Abstract

Fresnel zone plates produced by electron beam lithography and planar etching techniques provide a resolving power of about 10 nm. An alternative zone plate fabrication approach is based on alternately coating a micro-wire with two different materials. With this process, very thin zone layers with very high aspect ratios can be deposited. However, depending on the fabrication method, random zone positioning errors may introduce strong aberrations. We simulate the effect of positioning errors using different random fluctuations and study their influence on zone plate resolution. We find that random errors significantly decrease the contrast transfer of X-ray microscopes. Additionally, we derive an upper bound for the mean acceptable variance of the deposition rate.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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2014 (1)

S. Werner, S. Rehbein, P. Guttmann, and G. Schneider, “Three-dimensional structured on-chip stacked zone plates for nanoscale X-ray imaging with high efficiency,” Nano Res. 7(4), 528–535 (2014).
[Crossref]

2013 (1)

2012 (2)

W. Chao, P. Fischer, T. Tyliszczak, S. Rekawa, E. Anderson, and P. Naulleau, “Real space soft x-ray imaging at 10 nm spatial resolution,” Opt. Express 20(9), 9777–9783 (2012).
[Crossref] [PubMed]

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

2010 (1)

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

2009 (4)

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. Express 17(20), 17669–17677 (2009).
[Crossref] [PubMed]

M. Lindblom, J. Reinspach, O. von Hofsten, M. Bertilson, H. M. Hertz, and A. Holmberg, “High-aspect-ratio germanium zone plates fabricated by reactive ion etching in chlorine,” J. Vac. Sci. Technol. B 27(2), L1–L3 (2009).
[Crossref]

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-Resolution Soft-X-Ray Microscopy With Zone Plates in High Orders of Diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[Crossref] [PubMed]

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

2007 (1)

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

2004 (2)

2001 (1)

M. Peuker, “High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width,” Appl. Phys. Lett. 78(15), 2208 (2001).
[Crossref]

1997 (1)

G. Schneider, “Zone plates with high efficiency in high orders of diffraction described by dynamical theory,” Appl. Phys. Lett. 71(16), 2242 (1997).
[Crossref]

1996 (1)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).
[Crossref]

1988 (1)

Y. Vladimirsky and H. W. P. Koops, “MOIRE METHOD AND ZONE PLATE PATTERN INACCURACIES,” J. Vac. Sci. Technol. B 6(6), 2142–2146 (1988).
[Crossref]

1984 (1)

M. J. Simpson and A. G. Michette, “Imaging Properties of Modified Fresnel Zone Plates,” Opt. Acta (Lond.) 31(4), 403–413 (1984).
[Crossref]

Anderson, E.

Anderson, E. H.

Bartels, M.

Bertilson, M.

M. Lindblom, J. Reinspach, O. von Hofsten, M. Bertilson, H. M. Hertz, and A. Holmberg, “High-aspect-ratio germanium zone plates fabricated by reactive ion etching in chlorine,” J. Vac. Sci. Technol. B 27(2), L1–L3 (2009).
[Crossref]

Cao, Q.

Chao, W.

Chen, S.

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

David, C.

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Döring, F.

Eberl, C.

Feng, Y.

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

Feser, M.

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

Fink, R. H.

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Fischer, P.

Guizar-Sicairos, M.

Gutiérrez-Vega, J. C.

Guttmann, P.

S. Werner, S. Rehbein, P. Guttmann, and G. Schneider, “Three-dimensional structured on-chip stacked zone plates for nanoscale X-ray imaging with high efficiency,” Nano Res. 7(4), 528–535 (2014).
[Crossref]

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-Resolution Soft-X-Ray Microscopy With Zone Plates in High Orders of Diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[Crossref] [PubMed]

Heim, S.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-Resolution Soft-X-Ray Microscopy With Zone Plates in High Orders of Diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[Crossref] [PubMed]

Hertz, H. M.

