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

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]

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).

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. 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]

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. 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]

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. 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]

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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