Abstract

We proposed an iterative method for phase retrieval and diffractive imaging based on Babinet's principle and complementary random sampling (CRS). We demonstrated that the whole complex amplitude (not sieved) of an object wave can be accurately retrieved from the diffraction intensities of the object wave sampled by a group of binary CRS masks and the diffractive imaging for the object can be realized through a single digital inverse diffraction. Some experimental results are given for the demonstration. Our experimental results reveal that, using CRS, the influence of a binary random sampling mask on the retrieved field can be well eliminated, and the accuracy and efficiency of the phase retrieval can be greatly improved.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging

Tatiana Latychevskaia, Jean-Nicolas Longchamp, and Hans-Werner Fink
Opt. Express 19(20) 19330-19339 (2011)

Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint

Cheng Shen, Xuejing Bao, Jiubin Tan, Shutian Liu, and Zhengjun Liu
Opt. Express 25(14) 16235-16249 (2017)

Understanding the twin-image problem in phase retrieval

Manuel Guizar-Sicairos and James R. Fienup
J. Opt. Soc. Am. A 29(11) 2367-2375 (2012)

References

  • View by:
  • |
  • |
  • |

  1. J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
    [Crossref] [PubMed]
  2. A. Rosenhahn, R. Barth, F. Staier, T. Simpson, S. Mittler, S. Eisebitt, and M. Grunze, “Digital in-line soft x-ray holography with element contrast,” J. Opt. Soc. Am. A 25(2), 416–422 (2008).
    [Crossref] [PubMed]
  3. M. Guizar-Sicairos and J. R. Fienup, “Holography with extended reference by autocorrelation linear differential operation,” Opt. Express 15(26), 17592–17612 (2007).
    [Crossref] [PubMed]
  4. S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
    [Crossref]
  5. M. Guizar-Sicairos and J. R. Fienup, “Direct image reconstruction from a Fourier intensity pattern using HERALDO,” Opt. Lett. 33(22), 2668–2670 (2008).
    [Crossref] [PubMed]
  6. R. L. Sandberg, D. A. Raymondson, C. La-O-Vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, H. C. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. 34(11), 1618–1620 (2009).
    [Crossref] [PubMed]
  7. J. Geilhufe, C. Tieg, B. Pfau, C. M. Günther, E. Guehrs, S. Schaffert, and S. Eisebitt, “Extracting depth information of 3-dimensional structures from a single-view X-ray Fourier-transform hologram,” Opt. Express 22(21), 24959–24969 (2014).
    [Crossref] [PubMed]
  8. X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33(8), 776–778 (2008).
    [Crossref] [PubMed]
  9. J. Deng, H. Wang, D. Zhang, L. Zhong, J. Fan, and X. Lu, “Phase shift extraction algorithm based on Euclidean matrix norm,” Opt. Lett. 38(9), 1506–1508 (2013).
    [Crossref] [PubMed]
  10. N. T. Shaked, Y. Zhu, M. T. Rinehart, and A. Wax, “Two-step-only phase-shifting interferometry with optimized detector bandwidth for microscopy of live cells,” Opt. Express 17(18), 15585–15591 (2009).
    [Crossref] [PubMed]
  11. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
    [Crossref] [PubMed]
  12. U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
    [Crossref] [PubMed]
  13. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
    [Crossref] [PubMed]
  14. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
    [Crossref]
  15. M. Agour, P. F. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using SLM-based phase retrieval and a phase diffuser,” J. Europ. Opt. Soc. 7, 12046 (2012).
    [Crossref]
  16. J. A. Rodrigo, H. Duadi, T. Alieva, and Z. Zalevsky, “Multi-stage phase retrieval algorithm based upon the gyrator transform,” Opt. Express 18(2), 1510–1520 (2010).
    [Crossref] [PubMed]
  17. H. I. Campbell, S. Zhang, A. H. Greenaway, and S. Restaino, “Generalized phase diversity for wave-front sensing,” Opt. Lett. 29(23), 2707–2709 (2004).
    [Crossref] [PubMed]
  18. H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
