Abstract

It is proposed in this paper that an x-ray Gabor zone plate can be realized by properly arranging annulus-sector-shaped nanometer structure apertures along each zone. This provides a new coding methodology which can be used to fabricate a binary zone plate with single order foci only. Numerical simulation results show good agreement with the physical design.

© 2011 OSA

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References

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  1. G. Andersen, “Large optical photon sieve,” Opt. Lett. 30(22), 2976–2978 (2005).
    [CrossRef] [PubMed]
  2. Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
    [CrossRef] [PubMed]
  3. 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,” Nature 414(6860), 184–188 (2001).
    [CrossRef] [PubMed]
  4. A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
    [CrossRef]
  5. 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. B 27(6), 2606 (2009).
    [CrossRef]
  6. 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,” Nature 401(6756), 895–898 (1999).
    [CrossRef]
  7. H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
    [CrossRef]
  8. E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11(19), 2278–2288 (2003).
    [CrossRef] [PubMed]
  9. G. S. Waldman, “Variations on the Fresnel Zone Plate,” J. Opt. Soc. Am. 56(2), 215–217 (1966).
    [CrossRef]
  10. M. H. Horman and H. H. M. Chau, “Zone plate theory based on holography,” Appl. Opt. 6(2), 317–322 (1967).
    [CrossRef] [PubMed]
  11. T. D. Beynon, I. Kirk, and T. R. Mathews, “Gabor zone plate with binary transmittance values,” Opt. Lett. 17(7), 544–546 (1992).
    [CrossRef] [PubMed]
  12. C. M. Choy and L. M. Cheng, “High-efficiency cosine-approximated binary Gabor zone plate,” Appl. Opt. 33(5), 794–799 (1994).
    [CrossRef] [PubMed]
  13. http://henke.lbl.gov/optical_constants/filter2.html
  14. X. Wang and J. 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).

2011 (1)

X. Wang and J. 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).

2010 (1)

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[CrossRef]

2009 (1)

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. B 27(6), 2606 (2009).
[CrossRef]

2008 (1)

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

2005 (1)

2003 (2)

2001 (1)

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,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

1999 (1)

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,” Nature 401(6756), 895–898 (1999).
[CrossRef]

1994 (1)

1992 (1)

1967 (1)

1966 (1)

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,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Andersen, G.

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. B 27(6), 2606 (2009).
[CrossRef]

Attwood, D.

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[CrossRef]

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,” Nature 401(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,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Beynon, T. D.

Cabrini, S.

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11(19), 2278–2288 (2003).
[CrossRef] [PubMed]

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,” Nature 401(6756), 895–898 (1999).
[CrossRef]

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. B 27(6), 2606 (2009).
[CrossRef]

Chau, H. H. M.

Cheng, L. M.

Choy, C. M.

Cojoc, D.

Conley, R.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Di Fabrizio, E.

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11(19), 2278–2288 (2003).
[CrossRef] [PubMed]

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,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Facci, P.

Fischer, P.

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. B 27(6), 2606 (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,” Nature 401(6756), 895–898 (1999).
[CrossRef]

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,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Holt, M.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Horman, M. H.

Jacobsen, C.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
[CrossRef] [PubMed]

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,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Kang, H.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Kaulich, B.

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11(19), 2278–2288 (2003).
[CrossRef] [PubMed]

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,” Nature 401(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. B 27(6), 2606 (2009).
[CrossRef]

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,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Kirk, I.

Liu, C.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Macrander, A.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Maser, J.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Mathews, T. R.

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. B 27(6), 2606 (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,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Sakdinawat, A.

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[CrossRef]

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,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

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,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Stephenson, G.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Susini, J.

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11(19), 2278–2288 (2003).
[CrossRef] [PubMed]

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,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Vogt, S.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Waldman, G. S.

Wang, J.

X. Wang and J. 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.

X. Wang and J. 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.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
[CrossRef] [PubMed]

Wilhein, T.

