Abstract

Optical elements based on Fresnel zones are used in a range of applications, from X-ray telescopy to microscopy and recently also in the manipulation of de Broglie matter waves. In 1992 Beynon and co-workers presented a binary Gabor type zone plate (henceforth referred to as the Beynon Gabor zone plate). Because this zone plate has no higher order foci, it is in principle a very attractive candidate for focusing of de Broglie matter waves and in some cases X-rays. So far the Beynon Gabor zone plate investigations presented in the literature have concentrated on the intensity distribution along the optical axis and in the focal plane. Here we present a detailed numerical investigation of the Beynon Gabor zone plate, including an investigation of the off-optical axis, off focal plane intensity distribution for point source illumination. We show that at integer fractions of the focal length, the beam becomes nearly toroidal (doughnut-shaped). This offers potentially interesting new possibilities for de Broglie matter wave and X-ray optics, for example in STED-like applications. We further show that the increased intensity at the focal point predicted in the literature for a particular Beynon Gabor zone plate transmission function configuration is an artifact due to the lack of sampling nodes. We support our calculations with experimental measurements in the visible light range, using a Beynon Gabor zone plate fabricated with electron beam lithography.

© 2013 OSA

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2013 (2)

M. M. Greve, B. Holst, “Optimization of an electron beam lithography instrument for fast, large area writing at 10 kv acceleration voltage,” J. Vac. Sci. Technol B 31, 043202 (2013).
[CrossRef]

W. Fan, L. Wei, L. Zang, H., Cao, B. Zhu, X. Zhu, C. Xie, Y. Gao, Z. Zhao, Y. Gu, “Realizing a gabor zone plate with quasi-random distributed hexagon dots,” Opt. Express 21, 1473–1478 (2013).
[CrossRef] [PubMed]

2012 (2)

S.-R. Wu, Y. Hwy, G. Margaritondo, “Hard-x-ray zone plates: Recent progress,” Materials 5, 1752–1733 (2012).
[CrossRef]

T. Reisinger, M. Greve, S. Eder, G. Bracco, B. Holst, “Brightness and virtual source size of a supersonic-expansion deuterium beam,” Phys. Rev. A 86, 043804 (2012).
[CrossRef]

2011 (2)

T. Reisinger, G. Bracco, B. Holst, “Particle-wave discrimination in poisson spot experiments,” New Journal of Physics 13, 065016 (2011).
[CrossRef]

L. Wei, L. Kuang, W. Fan, H. Zang, L. Cao, Y. Gu, X. Wang, “Annulus-sector-element coded gabor zone plate at the x-ray wavelength,” Opt. Express 19, 21419–21424 (2011).
[CrossRef] [PubMed]

2010 (1)

T. Reisinger, S. Eder, M. M. Greve, H. I. Smith, B. Holst, “Free-standing silicon-nitride zoneplates for neutral-helium microscopy,” Microelectron. Eng. 87, 1011–1014 (2010).
[CrossRef]

2009 (1)

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

2008 (1)

M. Koch, S. Rehbein, G. Schmahl, T. Reisinger, G. Bracco, W. E. Ernst, B. Holst, “Imaging with neutral atoms: a new matter-wave microscope,” J. Micros. 229, 1–5 (2008).
[CrossRef]

2007 (2)

T. Reisinger, G. Bracco, S. Rehbein, G. Schmahl, W. E. Ernst, B. Holst, “Direct images of the virtual source in a supersonic expansion,” J. Phys. Chem. A 111, 12620–12628 (2007).
[CrossRef] [PubMed]

G. Andersen, D. Tullson, “Broadband antihole photon sieve telescope,” Appl. Opt. 46, 3706–3708 (2007).
[CrossRef] [PubMed]

2004 (1)

D. J. Velleman, “Simpson symmetrized and surpassed,” Mathematics Magazine 77, 31–45 (2004).
[CrossRef]

2003 (1)

J. Ding, M. Tang, Z. Jin, G. Wenqi, “Modified binary gabor zone plates,” Opt. Commun. 217, 97–103 (2003).
[CrossRef]

2001 (1)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seeman, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

1999 (1)

