Abstract

Compound lenses made from low-Z materials (e.g., Be, B, C, and Al) set up as a linear array of refractive lenses are proposed for submicrometer focusing of high-energy x rays (>5 keV) in one or two dimensions. A theory of focusing based on Maxwell’s equation and the Fresnel–Kirchhoff approach is presented. Compound refractive lenses were manufactured by drilling into an Al block a linear array of 200 closely spaced holes 0.5 mm in diameter for linear focusing and two crossed arrays of 100 holes each for point focusing. Focal spots of 3.7 μm and 8 μm × 18 μm were obtained at 30 keV for linear and two-dimensional lenses, respectively. Different technologies of manufacturing and possible applications of the proposed lenses are discussed.

© 1998 Optical Society of America

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References

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  1. P. J. Eng, M. L. Rivers, B. X. Yang, W. Schildkamp, “Microfocusing 4-keV to 65-keV x rays with bent Kirkpatrick–Baez mirrors,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 41–51 (1995).
    [CrossRef]
  2. F. Van Langevelde, D. K. Bowen, G. H. J. Tros, R. D. Vis, A. Huizing, K. G. De Boer, “Ellipsoid x-ray focusing for microprobe analysis at the SRS, Daresbury, UK,” Nucl. Instrum. Methods A 292, 719–727 (1990).
    [CrossRef]
  3. J. H. Underwood, A. C. Thomson, Y. Wu, R. D. Giauque, “X-ray microprobe using multilayer mirrors,” Nucl. Instrum. Methods A 266, 296–302 (1988).
    [CrossRef]
  4. B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
    [CrossRef]
  5. A. Snigirev, V. Kohn, “Bragg–Fresnel optics at the ESRF: microdiffraction and microimaging applications,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 27–37 (1995).
    [CrossRef]
  6. D. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction experiments,” Science 263, 201–203 (1994).
    [CrossRef] [PubMed]
  7. M. Kumakhov, V. A. Sharov, “A neutron lens,” Nature (London) 357, 390–391 (1992).
    [CrossRef]
  8. P. Kirkpatrick, A. V. Baez, “Formation of optical images by x rays,” J. Opt. Soc. Am. 38, 766–774 (1948).
    [CrossRef] [PubMed]
  9. S. Suehiro, H. Miyaji, H. Hayashi, “Refractive lens for x-ray focus,” Nature (London) 352, 385–386 (1991).
    [CrossRef]
  10. A. G. Michette, “No x-ray lens,” Nature (London) 353, 510 (1991).
    [CrossRef]
  11. B. X. Yang, “Fresnel and refractive lenses for x rays,” Nucl. Instrum. Methods A 328, 578–587 (1993).
    [CrossRef]
  12. A. Snigirev, V. Kohn, I. Snigireva, B. Lengeler, “A compound refractive lens for focusing high energy x-rays,” Nature (London) 384, 49–51 (1996).
    [CrossRef]
  13. J. Cowley, Diffraction Physics (North-Holland, Amsterdam, 1975).
  14. H. Jeffreys, B. Swirles, Method of Mathematical Physics (Cambridge U. Press, Cambridge, UK, 1966).
  15. H. Lehr, W. J. Erfeld, “Advanced microstructure products by synchrotron radiation lithography,” J. Phys. IV Colloque 9, 229–236 (1994).
  16. P. Elleaume, “Two-plane focusing of 30 keV undulator radiation with refractive lens,” ESRF Newsletter 38, 33–35 (1997).
  17. A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).
  18. B. Filseth, B. Lengeler, A. Snigirev, I. Snigireva, A. Souvorov, J. Tümmler, “Microfocusing of hard x-rays with beryllium lens,” to be published.

1997 (1)

P. Elleaume, “Two-plane focusing of 30 keV undulator radiation with refractive lens,” ESRF Newsletter 38, 33–35 (1997).

1996 (1)

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

1994 (2)

H. Lehr, W. J. Erfeld, “Advanced microstructure products by synchrotron radiation lithography,” J. Phys. IV Colloque 9, 229–236 (1994).

D. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction experiments,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

1993 (1)

B. X. Yang, “Fresnel and refractive lenses for x rays,” Nucl. Instrum. Methods A 328, 578–587 (1993).
[CrossRef]

1992 (2)

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

M. Kumakhov, V. A. Sharov, “A neutron lens,” Nature (London) 357, 390–391 (1992).
[CrossRef]

1991 (2)

S. Suehiro, H. Miyaji, H. Hayashi, “Refractive lens for x-ray focus,” Nature (London) 352, 385–386 (1991).
[CrossRef]

A. G. Michette, “No x-ray lens,” Nature (London) 353, 510 (1991).
[CrossRef]

1990 (1)

F. Van Langevelde, D. K. Bowen, G. H. J. Tros, R. D. Vis, A. Huizing, K. G. De Boer, “Ellipsoid x-ray focusing for microprobe analysis at the SRS, Daresbury, UK,” Nucl. Instrum. Methods A 292, 719–727 (1990).
[CrossRef]

1988 (1)

J. H. Underwood, A. C. Thomson, Y. Wu, R. D. Giauque, “X-ray microprobe using multilayer mirrors,” Nucl. Instrum. Methods A 266, 296–302 (1988).
[CrossRef]

1948 (1)

Baciocchi, M.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Baez, A. V.

Bajikar, S.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Bilderback, D.

D. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction experiments,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

Bowen, D. K.

F. Van Langevelde, D. K. Bowen, G. H. J. Tros, R. D. Vis, A. Huizing, K. G. De Boer, “Ellipsoid x-ray focusing for microprobe analysis at the SRS, Daresbury, UK,” Nucl. Instrum. Methods A 292, 719–727 (1990).
[CrossRef]

Cerrina, F.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Chrzas, J.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Cowley, J.

J. Cowley, Diffraction Physics (North-Holland, Amsterdam, 1975).

De Boer, K. G.

F. Van Langevelde, D. K. Bowen, G. H. J. Tros, R. D. Vis, A. Huizing, K. G. De Boer, “Ellipsoid x-ray focusing for microprobe analysis at the SRS, Daresbury, UK,” Nucl. Instrum. Methods A 292, 719–727 (1990).
[CrossRef]

Denton, D.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Di. Fabrizio, E.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Elleaume, P.

P. Elleaume, “Two-plane focusing of 30 keV undulator radiation with refractive lens,” ESRF Newsletter 38, 33–35 (1997).

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

Eng, P. J.

P. J. Eng, M. L. Rivers, B. X. Yang, W. Schildkamp, “Microfocusing 4-keV to 65-keV x rays with bent Kirkpatrick–Baez mirrors,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 41–51 (1995).
[CrossRef]

Erfeld, W. J.

H. Lehr, W. J. Erfeld, “Advanced microstructure products by synchrotron radiation lithography,” J. Phys. IV Colloque 9, 229–236 (1994).

Filseth, B.

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

B. Filseth, B. Lengeler, A. Snigirev, I. Snigireva, A. Souvorov, J. Tümmler, “Microfocusing of hard x-rays with beryllium lens,” to be published.

Gentilli, M.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Giauque, R. D.

J. H. Underwood, A. C. Thomson, Y. Wu, R. D. Giauque, “X-ray microprobe using multilayer mirrors,” Nucl. Instrum. Methods A 266, 296–302 (1988).
[CrossRef]

Grella, L.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Hayashi, H.

S. Suehiro, H. Miyaji, H. Hayashi, “Refractive lens for x-ray focus,” Nature (London) 352, 385–386 (1991).
[CrossRef]

Hoffman, S. A.

D. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction experiments,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

Huizing, A.

F. Van Langevelde, D. K. Bowen, G. H. J. Tros, R. D. Vis, A. Huizing, K. G. De Boer, “Ellipsoid x-ray focusing for microprobe analysis at the SRS, Daresbury, UK,” Nucl. Instrum. Methods A 292, 719–727 (1990).
[CrossRef]

Jeffreys, H.

H. Jeffreys, B. Swirles, Method of Mathematical Physics (Cambridge U. Press, Cambridge, UK, 1966).

Kirkpatrick, P.

Klocke, T.

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

Kohn, V.

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

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

A. Snigirev, V. Kohn, “Bragg–Fresnel optics at the ESRF: microdiffraction and microimaging applications,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 27–37 (1995).
[CrossRef]

Kumakhov, M.

M. Kumakhov, V. A. Sharov, “A neutron lens,” Nature (London) 357, 390–391 (1992).
[CrossRef]

Lai, B.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Legnini, D.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Lehr, H.

H. Lehr, W. J. Erfeld, “Advanced microstructure products by synchrotron radiation lithography,” J. Phys. IV Colloque 9, 229–236 (1994).

Lengeler, B.

