Shaping coherent x-rays with binary optics

Stefano Marchesini; Anne Sakdinawat

doi:10.1364/OE.27.000907

Shaping coherent x-rays with binary optics

Stefano Marchesini and Anne Sakdinawat

Optics Express
Vol. 27,
Issue 2,
pp. 907-917
(2019)
•https://doi.org/10.1364/OE.27.000907

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Stefano Marchesini and Anne Sakdinawat, "Shaping coherent x-rays with binary optics," Opt. Express 27, 907-917 (2019)

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Related Topics
Table of Contents Category
- Terahertz and X-ray Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: November 8, 2018
- Revised Manuscript: December 7, 2018
- Manuscript Accepted: December 7, 2018
- Published: January 11, 2019

Accessible

Open Access

Abstract

Diffractive lenses fabricated by lithographic methods are one of the most popular image forming optics in the x-ray regime. Most commonly, binary diffractive optics, such as Fresnel zone plates, are used due to their ability to focus at high resolution and to manipulate the x-ray wavefront. We report here a binary zone plate design strategy to form arbitrary illuminations for coherent multiplexing, structured illumination, and wavefront shaping experiments. Given a desired illumination, we adjust the duty cycle, harmonic order, and zone placement to vary both the amplitude and phase of the wavefront at the lens. This enables the binary lithographic pattern to generate arbitrary structured illumination optimized for a variety of applications such as holography, interferometry, ptychography, imaging, and others.

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References

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Author
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Publication

K. J. Kim, Z. Huang, and R. Lindberg, Synchrotron raidation and free-electron lasers: Principles of coherent X-ray generation(Cambridge University Press, 2017).
[Crossref]
P. Schmüser, M. Dohlus, J. Rossbach, and C. Behrens, Free-Electron Lasers in the Ultraviolet and X-ray Regime (Springer, 2014).
[Crossref]
M. Eriksson, J. F. van der Veen, and C. Quitmann, “Diffraction-limited storage rings - a window to the science of tomorrow,” J. Synchr. Rad. 21, 837 (2014).
[Crossref]
D. Attwood and A. Sakdinawat, X-rays and Extreme Ultraviolet Radiation: Principles and Applications(Cambridge University Press, 2017).
K. A. Nugent, “Coherent methods in the x-ray sciences,” Advances in Physics 59, 1–99 (2010).
[Crossref]
A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett. 32, 2635–2637 (2007).
[Crossref] [PubMed]
W.-H. Lee, “Binary computer-generated holograms,” Applied Optics 18, 3661–3669 (1979).
[Crossref] [PubMed]
J. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Optical Engineering 19, 193297 (1980).
[Crossref]
C. Xie, X. Zhu, H. Li, L. Shi, Y. Hua, and M. Liu, “Toward two-dimensional nanometer resolution hard x-ray differential-interference-contrast imaging using modified photon sieves,” Optics letters 37, 749–751 (2012).
[Crossref] [PubMed]
C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 kev using compound photon sieves,” Optics letters 35, 4048–4050 (2010).
[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, and et al., “Massively parallel x-ray holography,” Nature photonics 2, 560 (2008).
[Crossref]
E. D. Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11, 2278–2288 (2003).
[Crossref] [PubMed]
E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]
C. Chang, A. Sakdinawat, P. Fischer, E. Anderson, and D. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Opt. Lett. 31, 1564–1566 (2006).
[Crossref] [PubMed]
O. von Hofsten, M. Bertilson, and U. Vogt, “Theoretical development of a high-resolution differential-interference-contrast optic for x-ray microscopy,” Opt. Express 16, 1132–1141 (2008).
[Crossref] [PubMed]
M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific reports 3, 1927 (2013).
[Crossref] [PubMed]
G. Morrison, F. Zhang, A. Gianoncelli, and I. Robinson, “X-ray ptychography using randomized zone plates,” Optics Express 26, 14915–14927 (2018).
[Crossref] [PubMed]
P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Problems 34, 025003 (2018).
[Crossref]
S. Marchesini, Y.-C. Tu, and H.-t. Wu, “Alternating projection, ptychographic imaging and phase synchronization,” Applied and Computational Harmonic Analysis 41, 815–851 (2016).
[Crossref]
A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nature communications 4, 1669 (2013).
[Crossref] [PubMed]
D. Gabor, “A new microscopic principle,” Nature 161, 777 (1948).
[Crossref] [PubMed]
E. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” Journal of the Optical Society of America 52, 1123–1130 (1962).
[Crossref]
W.-H. Lee, “Binary synthetic holograms,” Applied optics 13, 1677–1682 (1974).
[Crossref] [PubMed]
S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
[Crossref] [PubMed]
W. K. Cheung, P. Tsang, T. Poon, and C. Zhou, “Enhanced method for the generation of binary fresnel holograms based on grid-cross downsampling,” Chinese Optics Letters 9, 120005 (2011).
[Crossref]
P. W. M. Tsang, “Generation of binary off-axis digital fresnel hologram with enhanced quality,” ICT Express 1, 26–29 (2015).
[Crossref]
E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Applied optics 17, 337–347 (1978).
[Crossref] [PubMed]
L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE transactions on image processing 2, 176–201 (1993).
[Crossref] [PubMed]
J. Vila-Comamala, S. Gorelick, E. Färm, C. Kewish, A. Diaz, R. Barrett, V. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Optics Express 19, 175–184 (2011).
[Crossref] [PubMed]
C. Chang and A. Sakdinawat, “Ultra-high aspect ratio high-resolution nanofabrication for hard x-ray diffractive optics,” Nat. Comm. 5, 4243 (2014).
[Crossref]
I. Mohacsi, I. Vartiainen, M. Guizar-Sicairos, P. Karvinen, C. Kewish, A. Somogyi, V. Guzenko, E. Müller, E. Färm, M. Ritala, and C. David, “Double-sided diffractive x-ray optics for hard x-ray microscopy,” Optics Express 23, 776 (2015).
[Crossref]
C. David, S. Gorelick, S. Rutishauser, J. Krzywinski, J. Vila-Comamala, V. Guzenko, O. Bunk, E. Färm, M. Ritala, M. Cammarata, D. Fritz, R. Barrett, L. Samoylova, J. Grünert, and H. Sinn, “Nanofocusing of hard x-ray free electron laser pulses using diamond based fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