R. B. Doak, R. E. Grisenti, S. Rehbein, G. Schmahl, J. P. Toennies, C. Wöll, “Towards realization of an atomic de broglie microscope: Helium atom focusing using fresnel zone plates,” Phys. Rev. Lett. 83, 4229–4232 (1999).
[CrossRef]

1994 (2)

1992 (1)

1991 (1)

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

1975 (1)

J. P. Ballantyne, “Electron beam fabrication of chromium master masks,” J. Vac. Sci. Technol. 12, 1257–1260 (1975).
[CrossRef]

1969 (1)

1967 (2)

1950 (1)

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166, 237 (1950).
[CrossRef] [PubMed]

1949 (1)

D. Gabor, “Microscopy by Reconstructed Wave-Fronts,” The Royal Society 197, 454–487 (1949).
[CrossRef]

1948 (1)

D. Garbor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef]

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seeman, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

Als-Nielsen, J.

J. Als-Nielsen, D. McMorrow, Elements of Modern X-ray Physics (John Wiley and Sons, Ltd, 2001).

Andersen, G.

Ballantyne, J. P.

J. P. Ballantyne, “Electron beam fabrication of chromium master masks,” J. Vac. Sci. Technol. 12, 1257–1260 (1975).
[CrossRef]

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seeman, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

Beynon, T. D.

Born, M.

M. Born, E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Cambridge University Press, 1999).
[CrossRef]

Bracco, G.

T. Reisinger, M. Greve, S. Eder, G. Bracco, B. Holst, “Brightness and virtual source size of a supersonic-expansion deuterium beam,” Phys. Rev. A 86, 043804 (2012).
[CrossRef]

T. Reisinger, G. Bracco, B. Holst, “Particle-wave discrimination in poisson spot experiments,” New Journal of Physics 13, 065016 (2011).
[CrossRef]

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

M. Koch, S. Rehbein, G. Schmahl, T. Reisinger, G. Bracco, W. E. Ernst, B. Holst, “Imaging with neutral atoms: a new matter-wave microscope,” J. Micros. 229, 1–5 (2008).
[CrossRef]

T. Reisinger, G. Bracco, S. Rehbein, G. Schmahl, W. E. Ernst, B. Holst, “Direct images of the virtual source in a supersonic expansion,” J. Phys. Chem. A 111, 12620–12628 (2007).
[CrossRef] [PubMed]

Cao,

Cao, L.

Carnal, O.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Chau, H. H. M.

Cheng, L.

Choy, C.

Ding, J.

J. Ding, M. Tang, Z. Jin, G. Wenqi, “Modified binary gabor zone plates,” Opt. Commun. 217, 97–103 (2003).
[CrossRef]

Doak, R. B.

R. B. Doak, R. E. Grisenti, S. Rehbein, G. Schmahl, J. P. Toennies, C. Wöll, “Towards realization of an atomic de broglie microscope: Helium atom focusing using fresnel zone plates,” Phys. Rev. Lett. 83, 4229–4232 (1999).
[CrossRef]

Eder, S.

T. Reisinger, M. Greve, S. Eder, G. Bracco, B. Holst, “Brightness and virtual source size of a supersonic-expansion deuterium beam,” Phys. Rev. A 86, 043804 (2012).
[CrossRef]

T. Reisinger, S. Eder, M. M. Greve, H. I. Smith, B. Holst, “Free-standing silicon-nitride zoneplates for neutral-helium microscopy,” Microelectron. Eng. 87, 1011–1014 (2010).
[CrossRef]

Ernst, W. E.

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

M. Koch, S. Rehbein, G. Schmahl, T. Reisinger, G. Bracco, W. E. Ernst, B. Holst, “Imaging with neutral atoms: a new matter-wave microscope,” J. Micros. 229, 1–5 (2008).
[CrossRef]

T. Reisinger, G. Bracco, S. Rehbein, G. Schmahl, W. E. Ernst, B. Holst, “Direct images of the virtual source in a supersonic expansion,” J. Phys. Chem. A 111, 12620–12628 (2007).
[CrossRef] [PubMed]

Fan, W.

Fladischer, K.

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

Gabor, D.

