Abstract

In this paper a novel single-focus x-ray zone plate is proposed by stagger arrangement of zones, which would be technically easier to manufacture. Theoretical design shows that the transmission function of the plate is a cosine function of radius, like that of a Gabor zone plate. Numerical simulation at the wavelength of 0.275 nm shows that the plate is of single-order focusing, with spatial resolution limit the same as that of the corresponding conventional zone plate, and the first-order diffraction efficiency of 11.5%. The plate can also work for single-order focusing at other x-ray wavelengths.

© 2013 Optical Society of America

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A. Takeuchi, Y. Suzuki, K. Uesugi, I. Okada, and H. Iriguchi, “Performance test and evaluation of multilevel Fresnel zone plate with three-step profile fabricated with electron-beam lithography,” Jpn. J. Appl. Phys.51(2), 022502 (2012).
[CrossRef]

X.-F. Wang, J.-Y. Wang, X.-H. Chen, X.-G. Chen, and L. Wei, “Large field-of-view X-ray imaging by using a Fresnel zone plate,” Laser Part. Beams30(1), 87–93 (2012).
[CrossRef]

2011

X.-F. Wang and J.-Y. Wang, “Analysis of high-resolution X-ray imaging of an inertial-confinement-fusion target by using a Fresnel zone plate,” Acta Phys. Sin.60(2), 025212 (2011).

L. Wei, L. Kuang, W. Fan, H. Zang, L. Cao, Y. Gu, and X. Wang, “Annulus-sector-element coded Gabor zone plate at the x-ray wavelength,” Opt. Express19(22), 21419–21424 (2011).
[CrossRef] [PubMed]

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

2010

2009

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express17(20), 17669–17677 (2009).
[CrossRef] [PubMed]

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. Anderson, “Hydrogen silsesquioxane double patterning process for 12 nm resolution x-ray zone plates,” J. Vac. Sci. Technol. B27(6), 2606–2611 (2009).
[CrossRef]

2005

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

2001

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature414(6860), 184–188 (2001).
[CrossRef] [PubMed]

2000

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva, and A. Snigirev, “Microscopic imaging and holography with hard X-rays using Fresnel zone-plates,” Opt. Commun.180(4–6), 233–238 (2000).
[CrossRef]

1999

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature401(6756), 895–898 (1999).
[CrossRef]

1994

1992

1974

1967

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Anderson, E.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. Anderson, “Hydrogen silsesquioxane double patterning process for 12 nm resolution x-ray zone plates,” J. Vac. Sci. Technol. B27(6), 2606–2611 (2009).
[CrossRef]

Anderson, E. H.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express17(20), 17669–17677 (2009).
[CrossRef] [PubMed]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Attwood, D.

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics4(12), 840–848 (2010).
[CrossRef]

Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Baretzky, B.

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

Barrett, R.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature401(6756), 895–898 (1999).
[CrossRef]

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Beynon, T. D.

Cabrini, S.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature401(6756), 895–898 (1999).
[CrossRef]

Cao, L.

Chao, W.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express17(20), 17669–17677 (2009).
[CrossRef] [PubMed]

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. Anderson, “Hydrogen silsesquioxane double patterning process for 12 nm resolution x-ray zone plates,” J. Vac. Sci. Technol. B27(6), 2606–2611 (2009).
[CrossRef]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Chen, X.-G.

X.-F. Wang, J.-Y. Wang, X.-H. Chen, X.-G. Chen, and L. Wei, “Large field-of-view X-ray imaging by using a Fresnel zone plate,” Laser Part. Beams30(1), 87–93 (2012).
[CrossRef]

Chen, X.-H.

X.-F. Wang, J.-Y. Wang, X.-H. Chen, X.-G. Chen, and L. Wei, “Large field-of-view X-ray imaging by using a Fresnel zone plate,” Laser Part. Beams30(1), 87–93 (2012).
[CrossRef]

Cheng, L. M.

Choy, C. M.

Di Fabrizio, E.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature401(6756), 895–898 (1999).
[CrossRef]

Drakopoulos, M.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva, and A. Snigirev, “Microscopic imaging and holography with hard X-rays using Fresnel zone-plates,” Opt. Commun.180(4–6), 233–238 (2000).
[CrossRef]

Fan, W.