2018 (2)

G. Morrison, F. Zhang, A. Gianoncelli, and I. Robinson, “X-ray ptychography using randomized zone plates,” Optics Express 26, 14915–14927 (2018).
[Crossref] [PubMed]

P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Problems 34, 025003 (2018).
[Crossref]

2016 (1)

S. Marchesini, Y.-C. Tu, and H.-t. Wu, “Alternating projection, ptychographic imaging and phase synchronization,” Applied and Computational Harmonic Analysis 41, 815–851 (2016).
[Crossref]

2015 (2)

P. W. M. Tsang, “Generation of binary off-axis digital fresnel hologram with enhanced quality,” ICT Express 1, 26–29 (2015).
[Crossref]

I. Mohacsi, I. Vartiainen, M. Guizar-Sicairos, P. Karvinen, C. Kewish, A. Somogyi, V. Guzenko, E. Müller, E. Färm, M. Ritala, and C. David, “Double-sided diffractive x-ray optics for hard x-ray microscopy,” Optics Express 23, 776 (2015).
[Crossref]

2014 (2)

C. Chang and A. Sakdinawat, “Ultra-high aspect ratio high-resolution nanofabrication for hard x-ray diffractive optics,” Nat. Comm. 5, 4243 (2014).
[Crossref]

M. Eriksson, J. F. van der Veen, and C. Quitmann, “Diffraction-limited storage rings - a window to the science of tomorrow,” J. Synchr. Rad. 21, 837 (2014).
[Crossref]

2013 (2)

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nature communications 4, 1669 (2013).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific reports 3, 1927 (2013).
[Crossref] [PubMed]

2012 (1)

C. Xie, X. Zhu, H. Li, L. Shi, Y. Hua, and M. Liu, “Toward two-dimensional nanometer resolution hard x-ray differential-interference-contrast imaging using modified photon sieves,” Optics letters 37, 749–751 (2012).
[Crossref] [PubMed]

2011 (3)

