Abstract

Ptychography is a coherent imaging technique that enables an image of a specimen to be generated from a set of diffraction patterns. One limitation of the technique is the assumption of a multiplicative interaction between the illuminating coherent beam and the specimen, which restricts ptychography to samples no thicker than a few tens of micrometers in the case of visible-light imaging at micron-scale resolution. By splitting a sample into axial sections, we demonstrated in recent work that this thickness restriction can be relaxed and whats-more, that coarse optical sectioning can be realized using a single ptychographic data set. Here we apply our technique to data collected from a modified optical microscope to realize a reduction in the optical sectioning depth to 2 μm in the axial direction for samples up to 150 μm thick. Furthermore, we increase the number of sections that are imaged from 5 in our previous work to 34 here. Our results compare well with sectioned images collected from a confocal microscope but have the added advantage of strong phase contrast, which removes the need for sample staining.

© 2014 Optical Society of America

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  1. J. Marrison, L. Raty, P. Marriott, P. O’Toole, “Ptychography a label free, high-contrast imaging technique for live cells using quantitative phase information,” Nature Scientific Reports 3, 1–7 (2013).
  2. H. M. L. Faulkner, J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
    [CrossRef] [PubMed]
  3. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
    [CrossRef] [PubMed]
  4. M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nature Comms. 3, 730 (2012).
    [CrossRef]
  5. M. Guizar-Sicairos, J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008).
    [CrossRef] [PubMed]
  6. A. M. Maiden, J.M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
    [CrossRef] [PubMed]
  7. A. M. Maiden, M. J. Humphry, F. Zhang, J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28, 604–612 (2011).
    [CrossRef]
  8. P. Thibault, A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
    [CrossRef] [PubMed]
  9. P. Thibault, M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys 14, 063004 (2012).
    [CrossRef]
  10. H. Liu, Z. Xu, X. Zhang, Y. Wu, Z. Guo, R. Tai, “Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging,” Applied Optics 52, 2416–2427 (2013).
    [CrossRef] [PubMed]
  11. D. J. Batey, D. Claus, J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
    [CrossRef] [PubMed]
  12. A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
    [CrossRef] [PubMed]
  13. M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
    [CrossRef] [PubMed]
  14. F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, J. M. Rodenburg, “Translation position determination in ptychographic coherent diffractive imaging,” Opt. Express 21, 13592–13606 (2013).
    [CrossRef] [PubMed]
  15. A. Tripathi, I. McNulty, O. G. Shpyrko, “Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods,” Opt. Express 22(2), 1452–1466 (2014).
    [CrossRef] [PubMed]
  16. P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. Sec. A 62, 248–261 (2006).
    [CrossRef]
  17. A. M. Maiden, M. J. Humphry, J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614, (2012).
    [CrossRef]
  18. A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
    [CrossRef] [PubMed]
  19. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
    [CrossRef] [PubMed]
  20. Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photonics 7, 113–117 (2013).
    [CrossRef]
  21. J. M. Rodenburg, R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339, 521 (1992).
    [CrossRef]
  22. J. M. Cowley, A. F. Moodie, “The scattering of electrons by atoms and crystals. A new theoretical approach,” Acta Crystallogr. Sec. A 10, 609–619 (1957).
  23. J. W. Goodman, Introduction to Fourier Optics3rd edition (Roberts and Company Publishers, 2005) pp. 55–73
  24. M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
    [CrossRef]
  25. C. L. Wenzel, J. Marrison, J. Mattsson, J. Haseloff, S. M. Bougourd, “Ectopic divisions in vascular and ground tissues of Arabidopsis Thaliana result in distinct leaf venation defects,” J. Exp. Bot. 63, 5351–5363 (2012).
    [CrossRef] [PubMed]

2014 (3)

D. J. Batey, D. Claus, J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[CrossRef] [PubMed]

A. Tripathi, I. McNulty, O. G. Shpyrko, “Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods,” Opt. Express 22(2), 1452–1466 (2014).
[CrossRef] [PubMed]

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[CrossRef] [PubMed]

2013 (6)

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

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, J. M. Rodenburg, “Translation position determination in ptychographic coherent diffractive imaging,” Opt. Express 21, 13592–13606 (2013).
[CrossRef] [PubMed]

H. Liu, Z. Xu, X. Zhang, Y. Wu, Z. Guo, R. Tai, “Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging,” Applied Optics 52, 2416–2427 (2013).
[CrossRef] [PubMed]

J. Marrison, L. Raty, P. Marriott, P. O’Toole, “Ptychography a label free, high-contrast imaging technique for live cells using quantitative phase information,” Nature Scientific Reports 3, 1–7 (2013).