    [Crossref] [PubMed]
  19. J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
    [Crossref] [PubMed]
  20. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
    [Crossref] [PubMed]
  21. J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107(2-3), 227–231 (2007).
    [Crossref] [PubMed]
  22. A. Anand, G. Pedrini, W. Osten, and P. Almoro, “Wavefront sensing with random amplitude mask and phase retrieval,” Opt. Lett. 32(11), 1584–1586 (2007).
    [Crossref] [PubMed]
  23. A. Fannjiang, “Absolute uniqueness of phase retrieval with random illumination,” Inverse Probl. 28(7), 075008 (2012).
    [Crossref]
  24. E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” SIAM J. Imaging Sci. 6(1), 199–225 (2013).
    [Crossref]
  25. I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
    [Crossref] [PubMed]
  26. F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
    [Crossref]
  27. C. Falldorf, M. Agour, C. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system,” Appl. Opt. 49(10), 1826–1830 (2010).
    [Crossref] [PubMed]
  28. A. Fannjiang and W. Liao, “Phase retrieval with random phase illumination,” J. Opt. Soc. Am. A 29(9), 1847–1859 (2012).
    [Crossref] [PubMed]
  29. H. Tao, S. P. Veetil, J. Cheng, X. Pan, H. Wang, C. Liu, and J.-Q. Zhu, “Measurement of the complex transmittance of large optical elements with modulation coherent imaging,” Appl. Opt. 54(7), 1776–1781 (2015).
    [Crossref]
  30. H.-Y. Wang, C. Liu, S. P. Veetil, X.-C. Pan, and J.-Q. Zhu, “Measurement of the complex transmittance of large optical elements with Ptychographical Iterative Engine,” Opt. Express 22(2), 2159–2166 (2014).
    [Crossref] [PubMed]
  31. R. Horisaki, Y. Ogura, M. Aino, and J. Tanida, “Single-shot phase imaging with a coded aperture,” Opt. Lett. 39(22), 6466–6469 (2014).
    [Crossref] [PubMed]
  32. R. Horisaki and J. Tanida, “Multidimensional object acquisition by single-shot phase imaging with a coded aperture,” Opt. Express 23(8), 9696–9704 (2015).
    [Crossref] [PubMed]
  33. Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp.Technol. 6(10), 506–509 (2010).
    [Crossref]
  34. G. Rodriguez-Zurita, C. Rickenstorff, R. Pastrana-Sánchez, J. F. Vázquez-Castillo, C. Robledo-Sanchez, C. Meneses-Fabian, and N. I. Toto-Arellano, “Babinet’s principle for scalar complex objects in the far field,” J. Opt. 16(10), 105707 (2014).
    [Crossref]
  35. C. Martinez, O. Lemonnier, F. Laulagnet, A. Fargeix, F. Tissot, and M. F. Armand, “Complementary computer generated holography for aesthetic watermarking,” Opt. Express 20(5), 5547–5556 (2012).
    [Crossref] [PubMed]
  36. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
  37. M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, “Quantitative phase imaging,” Prog. Opt. 57, 133–217 (2012).
    [Crossref]
  38. T. H. Nguyen, C. Edwards, L. L. Goddard, and G. Popescu, “Quantitative phase imaging with partially coherent illumination,” Opt. Lett. 39(19), 5511–5514 (2014).
    [Crossref] [PubMed]
  39. T. Harada, H. Hashimoto, Y. Tanaka, T. Amano, T. Watanabe, and H. Kinoshita, “Quantitative phase imaging of a small phase structure on an extreme-ultraviolet mask by coherent diffraction imaging,” Appl. Phys. Express 8(5), 055202 (2015).
    [Crossref]

2015 (4)

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

H. Tao, S. P. Veetil, J. Cheng, X. Pan, H. Wang, C. Liu, and J.-Q. Zhu, “Measurement of the complex transmittance of large optical elements with modulation coherent imaging,” Appl. Opt. 54(7), 1776–1781 (2015).
[Crossref]

R. Horisaki and J. Tanida, “Multidimensional object acquisition by single-shot phase imaging with a coded aperture,” Opt. Express 23(8), 9696–9704 (2015).
[Crossref] [PubMed]

T. Harada, H. Hashimoto, Y. Tanaka, T. Amano, T. Watanabe, and H. Kinoshita, “Quantitative phase imaging of a small phase structure on an extreme-ultraviolet mask by coherent diffraction imaging,” Appl. Phys. Express 8(5), 055202 (2015).
[Crossref]