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

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

B. Filseth, B. Lengeler, A. Snigirev, I. Snigireva, A. Souvorov, J. Tümmler, “Microfocusing of hard x-rays with beryllium lens,” to be published.

Michette, A. G.

A. G. Michette, “No x-ray lens,” Nature (London) 353, 510 (1991).
[CrossRef]

Miyaji, H.

S. Suehiro, H. Miyaji, H. Hayashi, “Refractive lens for x-ray focus,” Nature (London) 352, 385–386 (1991).
[CrossRef]

Rivers, M. L.

P. J. Eng, M. L. Rivers, B. X. Yang, W. Schildkamp, “Microfocusing 4-keV to 65-keV x rays with bent Kirkpatrick–Baez mirrors,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 41–51 (1995).
[CrossRef]

Schildkamp, W.

P. J. Eng, M. L. Rivers, B. X. Yang, W. Schildkamp, “Microfocusing 4-keV to 65-keV x rays with bent Kirkpatrick–Baez mirrors,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 41–51 (1995).
[CrossRef]

Sharov, V. A.

M. Kumakhov, V. A. Sharov, “A neutron lens,” Nature (London) 357, 390–391 (1992).
[CrossRef]

Snigirev, A.

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

B. Filseth, B. Lengeler, A. Snigirev, I. Snigireva, A. Souvorov, J. Tümmler, “Microfocusing of hard x-rays with beryllium lens,” to be published.

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

A. Snigirev, V. Kohn, “Bragg–Fresnel optics at the ESRF: microdiffraction and microimaging applications,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 27–37 (1995).
[CrossRef]

Snigireva, I.

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

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

B. Filseth, B. Lengeler, A. Snigirev, I. Snigireva, A. Souvorov, J. Tümmler, “Microfocusing of hard x-rays with beryllium lens,” to be published.

Souvorov, A.

B. Filseth, B. Lengeler, A. Snigirev, I. Snigireva, A. Souvorov, J. Tümmler, “Microfocusing of hard x-rays with beryllium lens,” to be published.

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

Suehiro, S.

S. Suehiro, H. Miyaji, H. Hayashi, “Refractive lens for x-ray focus,” Nature (London) 352, 385–386 (1991).
[CrossRef]

Swirles, B.

H. Jeffreys, B. Swirles, Method of Mathematical Physics (Cambridge U. Press, Cambridge, UK, 1966).

Thiel, D. J.

D. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction experiments,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

Thomson, A. C.

J. H. Underwood, A. C. Thomson, Y. Wu, R. D. Giauque, “X-ray microprobe using multilayer mirrors,” Nucl. Instrum. Methods A 266, 296–302 (1988).
[CrossRef]

Tros, G. H. J.

F. Van Langevelde, D. K. Bowen, G. H. J. Tros, R. D. Vis, A. Huizing, K. G. De Boer, “Ellipsoid x-ray focusing for microprobe analysis at the SRS, Daresbury, UK,” Nucl. Instrum. Methods A 292, 719–727 (1990).
[CrossRef]

Tümmler, J.

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

B. Filseth, B. Lengeler, A. Snigirev, I. Snigireva, A. Souvorov, J. Tümmler, “Microfocusing of hard x-rays with beryllium lens,” to be published.

Underwood, J. H.

J. H. Underwood, A. C. Thomson, Y. Wu, R. D. Giauque, “X-ray microprobe using multilayer mirrors,” Nucl. Instrum. Methods A 266, 296–302 (1988).
[CrossRef]

Van Langevelde, F.

F. Van Langevelde, D. K. Bowen, G. H. J. Tros, R. D. Vis, A. Huizing, K. G. De Boer, “Ellipsoid x-ray focusing for microprobe analysis at the SRS, Daresbury, UK,” Nucl. Instrum. Methods A 292, 719–727 (1990).
[CrossRef]

Viccaro, P. J.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Vis, R. D.

F. Van Langevelde, D. K. Bowen, G. H. J. Tros, R. D. Vis, A. Huizing, K. G. De Boer, “Ellipsoid x-ray focusing for microprobe analysis at the SRS, Daresbury, UK,” Nucl. Instrum. Methods A 292, 719–727 (1990).
[CrossRef]

White, V.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Wu, Y.

J. H. Underwood, A. C. Thomson, Y. Wu, R. D. Giauque, “X-ray microprobe using multilayer mirrors,” Nucl. Instrum. Methods A 266, 296–302 (1988).
[CrossRef]

Xiao, Y.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Yang, B. X.