D. Gabor, “Microscopy by Reconstructed Wave-Fronts,” The Royal Society 197, 454–487 (1949).
[CrossRef]

Gao, Y.

Garbor, D.

D. Garbor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef]

Greve, M.

T. Reisinger, M. Greve, S. Eder, G. Bracco, B. Holst, “Brightness and virtual source size of a supersonic-expansion deuterium beam,” Phys. Rev. A 86, 043804 (2012).
[CrossRef]

Greve, M. M.

M. M. Greve, B. Holst, “Optimization of an electron beam lithography instrument for fast, large area writing at 10 kv acceleration voltage,” J. Vac. Sci. Technol B 31, 043202 (2013).
[CrossRef]

T. Reisinger, S. Eder, M. M. Greve, H. I. Smith, B. Holst, “Free-standing silicon-nitride zoneplates for neutral-helium microscopy,” Microelectron. Eng. 87, 1011–1014 (2010).
[CrossRef]

Grisenti, R. E.

R. B. Doak, R. E. Grisenti, S. Rehbein, G. Schmahl, J. P. Toennies, C. Wöll, “Towards realization of an atomic de broglie microscope: Helium atom focusing using fresnel zone plates,” Phys. Rev. Lett. 83, 4229–4232 (1999).
[CrossRef]

Gu, Y.

H.,

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seeman, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

Hell, S.

Holst, B.

M. M. Greve, B. Holst, “Optimization of an electron beam lithography instrument for fast, large area writing at 10 kv acceleration voltage,” J. Vac. Sci. Technol B 31, 043202 (2013).
[CrossRef]

T. Reisinger, M. Greve, S. Eder, G. Bracco, B. Holst, “Brightness and virtual source size of a supersonic-expansion deuterium beam,” Phys. Rev. A 86, 043804 (2012).
[CrossRef]

T. Reisinger, G. Bracco, B. Holst, “Particle-wave discrimination in poisson spot experiments,” New Journal of Physics 13, 065016 (2011).
[CrossRef]

T. Reisinger, S. Eder, M. M. Greve, H. I. Smith, B. Holst, “Free-standing silicon-nitride zoneplates for neutral-helium microscopy,” Microelectron. Eng. 87, 1011–1014 (2010).
[CrossRef]

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

M. Koch, S. Rehbein, G. Schmahl, T. Reisinger, G. Bracco, W. E. Ernst, B. Holst, “Imaging with neutral atoms: a new matter-wave microscope,” J. Micros. 229, 1–5 (2008).
[CrossRef]

T. Reisinger, G. Bracco, S. Rehbein, G. Schmahl, W. E. Ernst, B. Holst, “Direct images of the virtual source in a supersonic expansion,” J. Phys. Chem. A 111, 12620–12628 (2007).
[CrossRef] [PubMed]

Horman, M. H.

Hwy, Y.

S.-R. Wu, Y. Hwy, G. Margaritondo, “Hard-x-ray zone plates: Recent progress,” Materials 5, 1752–1733 (2012).
[CrossRef]

Janesick, J. R.

J. R. Janesick, Scientific Charge-Coupled Devices, vol. PM83 (SPIE Press, Washington, 2001).
[CrossRef]

Jin, Z.

J. Ding, M. Tang, Z. Jin, G. Wenqi, “Modified binary gabor zone plates,” Opt. Commun. 217, 97–103 (2003).
[CrossRef]

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seeman, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seeman, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

Kirk, I.

Koch, M.

M. Koch, S. Rehbein, G. Schmahl, T. Reisinger, G. Bracco, W. E. Ernst, B. Holst, “Imaging with neutral atoms: a new matter-wave microscope,” J. Micros. 229, 1–5 (2008).
[CrossRef]

Kuang, L.

Margaritondo, G.

S.-R. Wu, Y. Hwy, G. Margaritondo, “Hard-x-ray zone plates: Recent progress,” Materials 5, 1752–1733 (2012).
[CrossRef]

Mathews, T. R.

McMorrow, D.

J. Als-Nielsen, D. McMorrow, Elements of Modern X-ray Physics (John Wiley and Sons, Ltd, 2001).

Michette, A. G.