M. Lindblom, J. Reinspach, O. von Hofsten, M. Bertilson, H. M. Hertz, and A. Holmberg, “High-aspect-ratio germanium zone plates fabricated by reactive ion etching in chlorine,” J. Vac. Sci. Technol. B 27(2), L1–L3 (2009).
[Crossref]

Heymann, J. B.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Hoffmann, S.

Holmberg, A.

M. Lindblom, J. Reinspach, O. von Hofsten, M. Bertilson, H. M. Hertz, and A. Holmberg, “High-aspect-ratio germanium zone plates fabricated by reactive ion etching in chlorine,” J. Vac. Sci. Technol. B 27(2), L1–L3 (2009).
[Crossref]

Ito, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Jahns, J.

Jefimovs, K.

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Kim, J.

Kohn, V.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).
[Crossref]

Koops, H. W. P.

Y. Vladimirsky and H. W. P. Koops, “MOIRE METHOD AND ZONE PLATE PATTERN INACCURACIES,” J. Vac. Sci. Technol. B 6(6), 2142–2146 (1988).
[Crossref]

Krebs, H. U.

Lengeler, B.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).
[Crossref]

Liese, T.

Lindblom, M.

M. Lindblom, J. Reinspach, O. von Hofsten, M. Bertilson, H. M. Hertz, and A. Holmberg, “High-aspect-ratio germanium zone plates fabricated by reactive ion etching in chlorine,” J. Vac. Sci. Technol. B 27(2), L1–L3 (2009).
[Crossref]

Lyon, A.

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

Maaßdorf, A.

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Masuda, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

McNally, J. G.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Michette, A. G.

M. J. Simpson and A. G. Michette, “Imaging Properties of Modified Fresnel Zone Plates,” Opt. Acta (Lond.) 31(4), 403–413 (1984).
[Crossref]

Mueller, F.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Müller, W. G.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Nagashima, K.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Naulleau, P.

Nishitsuji, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Okada, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Osterhoff, M.

Peuker, M.

M. Peuker, “High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width,” Appl. Phys. Lett. 78(15), 2208 (2001).
[Crossref]

Pilvi, T.

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Raabe, J.

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Rehbein, S.

S. Werner, S. Rehbein, P. Guttmann, and G. Schneider, “Three-dimensional structured on-chip stacked zone plates for nanoscale X-ray imaging with high efficiency,” Nano Res. 7(4), 528–535 (2014).
[Crossref]

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-Resolution Soft-X-Ray Microscopy With Zone Plates in High Orders of Diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[Crossref] [PubMed]

Reinspach, J.

M. Lindblom, J. Reinspach, O. von Hofsten, M. Bertilson, H. M. Hertz, and A. Holmberg, “High-aspect-ratio germanium zone plates fabricated by reactive ion etching in chlorine,” J. Vac. Sci. Technol. B 27(2), L1–L3 (2009).
[Crossref]

Rekawa, S.

Rishton, S.

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

Ritala, M.

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Robisch, A. L.

Ruhlandt, A.

Sakurai, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Salditt, T.

Sassolini, S.

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

Schlenkrich, F.

Schneider, G.

S. Werner, S. Rehbein, P. Guttmann, and G. Schneider, “Three-dimensional structured on-chip stacked zone plates for nanoscale X-ray imaging with high efficiency,” Nano Res. 7(4), 528–535 (2014).
[Crossref]

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-Resolution Soft-X-Ray Microscopy With Zone Plates in High Orders of Diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[Crossref] [PubMed]

G. Schneider, “Zone plates with high efficiency in high orders of diffraction described by dynamical theory,” Appl. Phys. Lett. 71(16), 2242 (1997).
[Crossref]

Senoner, M.

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Shimobaba, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Shiraki, A.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Simpson, M. J.

M. J. Simpson and A. G. Michette, “Imaging Properties of Modified Fresnel Zone Plates,” Opt. Acta (Lond.) 31(4), 403–413 (1984).
[Crossref]

Snigirev, A.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).
[Crossref]

Snigireva, I.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).
[Crossref]

Takada, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Tyliszczak, T.