2014 (5)

2013 (2)

J. Deng, H. Wang, D. Zhang, L. Zhong, J. Fan, and X. Lu, “Phase shift extraction algorithm based on Euclidean matrix norm,” Opt. Lett. 38(9), 1506–1508 (2013).
[Crossref] [PubMed]

E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” SIAM J. Imaging Sci. 6(1), 199–225 (2013).
[Crossref]

2012 (5)

A. Fannjiang, “Absolute uniqueness of phase retrieval with random illumination,” Inverse Probl. 28(7), 075008 (2012).
[Crossref]

A. Fannjiang and W. Liao, “Phase retrieval with random phase illumination,” J. Opt. Soc. Am. A 29(9), 1847–1859 (2012).
[Crossref] [PubMed]

C. Martinez, O. Lemonnier, F. Laulagnet, A. Fargeix, F. Tissot, and M. F. Armand, “Complementary computer generated holography for aesthetic watermarking,” Opt. Express 20(5), 5547–5556 (2012).
[Crossref] [PubMed]

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, “Quantitative phase imaging,” Prog. Opt. 57, 133–217 (2012).
[Crossref]

M. Agour, P. F. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using SLM-based phase retrieval and a phase diffuser,” J. Europ. Opt. Soc. 7, 12046 (2012).
[Crossref]

2010 (4)

2009 (2)

2008 (6)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33(8), 776–778 (2008).
[Crossref] [PubMed]

A. Rosenhahn, R. Barth, F. Staier, T. Simpson, S. Mittler, S. Eisebitt, and M. Grunze, “Digital in-line soft x-ray holography with element contrast,” J. Opt. Soc. Am. A 25(2), 416–422 (2008).
[Crossref] [PubMed]

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

M. Guizar-Sicairos and J. R. Fienup, “Direct image reconstruction from a Fourier intensity pattern using HERALDO,” Opt. Lett. 33(22), 2668–2670 (2008).
[Crossref] [PubMed]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

2007 (4)

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107(2-3), 227–231 (2007).
[Crossref] [PubMed]

A. Anand, G. Pedrini, W. Osten, and P. Almoro, “Wavefront sensing with random amplitude mask and phase retrieval,” Opt. Lett. 32(11), 1584–1586 (2007).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Holography with extended reference by autocorrelation linear differential operation,” Opt. Express 15(26), 17592–17612 (2007).
[Crossref] [PubMed]

2005 (1)

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

2004 (2)

H. I. Campbell, S. Zhang, A. H. Greenaway, and S. Restaino, “Generalized phase diversity for wave-front sensing,” Opt. Lett. 29(23), 2707–2709 (2004).
[Crossref] [PubMed]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

2002 (1)

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

1998 (1)

1982 (1)

Agour, M.

M. Agour, P. F. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using SLM-based phase retrieval and a phase diffuser,” J. Europ. Opt. Soc. 7, 12046 (2012).
[Crossref]

C. Falldorf, M. Agour, C. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system,” Appl. Opt. 49(10), 1826–1830 (2010).
[Crossref] [PubMed]

Aino, M.

Alieva, T.

Almoro, P.

Almoro, P. F.

M. Agour, P. F. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using SLM-based phase retrieval and a phase diffuser,” J. Europ. Opt. Soc. 7, 12046 (2012).
[Crossref]

Amano, T.

T. Harada, H. Hashimoto, Y. Tanaka, T. Amano, T. Watanabe, and H. Kinoshita, “Quantitative phase imaging of a small phase structure on an extreme-ultraviolet mask by coherent diffraction imaging,” Appl. Phys. Express 8(5), 055202 (2015).
[Crossref]

Anand, A.

Armand, M. F.

Bajt, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Barth, R.

Barty, A.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Beetz, T.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Bergmann, R. B.

Bhaduri, B.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, “Quantitative phase imaging,” Prog. Opt. 57, 133–217 (2012).
[Crossref]

Bogan, M. J.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Boutet, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Bunk, O.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Cai, L. Z.

Campbell, H. I.

Candès, E. J.

E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” SIAM J. Imaging Sci. 6(1), 199–225 (2013).
[Crossref]

Chapman, H. N.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[Crossref]

Chen, Q.

