Abstract

An autofocusing algorithm for ptychography is proposed. The method optimizes a sharpness metric that would be observed in a differential interference microscope and is valid for both amplitude and phase modulating specimens. We experimentally demonstrate that the algorithm, based on the extended ptychographic iterative engine (ePIE), calibrates the sample–detector distance with an accuracy within the depth of field of the ptychographic microscope. We show that the method can be used to determine slice separation in multislice ptychography, provided there are isolated regions on each slice of the specimen that do not axially overlap.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  2. F. Pfeiffer, Nat. Photonics 12, 9 (2018).
    [Crossref]
  3. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
    [Crossref]
  4. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
    [Crossref]
  5. A. M. Maiden and J. M. Rodenburg, Ultramicroscopy 109, 1256 (2009).
    [Crossref]
  6. P. Thibault and A. Menzel, Nature 494, 68 (2013).
    [Crossref]
  7. D. J. Batey, D. Claus, and J. M. Rodenburg, Ultramicroscopy 138, 13 (2014).
    [Crossref]
  8. B. Enders, “Development and application of decoherence models in ptychographic diffraction imaging,” Ph.D. dissertation (Technical University Munich, 2016).
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    [Crossref]
  11. A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, Ultramicroscopy 120, 64 (2012).
    [Crossref]
  12. M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, Ultramicroscopy 126, 44 (2013).
    [Crossref]
  13. F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, Opt. Express 21, 13592 (2013).
    [Crossref]
  14. L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
    [Crossref]
  15. A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, J. Opt. Soc. Am. A 29, 1606 (2012).
    [Crossref]
  16. E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, Opt. Express 24, 29089 (2016).
    [Crossref]
  17. J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, Opt. Laser Eng. 98, 56 (2017).
    [Crossref]
  18. J. W. Goodman, Introduction to Fourier Optics, 4th ed. (WH Freeman, 2017).
  19. J. M. Rodenburg and R. H. T. Bates, Philos. Trans. R. Soc. London, Ser. A 339, 521 (1992).
    [Crossref]
  20. D. D. Nolte, Optical Interferometry for Biology and Medicine (Springer, 2011).
  21. A. Maiden, D. Johnson, and P. Li, Optica 4, 736 (2017).
    [Crossref]
  22. O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
    [Crossref]
  23. A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, Opt. Lett. 35, 2585 (2010).
    [Crossref]
  24. M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 1 (2012).
    [Crossref]
  25. M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
    [Crossref]
  26. M. Odstrcil, A. Menzel, and M. Guizar-Sicairos, Opt. Express 26, 3108 (2018).
    [Crossref]

2018 (3)

F. Pfeiffer, Nat. Photonics 12, 9 (2018).
[Crossref]

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

M. Odstrcil, A. Menzel, and M. Guizar-Sicairos, Opt. Express 26, 3108 (2018).
[Crossref]

2017 (2)

A. Maiden, D. Johnson, and P. Li, Optica 4, 736 (2017).
[Crossref]

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, Opt. Laser Eng. 98, 56 (2017).
[Crossref]

2016 (1)

2014 (1)

D. J. Batey, D. Claus, and J. M. Rodenburg, Ultramicroscopy 138, 13 (2014).
[Crossref]

2013 (4)

P. Thibault and A. Menzel, Nature 494, 68 (2013).
[Crossref]

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, Ultramicroscopy 126, 44 (2013).
[Crossref]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, Opt. Express 21, 13592 (2013).
[Crossref]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
[Crossref]

2012 (3)

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 1 (2012).
[Crossref]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, J. Opt. Soc. Am. A 29, 1606 (2012).
[Crossref]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

2010 (1)

2009 (2)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[Crossref]

A. M. Maiden and J. M. Rodenburg, Ultramicroscopy 109, 1256 (2009).
[Crossref]

2008 (3)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

M. Guizar-Sicairos and J. R. Fienup, Opt. Express 16, 7264 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

2004 (1)

J. M. Rodenburg and H. M. L. Faulkner, Appl. Phys. Lett. 85, 4795 (2004).
[Crossref]

1992 (1)

J. M. Rodenburg and R. H. T. Bates, Philos. Trans. R. Soc. London, Ser. A 339, 521 (1992).
[Crossref]

Baluktsian, M.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Bates, R. H. T.

J. M. Rodenburg and R. H. T. Bates, Philos. Trans. R. Soc. London, Ser. A 339, 521 (1992).
[Crossref]

Batey, D. J.

D. J. Batey, D. Claus, and J. M. Rodenburg, Ultramicroscopy 138, 13 (2014).
[Crossref]

Bean, R.