Vila-Comamala, J.

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Vladimirsky, Y.

Y. Vladimirsky and H. W. P. Koops, “MOIRE METHOD AND ZONE PLATE PATTERN INACCURACIES,” J. Vac. Sci. Technol. B 6(6), 2142–2146 (1988).
[Crossref]

von Hofsten, O.

M. Lindblom, J. Reinspach, O. von Hofsten, M. Bertilson, H. M. Hertz, and A. Holmberg, “High-aspect-ratio germanium zone plates fabricated by reactive ion etching in chlorine,” J. Vac. Sci. Technol. B 27(2), L1–L3 (2009).
[Crossref]

Weng, J.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

Werner, S.

S. Werner, S. Rehbein, P. Guttmann, and G. Schneider, “Three-dimensional structured on-chip stacked zone plates for nanoscale X-ray imaging with high efficiency,” Nano Res. 7(4), 528–535 (2014).
[Crossref]

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-Resolution Soft-X-Ray Microscopy With Zone Plates in High Orders of Diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[Crossref] [PubMed]

Yun, W.

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

Zeng, X.

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

Appl. Phys. Lett. (2)

M. Peuker, “High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width,” Appl. Phys. Lett. 78(15), 2208 (2001).
[Crossref]

G. Schneider, “Zone plates with high efficiency in high orders of diffraction described by dynamical theory,” Appl. Phys. Lett. 71(16), 2242 (1997).
[Crossref]

Comput. Phys. Commun. (1)

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. 183(5), 1124–1138 (2012).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. B (2)

Y. Vladimirsky and H. W. P. Koops, “MOIRE METHOD AND ZONE PLATE PATTERN INACCURACIES,” J. Vac. Sci. Technol. B 6(6), 2142–2146 (1988).
[Crossref]

M. Lindblom, J. Reinspach, O. von Hofsten, M. Bertilson, H. M. Hertz, and A. Holmberg, “High-aspect-ratio germanium zone plates fabricated by reactive ion etching in chlorine,” J. Vac. Sci. Technol. B 27(2), L1–L3 (2009).
[Crossref]

Microelectron. Nano. Struct. (1)

Y. Feng, M. Feser, A. Lyon, S. Rishton, X. Zeng, S. Chen, S. Sassolini, and W. Yun, “Nanofabrication of high aspect ratio 24 nm x-ray zone plates for x-ray imaging applications,” Microelectron. Nano. Struct. 25(6), 2004 (2007).

Nano Res. (1)

S. Werner, S. Rehbein, P. Guttmann, and G. Schneider, “Three-dimensional structured on-chip stacked zone plates for nanoscale X-ray imaging with high efficiency,” Nano Res. 7(4), 528–535 (2014).
[Crossref]

Nat. Methods (1)

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Nature (1)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).
[Crossref]

Opt. Acta (Lond.) (1)

M. J. Simpson and A. G. Michette, “Imaging Properties of Modified Fresnel Zone Plates,” Opt. Acta (Lond.) 31(4), 403–413 (1984).
[Crossref]

Opt. Express (3)

Phys. Rev. Lett. (1)

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-Resolution Soft-X-Ray Microscopy With Zone Plates in High Orders of Diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[Crossref] [PubMed]

Ultramicroscopy (1)

J. Vila-Comamala, K. Jefimovs, J. Raabe, T. Pilvi, R. H. Fink, M. Senoner, A. Maaßdorf, M. Ritala, and C. David, “Advanced thin film technology for ultrahigh resolution X-ray microscopy,” Ultramicroscopy 109(11), 1360–1364 (2009).
[Crossref] [PubMed]

Other (2)

D. Rudolph, B. Niemann, and G. Schmahl, “Status Of The Sputtered Sliced Zone Plates For X-Ray Microscopy,” (1982), pp. 103–105.

A. Duvel, D. Rudolph, and G. Schmahl, “Fabrication of thick zone plates for multi-kilovolt X-rays,” in X-Ray Microscopy, Proceedings, W. MeyerIlse, T. Warwick, and D. Attwood, eds. (2000), pp. 607–614.