Winarski, R.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Yan, H.

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

Yun, W.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
[CrossRef] [PubMed]

Acta Phys. Sin. (1)

X. Wang and J. 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. (2)

Appl. Phys. Lett. (1)

H. Kang, H. Yan, R. Winarski, M. Holt, J. Maser, C. Liu, R. Conley, S. Vogt, A. Macrander, and G. Stephenson, “Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens,” Appl. Phys. Lett. 92(22), 221114 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. B (1)

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. B 27(6), 2606 (2009).
[CrossRef]

Nat. Photonics (1)

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[CrossRef]

Nature (3)

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,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
[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,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Other (1)

http://henke.lbl.gov/optical_constants/filter2.html

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Figures (3)

Fig. 1
Fig. 1

(a) shows the ASZP pattern for 50 zone pairs and 100 elements in each zone pair. (b) shows the detailed structures of a zone pair. (c) shows an annulus-sector-shaped element.

Fig. 2
Fig. 2

(a) Intensity distribution along the optical axis of an ASZP. (b) The intensity profile along the radial direction on the focal plane.

Fig. 3
Fig. 3

(a) Coordinate system for simulating the ASZP off-axis imaging. (b) The intensity profiles of the ASZP imaging for a point source at different off-axis distances along the x axis. Solid curve: (0 mm). Dash curve: (13 mm). Dash-dot curve: (17 mm).

Tables (1)

Tables Icon

Table 1 Parameters of the ASZP and in the simulation.

Equations (16)

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U( z )=( A 0 /2iλz )exp( ikz ) 0 2π 0 R t( r,θ ) exp( iπ r 2 /λz )d r 2 dθ
U( z )=( A 0 π/iλz )exp( ikz ) 0 R t( r ) exp( iπ r 2 /λz )d r 2 .
t( r )=( 1/2 )[ 1+cos( π r 2 / r 1 2 ) ].
r=r r n + r n ;( r n r r n+1 )
r n = ( 2n1 ) 1/2 r 1
t( r )=( 1/2 ){ 1+cos[ π( 2n1 ) ( 1+ r r n r 1 ( 2n1 ) 1/2 ) 2 ] }.
cos[ π( 2n1 ) ( 1+ r r n r 1 ( 2n1 ) 1/2 ) 2 ]cos[ π( 2n1 )( 1+ 2( r r n ) r 1 ( 2n1 ) 1/2 ) ] cos[ 2π( r r n ) r 1 2n1 ]cos[ 2π( r r n ) 2 r 1 ( 2n1 + 2n+1 ) ] =cos[ 2π( r r n ) r n+1 r n ]                                                                             
t( r )=( 1/2 ){ 1cos[ 2π( r r n )/( r n+1 r n ) ] }.
f n (r)= πN D sin( 2π r r n D 4 D )
r n +D/4 r n +3D/4 f n ( r )dr=N
πNsin[ 2π( r i r n D/4 )/D ]Δ r i /D
l( r 0 )= 0 2π l( r 0 ,θ ) = i 2π N r 0 πN D sin[ 2π( r i r n D/4 )/D ]Δ r i
t( r 0 )= l( r 0 ) 2π r 0 ={ π D r n +D/4 r 0 +D/4 sin[ 2π( r i r n D/4 )/D ]d r i π D r 0 D/4 r n +3D/4 sin[ 2π( r i r n D/4 )/D ]d r i r n < r 0 < r n +D/2 r n +D/2< r 0 < r n+1 .
t( r 0 )=( 1/2 ){ 1cos[ 2π( r 0 r n )/D ] }
t ~ ={ 1 exp[ kd( β+iδ ) ] the open zone the opaque zone
U( P )= iA 2λ S exp[ ik( r+s ) ] t ˜ ( S ) rs [ cos( n,s )cos( n,r ) ]dS           

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