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Cheng, J.

Cheng, X. C.

Cui, C.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107(2-3), 227–231 (2007).
[Crossref] [PubMed]

David, C.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Deng, J.

Dierolf, M.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Dobson, B. R.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Dong, G. Y.

Duadi, H.

Edwards, C.

Eisebitt, S.

Eldar, Y. C.

E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” SIAM J. Imaging Sci. 6(1), 199–225 (2013).
[Crossref]

Elser, V.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Falldorf, C.

M. Agour, P. F. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using SLM-based phase retrieval and a phase diffuser,” J. Europ. Opt. Soc. 7, 12046 (2012).
[Crossref]

C. Falldorf, M. Agour, C. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system,” Appl. Opt. 49(10), 1826–1830 (2010).
[Crossref] [PubMed]

Fan, J.

Fannjiang, A.

A. Fannjiang and W. Liao, “Phase retrieval with random phase illumination,” J. Opt. Soc. Am. A 29(9), 1847–1859 (2012).
[Crossref] [PubMed]

A. Fannjiang, “Absolute uniqueness of phase retrieval with random illumination,” Inverse Probl. 28(7), 075008 (2012).
[Crossref]

Fargeix, A.

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Fienup, J. R.

Frank, M.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Geilhufe, J.

Goddard, L. L.

Gray, J.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

Greenaway, A. H.

Grunze, M.

Guehrs, E.

Guizar-Sicairos, M.

Günther, C. M.

Hajdu, J.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Harada, T.

T. Harada, H. Hashimoto, Y. Tanaka, T. Amano, T. Watanabe, and H. Kinoshita, “Quantitative phase imaging of a small phase structure on an extreme-ultraviolet mask by coherent diffraction imaging,” Appl. Phys. Express 8(5), 055202 (2015).
[Crossref]

Hashimoto, H.

T. Harada, H. Hashimoto, Y. Tanaka, T. Amano, T. Watanabe, and H. Kinoshita, “Quantitative phase imaging of a small phase structure on an extreme-ultraviolet mask by coherent diffraction imaging,” Appl. Phys. Express 8(5), 055202 (2015).
[Crossref]

Hau-Riege, S. P.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Horisaki, R.

Howells, M.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Howells, M. R.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Hurst, A. C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107(2-3), 227–231 (2007).
[Crossref] [PubMed]

Isaacson, M.

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Ishikawa, T.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

Jacobsen, C.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp.Technol. 6(10), 506–509 (2010).
[Crossref]

Jefimovs, K.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Johnson, I.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Kapteyn, H. C.

Kinoshita, H.

T. Harada, H. Hashimoto, Y. Tanaka, T. Amano, T. Watanabe, and H. Kinoshita, “Quantitative phase imaging of a small phase structure on an extreme-ultraviolet mask by coherent diffraction imaging,” Appl. Phys. Express 8(5), 055202 (2015).
[Crossref]

Kirz, J.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Kopylow, C.

La-O-Vorakiat, C.

Laulagnet, F.

Lee, J. Y.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Lemonnier, O.

Liao, W.

Lima, E.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Liu, C.

Lu, X.

Marchesini, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Martinez, C.

Meneses-Fabian, C.

G. Rodriguez-Zurita, C. Rickenstorff, R. Pastrana-Sánchez, J. F. Vázquez-Castillo, C. Robledo-Sanchez, C. Meneses-Fabian, and N. I. Toto-Arellano, “Babinet’s principle for scalar complex objects in the far field,” J. Opt. 16(10), 105707 (2014).
[Crossref]

Meng, X. F.

Menzel, A.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Miao, H.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Miao, J.

Mir, M.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, “Quantitative phase imaging,” Prog. Opt. 57, 133–217 (2012).
[Crossref]

Mittler, S.

Murnane, M. M.

Neiman, A. M.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Nguyen, T. H.

Ogura, Y.

Osten, W.

Pan, X.

Pan, X.-C.

Panepucci, R. R.

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Pastrana-Sánchez, R.