A. G. Michette, Optical Systems for Soft X rays (Plenum Press, 1986).
[CrossRef]

Mlynek, J.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Patel, A. A.

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

Rehbein, S.

M. Koch, S. Rehbein, G. Schmahl, T. Reisinger, G. Bracco, W. E. Ernst, B. Holst, “Imaging with neutral atoms: a new matter-wave microscope,” J. Micros. 229, 1–5 (2008).
[CrossRef]

T. Reisinger, G. Bracco, S. Rehbein, G. Schmahl, W. E. Ernst, B. Holst, “Direct images of the virtual source in a supersonic expansion,” J. Phys. Chem. A 111, 12620–12628 (2007).
[CrossRef] [PubMed]

R. B. Doak, R. E. Grisenti, S. Rehbein, G. Schmahl, J. P. Toennies, C. Wöll, “Towards realization of an atomic de broglie microscope: Helium atom focusing using fresnel zone plates,” Phys. Rev. Lett. 83, 4229–4232 (1999).
[CrossRef]

Reingruber, H.

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

Reisinger, T.

T. Reisinger, M. Greve, S. Eder, G. Bracco, B. Holst, “Brightness and virtual source size of a supersonic-expansion deuterium beam,” Phys. Rev. A 86, 043804 (2012).
[CrossRef]

T. Reisinger, G. Bracco, B. Holst, “Particle-wave discrimination in poisson spot experiments,” New Journal of Physics 13, 065016 (2011).
[CrossRef]

T. Reisinger, S. Eder, M. M. Greve, H. I. Smith, B. Holst, “Free-standing silicon-nitride zoneplates for neutral-helium microscopy,” Microelectron. Eng. 87, 1011–1014 (2010).
[CrossRef]

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

M. Koch, S. Rehbein, G. Schmahl, T. Reisinger, G. Bracco, W. E. Ernst, B. Holst, “Imaging with neutral atoms: a new matter-wave microscope,” J. Micros. 229, 1–5 (2008).
[CrossRef]

T. Reisinger, G. Bracco, S. Rehbein, G. Schmahl, W. E. Ernst, B. Holst, “Direct images of the virtual source in a supersonic expansion,” J. Phys. Chem. A 111, 12620–12628 (2007).
[CrossRef] [PubMed]

Rogers, G. L.

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166, 237 (1950).
[CrossRef] [PubMed]

Schmahl, G.

M. Koch, S. Rehbein, G. Schmahl, T. Reisinger, G. Bracco, W. E. Ernst, B. Holst, “Imaging with neutral atoms: a new matter-wave microscope,” J. Micros. 229, 1–5 (2008).
[CrossRef]

T. Reisinger, G. Bracco, S. Rehbein, G. Schmahl, W. E. Ernst, B. Holst, “Direct images of the virtual source in a supersonic expansion,” J. Phys. Chem. A 111, 12620–12628 (2007).
[CrossRef] [PubMed]

R. B. Doak, R. E. Grisenti, S. Rehbein, G. Schmahl, J. P. Toennies, C. Wöll, “Towards realization of an atomic de broglie microscope: Helium atom focusing using fresnel zone plates,” Phys. Rev. Lett. 83, 4229–4232 (1999).
[CrossRef]

Seeman, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seeman, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

Sigel, M.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seeman, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

Sleator, T.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Smith, H. I.

T. Reisinger, S. Eder, M. M. Greve, H. I. Smith, B. Holst, “Free-standing silicon-nitride zoneplates for neutral-helium microscopy,” Microelectron. Eng. 87, 1011–1014 (2010).
[CrossRef]

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

Takuma, H.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Tang, M.

J. Ding, M. Tang, Z. Jin, G. Wenqi, “Modified binary gabor zone plates,” Opt. Commun. 217, 97–103 (2003).
[CrossRef]

Toennies, J. P.

R. B. Doak, R. E. Grisenti, S. Rehbein, G. Schmahl, J. P. Toennies, C. Wöll, “Towards realization of an atomic de broglie microscope: Helium atom focusing using fresnel zone plates,” Phys. Rev. Lett. 83, 4229–4232 (1999).
[CrossRef]

Tullson, D.