C. David, S. Gorelick, S. Rutishauser, J. Krzywinski, J. Vila-Comamala, V. Guzenko, O. Bunk, E. Färm, M. Ritala, M. Cammarata, D. Fritz, R. Barrett, L. Samoylova, J. Grünert, and H. Sinn, “Nanofocusing of hard x-ray free electron laser pulses using diamond based fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

J. Vila-Comamala, S. Gorelick, E. Färm, C. Kewish, A. Diaz, R. Barrett, V. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Optics Express 19, 175–184 (2011).
[Crossref] [PubMed]

W. K. Cheung, P. Tsang, T. Poon, and C. Zhou, “Enhanced method for the generation of binary fresnel holograms based on grid-cross downsampling,” Chinese Optics Letters 9, 120005 (2011).
[Crossref]

2010 (2)

C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 kev using compound photon sieves,” Optics letters 35, 4048–4050 (2010).
[Crossref] [PubMed]

K. A. Nugent, “Coherent methods in the x-ray sciences,” Advances in Physics 59, 1–99 (2010).
[Crossref]

2008 (2)

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, and et al., “Massively parallel x-ray holography,” Nature photonics 2, 560 (2008).
[Crossref]

O. von Hofsten, M. Bertilson, and U. Vogt, “Theoretical development of a high-resolution differential-interference-contrast optic for x-ray microscopy,” Opt. Express 16, 1132–1141 (2008).
[Crossref] [PubMed]

E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]

1994 (1)

S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
[Crossref] [PubMed]

1993 (1)

L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE transactions on image processing 2, 176–201 (1993).
[Crossref] [PubMed]

1980 (1)

J. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Optical Engineering 19, 193297 (1980).
[Crossref]

1979 (1)

W.-H. Lee, “Binary computer-generated holograms,” Applied Optics 18, 3661–3669 (1979).
[Crossref] [PubMed]

1978 (1)

E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Applied optics 17, 337–347 (1978).
[Crossref] [PubMed]

1974 (1)

W.-H. Lee, “Binary synthetic holograms,” Applied optics 13, 1677–1682 (1974).
[Crossref] [PubMed]

1962 (1)

E. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” Journal of the Optical Society of America 52, 1123–1130 (1962).
[Crossref]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777 (1948).
[Crossref] [PubMed]

Altissimo, M.

Anderson, E.

Attwood, D.

D. Attwood and A. Sakdinawat, X-rays and Extreme Ultraviolet Radiation: Principles and Applications(Cambridge University Press, 2017).

Bajt, S.

Barrett, R.

Barty, A.

Behrens, C.

P. Schmüser, M. Dohlus, J. Rossbach, and C. Behrens, Free-Electron Lasers in the Ultraviolet and X-ray Regime (Springer, 2014).
[Crossref]

Bertilson, M.

Bogan, M. J.

Boutet, S.

Bunk, O.

Businaro, L.

Cabrini, S.

Cammarata, M.

Cannon, T. M.

E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Applied optics 17, 337–347 (1978).
[Crossref] [PubMed]

Chang, C.

C. Chang and A. Sakdinawat, “Ultra-high aspect ratio high-resolution nanofabrication for hard x-ray diffractive optics,” Nat. Comm. 5, 4243 (2014).
[Crossref]

Chapman, H. N.

Chen, P.

P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Problems 34, 025003 (2018).
[Crossref]

Cheung, W. K.

Cingolani, R.

Cloetens, P.

Cojoc, D.

David, C.

De Vittorio, M.

Diaz, A.

Dierolf, M.

Dixit, S.

S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
[Crossref] [PubMed]

Dohlus, M.

P. Schmüser, M. Dohlus, J. Rossbach, and C. Behrens, Free-Electron Lasers in the Ultraviolet and X-ray Regime (Springer, 2014).
[Crossref]

Enders, B.

Eriksson, M.

M. Eriksson, J. F. van der Veen, and C. Quitmann, “Diffraction-limited storage rings - a window to the science of tomorrow,” J. Synchr. Rad. 21, 837 (2014).
[Crossref]

Fabrizio, E. D.

Fabrizio, E. Di

Facci, P.

Fannjiang, A.

P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Problems 34, 025003 (2018).
[Crossref]

Färm, E.

Fenimore, E. E.

E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Applied optics 17, 337–347 (1978).
[Crossref] [PubMed]

Fienup, J.

J. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Optical Engineering 19, 193297 (1980).
[Crossref]

Fischer, P.

Frank, M.

Fritz, D.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777 (1948).
[Crossref] [PubMed]

Gianoncelli, A.

G. Morrison, F. Zhang, A. Gianoncelli, and I. Robinson, “X-ray ptychography using randomized zone plates,” Optics Express 26, 14915–14927 (2018).
[Crossref] [PubMed]

Gigli, G.

Gorelick, S.

Grünert, J.

Guizar-Sicairos, M.

Guzenko, V.

Hau-Riege, S. P.

Hua, Y.

Huang, Z.

K. J. Kim, Z. Huang, and R. Lindberg, Synchrotron raidation and free-electron lasers: Principles of coherent X-ray generation(Cambridge University Press, 2017).
[Crossref]

Karvinen, P.

Kaulich, B.

Kewish, C.

Kim, K. J.

K. J. Kim, Z. Huang, and R. Lindberg, Synchrotron raidation and free-electron lasers: Principles of coherent X-ray generation(Cambridge University Press, 2017).
[Crossref]

Krzywinski, J.

Lawson, J.

S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
[Crossref] [PubMed]

Lee, W.-H.

W.-H. Lee, “Binary computer-generated holograms,” Applied Optics 18, 3661–3669 (1979).
[Crossref] [PubMed]

W.-H. Lee, “Binary synthetic holograms,” Applied optics 13, 1677–1682 (1974).
[Crossref] [PubMed]

Leith, E.

E. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” Journal of the Optical Society of America 52, 1123–1130 (1962).
[Crossref]

Li, H.

C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 kev using compound photon sieves,” Optics letters 35, 4048–4050 (2010).
[Crossref] [PubMed]

Lindberg, R.

K. J. Kim, Z. Huang, and R. Lindberg, Synchrotron raidation and free-electron lasers: Principles of coherent X-ray generation(Cambridge University Press, 2017).
[Crossref]

Liu, M.

Liu, Y.

A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett. 32, 2635–2637 (2007).
[Crossref] [PubMed]

Maiden, A.

Manes, K.

S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
[Crossref] [PubMed]

Marchesini, S.

S. Marchesini, Y.-C. Tu, and H.-t. Wu, “Alternating projection, ptychographic imaging and phase synchronization,” Applied and Computational Harmonic Analysis 41, 815–851 (2016).
[Crossref]

Mohacsi, I.

Morrison, G.

G. Morrison, F. Zhang, A. Gianoncelli, and I. Robinson, “X-ray ptychography using randomized zone plates,” Optics Express 26, 14915–14927 (2018).
[Crossref] [PubMed]

Müller, E.

Nugent, K.

S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
[Crossref] [PubMed]

Nugent, K. A.

K. A. Nugent, “Coherent methods in the x-ray sciences,” Advances in Physics 59, 1–99 (2010).
[Crossref]

Pfeiffer, F.

Poon, T.

Powell, H.

S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
[Crossref] [PubMed]

Quitmann, C.

M. Eriksson, J. F. van der Veen, and C. Quitmann, “Diffraction-limited storage rings - a window to the science of tomorrow,” J. Synchr. Rad. 21, 837 (2014).
[Crossref]

Ritala, M.

Robinson, I.

G. Morrison, F. Zhang, A. Gianoncelli, and I. Robinson, “X-ray ptychography using randomized zone plates,” Optics Express 26, 14915–14927 (2018).
[Crossref] [PubMed]

Rodenburg, J.

Romanato, F.

Rossbach, J.

P. Schmüser, M. Dohlus, J. Rossbach, and C. Behrens, Free-Electron Lasers in the Ultraviolet and X-ray Regime (Springer, 2014).
[Crossref]

Rutishauser, S.

Sakdinawat, A.

C. Chang and A. Sakdinawat, “Ultra-high aspect ratio high-resolution nanofabrication for hard x-ray diffractive optics,” Nat. Comm. 5, 4243 (2014).
[Crossref]

A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett. 32, 2635–2637 (2007).
[Crossref] [PubMed]

D. Attwood and A. Sakdinawat, X-rays and Extreme Ultraviolet Radiation: Principles and Applications(Cambridge University Press, 2017).