G. Rodriguez-Zurita, C. Rickenstorff, R. Pastrana-Sánchez, J. F. Vázquez-Castillo, C. Robledo-Sanchez, C. Meneses-Fabian, and N. I. Toto-Arellano, “Babinet’s principle for scalar complex objects in the far field,” J. Opt. 16(10), 105707 (2014).
[Crossref]

Paul, A.

Pedrini, G.

Pfau, B.

Pfeiffer, F.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Popescu, G.

Raines, K. S.

Raymondson, D. A.

Renker, D.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

Restaino, S.

Rickenstorff, C.

G. Rodriguez-Zurita, C. Rickenstorff, R. Pastrana-Sánchez, J. F. Vázquez-Castillo, C. Robledo-Sanchez, C. Meneses-Fabian, and N. I. Toto-Arellano, “Babinet’s principle for scalar complex objects in the far field,” J. Opt. 16(10), 105707 (2014).
[Crossref]

Rinehart, M. T.

Rivenson, Y.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp.Technol. 6(10), 506–509 (2010).
[Crossref]

Robinson, I. K.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

Robledo-Sanchez, C.

G. Rodriguez-Zurita, C. Rickenstorff, R. Pastrana-Sánchez, J. F. Vázquez-Castillo, C. Robledo-Sanchez, C. Meneses-Fabian, and N. I. Toto-Arellano, “Babinet’s principle for scalar complex objects in the far field,” J. Opt. 16(10), 105707 (2014).
[Crossref]

Rodenburg, J. M.

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107(2-3), 227–231 (2007).
[Crossref] [PubMed]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Rodrigo, J. A.

Rodriguez-Zurita, G.

G. Rodriguez-Zurita, C. Rickenstorff, R. Pastrana-Sánchez, J. F. Vázquez-Castillo, C. Robledo-Sanchez, C. Meneses-Fabian, and N. I. Toto-Arellano, “Babinet’s principle for scalar complex objects in the far field,” J. Opt. 16(10), 105707 (2014).
[Crossref]

Rosenhahn, A.

Sakdinawat, A. E.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Sandberg, R. L.

Sayre, D.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[Crossref]

Schaffert, S.

Schlotter, W. F.

Seibert, M. M.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Shaevitz, J. W.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Shaked, N. T.

Shapiro, D.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Shapiro, D. A.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Shen, X. X.

Simpson, T.

Spence, J. C. H.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Staier, F.

Stern, A.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp.Technol. 6(10), 506–509 (2010).
[Crossref]

Strohmer, T.

E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” SIAM J. Imaging Sci. 6(1), 199–225 (2013).
[Crossref]

Sun, W. J.

Szöke, A.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Tanaka, Y.

T. Harada, H. Hashimoto, Y. Tanaka, T. Amano, T. Watanabe, and H. Kinoshita, “Quantitative phase imaging of a small phase structure on an extreme-ultraviolet mask by coherent diffraction imaging,” Appl. Phys. Express 8(5), 055202 (2015).
[Crossref]

Tanida, J.

Tao, H.

Thibault, P.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Tieg, C.

Tissot, F.

Toto-Arellano, N. I.

G. Rodriguez-Zurita, C. Rickenstorff, R. Pastrana-Sánchez, J. F. Vázquez-Castillo, C. Robledo-Sanchez, C. Meneses-Fabian, and N. I. Toto-Arellano, “Babinet’s principle for scalar complex objects in the far field,” J. Opt. 16(10), 105707 (2014).
[Crossref]

Vázquez-Castillo, J. F.

G. Rodriguez-Zurita, C. Rickenstorff, R. Pastrana-Sánchez, J. F. Vázquez-Castillo, C. Robledo-Sanchez, C. Meneses-Fabian, and N. I. Toto-Arellano, “Babinet’s principle for scalar complex objects in the far field,” J. Opt. 16(10), 105707 (2014).
[Crossref]

Veetil, S. P.

Voroninski, V.

E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” SIAM J. Imaging Sci. 6(1), 199–225 (2013).
[Crossref]

Wang, H.

Wang, H.-Y.

Wang, R.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, “Quantitative phase imaging,” Prog. Opt. 57, 133–217 (2012).
[Crossref]

Wang, Y. R.

Watanabe, T.