P. Thibault, A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[CrossRef] [PubMed]

2012 (5)

P. Thibault, M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys 14, 063004 (2012).
[CrossRef]

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

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[CrossRef] [PubMed]

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

C. L. Wenzel, J. Marrison, J. Mattsson, J. Haseloff, S. M. Bougourd, “Ectopic divisions in vascular and ground tissues of Arabidopsis Thaliana result in distinct leaf venation defects,” J. Exp. Bot. 63, 5351–5363 (2012).
[CrossRef] [PubMed]

2011 (1)

2010 (2)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

2009 (1)

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

2008 (2)

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

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

2006 (1)

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. Sec. A 62, 248–261 (2006).
[CrossRef]

2004 (1)

H. M. L. Faulkner, J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

1992 (1)

J. M. Rodenburg, R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339, 521 (1992).
[CrossRef]

1957 (1)

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

Bates, R. H. T.

J. M. Rodenburg, R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339, 521 (1992).
[CrossRef]

Batey, D. J.

D. J. Batey, D. Claus, J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[CrossRef] [PubMed]

Bean, R.

Beckers, M.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Berenguer, F.

Boss, D.

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

Bougourd, S. M.

C. L. Wenzel, J. Marrison, J. Mattsson, J. Haseloff, S. M. Bougourd, “Ectopic divisions in vascular and ground tissues of Arabidopsis Thaliana result in distinct leaf venation defects,” J. Exp. Bot. 63, 5351–5363 (2012).
[CrossRef] [PubMed]

Bunk, O.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

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

Chen, B.

Claus, D.

D. J. Batey, D. Claus, J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[CrossRef] [PubMed]

Cotte, Y.

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

Cowley, J. M.

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

David, C.

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

Depeursinge, C.

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

Diaz, A.

Dierolf, M.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

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

Elser, V.

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. Sec. A 62, 248–261 (2006).
[CrossRef]

Faulkner, H. M. L.

H. M. L. Faulkner, J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

Fienup, J. R.

Furutaku, S.

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[CrossRef] [PubMed]

Giewekemeyer, K.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics3rd edition (Roberts and Company Publishers, 2005) pp. 55–73

Gorniak, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Guizar-Sicairos, M.

P. Thibault, M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys 14, 063004 (2012).
[CrossRef]

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

Guo, Z.

H. Liu, Z. Xu, X. Zhang, Y. Wu, Z. Guo, R. Tai, “Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging,” Applied Optics 52, 2416–2427 (2013).
[CrossRef] [PubMed]

Haseloff, J.

C. L. Wenzel, J. Marrison, J. Mattsson, J. Haseloff, S. M. Bougourd, “Ectopic divisions in vascular and ground tissues of Arabidopsis Thaliana result in distinct leaf venation defects,” J. Exp. Bot. 63, 5351–5363 (2012).
[CrossRef] [PubMed]

Humphry, M. J.

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

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[CrossRef] [PubMed]

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

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

Hurst, A. C.

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

Ishikawa, T.

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[CrossRef] [PubMed]

Jacobsen, C.

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. Sec. A 62, 248–261 (2006).
[CrossRef]

Jefimovs, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

Jourdain, P.

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

Kewish, C. M.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

Kohmura, Y.

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[CrossRef] [PubMed]

Kraus, B.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[CrossRef] [PubMed]

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

Liu, H.

H. Liu, Z. Xu, X. Zhang, Y. Wu, Z. Guo, R. Tai, “Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging,” Applied Optics 52, 2416–2427 (2013).
[CrossRef] [PubMed]

Magistretti, P.

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

Maiden, A. M.

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

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[CrossRef] [PubMed]

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

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

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

Marquet, P.

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

Marriott, P.

J. Marrison, L. Raty, P. Marriott, P. O’Toole, “Ptychography a label free, high-contrast imaging technique for live cells using quantitative phase information,” Nature Scientific Reports 3, 1–7 (2013).

Marrison, J.

J. Marrison, L. Raty, P. Marriott, P. O’Toole, “Ptychography a label free, high-contrast imaging technique for live cells using quantitative phase information,” Nature Scientific Reports 3, 1–7 (2013).

C. L. Wenzel, J. Marrison, J. Mattsson, J. Haseloff, S. M. Bougourd, “Ectopic divisions in vascular and ground tissues of Arabidopsis Thaliana result in distinct leaf venation defects,” J. Exp. Bot. 63, 5351–5363 (2012).
[CrossRef] [PubMed]

Mattsson, J.