B. X. Yang, “Fresnel and refractive lenses for x rays,” Nucl. Instrum. Methods A 328, 578–587 (1993).
[CrossRef]

P. J. Eng, M. L. Rivers, B. X. Yang, W. Schildkamp, “Microfocusing 4-keV to 65-keV x rays with bent Kirkpatrick–Baez mirrors,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 41–51 (1995).
[CrossRef]

Yun, B.

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

B. Lai, B. Yun, D. Legnini, Y. Xiao, J. Chrzas, P. J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di. Fabrizio, M. Gentilli, L. Grella, M. Baciocchi, “Hard x-ray zone plate fabricated by lithographic techniques,” Appl. Phys. Lett. 61, 1877–1879 (1992).
[CrossRef]

ESRF Newsletter (1)

P. Elleaume, “Two-plane focusing of 30 keV undulator radiation with refractive lens,” ESRF Newsletter 38, 33–35 (1997).

J. Opt. Soc. Am. (1)

J. Phys. IV Colloque (1)

H. Lehr, W. J. Erfeld, “Advanced microstructure products by synchrotron radiation lithography,” J. Phys. IV Colloque 9, 229–236 (1994).

Nature (London) (4)

M. Kumakhov, V. A. Sharov, “A neutron lens,” Nature (London) 357, 390–391 (1992).
[CrossRef]

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

S. Suehiro, H. Miyaji, H. Hayashi, “Refractive lens for x-ray focus,” Nature (London) 352, 385–386 (1991).
[CrossRef]

A. G. Michette, “No x-ray lens,” Nature (London) 353, 510 (1991).
[CrossRef]

Nucl. Instrum. Methods A (3)

B. X. Yang, “Fresnel and refractive lenses for x rays,” Nucl. Instrum. Methods A 328, 578–587 (1993).
[CrossRef]

F. Van Langevelde, D. K. Bowen, G. H. J. Tros, R. D. Vis, A. Huizing, K. G. De Boer, “Ellipsoid x-ray focusing for microprobe analysis at the SRS, Daresbury, UK,” Nucl. Instrum. Methods A 292, 719–727 (1990).
[CrossRef]

J. H. Underwood, A. C. Thomson, Y. Wu, R. D. Giauque, “X-ray microprobe using multilayer mirrors,” Nucl. Instrum. Methods A 266, 296–302 (1988).
[CrossRef]

Science (1)

D. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction experiments,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

Other (6)

P. J. Eng, M. L. Rivers, B. X. Yang, W. Schildkamp, “Microfocusing 4-keV to 65-keV x rays with bent Kirkpatrick–Baez mirrors,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 41–51 (1995).
[CrossRef]

J. Cowley, Diffraction Physics (North-Holland, Amsterdam, 1975).

H. Jeffreys, B. Swirles, Method of Mathematical Physics (Cambridge U. Press, Cambridge, UK, 1966).

A. Snigirev, B. Filseth, P. Elleaume, T. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tümmler, “Refractive lenses for high energy X-ray focusing,” in High Heat Flux Engineering IV, A. Khounsary, ed., Proc. SPIE3151A, (1997).

B. Filseth, B. Lengeler, A. Snigirev, I. Snigireva, A. Souvorov, J. Tümmler, “Microfocusing of hard x-rays with beryllium lens,” to be published.

A. Snigirev, V. Kohn, “Bragg–Fresnel optics at the ESRF: microdiffraction and microimaging applications,” in X-Ray Microbeam Technology and Applications, W. Yun, ed., Proc. SPIE2516, 27–37 (1995).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic view of the compound refractive lens as an array of air (vacuum) cylindrical holes: R, radius of the holes; d, minimum spacing between the holes; N, number of holes; λ, wavelength of x rays to be focused; f, focus distance; δ, decrement of the refractive index of the lens material; p, distance between the centers of the two neighboring holes: (a) single refractive lens, (b) compound refractive lens for linear focusing, (c) compound refractive lens for two-dimensional focusing in crossed geometry.

Fig. 2
Fig. 2

Schematic display of the experimental setup and geometric parameters of the optical scheme. The x rays from the bending magnet were selected by an Si (111) monochromator. The single-crystal Si mirror was used to cut the high order of harmonics. The lens was placed 40 m from the source. Focusing was detected in the focal plane of the CRL by a pin diode and scintillator counting detectors.

