Abstract

A compound refractive lens (CRL), consisting of a series of N closely spaced lens elements each of which contributes a small fraction of the total focusing, can be used to focus x rays or neutrons. The thickness of a CRL can be comparable to its focal length, whereupon a thick-lens analysis must be performed. In contrast with the conventional optical lens, where the ray inside the lens follows a straight line, the ray inside the CRL is continually changing direction because of the multiple refracting surfaces. Thus the matrix representation for the thick CRL is quite different from that for the thick optical lens. Principal planes can be defined such that the thick-lens matrix can be converted to that of a thin lens. For a thick lens the focal length is greater than for a thin lens with the same lens curvature, but this lengthening effect is less for the CRL than for the conventional optical lens.

© 2003 Optical Society of America

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References

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  1. T. Tomie, “X-ray lens,” Japan patent6-045288 (18February1994).
  2. T. Tomie, “X-ray lens,” U.S. patent5,594,773 (14January1997).
  3. T. Tomie, “X-ray lens,” U.S. patent5,684,852 (4November1997).
  4. 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]
  5. B. X. Yang, “Fresnel and refractive lenses for x-rays,” Nucl. Instrum. Methods Phys. Res. A 328, 578–587 (1993).
    [CrossRef]
  6. R. K. Smither, A. M. Khounsary, S. Xu, “Potential of a beryllium x-ray lens,” in High Heat Flux and Synchrotron Radiation Beamlines, A. T. Macrander, A. M. Khounsary, eds., Proc. SPIE3151, 150–163 (1997).
    [CrossRef]
  7. P. Ellaume, “Two-plane focusing of 30 keV undulator radiation,” J. Synchrotron Radiat. 5, 1–5 (1998).
    [CrossRef]
  8. B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
    [CrossRef]
  9. J. T. Cremer, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, R. H. Pantell, R. Tatchyn, “Cylindrical compound refractive x-ray lenses using plastic substrates,” Rev. Sci. Instrum. 70, 3545–3548 (1999).
    [CrossRef]
  10. H. R. Beguiristain, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. T. Cremer, “Development of compound refractive lenses for x-rays,” in Synchrotron Radiation Instrumentation: Eleventh Proceedings of the U.S. National Conference, P. Pianetta, J. Arthur, S. Brennan, eds. (American Institute of Physics, New York, 2000), Vol. 521, pp. 258–266.
  11. H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. Feinstein, “Compound x-ray refractive lenses made of polyimide,” in Advances in Laboratory-based X-Ray Sources and Optics, C. A. MacDonald, A. M. Khounsary, eds., Proc. SPIE4144, 155–164 (2000).
    [CrossRef]
  12. M. A. Piestrup, R. H. Pantell, J. T. Cremer, H. R. Beguiristain, “Compound refractive lens,” U.S. patent6,269,145 (31July2001).
  13. R. H. Pantell, J. Feinstein, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, “The effect of unit lens alignment and surface quality on compound refractive lens performance,” Rev. Sci. Instrum. 72, 48–52 (2001).
    [CrossRef]
  14. M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, R. H. Pantell, “Two-dimensional x-ray focusing from compound lenses made of plastic,” Rev. Sci. Instrum. 71, 4375–4379 (2000).
    [CrossRef]
  15. H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, C. K. Gary, “X-ray focusing with compound lenses made from beryllium,” Opt. Lett. 27, 778–780 (2002).
    [CrossRef]
  16. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), p. 171 ff.
  17. V. V. Protopopov, K. A. Valiev, “Theory of an ideal compound x-ray lens,” Opt. Commun. 151, 297–312 (1998).
    [CrossRef]

2002 (1)

2001 (1)

R. H. Pantell, J. Feinstein, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, “The effect of unit lens alignment and surface quality on compound refractive lens performance,” Rev. Sci. Instrum. 72, 48–52 (2001).
[CrossRef]

2000 (1)

M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, R. H. Pantell, “Two-dimensional x-ray focusing from compound lenses made of plastic,” Rev. Sci. Instrum. 71, 4375–4379 (2000).
[CrossRef]

1999 (2)

B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
[CrossRef]

J. T. Cremer, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, R. H. Pantell, R. Tatchyn, “Cylindrical compound refractive x-ray lenses using plastic substrates,” Rev. Sci. Instrum. 70, 3545–3548 (1999).
[CrossRef]

1998 (2)

V. V. Protopopov, K. A. Valiev, “Theory of an ideal compound x-ray lens,” Opt. Commun. 151, 297–312 (1998).
[CrossRef]

P. Ellaume, “Two-plane focusing of 30 keV undulator radiation,” J. Synchrotron Radiat. 5, 1–5 (1998).
[CrossRef]

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]

1993 (1)

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

Beguiristain, H. R.