Sakdinawat, A. E.

Samoylova, L.

Schmüser, P.

P. Schmüser, M. Dohlus, J. Rossbach, and C. Behrens, Free-Electron Lasers in the Ultraviolet and X-ray Regime (Springer, 2014).
[Crossref]

Shi, L.

C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 kev using compound photon sieves,” Optics letters 35, 4048–4050 (2010).
[Crossref] [PubMed]

Sinn, H.

Somogyi, A.

Stockmar, M.

Susini, J.

Szöke, A.

Thibault, P.

Tsang, P.

Tsang, P. W. M.

P. W. M. Tsang, “Generation of binary off-axis digital fresnel hologram with enhanced quality,” ICT Express 1, 26–29 (2015).
[Crossref]

Tu, Y.-C.

S. Marchesini, Y.-C. Tu, and H.-t. Wu, “Alternating projection, ptychographic imaging and phase synchronization,” Applied and Computational Harmonic Analysis 41, 815–851 (2016).
[Crossref]

Upatnieks, J.

E. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” Journal of the Optical Society of America 52, 1123–1130 (1962).
[Crossref]

van der Veen, J. F.

M. Eriksson, J. F. van der Veen, and C. Quitmann, “Diffraction-limited storage rings - a window to the science of tomorrow,” J. Synchr. Rad. 21, 837 (2014).
[Crossref]

Vartiainen, I.

Vila-Comamala, J.

Vincent, L.

L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE transactions on image processing 2, 176–201 (1993).
[Crossref] [PubMed]

Vitale, E.

Vogt, U.

von Hofsten, O.

Wang, Y.

C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 kev using compound photon sieves,” Optics letters 35, 4048–4050 (2010).
[Crossref] [PubMed]

Wilhein, T.

Wu, H.-t.

S. Marchesini, Y.-C. Tu, and H.-t. Wu, “Alternating projection, ptychographic imaging and phase synchronization,” Applied and Computational Harmonic Analysis 41, 815–851 (2016).
[Crossref]

Xie, C.

C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 kev using compound photon sieves,” Optics letters 35, 4048–4050 (2010).
[Crossref] [PubMed]

Zanette, I.

Zhang, F.

G. Morrison, F. Zhang, A. Gianoncelli, and I. Robinson, “X-ray ptychography using randomized zone plates,” Optics Express 26, 14915–14927 (2018).
[Crossref] [PubMed]

Zhou, C.

Zhu, X.

C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 kev using compound photon sieves,” Optics letters 35, 4048–4050 (2010).
[Crossref] [PubMed]

Advances in Physics (1)

K. A. Nugent, “Coherent methods in the x-ray sciences,” Advances in Physics 59, 1–99 (2010).
[Crossref]

Applied and Computational Harmonic Analysis (1)

S. Marchesini, Y.-C. Tu, and H.-t. Wu, “Alternating projection, ptychographic imaging and phase synchronization,” Applied and Computational Harmonic Analysis 41, 815–851 (2016).
[Crossref]

Applied optics (2)

W.-H. Lee, “Binary synthetic holograms,” Applied optics 13, 1677–1682 (1974).
[Crossref] [PubMed]

W.-H. Lee, “Binary computer-generated holograms,” Applied Optics 18, 3661–3669 (1979).
[Crossref] [PubMed]

E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Applied optics 17, 337–347 (1978).
[Crossref] [PubMed]

Chinese Optics Letters (1)

ICT Express (1)

P. W. M. Tsang, “Generation of binary off-axis digital fresnel hologram with enhanced quality,” ICT Express 1, 26–29 (2015).
[Crossref]

IEEE transactions on image processing (1)

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Fig. 1 On axis and off axis Zone plates with order sorting apertures

Download Full Size | PPT Slide | PDF

Fig. 2 Uniformly redundant array illumination. Top row: desired amplitude, phase at the lens, and at the sample plane complex-HSV representation and amplitude. Following Rows, from top to bottom,

W_{{ZP}_{0}}

W_{{ZP}_{1 d c}}

W_{{ZP}_{2 h y b}}

, and

W_{{ZP}_{3 g r a t}}

. Columns, from left to right: the zone plate, magnified portion of zone plate, focal plane overview, and the focal spot.

