. Krenkel, M. Bartels, and T. Salditt, “Transport of intensity phase reconstruction to solve the twin image problem in holographic x–ray imaging,” Opt. Express 21, 2220–2235 (2013).
[CrossRef] [PubMed]

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
[CrossRef] [PubMed]

K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, “X–ray propagation microscopy of biological cells using waveguides as a quasipoint source,” Phys. Rev. A 83, 023804 (2011).
[CrossRef]

Beck, M.

N. Banterle, K. Huy Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super–resolution microscopy,” J. Struct. Biol. 183, 363–367 (2013).
[CrossRef] [PubMed]

Beerlink, A.

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
[CrossRef] [PubMed]

Beta, C.

K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, “X–ray propagation microscopy of biological cells using waveguides as a quasipoint source,” Phys. Rev. A 83, 023804 (2011).
[CrossRef]

Buffière, J.-Y.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick–Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

Bunk, O.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103(R) (2012).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

Clark, J. N.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

Cloetens, P.

J. Hagemann, A. L. Robisch, D. R. Luke, C. Homann, T. Hohage, P. Cloetens, H. Suhonen, and T. Salditt, “Reconstruction of wave front and object for inline holography from a set of detection planes,” Opt. Express 22, 11552–11569 (2014).
[CrossRef]

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, 1927 (2013).

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick–Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

De Fanis, A.

C. Rau, U. Wagner, Z. Pesic, and A. De Fanis, “Coherent imaging at the Diamond beamline I13,” Phys. Status Solidi A 208, 2522–2525 (2011).
[CrossRef]

de Jonge, M.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

Diaz, A.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103(R) (2012).
[CrossRef]

Dierolf, M.

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, 1927 (2013).

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

Elser, V.

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, 1927 (2013).

Fienup, J. R.

Giewekemeyer, K.

K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, “X–ray propagation microscopy of biological cells using waveguides as a quasipoint source,” Phys. Rev. A 83, 023804 (2011).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, 1996).

Guizar-Sicairos, M.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103(R) (2012).
[CrossRef]

Gureyev, T. E.

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).
[CrossRef]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef] [PubMed]

Hagemann, J.

Hohage, T.

Holler, M.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103(R) (2012).
[CrossRef]

Homann, C.

Huy Bui, K.

N. Banterle, K. Huy Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super–resolution microscopy,” J. Struct. Biol. 183, 363–367 (2013).
[CrossRef] [PubMed]

Kalbfleisch, S.

K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, “X–ray propagation microscopy of biological cells using waveguides as a quasipoint source,” Phys. Rev. A 83, 023804 (2011).
[CrossRef]

Krenkel, M.

M. Krenkel, M. Bartels, and T. Salditt, “Transport of intensity phase reconstruction to solve the twin image problem in holographic x–ray imaging,” Opt. Express 21, 2220–2235 (2013).
[CrossRef] [PubMed]

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
[CrossRef] [PubMed]

Krüger, S. P.

K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, “X–ray propagation microscopy of biological cells using waveguides as a quasipoint source,” Phys. Rev. A 83, 023804 (2011).
[CrossRef]

Lemke, E. A.

N. Banterle, K. Huy Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super–resolution microscopy,” J. Struct. Biol. 183, 363–367 (2013).
[CrossRef] [PubMed]

Ludwig, W.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick–Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

Luke, D. R.

Maiden, A. M.

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

Maire, E.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick–Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

Mayo, S. C.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef] [PubMed]

McNulty, I.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

Menzel, A.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103(R) (2012).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

Miller, P. R.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef] [PubMed]

Mokso, R.

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
[CrossRef] [PubMed]

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick–Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

Nugent, K. A.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

Olendrowitz, C.

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
[CrossRef] [PubMed]

Paganin, D.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef] [PubMed]

Paganin, D. M.

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).
[CrossRef]

D. M. Paganin, Coherent X–Ray Optics (Oxford University Press, 2006).
[CrossRef]

Peele, A. G.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

Pesic, Z.

C. Rau, U. Wagner, Z. Pesic, and A. De Fanis, “Coherent imaging at the Diamond beamline I13,” Phys. Status Solidi A 208, 2522–2525 (2011).
[CrossRef]

Pfeifer, M. A.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

Pfeiffer, F.

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, 1927 (2013).

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

Pogany, A.

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).
[CrossRef]

Rau, C.

C. Rau, U. Wagner, Z. Pesic, and A. De Fanis, “Coherent imaging at the Diamond beamline I13,” Phys. Status Solidi A 208, 2522–2525 (2011).
[CrossRef]

Robisch, A. L.

Rodenburg, J. M.

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

Salditt, T.

J. Hagemann, A. L. Robisch, D. R. Luke, C. Homann, T. Hohage, P. Cloetens, H. Suhonen, and T. Salditt, “Reconstruction of wave front and object for inline holography from a set of detection planes,” Opt. Express 22, 11552–11569 (2014).
[CrossRef]

M. Krenkel, M. Bartels, and T. Salditt, “Transport of intensity phase reconstruction to solve the twin image problem in holographic x–ray imaging,” Opt. Express 21, 2220–2235 (2013).
[CrossRef] [PubMed]

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
[CrossRef] [PubMed]

K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, “X–ray propagation microscopy of biological cells using waveguides as a quasipoint source,” Phys. Rev. A 83, 023804 (2011).
[CrossRef]

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE Press, 2010).