T. Harada, H. Hashimoto, Y. Tanaka, T. Amano, T. Watanabe, and H. Kinoshita, “Quantitative phase imaging of a small phase structure on an extreme-ultraviolet mask by coherent diffraction imaging,” Appl. Phys. Express 8(5), 055202 (2015).
[Crossref]

Wax, A.

Weierstall, U.

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

Xu, X. F.

Zalevsky, Z.

Zhang, D.

Zhang, F.

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[Crossref]

Zhang, H.

Zhang, S.

Zhong, L.

Zhu, J.-Q.

Zhu, R.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, “Quantitative phase imaging,” Prog. Opt. 57, 133–217 (2012).
[Crossref]

Zhu, Y.

Appl. Opt. (3)

Appl. Phys. Express (1)

T. Harada, H. Hashimoto, Y. Tanaka, T. Amano, T. Watanabe, and H. Kinoshita, “Quantitative phase imaging of a small phase structure on an extreme-ultraviolet mask by coherent diffraction imaging,” Appl. Phys. Express 8(5), 055202 (2015).
[Crossref]

Inverse Probl. (1)

A. Fannjiang, “Absolute uniqueness of phase retrieval with random illumination,” Inverse Probl. 28(7), 075008 (2012).
[Crossref]

J. Disp.Technol. (1)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel Holography,” J. Disp.Technol. 6(10), 506–509 (2010).
[Crossref]

J. Europ. Opt. Soc. (1)

M. Agour, P. F. Almoro, and C. Falldorf, “Investigation of smooth wave fronts using SLM-based phase retrieval and a phase diffuser,” J. Europ. Opt. Soc. 7, 12046 (2012).
[Crossref]

J. Opt. (1)

G. Rodriguez-Zurita, C. Rickenstorff, R. Pastrana-Sánchez, J. F. Vázquez-Castillo, C. Robledo-Sanchez, C. Meneses-Fabian, and N. I. Toto-Arellano, “Babinet’s principle for scalar complex objects in the far field,” J. Opt. 16(10), 105707 (2014).
[Crossref]

J. Opt. Soc. Am. A (3)

Nat. Photonics (1)

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2(9), 560–563 (2008).
[Crossref]

Opt. Express (7)

N. T. Shaked, Y. Zhu, M. T. Rinehart, and A. Wax, “Two-step-only phase-shifting interferometry with optimized detector bandwidth for microscopy of live cells,” Opt. Express 17(18), 15585–15591 (2009).
[Crossref] [PubMed]

J. A. Rodrigo, H. Duadi, T. Alieva, and Z. Zalevsky, “Multi-stage phase retrieval algorithm based upon the gyrator transform,” Opt. Express 18(2), 1510–1520 (2010).
[Crossref] [PubMed]

C. Martinez, O. Lemonnier, F. Laulagnet, A. Fargeix, F. Tissot, and M. F. Armand, “Complementary computer generated holography for aesthetic watermarking,” Opt. Express 20(5), 5547–5556 (2012).
[Crossref] [PubMed]

H.-Y. Wang, C. Liu, S. P. Veetil, X.-C. Pan, and J.-Q. Zhu, “Measurement of the complex transmittance of large optical elements with Ptychographical Iterative Engine,” Opt. Express 22(2), 2159–2166 (2014).
[Crossref] [PubMed]

J. Geilhufe, C. Tieg, B. Pfau, C. M. Günther, E. Guehrs, S. Schaffert, and S. Eisebitt, “Extracting depth information of 3-dimensional structures from a single-view X-ray Fourier-transform hologram,” Opt. Express 22(21), 24959–24969 (2014).
[Crossref] [PubMed]

R. Horisaki and J. Tanida, “Multidimensional object acquisition by single-shot phase imaging with a coded aperture,” Opt. Express 23(8), 9696–9704 (2015).
[Crossref] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Holography with extended reference by autocorrelation linear differential operation,” Opt. Express 15(26), 17592–17612 (2007).
[Crossref] [PubMed]

Opt. Lett. (8)

R. Horisaki, Y. Ogura, M. Aino, and J. Tanida, “Single-shot phase imaging with a coded aperture,” Opt. Lett. 39(22), 6466–6469 (2014).
[Crossref] [PubMed]