Fischer, P.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express17(20), 17669–17677 (2009).
[CrossRef] [PubMed]

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. Anderson, “Hydrogen silsesquioxane double patterning process for 12 nm resolution x-ray zone plates,” J. Vac. Sci. Technol. B27(6), 2606–2611 (2009).
[CrossRef]

Gentili, M.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature401(6756), 895–898 (1999).
[CrossRef]

Grévent, C.

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

Gu, Y.

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Harteneck, B. D.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Iriguchi, H.

A. Takeuchi, Y. Suzuki, K. Uesugi, I. Okada, and H. Iriguchi, “Performance test and evaluation of multilevel Fresnel zone plate with three-step profile fabricated with electron-beam lithography,” Jpn. J. Appl. Phys.51(2), 022502 (2012).
[CrossRef]

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Kaulich, B.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature401(6756), 895–898 (1999).
[CrossRef]

Kim, J.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. Anderson, “Hydrogen silsesquioxane double patterning process for 12 nm resolution x-ray zone plates,” J. Vac. Sci. Technol. B27(6), 2606–2611 (2009).
[CrossRef]

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express17(20), 17669–17677 (2009).
[CrossRef] [PubMed]

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Kirk, I.

Kirz, J.

Knez, M.

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

Kuang, L.

Leitenberger, W.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva, and A. Snigirev, “Microscopic imaging and holography with hard X-rays using Fresnel zone-plates,” Opt. Commun.180(4–6), 233–238 (2000).
[CrossRef]

Li, H.

Liddle, J. A.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Mathews, T. R.

Mayer, M.

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

Mittra, R.

Okada, I.

A. Takeuchi, Y. Suzuki, K. Uesugi, I. Okada, and H. Iriguchi, “Performance test and evaluation of multilevel Fresnel zone plate with three-step profile fabricated with electron-beam lithography,” Jpn. J. Appl. Phys.51(2), 022502 (2012).
[CrossRef]

Rehbein, S.

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

Rekawa, S.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. Anderson, “Hydrogen silsesquioxane double patterning process for 12 nm resolution x-ray zone plates,” J. Vac. Sci. Technol. B27(6), 2606–2611 (2009).
[CrossRef]

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express17(20), 17669–17677 (2009).
[CrossRef] [PubMed]

Romanato, F.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature401(6756), 895–898 (1999).
[CrossRef]

Sakdinawat, A.

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics4(12), 840–848 (2010).
[CrossRef]

Schneider, G.

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

Schütz, G.

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

Seemann, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Semonin, R. G.

Shi, L.

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Snigirev, A.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva, and A. Snigirev, “Microscopic imaging and holography with hard X-rays using Fresnel zone-plates,” Opt. Commun.180(4–6), 233–238 (2000).
[CrossRef]

Snigireva, I.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva, and A. Snigirev, “Microscopic imaging and holography with hard X-rays using Fresnel zone-plates,” Opt. Commun.180(4–6), 233–238 (2000).
[CrossRef]

Stigliani, D. J.

Susini, J.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature401(6756), 895–898 (1999).
[CrossRef]

Suzuki, Y.

A. Takeuchi, Y. Suzuki, K. Uesugi, I. Okada, and H. Iriguchi, “Performance test and evaluation of multilevel Fresnel zone plate with three-step profile fabricated with electron-beam lithography,” Jpn. J. Appl. Phys.51(2), 022502 (2012).
[CrossRef]

Szeghalmi, A.

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

Takeuchi, A.

A. Takeuchi, Y. Suzuki, K. Uesugi, I. Okada, and H. Iriguchi, “Performance test and evaluation of multilevel Fresnel zone plate with three-step profile fabricated with electron-beam lithography,” Jpn. J. Appl. Phys.51(2), 022502 (2012).
[CrossRef]

Uesugi, K.

A. Takeuchi, Y. Suzuki, K. Uesugi, I. Okada, and H. Iriguchi, “Performance test and evaluation of multilevel Fresnel zone plate with three-step profile fabricated with electron-beam lithography,” Jpn. J. Appl. Phys.51(2), 022502 (2012).
[CrossRef]

Wang, J.-Y.

X.-F. Wang, J.-Y. Wang, X.-H. Chen, X.-G. Chen, and L. Wei, “Large field-of-view X-ray imaging by using a Fresnel zone plate,” Laser Part. Beams30(1), 87–93 (2012).
[CrossRef]

X.-F. Wang and J.-Y. Wang, “Analysis of high-resolution X-ray imaging of an inertial-confinement-fusion target by using a Fresnel zone plate,” Acta Phys. Sin.60(2), 025212 (2011).