Sprung, M.

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
[CrossRef] [PubMed]

Stockmar, M.

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, 1927 (2013).

Suhonen, H.

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, 1927 (2013).

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

Vila-Comamala, J.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103(R) (2012).
[CrossRef]

Wagner, U.

C. Rau, U. Wagner, Z. Pesic, and A. De Fanis, “Coherent imaging at the Diamond beamline I13,” Phys. Status Solidi A 208, 2522–2525 (2011).
[CrossRef]

Wilkins, S. W.

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).
[CrossRef]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef] [PubMed]

Williams, G. J.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

Zanette, I.

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, 1927 (2013).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick–Baez optics,” Appl. Phys. Lett. 90, 144104 (2007).
[CrossRef]

J. Microsc. (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

J. Struct. Biol. (1)

N. Banterle, K. Huy Bui, E. A. Lemke, and M. Beck, “Fourier ring correlation as a resolution criterion for super–resolution microscopy,” J. Struct. Biol. 183, 363–367 (2013).
[CrossRef] [PubMed]

Nat. Phys. (1)

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[CrossRef]

Opt. Commun. (1)

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).
[CrossRef]

Opt. Express (2)

Phys. Med. Biol. (1)

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase–contrast x–ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57, 5309–5323 (2012).
[CrossRef] [PubMed]

Phys. Rev. A (1)

K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, “X–ray propagation microscopy of biological cells using waveguides as a quasipoint source,” Phys. Rev. A 83, 023804 (2011).
[CrossRef]

Phys. Rev. B (1)

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103(R) (2012).
[CrossRef]

Phys. Status Solidi A (1)

C. Rau, U. Wagner, Z. Pesic, and A. De Fanis, “Coherent imaging at the Diamond beamline I13,” Phys. Status Solidi A 208, 2522–2525 (2011).
[CrossRef]

Sci. Rep. (1)

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, 1927 (2013).

Ultramicroscopy (2)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

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

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw–Hill, 1996).

D. M. Paganin, Coherent X–Ray Optics (Oxford University Press, 2006).
[CrossRef]

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE Press, 2010).

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 (8)

Fig. 1
Fig. 1

Schematic diagram of 1D–PIE methods.

Fig. 2
Fig. 2

Simulated sample amplitude (a) and phase shift (b) maps. Simulated beam amplitude (c) and phase (d) maps. Retrieved sample (e, f) and beam (g, h) in the case of 1% Gaussian noise. Retrieved sample (i, l) and beam (m, n) in the case of 10% Gaussian noise. All the original photographs used to simulate the sample amplitude and phase shift maps were taken by F.A.V..

Fig. 3
Fig. 3

Evolution of the RMS error εn. The solid (blue) line refers to the case of 1% noise, the dashed (black) line refers to the case of 10% noise.

Fig. 4
Fig. 4

Reconstructed (dotted, green) and theoretical (solid, black) phase shift of a PEEK monofilament in water.

Fig. 5
Fig. 5

Reconstructed results of a spider leg. Retrieved sample amplitude (a) and phase shift (b) maps. Retrieved beam amplitude (c) and phase (d) maps. The lateral inserts show an enlargement of the regions in the white squares; red arrows show some of the very small details (≈5μm) visible in the reconstructed images, and how these appear sharper in the phase image.

Fig. 6
Fig. 6

Evolution of the RMS error En.

Fig. 7
Fig. 7

(a) Division of the Fourier space for the calculation of the FRC curves. FRC curves (solid) and 2σ criterion (dashed) for 1% noise along x (b) and y (c), and for 10% noise along x (d) and y (e).

Fig. 8
Fig. 8

Mean radial Fourier spectrum of the spider leg transmission function (Fig. 5) along the x (a) and y (b) directions (solid lines) and relative thresholds (dashed lines) used to estimate the experimental resolution.

Tables (1)

Tables Icon

Table 1 Estimated resolution values of the reconstructed sample transmission function for the simulated case, using the FRC and the 2σ criterion.

Equations (10)

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

ψ ( x , y ) = O ( x , y ) B ( x , y ) .
Ψ ( x , y ) = 𝒫 x y [ ψ ] ( x , y ) = ψ ( x , y ) * H p ( x , y ) ,
H p ( x , y ) = exp ( i k z p ) i λ z p exp ( i k x 2 + y 2 2 z p ) ,
H p ( x , y ) exp ( i k x 2 2 z p ) exp ( i k y 2 2 z p ) = h p ( x ) h p ( y ) .
Ψ ( x , y ) = 𝒫 x [ 𝒫 y [ ψ ] ] ( x , y ) ,
𝒫 x [ f ] ( x , y ) = f ( r , y ) h p ( x r ) d r ,
𝒫 x [ f ] ( x , y ) = h p ( x ) r [ f ( r , y ) h p ( r ) ] ( x λ z p ) ,
𝒫 y [ f ] ( x , y ) = η 1 [ s [ f ( x , s ) ] ( η ) h ^ p ( η ) ] ( y ) ,
ε n = x , y | O ( x , y ) O n ( x , y ) | 2 x , y | O ( x , y ) | 2 ,
E n = j x , y | I j ( x , y ) | Ψ j ( x , y ) | | 2 j x , y I j ( x , y ) ,

Metrics