Velleman, D. J.

D. J. Velleman, “Simpson symmetrized and surpassed,” Mathematics Magazine 77, 31–45 (2004).
[CrossRef]

Wang, X.

Wei, L.

Wenqi, G.

J. Ding, M. Tang, Z. Jin, G. Wenqi, “Modified binary gabor zone plates,” Opt. Commun. 217, 97–103 (2003).
[CrossRef]

Wichmann, J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Cambridge University Press, 1999).
[CrossRef]

Wöll, C.

R. B. Doak, R. E. Grisenti, S. Rehbein, G. Schmahl, J. P. Toennies, C. Wöll, “Towards realization of an atomic de broglie microscope: Helium atom focusing using fresnel zone plates,” Phys. Rev. Lett. 83, 4229–4232 (1999).
[CrossRef]

Wu, S.-R.

S.-R. Wu, Y. Hwy, G. Margaritondo, “Hard-x-ray zone plates: Recent progress,” Materials 5, 1752–1733 (2012).
[CrossRef]

Xie, C.

Zang, H.

Zang, L.

Zhao, Z.

Zhu, B.

Zhu, X.

Appl. Opt. (5)

J. Micros. (1)

M. Koch, S. Rehbein, G. Schmahl, T. Reisinger, G. Bracco, W. E. Ernst, B. Holst, “Imaging with neutral atoms: a new matter-wave microscope,” J. Micros. 229, 1–5 (2008).
[CrossRef]

J. Phys. Chem. A (1)

T. Reisinger, G. Bracco, S. Rehbein, G. Schmahl, W. E. Ernst, B. Holst, “Direct images of the virtual source in a supersonic expansion,” J. Phys. Chem. A 111, 12620–12628 (2007).
[CrossRef] [PubMed]

J. Vac. Sci. Technol B (1)

M. M. Greve, B. Holst, “Optimization of an electron beam lithography instrument for fast, large area writing at 10 kv acceleration voltage,” J. Vac. Sci. Technol B 31, 043202 (2013).
[CrossRef]

J. Vac. Sci. Technol. (1)

J. P. Ballantyne, “Electron beam fabrication of chromium master masks,” J. Vac. Sci. Technol. 12, 1257–1260 (1975).
[CrossRef]

Materials (1)

S.-R. Wu, Y. Hwy, G. Margaritondo, “Hard-x-ray zone plates: Recent progress,” Materials 5, 1752–1733 (2012).
[CrossRef]

Mathematics Magazine (1)

D. J. Velleman, “Simpson symmetrized and surpassed,” Mathematics Magazine 77, 31–45 (2004).
[CrossRef]

Microelectron. Eng. (1)

T. Reisinger, S. Eder, M. M. Greve, H. I. Smith, B. Holst, “Free-standing silicon-nitride zoneplates for neutral-helium microscopy,” Microelectron. Eng. 87, 1011–1014 (2010).
[CrossRef]

Nature (3)

D. Garbor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef]

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166, 237 (1950).
[CrossRef] [PubMed]

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seeman, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

New Journal of Physics (1)

T. Reisinger, G. Bracco, B. Holst, “Particle-wave discrimination in poisson spot experiments,” New Journal of Physics 13, 065016 (2011).
[CrossRef]

Opt. Commun. (1)

J. Ding, M. Tang, Z. Jin, G. Wenqi, “Modified binary gabor zone plates,” Opt. Commun. 217, 97–103 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

T. Reisinger, M. Greve, S. Eder, G. Bracco, B. Holst, “Brightness and virtual source size of a supersonic-expansion deuterium beam,” Phys. Rev. A 86, 043804 (2012).
[CrossRef]

Phys. Rev. A. (1)

T. Reisinger, A. A. Patel, H. Reingruber, K. Fladischer, W. E. Ernst, G. Bracco, H. I. Smith, B. Holst, “Poisson’s spot with molecules,” Phys. Rev. A. 79, 053823 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

R. B. Doak, R. E. Grisenti, S. Rehbein, G. Schmahl, J. P. Toennies, C. Wöll, “Towards realization of an atomic de broglie microscope: Helium atom focusing using fresnel zone plates,” Phys. Rev. Lett. 83, 4229–4232 (1999).
[CrossRef]

The Royal Society (1)

D. Gabor, “Microscopy by Reconstructed Wave-Fronts,” The Royal Society 197, 454–487 (1949).
[CrossRef]

Other (4)

A. G. Michette, Optical Systems for Soft X rays (Plenum Press, 1986).
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J. Als-Nielsen, D. McMorrow, Elements of Modern X-ray Physics (John Wiley and Sons, Ltd, 2001).