Wang, X.

Wang, X.-F.

X.-F. Wang, J.-Y. Wang, X.-H. Chen, X.-G. Chen, and L. Wei, “Large field-of-view X-ray imaging by using a Fresnel zone plate,” Laser Part. Beams30(1), 87–93 (2012).
[CrossRef]

X.-F. Wang and J.-Y. Wang, “Analysis of high-resolution X-ray imaging of an inertial-confinement-fusion target by using a Fresnel zone plate,” Acta Phys. Sin.60(2), 025212 (2011).

Wang, Y.

Wei, L.

X.-F. Wang, J.-Y. Wang, X.-H. Chen, X.-G. Chen, and L. Wei, “Large field-of-view X-ray imaging by using a Fresnel zone plate,” Laser Part. Beams30(1), 87–93 (2012).
[CrossRef]

L. Wei, L. Kuang, W. Fan, H. Zang, L. Cao, Y. Gu, and X. Wang, “Annulus-sector-element coded Gabor zone plate at the x-ray wavelength,” Opt. Express19(22), 21419–21424 (2011).
[CrossRef] [PubMed]

Weigand, M.

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

Weitkamp, T.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva, and A. Snigirev, “Microscopic imaging and holography with hard X-rays using Fresnel zone-plates,” Opt. Commun.180(4–6), 233–238 (2000).
[CrossRef]

Xie, C.

Zang, H.

Zhu, X.

Acta Phys. Sin.

X.-F. Wang and J.-Y. Wang, “Analysis of high-resolution X-ray imaging of an inertial-confinement-fusion target by using a Fresnel zone plate,” Acta Phys. Sin.60(2), 025212 (2011).

Appl. Opt.

J. Opt. Soc. Am.

J. Vac. Sci. Technol. B

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. Anderson, “Hydrogen silsesquioxane double patterning process for 12 nm resolution x-ray zone plates,” J. Vac. Sci. Technol. B27(6), 2606–2611 (2009).
[CrossRef]

Jpn. J. Appl. Phys.

A. Takeuchi, Y. Suzuki, K. Uesugi, I. Okada, and H. Iriguchi, “Performance test and evaluation of multilevel Fresnel zone plate with three-step profile fabricated with electron-beam lithography,” Jpn. J. Appl. Phys.51(2), 022502 (2012).
[CrossRef]

Laser Part. Beams

X.-F. Wang, J.-Y. Wang, X.-H. Chen, X.-G. Chen, and L. Wei, “Large field-of-view X-ray imaging by using a Fresnel zone plate,” Laser Part. Beams30(1), 87–93 (2012).
[CrossRef]

Nat. Photonics

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics4(12), 840–848 (2010).
[CrossRef]

Nature

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature401(6756), 895–898 (1999).
[CrossRef]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Opt. Commun.

W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva, and A. Snigirev, “Microscopic imaging and holography with hard X-rays using Fresnel zone-plates,” Opt. Commun.180(4–6), 233–238 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Ultramicroscopy

M. Mayer, C. Grévent, A. Szeghalmi, M. Knez, M. Weigand, S. Rehbein, G. Schneider, B. Baretzky, and G. Schütz, “Multilayer Fresnel zone plate for soft X-ray microscopy resolves sub-39 nm structures,” Ultramicroscopy111(12), 1706–1711 (2011).
[CrossRef] [PubMed]

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http://henke.lbl.gov/optical_constants/ ; http://www.nist.gov/pml/data/ffast/index.cfm .

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Figures (6)

Fig. 1
Fig. 1

The first pair of staggered zones. The red-shaded area and blue-shaded area stand for the transparent part and the opaque part, respectively. The dash circles show the outer boundaries of the 1st and the 2nd half-wave zones of a conventional FZP.

Fig. 2
Fig. 2

(a) Azimuthally random arrangement of the first and the second pair of staggered zones. (b) An SZP of 50 zone pairs. The red-shaded area and blue-shaded area stand for the transparent part and the opaque part, respectively.

Fig. 3
Fig. 3

The schematic diagram of diffractions by the SZP. The z-axis is the optical axis that goes through the SZP center.

Fig. 4
Fig. 4

(a) The normalized intensity distribution along the optical axis of an SZP. (b) Profile of the Airy pattern along the x-direction on the focal plane. The inset shows the profile in a wider range. (c) The fraction of energy contained within a circle of radius rc. The dash line shows 62.6%, the total transmission of the SZP.