C. L. Wenzel, J. Marrison, J. Mattsson, J. Haseloff, S. M. Bougourd, “Ectopic divisions in vascular and ground tissues of Arabidopsis Thaliana result in distinct leaf venation defects,” J. Exp. Bot. 63, 5351–5363 (2012).
[CrossRef] [PubMed]

McNulty, I.

Menzel, A.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, J. M. Rodenburg, “Translation position determination in ptychographic coherent diffractive imaging,” Opt. Express 21, 13592–13606 (2013).
[CrossRef] [PubMed]

P. Thibault, A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

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

Moodie, A. F.

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

O’Toole, P.

J. Marrison, L. Raty, P. Marriott, P. O’Toole, “Ptychography a label free, high-contrast imaging technique for live cells using quantitative phase information,” Nature Scientific Reports 3, 1–7 (2013).

Pavillon, N.

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

Peterson, I.

Pfeiffer, F.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

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

Raty, L.

J. Marrison, L. Raty, P. Marriott, P. O’Toole, “Ptychography a label free, high-contrast imaging technique for live cells using quantitative phase information,” Nature Scientific Reports 3, 1–7 (2013).

Robinson, I. K.

Rodenburg, J. M.

D. J. Batey, D. Claus, J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[CrossRef] [PubMed]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, J. M. Rodenburg, “Translation position determination in ptychographic coherent diffractive imaging,” Opt. Express 21, 13592–13606 (2013).
[CrossRef] [PubMed]

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

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

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

H. M. L. Faulkner, J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

J. M. Rodenburg, R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339, 521 (1992).
[CrossRef]

Rodenburg, J.M.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[CrossRef] [PubMed]

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

Rosenhahn, A.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Salditt, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Sarahan, M. C.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[CrossRef] [PubMed]

Sayre, D.

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. Sec. A 62, 248–261 (2006).
[CrossRef]

Schlichting, I.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

Schneider, P.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

Senkbeil, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Shapiro, D.

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. Sec. A 62, 248–261 (2006).
[CrossRef]

Shimomura, K.

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[CrossRef] [PubMed]

Shpyrko, O. G.

Suzuki, A.

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[CrossRef] [PubMed]

Tai, R.

H. Liu, Z. Xu, X. Zhang, Y. Wu, Z. Guo, R. Tai, “Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging,” Applied Optics 52, 2416–2427 (2013).
[CrossRef] [PubMed]

Takahashi, Y.

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[CrossRef] [PubMed]

Thibault, P.

P. Thibault, A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[CrossRef] [PubMed]

P. Thibault, M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys 14, 063004 (2012).
[CrossRef]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

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

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. Sec. A 62, 248–261 (2006).
[CrossRef]

Toy, F.

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

Tripathi, A.

Vila-Comamala, J.

Von Konig, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

Wenzel, C. L.

C. L. Wenzel, J. Marrison, J. Mattsson, J. Haseloff, S. M. Bougourd, “Ectopic divisions in vascular and ground tissues of Arabidopsis Thaliana result in distinct leaf venation defects,” J. Exp. Bot. 63, 5351–5363 (2012).
[CrossRef] [PubMed]

Wepf, R.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

Wu, Y.

H. Liu, Z. Xu, X. Zhang, Y. Wu, Z. Guo, R. Tai, “Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging,” Applied Optics 52, 2416–2427 (2013).
[CrossRef] [PubMed]

Xu, Z.

H. Liu, Z. Xu, X. Zhang, Y. Wu, Z. Guo, R. Tai, “Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging,” Applied Optics 52, 2416–2427 (2013).
[CrossRef] [PubMed]

Yamauchi, K.

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[CrossRef] [PubMed]

Zhang, F.

Zhang, X.