Beckers, M.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, Ultramicroscopy 126, 44 (2013).
[Crossref]

Bunk, O.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 1 (2012).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Bykova, I.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Chen, B.

Claus, D.

D. J. Batey, D. Claus, and J. M. Rodenburg, Ultramicroscopy 138, 13 (2014).
[Crossref]

Cloetens, P.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
[Crossref]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Diaz, A.

Dierolf, M.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Dogan, G.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Dou, J.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, Opt. Laser Eng. 98, 56 (2017).
[Crossref]

Enders, B.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
[Crossref]

B. Enders, “Development and application of decoherence models in ptychographic diffraction imaging,” Ph.D. dissertation (Technical University Munich, 2016).

Faulkner, H. M. L.

J. M. Rodenburg and H. M. L. Faulkner, Appl. Phys. Lett. 85, 4795 (2004).
[Crossref]

Fienup, J. R.

Gao, Z.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, Opt. Laser Eng. 98, 56 (2017).
[Crossref]

Giewekemeyer, K.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, Ultramicroscopy 126, 44 (2013).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 4th ed. (WH Freeman, 2017).

Gorniak, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, Ultramicroscopy 126, 44 (2013).
[Crossref]

Guizar-Sicairos, M.

Holler, M.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 1 (2012).
[Crossref]

Humphry, M. J.

Johnson, D.

Johnson, I.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Keskinbora, K.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Kraus, B.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

Kynde, S.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Li, P.

Loetgering, L.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Ma, J.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, Opt. Laser Eng. 98, 56 (2017).
[Crossref]

Maiden, A.

Maiden, A. M.

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, J. Opt. Soc. Am. A 29, 1606 (2012).
[Crossref]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, Opt. Lett. 35, 2585 (2010).
[Crossref]

A. M. Maiden and J. M. Rodenburg, Ultramicroscopy 109, 1256 (2009).
[Crossref]

Marti, O.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Menzel, A.

M. Odstrcil, A. Menzel, and M. Guizar-Sicairos, Opt. Express 26, 3108 (2018).
[Crossref]

E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, Opt. Express 24, 29089 (2016).
[Crossref]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, Opt. Express 21, 13592 (2013).
[Crossref]

P. Thibault and A. Menzel, Nature 494, 68 (2013).
[Crossref]

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 1 (2012).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Nolte, D. D.

D. D. Nolte, Optical Interferometry for Biology and Medicine (Springer, 2011).

Odstrcil, M.

M. Odstrcil, A. Menzel, and M. Guizar-Sicairos, Opt. Express 26, 3108 (2018).
[Crossref]

M. Odstrčil, “Coherent diffractive imaging using table-top sources,” Ph.D. Thesis (University of Southampton, 2017).

Peterson, I.

Pfeiffer, F.

F. Pfeiffer, Nat. Photonics 12, 9 (2018).
[Crossref]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Robinson, I. K.

Rodenburg, J. M.

D. J. Batey, D. Claus, and J. M. Rodenburg, Ultramicroscopy 138, 13 (2014).
[Crossref]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, Opt. Express 21, 13592 (2013).
[Crossref]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, J. Opt. Soc. Am. A 29, 1606 (2012).
[Crossref]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, Opt. Lett. 35, 2585 (2010).
[Crossref]

A. M. Maiden and J. M. Rodenburg, Ultramicroscopy 109, 1256 (2009).
[Crossref]

J. M. Rodenburg and H. M. L. Faulkner, Appl. Phys. Lett. 85, 4795 (2004).
[Crossref]

J. M. Rodenburg and R. H. T. Bates, Philos. Trans. R. Soc. London, Ser. A 339, 521 (1992).
[Crossref]

Rose, M.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Rosenhahn, A.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, Ultramicroscopy 126, 44 (2013).
[Crossref]

Salditt, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, Ultramicroscopy 126, 44 (2013).
[Crossref]

Sanli, U.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Sarahan, M. C.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

Schütz, G.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Senkbeil, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, Ultramicroscopy 126, 44 (2013).
[Crossref]

Stockmar, M.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
[Crossref]

Thibault, P.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
[Crossref]

P. Thibault and A. Menzel, Nature 494, 68 (2013).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Tsai, E. H. R.

Usov, I.

Vila-Comamala, J.

Wang, L.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, Opt. Laser Eng. 98, 56 (2017).
[Crossref]

Weigand, M.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Wilhein, T.

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Yang, Z.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, Opt. Laser Eng. 98, 56 (2017).
[Crossref]

Yuan, C.

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, Opt. Laser Eng. 98, 56 (2017).
[Crossref]

Zanette, I.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
[Crossref]

Zhang, F.