M. Born, E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Cambridge University Press, 1999).
[CrossRef]

J. R. Janesick, Scientific Charge-Coupled Devices, vol. PM83 (SPIE Press, Washington, 2001).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Radial Transmittances tav(r) of the 10th open zone for λ = 632.8 nm, f = 1 m and ξ0 = 3π/2. Full curve: Radial transmittance for GZP and BGZP as given by Eq. (1). Dashed curve: Radial transmittance for FZP as given by Eq. (2). It should be noted that after integration over the angle with sufficiently many points on the zone plate the transmittance does not appear binary in the plot.

Fig. 2
Fig. 2

(a)–(c): Simulation results of the amplitude probability in the focal plane for a 40 zones Beynon-type GZP with the transmittance represented by the two sinusoidal curves in Eqs. (5), λ = 632.8 nm and f = 1 m for N = 6, N = 30 and N = 60. Same spatial and amplitude scales for all figures. (d): Intensity (arbitrary units) in the focal plane of the central peak, same for any N.

Fig. 3
Fig. 3

Simulation results showing the amplitude of probability at z = 1/2 m of a 40-zones BGZP with the transmittance represented by the two sinusoidal curves in Eqs. (5), λ = 632.8 nm and f = 1 m. Same spatial and amplitude scales for (a): 30 sectors; (b): 60 sectors.

Fig. 4
Fig. 4

Stereo microscope (Nikon SMZ 1500) image of the Beynon Gabor zone plates fabricated by EBL. The transmittance used is that represented by the two sinusoidal curves in Eqs. (5) 4. The BGZP has 60 sectors (N = 60) and 40 zones. Note the central stop which is included to block the 0th order beam on the optical axis.

Fig. 5
Fig. 5

Experimental setup used for testing the Beynon Gabor zone plate.

Fig. 6
Fig. 6

To the left, experimental diffraction pattern obtained using the BGZP shown in Fig. 4 and the experimental setup shown in Fig. 5. The image is obtained with a parallel incident beam with wavelength 632.8 nm at the focal length of the BGZP = 1 m. To the right the corresponding simulated diffration pattern.

Fig. 7
Fig. 7

Experimental diffraction pattern obtained using the BGZP shown in Fig. 4 and the experimental setup shown in Fig. 5. The image is obtained with a parallel incident beam with wavelength 632.8 nm at distance f/2 =1/2 m. The predicted doughnut shape is clearly visible and in good agreement with the simulated results in Fig. 3. The center focus is believed to be due to an artifact related to the fabrication process (see discussion in main text). In order to highlight the doughnut an additional image Fig. 7(b) with increased brightness is included where the focusing effect is removed.

Equations (6)

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t G Z P ( r ) = 1 2 + 1 2 cos ( π r 2 λ f + ξ 0 )
t F Z P ( r ) = 1 2 + 1 2 sign ( cos ( π r 2 λ f + ξ 0 ) )
t a v ( r ) = t G Z P ( r ) = ( 1 / 2 π ) 0 2 π t ( r , ϕ ) d ϕ
ϕ k ( r p ) = A i λ 𝒜 ϕ k i ( r ) t ( r , ϕ ) e i k r r p r r p cos χ + cos θ 2 r d r d ϕ
ϕ i = i 2 π N
t ( r , ϕ ) = 0 r [ r A , r B ] if | ϕ ϕ i | π / N < sin ( π 2 r r A r B r A ) = 0 r [ r B , r C ] if | ϕ ϕ i | π / N < sin ( π 2 r r C r B r C ) = 100 % otherwise

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