Fig. 5
Fig. 5

The 1st-order diffraction efficiency versus x-ray photon energy. Solid curve: SZP. Dash dot curve: FZP.

Fig. 6
Fig. 6

The image’s intensity distributions along the x- and the y-direction, separately. The intensity is relative to that of the point source. Position 0 is the Airy pattern center. The inset shows the sidelobes. Solid curve: x-direction. Dot curve: y-direction. (a) The point source is on the optical axis. (b) The point source is, along the x-direction, 3 mm off the optical axis.

Tables (1)

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Table 1 Parameters of the SZP Used in the Simulation

Equations (19)

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U( P )= A 0 iλz exp(ikz) 0 2π 0 R t(ρ,θ)exp { iπ λz [ (xρcosθ) 2 + (yρsinθ) 2 ] } ρdρdθ,
U( z )= A 0 iλz exp(ikz) 0 R T(ρ)exp ( iπ λz ρ 2 )ρdρ,
T(ρ)= 0 2π t(ρ,θ) dθ.
t G = 1 2 (1cos π ρ 2 λf ).
U( z )= A 0 iλz exp(ikz) 0 2π 0 R 1 2 (1cos π ρ 2 λf )exp ( iπ λz ρ 2 )ρdρdθ = 2π A 0 iλz exp(ikz) 0 R 1 2 (1cos π ρ 2 λf )exp ( iπ λz ρ 2 )ρdρ
T=π(1cos π ρ 2 λf ),
T upper (ρ)= 0 π t(ρ,θ) dθ.
T upper (ρ)= 0 θ dθ=θ.
T=2θ.
r 1 :ρ= λf π [arccos(12 θ π )] 0<θπ.
T upper (ρ)= θ π dθ=πθ.
T=2(πθ).
r 2 :ρ= λf π [arccos(12 θ π )+π] 0<θπ
r 3 :ρ= λf π [arccos(32 θ π )] π<θ2π r 4 :ρ= λf π [arccos(32 θ π )+π] π<θ2π
t(ρ,θ)={ 10<θ< π 2 π 2 cos ρ 2 π λf ,0<ρ λf 1π<θ< 3π 2 π 2 cos ρ 2 π λf ,0<ρ λf 1 π 2 + π 2 cos ρ 2 π λf <θ<π, λf <ρ 2λf 1 3π 2 + π 2 cos ρ 2 π λf <θ<2π, λf <ρ 2λf 0theopaquezone .
T(ρ)= 0 2π t(ρ,θ) dθ={ 0 π 2 π 2 cos ρ 2 π λf t(ρ,θ) dθ+ π 3π 2 π 2 cos ρ 2 π λf t(ρ,θ) dθ,0<ρ λf π 2 + π 2 cos ρ 2 π λf π t(ρ,θ) dθ+ 3π 2 + π 2 cos ρ 2 π λf 2π t(ρ,θ) dθ, λf <ρ 2λf =π(1cos π ρ 2 λf ) .
t(ρ,θ,n)={ 10<θ θ n ' < π 2 π 2 cos( ρ 2 π λf ), 2nλf <ρ (2n+1)λf 1π<θ θ n ' < 3π 2 π 2 cos ρ 2 π λf , 2nλf <ρ (2n+1)λf 1 π 2 + π 2 cos ρ 2 π λf <θ θ n ' <π, (2n+1)λf <ρ (2n+2)λf 1 3π 2 + π 2 cos ρ 2 π λf <θ θ n ' <2π, (2n+1)λf <ρ (2n+2)λf 0theopaquezone ,
t(ρ,θ,n)={ 10<θ θ n ' < π 2 π 2 cos( ρ 2 π λf ), 2nλf <ρ (2n+1)λf 1π<θ θ n ' < 3π 2 π 2 cos ρ 2 π λf , 2nλf <ρ (2n+1)λf 1 π 2 + π 2 cos ρ 2 π λf <θ θ n ' <π, (2n+1)λf <ρ (2n+2)λf 1 3π 2 + π 2 cos ρ 2 π λf <θ θ n ' <2π, (2n+1)λf <ρ (2n+2)λf exp[kd(β+iδ)]theopaquezone ,
U(P)= i A 0 λ Σ t(ρ,θ) e ik(r+s) rs ρdρ dθ,

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