Download Full Size | PPT Slide | PDF

Fig. 3 Off-axis holographic illumination. Top row: desired amplitude, phase at the lens, and at the sample plane. Following Rows, from top to bottom,

W_{{ZP}_{0}}

W_{{ZP}_{1 d c}}

W_{{ZP}_{2 h y b}}

, and

W_{{ZP}_{3 g r a t}}

. Columns, from left to right: the zone plate, magnified portion of zone plate, focal plane overview, and the focal spot.

Download Full Size | PPT Slide | PDF

Fig. 4 Band Limited Random illumination. Top row: desired amplitude, phase at the lens, and at the sample represented in HSV color format with Hue=phase, Value=amplitude, and Saturation=1, and amplitude on the right. Following Rows, from top to bottom,

W_{{ZP}_{0}}

W_{{ZP}_{1 d c}}

W_{{ZP}_{2 h y b}}

, and

W_{{ZP}_{3 g r a t}}

. Columns, from left to right: the zone plate, magnified portion of zone plate, focal plane overview, and the focal spot.

Download Full Size | PPT Slide | PDF

Tables (1)

Table 1 The normalized mean square error (nmse), normalized mean square error after morphological opening (nmse-o), relative efficiency, 1/c, and mean power $‖ W ‖^{2}$ for the URA, holographic, and bandwidth limited random pytchography zone plates.

View Table

Equations (8)

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{ZP}_{0} (ϕ_{0}) = {\begin{array}{l} 1, if mod (ϕ_{0}, 2 π) < π \\ 0, otherwise, \end{array}

ε_{h} (L, p) = {\begin{array}{l} L / p, if h = 0 \\ \frac{1}{h π} sin (\frac{π h L}{p}), if | h | > 0 \end{array}

{ZP}_{1 dc} (ϕ_{w}, | W |) = {\begin{array}{l} 1, if mod (ϕ_{w} + ϕ_{W}, 2 π) < 2 ϕ_{W}, \\ 0, otherwise \end{array}

{ZP}_{1 h} (ϕ_{w}, | W |) = {\begin{array}{l} 1, if mod (ϕ_{w} + ϕ_{W}, 4 π) < 2 π + 2 ϕ_{W} \\ 0, otherwise \end{array}

{ZP}_{2 hyb} (ϕ_{w}, | W |) = {\begin{array}{l} {ZP}_{1 d c} (ϕ_{w}, | W |), if | W | > 1 / 2 \\ {ZP}_{1 h} (ϕ_{w}, 2 | W |), otherwise \end{array}

{ZP}_{3 grat} (ϕ_{w}, | W |) = {ZP}_{0} (ϕ_{w}) \circ T (| W |)

T (| W |) = {\begin{array}{l} 1, if mod (x / l - | W | / 2, 2) < | W | \\ 0, otherwise \end{array}

nmse = \min_{c} \frac{‖ w_{t r u t h} - c w_{Z P} ‖_{O S A}^{2}}{‖ w_{t r u t h} ‖_{O S A}^{2}},

lens	nmse	nmse-o	relative efficiency	$\frac{1}{c}$

URA
$‖ W ‖^{2} = 0.0062$

ZP₀	0.550	0.550	1	16
ZP $_{1 dc}$	0.0016	0.503	0.0072	1
ZP $_{2 hyb}$	0.146	0.165	0.0083	1.17
ZP $_{3 grat}$	0.0063	0.3092	0.0072	1.0

Holographic
$‖ W ‖^{2} = 0.0056$

ZP₀	0.648	0.649	1	22
ZP $_{1 dc}$	0.0016	0.363	0.0056	1
ZP $_{2 hyb}$	0.1965	0.197	0.0074	1.3
ZP $_{3 grat}$	0.0016	0.265	0.0058	1.03

Bandwidth Limited
Random Ptychography
$‖ W ‖^{2} = 0.39202$

ZP₀	0.0760	0.076	1	2.5808
ZP $_{1 dc}$	0.00031	0.0019	0.4003	1
ZP $_{2 hyb}$	0.00454	0.0045	0.4061	1.0047
ZP $_{3 grat}$	0.00141	0.0015	0.4056	1.0032

Abstract

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