T. H. Nguyen, C. Edwards, L. L. Goddard, and G. Popescu, “Quantitative phase imaging with partially coherent illumination,” Opt. Lett. 39(19), 5511–5514 (2014).
[Crossref] [PubMed]

J. Deng, H. Wang, D. Zhang, L. Zhong, J. Fan, and X. Lu, “Phase shift extraction algorithm based on Euclidean matrix norm,” Opt. Lett. 38(9), 1506–1508 (2013).
[Crossref] [PubMed]

H. I. Campbell, S. Zhang, A. H. Greenaway, and S. Restaino, “Generalized phase diversity for wave-front sensing,” Opt. Lett. 29(23), 2707–2709 (2004).
[Crossref] [PubMed]

A. Anand, G. Pedrini, W. Osten, and P. Almoro, “Wavefront sensing with random amplitude mask and phase retrieval,” Opt. Lett. 32(11), 1584–1586 (2007).
[Crossref] [PubMed]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33(8), 776–778 (2008).
[Crossref] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Direct image reconstruction from a Fourier intensity pattern using HERALDO,” Opt. Lett. 33(22), 2668–2670 (2008).
[Crossref] [PubMed]

R. L. Sandberg, D. A. Raymondson, C. La-O-Vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, H. C. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. 34(11), 1618–1620 (2009).
[Crossref] [PubMed]

Phys. Rev. B (1)

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[Crossref]

Phys. Rev. Lett. (3)

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100(15), 155503 (2008).
[Crossref] [PubMed]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[Crossref] [PubMed]

Prog. Opt. (1)

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, “Quantitative phase imaging,” Prog. Opt. 57, 133–217 (2012).
[Crossref]

Science (2)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

SIAM J. Imaging Sci. (1)

E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” SIAM J. Imaging Sci. 6(1), 199–225 (2013).
[Crossref]

Ultramicroscopy (2)

U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90(2-3), 171–195 (2002).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107(2-3), 227–231 (2007).
[Crossref] [PubMed]

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

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 (5)

Fig. 1
Fig. 1 Schematic diagram for lensless diffractive imaging based on random sampling.
Fig. 2
Fig. 2 Simulation results. (a) Phase distribution of the pure phase object to be measured. (b)-(e) Prepared a group of CRS masks with N = 4. (f) An example of the intensity distributions obtained in the recording plane. (g) and (h) Extracted amplitude and phase distributions of the object wave at the sampling plane based on our CRS-CDI method. (i) Phase distribution of the reconstructed image through an inverse diffraction of the extracted complex amplitude shown in (g) and (h). (j) An example of the reconstructed image through an inverse digital diffraction of the sieved field retrieved by the RS-CDI [25] using the intensity shown in (f). (k) An imaging example reconstructed when the initial phase of the iterative operations is randomly changed with different known intensity I n .
Fig. 3
Fig. 3 Phase profiles of the original object (black line) and the reconstructed image (red dashed line) along the red lines shown in Figs. 2(a) and 2(i).
Fig. 4
Fig. 4 Experimental results based on the CRS-CDI method. (a)-(d) are the recorded diffraction intensities when the CRS masks with the number of N = 4 are respectively placed on the sampling; (e) and (f) are the retrieved amplitude and phase at the sampling plane using CRS-CDI algorithm; (g) and (h) are the amplitude and phase of the final reconstructed image.
Fig. 5
Fig. 5 The PSNR of the CRS-CDI versus the number N of the CRS masks. As a comparison, the PSNR of the RS-CDI with a RS mask is also given (red point).

Equations (7)

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

I(u,v)= | F r z { S(x,y)o(x,y) } | 2 ,
S(x,y)o(x,y)Iter{ I(u,v),S(x,y) }
S n (p,q)={ 1, for R(p,q)=n 0, for R(p,q)n ,(n=1,2,,N),
n=1 N S n (p,q) =1.
I n (u,v)= | F r z { S n (p,q)o(p,q) } | 2 ,n=1,2,,N.
o ˜ n (p,q)= S n (p,q)o(p,q)exp(i δ n )Iter{ I n (u,v), S n (p,q) },n=1,2,,N,
n=1 N Iter{ I n (u,v),S(p,q) } o(p,q) n=1 N S n (p,q)exp(i δ n )= o(p,q)exp(i δ 0 ).

Metrics