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Figures (6)

Fig. 1
Fig. 1 X-ray optical setup of a scanning transmission X-ray microscope (STXM). An FZP with central stop forms a focal spot which is raster scanned in the object plane. The order sorting aperture blocks all orders except the diffraction order of the FZP used for imaging.
Fig. 2
Fig. 2 (a). Impact of the central stop on the focal spot pattern of an FZP. Four different central stop diameters are considered: 0 (brown), 25 (green), 50 (purple) and 75% (blue). Figure 2(b). Corresponding MTFs for the focal spot pattern in Fig. 2(a). The calculations were performed for an FZP with 5 nm outermost zone width and a focal length of 50 µm at λ = 0.157 nm.
Fig. 3
Fig. 3 Illustration of the different types of positioning errors which are considered in this paper. a) Random fluctuations in the deposited zone width. b) Systematic shift of the zones due to an elliptical wire substrate. c) Random positioning errors caused by the roughness of the substrate. The erroneous FZP pattern is shown in color. The zone positions for the ideal FZP pattern are also indicated (cross-hatched).
Fig. 4
Fig. 4 Simulated images showing the impact of the substrate roughness (right column, see also Fig. 3(c)) on the focal pattern (left column) and hence the resolution (middle column) of the STXM. The simulation was performed for FZPs with an outermost zone width of drN = 5 nm and a diameter of 1.594 µm at a wavelength of 0.157 nm (see also [17]). Figure 4(a) shows the results for a perfect FZP without central stop. Figures 4(b)-(e) show the results for FZPs with central stop of 0.9 µm and different rms-values of 0 nm, 3 nm, 6 nm and 10 nm, respectively.
Fig. 5
Fig. 5 Plots showing the mean MTFs of the same FZPs as shown in Figs. 4(a)-(e). With increasing rms-values of the micro-wire substrate, the MTFs already decrease strongly at moderate spatial frequencies. Note the increasing standard deviation with increasing rms-values which is caused by the angular dependency of the MTF of non-circular FZPs.
Fig. 6
Fig. 6 Plots showing the MTFs of d-FZPs and e-FZPs for different production parameters. The FZPs are assumed to consist of perfectly circular concentric rings that are alternately opaque and transparent. All FZPs have a diameter of 50 µm. The border of each ring is perturbed as described in the text. The percentage of the FZP area obscured by the micro-wire substrate is denoted by A. In the left plot (a), the standard deviation of the positioning error varied between 0.02 and 0.05 nm per each nm deposited. In this case, the condition dr N 2 > σ R 2 R 1 nm =0.05 nm*86.6=4.33 nm is not satisfied for σ R =0.05 nm (violet graph). In the green graph, the standard deviation is σ R =0.02 nm satisfying the condition dr N 2 > σ R 2 R 1 nm   =0.05 nm*86.6=1.73 nm . The brown line corresponds to a perfect FZP. The right plot (b) shows the MTFs of an e-FZP and two d-FZPs. The FZP-parameters for the FZP 4) and 5) are identical, but the simulated positioning errors correspond to a d-FZP in 4) and an e-FZP in 5). The fact that the d-FZP 6) does not satisfy the above given condition and has additionally a large central wire reduces the MTF below the level of the FZP 4) and 5) for a large part of the frequency range.

Equations (3)

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u( x,y, z 1 )= exp( i k( z 1 z 0 ) ) i λ ( z 1 z 0 )   +   u( x , y , z 0 )exp( i k 2 ( z 1 z 0 ) ( ( x x ) 2 + ( y y ) 2 ) )d x dy'
u( x,y, z 1 )= exp( i k( z 1 z 0 ) ) i λ ( z 1 z 0 ) 1  ( ( u( x , y , z 0 ) )( exp( i k 2 ( z 1 z 0 ) ( ( x x ) 2 + ( y y ) 2 ) ) ) )
d r N 2 > σ N 2 N+ σ R 2 R ΔR .

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