Appl. Phys. Lett. (1)

J. M. Rodenburg and H. M. L. Faulkner, Appl. Phys. Lett. 85, 4795 (2004).
[Crossref]

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

Nat. Photonics (1)

F. Pfeiffer, Nat. Photonics 12, 9 (2018).
[Crossref]

Nature (1)

P. Thibault and A. Menzel, Nature 494, 68 (2013).
[Crossref]

Opt. Eng. (1)

L. Loetgering, M. Rose, K. Keskinbora, M. Baluktsian, G. Dogan, U. Sanli, I. Bykova, M. Weigand, G. Schütz, and T. Wilhein, Opt. Eng. 57, 084106 (2018).
[Crossref]

Opt. Express (4)

Opt. Laser Eng. (1)

J. Dou, Z. Gao, J. Ma, C. Yuan, Z. Yang, and L. Wang, Opt. Laser Eng. 98, 56 (2017).
[Crossref]

Opt. Lett. (1)

Optica (1)

Philos. Trans. R. Soc. London, Ser. A (1)

J. M. Rodenburg and R. H. T. Bates, Philos. Trans. R. Soc. London, Ser. A 339, 521 (1992).
[Crossref]

Phys. Rev. B (1)

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 1 (2012).
[Crossref]

Sci. Rep. (1)

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, Sci. Rep. 3, 1927 (2013).
[Crossref]

Science (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Ultramicroscopy (6)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[Crossref]

A. M. Maiden and J. M. Rodenburg, Ultramicroscopy 109, 1256 (2009).
[Crossref]

D. J. Batey, D. Claus, and J. M. Rodenburg, Ultramicroscopy 138, 13 (2014).
[Crossref]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, Ultramicroscopy 126, 44 (2013).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Other (4)

J. W. Goodman, Introduction to Fourier Optics, 4th ed. (WH Freeman, 2017).

D. D. Nolte, Optical Interferometry for Biology and Medicine (Springer, 2011).

B. Enders, “Development and application of decoherence models in ptychographic diffraction imaging,” Ph.D. dissertation (Technical University Munich, 2016).

M. Odstrčil, “Coherent diffractive imaging using table-top sources,” Ph.D. Thesis (University of Southampton, 2017).

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Figures (5)

Fig. 1.
Fig. 1. Axial misalignment in the sample–detector distance results in scan grid miscalibration. The black coordinates (dashed line) illustrate an inflated scan grid as compared to the true encoder positions (gray coordinates, solid line). The depicted situation arises when underestimating the sample–detector distance, while an overestimation would result in a compressed scan grid.
Fig. 2.
Fig. 2. Experimental setup. A spatially filtered (L, lens; PH, pinhole) beam is focused to produce a divergent beam illuminating a sample mounted on a $xy$ translation stage. The diffraction data are recorded in a lensless geometry.
Fig. 3.
Fig. 3. Ptychographic reconstruction (a), (b) with autofocus and (c), (d) without autofocus using an initial object–detector distance of $ {z_0} = 35.5\;{\rm mm} $ . (e) Estimated sample–detector distance $ z $ versus iteration with varying initial estimates $ {z_0} $ . (a), (b) correspond to the central dotted-dashed line in (e).
Fig. 4.
Fig. 4. (a) Due to refraction at the glass–air interface and assumed free-space propagation from the sample to the detector, the autofocusing algorithm recovers a virtual point source inside the specimen. (b) Experimental geometry for multislice ptychography.
Fig. 5.
Fig. 5. Comparison of (a) single- and (b) multislice amplitude reconstructions of crossed fingerprints. (b) Both object slices projected into the same plane. (c) 3PIE beam reconstruction. Hue and brightness show phase and amplitude, respectively. (d) Overlay of back (green, illumination-sided) and front (red, detector-sided) slices of object reconstruction.

Tables (1)

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Algorithm 1. Axial position correction algorithm (zPIE)

Equations (7)

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p ¯ j = D r j λ ( z ± δ z ) p j D r j λ z 2 δ z ,
O ( x , y , z ) = F 1 H k Δ z ( f x , f y ) F O ( x , y , 0 ) ,
H k Δ z ( f x , f y ) = exp [ i 2 π / λ k Δ z 1 ( f x x ) 2 ( f y y ) 2 ] .
Δ z = λ ( 2 z / D ) 2 .
S ( z ) = | x O ( x , y , z ) | 2 + | y O ( x , y , z ) | 2 + ϵ d x d y ,
S ( z ) S ( z ) + ( z z ) z S ( z ) + 1 2 ( z z ) 2 z 2 S ( z ) ,
S ( z ) S ( z ) + 1 2 ( z z ) 2 z 2 S ( z ) .

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