H. Liu, Z. Xu, X. Zhang, Y. Wu, Z. Guo, R. Tai, “Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging,” Applied Optics 52, 2416–2427 (2013).
[CrossRef] [PubMed]

Acta Crystallogr. Sec. (1)

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. Sec. A 62, 248–261 (2006).
[CrossRef]

Acta Crystallogr. Sec. A (1)

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

Applied Optics (1)

H. Liu, Z. Xu, X. Zhang, Y. Wu, Z. Guo, R. Tai, “Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging,” Applied Optics 52, 2416–2427 (2013).
[CrossRef] [PubMed]

J. Exp. Bot. (1)

C. L. Wenzel, J. Marrison, J. Mattsson, J. Haseloff, S. M. Bougourd, “Ectopic divisions in vascular and ground tissues of Arabidopsis Thaliana result in distinct leaf venation defects,” J. Exp. Bot. 63, 5351–5363 (2012).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Nature (2)

P. Thibault, A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[CrossRef] [PubMed]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–440 (2010).
[CrossRef] [PubMed]

Nature Comms. (1)

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

Nature Photonics (1)

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

Nature Scientific Reports (1)

J. Marrison, L. Raty, P. Marriott, P. O’Toole, “Ptychography a label free, high-contrast imaging technique for live cells using quantitative phase information,” Nature Scientific Reports 3, 1–7 (2013).

New J. Phys (1)

P. Thibault, M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys 14, 063004 (2012).
[CrossRef]

New J. Phys. (1)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[CrossRef]

Opt. Express (3)

Phil. Trans. R. Soc. Lond. A (1)

J. M. Rodenburg, R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339, 521 (1992).
[CrossRef]

Phys. Rev. Lett. (2)

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[CrossRef] [PubMed]

H. M. L. Faulkner, J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

Science (1)

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

Ultramicroscopy (4)

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

D. J. Batey, D. Claus, J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[CrossRef] [PubMed]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[CrossRef] [PubMed]

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics3rd edition (Roberts and Company Publishers, 2005) pp. 55–73

Supplementary Material (4)

» Media 1: AVI (2307 KB)     
» Media 2: AVI (3589 KB)     
» Media 3: AVI (3887 KB)     
» Media 4: AVI (1095 KB)     

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Figures (6)

Fig. 1
Fig. 1

Experimental setup used for all measurements (not to scale). Lenses L1 and L2 project an image of a 400 μm diameter pinhole and diffuser onto the thick specimen which is mounted on an x–y translation stage. The scattered laser light is collected by a conventional optical microscope (lenses L3 and L4). The last plane of the specimen is located at the focal point, fobj, of the objective lens L3. The CCD is placed at a camera length CL = 67 mm from the image plane of the microscope, and collects a diffraction pattern from the specimen at each x–y position visited. A typical diffraction pattern is shown at the plane of the CCD.

Fig. 2
Fig. 2

Reconstructions of the complex transfer functions of two planar layers of polystyrene micro-spheres separated by 40 μm. (a) 10 μm spheres in plane one (b) 20 μm spheres in plane two. The insets in (a) and (b) show a cross-sectional profile of the phase of a single bead in each layer. (c) Reconstruction of the complex field of the illumination incident on plane one, namely the probe. The modulus and phase of the three images are represented by the saturation and hue respectively. This is shown with the color map in (b).

Fig. 3
Fig. 3

Selected slices from a reconstruction of the phase, (a)–(d), and modulus, (e)–(h), of the complex transfer function of a Spirogyra algae specimen. The separations between the slices are 15 μm, 10 μm, and 15 μm for slices (a)–(b), (b)–(c), and (c)–(d) respectively. The color-bars in (a) and (e) indicate the phase (radians) and modulus (a.u.) of the complex transfer function of the specimen relative to the mounting medium (see Media ( Media 1)).

Fig. 4
Fig. 4

3D volume render of a Spirogyra. Each image represents the total phase shift over 20 μm thick slices within the Spirogyra (see ( Media 2)).

Fig. 5
Fig. 5

Selected slices from a reconstruction of the phase of the complex transfer function of a Volvox algae specimen with total thickness 150 μm. The slices (a)–(h) correspond to planes 1, 3, 5, 11, 17, 21, 24 and 28 out of a total of 33. The separation between adjacent planes is 4.7 μm. The color-bar in (a) indicates the phase shift (radians) (see ( Media 3)).

Fig. 6
Fig. 6

(a)–(d) Selected slices from ptychographic reconstructions of the phase of the complex transfer function of embryonic leaf tip. (e)–(h) The same leaf tip measured on a fluorescence confocal microscope. Individual cells are highlighted in red in each panel in order to aid the comparison. The color-bar in (a) indicates the phase shift (radians). The color-bar in (e) indicates the florescence intensity (a.u.) (see ( Media 4)).

Equations (3)

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

I j ( u ) | d [ P ( r R j ) O ( r ) ] | 2
T < R a λ
I j ( u ) | d [ O 3 ( r ) 𝒫 z 2 [ O 2 ( r ) 𝒫 z 1 [ P ( r R j ) O 1 ( r ) ] ] ] | 2

Metrics