Fig. 3
Fig. 3

Schematic view of the parabolically shaped single and compound refractive lenses: R, radius of curvature; A, aperture of the lens; p, length of the single lens or the distance between the centers of the two neighboring holes for a compound lens. (a) Single parabolic refractive lens, (b) compound refractive lens with parabolically shaped holes, (c) compound refractive lens with parabolically shaped half-holes.

Fig. 4
Fig. 4

a, CRL 1. 200 cylindrical holes of 500-μm diameter and 3-mm depth were produced in an Al alloy plate with a computer-controlled drilling machine. Spacing in the thinnest part between the holes, ∼50 μm; length of the lens, 11 cm. b, CRL 2. 200 cylindrical holes of 500-μm diameter and 3-mm depth were produced in cross geometry in an Al alloy plate with a computer-controlled drilling machine. Spacing in the thinnest part between the holes, ∼50 μm; length of the lens, 11 cm.

Fig. 5
Fig. 5

a, 2D intensity mapping along the optical axis around the 5-cm focal distance. b, Single cross section of the focal line at a 1.2-m focal distance for CRL 1.

Fig. 6
Fig. 6

2D intensity mapping of the focal spot at a 2-m focal distance for CRL 2.

Fig. 7
Fig. 7

Theoretical calculations of the number of holes in the lens (solid curve) and real gain (dashed curve) versus energy for a lens with a 500-mm-hole radius from, a, boron and, b, aluminum at a fixed 1-m focal distance.

Fig. 8
Fig. 8

Theoretical calculation of the number of holes and real gain versus radius of the holes for a boron lens at 10 keV at a fixed 1-m focal distance.

Tables (1)

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Table 1 Calculated CRL Parameters for Boron and Aluminuma

Equations (22)

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E x 1 ,   y 1 ,   z 1 = a z 1 - z     d x d yP x 1 - x ,   z 1 - z × P y 1 - y ,   z 1 - z E x ,   y ,   z ,
a z = exp 2 i π   z λ ,     P x ,   z = 1 i λ z exp i π   x 2 λ z .
n x = 1 + η x = 1 + - δ + i β p - 1 × d + 2 R - R 2 - x 2 1 / 2 ,
d 2 d x 2 + d 2 d y 2 + d 2 d z 2 + 2 π λ   n x 2 E x ,   z = 0 ,
E sw x ,   y ,   z = 1 z exp 2 i π λ   h 0 x - x s ,   y - y s ,   z , h 0 x ,   t ,   z = z + x 2 + y 2 2 z .
E x ,   y ,   z = E sw x ,   y ,   z exp 2 i π λ   h x ,   z ,
h z = η - α h x + i λ 4 π h x + h z - 1 2 h x 2 + h z 2 - η 2
h x ,   z η x z - z b - α 2   η x x z - z b 2 - 1 6 η x x 2 z - z b 3 + i λ 8 π   η x x z - z b 2 .
η x - δ + i β p - 1 d + x 2 R + x 4 4 R 3 + .
Re   h x 0 ,   z b + L - 1 F 1 + L 3 F - L r s ,   Re 2 π i λ   h 0 ,   z b + L L 4 F .
f x exp 2 π i λ - δ + i β N d + x 2 R + x 4 4 R 3 + ,
E x d ,   y d = i λ a r t P x d - x s ,   r t P y d - y s ,   r t ×   d xP x d - x ,   r d C x d ,   x f x ,
C x d ,   x = r t r s 1 / 2 exp π i λ r t r t r s   x 2 - x d 2 , x d = x d + x s r d r s .
I 0 ,   r t I sw 0 ,   r t r t R r t R - 2 δ Nr s r d exp - μ Nd ,
A t = D 4   λ F R 2 1 / 4 < D .
A a = D 2 μ RN 1 / 2 < D .
I x d I sw x d A σ f 1 + r f r s exp - μ Nd sinc 2 π x d σ f ,
r f = F 1 - F / r s ,     σ f = λ r f A ,     sinc x = sin x x .
G = A σ f 1 + r f r s = A 2 λ r f 1 + r f r s .
A t = 2 R 1 2 λ δ R 1 1 / 4 N ,     A a = 2 R 1 2 μ R 1 1 / 2 .
N max = 1 μ λ F ,     G = 4 δ π β N N max ,     N < N max .
g = r s r f σ f σ s   G   exp - μ Nd = A σ s r s r f + 1 exp - μ Nd ,

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