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, C. K. Gary, “X-ray focusing with compound lenses made from beryllium,” Opt. Lett. 27, 778–780 (2002).
[CrossRef]

R. H. Pantell, J. Feinstein, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, “The effect of unit lens alignment and surface quality on compound refractive lens performance,” Rev. Sci. Instrum. 72, 48–52 (2001).
[CrossRef]

M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, R. H. Pantell, “Two-dimensional x-ray focusing from compound lenses made of plastic,” Rev. Sci. Instrum. 71, 4375–4379 (2000).
[CrossRef]

J. T. Cremer, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, R. H. Pantell, R. Tatchyn, “Cylindrical compound refractive x-ray lenses using plastic substrates,” Rev. Sci. Instrum. 70, 3545–3548 (1999).
[CrossRef]

H. R. Beguiristain, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. T. Cremer, “Development of compound refractive lenses for x-rays,” in Synchrotron Radiation Instrumentation: Eleventh Proceedings of the U.S. National Conference, P. Pianetta, J. Arthur, S. Brennan, eds. (American Institute of Physics, New York, 2000), Vol. 521, pp. 258–266.

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. Feinstein, “Compound x-ray refractive lenses made of polyimide,” in Advances in Laboratory-based X-Ray Sources and Optics, C. A. MacDonald, A. M. Khounsary, eds., Proc. SPIE4144, 155–164 (2000).
[CrossRef]

M. A. Piestrup, R. H. Pantell, J. T. Cremer, H. R. Beguiristain, “Compound refractive lens,” U.S. patent6,269,145 (31July2001).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), p. 171 ff.

Cremer, J. T.

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, C. K. Gary, “X-ray focusing with compound lenses made from beryllium,” Opt. Lett. 27, 778–780 (2002).
[CrossRef]

R. H. Pantell, J. Feinstein, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, “The effect of unit lens alignment and surface quality on compound refractive lens performance,” Rev. Sci. Instrum. 72, 48–52 (2001).
[CrossRef]

M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, R. H. Pantell, “Two-dimensional x-ray focusing from compound lenses made of plastic,” Rev. Sci. Instrum. 71, 4375–4379 (2000).
[CrossRef]

J. T. Cremer, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, R. H. Pantell, R. Tatchyn, “Cylindrical compound refractive x-ray lenses using plastic substrates,” Rev. Sci. Instrum. 70, 3545–3548 (1999).
[CrossRef]

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. Feinstein, “Compound x-ray refractive lenses made of polyimide,” in Advances in Laboratory-based X-Ray Sources and Optics, C. A. MacDonald, A. M. Khounsary, eds., Proc. SPIE4144, 155–164 (2000).
[CrossRef]

H. R. Beguiristain, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. T. Cremer, “Development of compound refractive lenses for x-rays,” in Synchrotron Radiation Instrumentation: Eleventh Proceedings of the U.S. National Conference, P. Pianetta, J. Arthur, S. Brennan, eds. (American Institute of Physics, New York, 2000), Vol. 521, pp. 258–266.

M. A. Piestrup, R. H. Pantell, J. T. Cremer, H. R. Beguiristain, “Compound refractive lens,” U.S. patent6,269,145 (31July2001).

Drakopolulos, M.

B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
[CrossRef]

Ellaume, P.

P. Ellaume, “Two-plane focusing of 30 keV undulator radiation,” J. Synchrotron Radiat. 5, 1–5 (1998).
[CrossRef]

Feinstein, J.

R. H. Pantell, J. Feinstein, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, “The effect of unit lens alignment and surface quality on compound refractive lens performance,” Rev. Sci. Instrum. 72, 48–52 (2001).
[CrossRef]

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. Feinstein, “Compound x-ray refractive lenses made of polyimide,” in Advances in Laboratory-based X-Ray Sources and Optics, C. A. MacDonald, A. M. Khounsary, eds., Proc. SPIE4144, 155–164 (2000).
[CrossRef]

Gary, C. K.

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, C. K. Gary, “X-ray focusing with compound lenses made from beryllium,” Opt. Lett. 27, 778–780 (2002).
[CrossRef]

R. H. Pantell, J. Feinstein, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, “The effect of unit lens alignment and surface quality on compound refractive lens performance,” Rev. Sci. Instrum. 72, 48–52 (2001).
[CrossRef]

M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, R. H. Pantell, “Two-dimensional x-ray focusing from compound lenses made of plastic,” Rev. Sci. Instrum. 71, 4375–4379 (2000).
[CrossRef]

J. T. Cremer, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, R. H. Pantell, R. Tatchyn, “Cylindrical compound refractive x-ray lenses using plastic substrates,” Rev. Sci. Instrum. 70, 3545–3548 (1999).
[CrossRef]

H. R. Beguiristain, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. T. Cremer, “Development of compound refractive lenses for x-rays,” in Synchrotron Radiation Instrumentation: Eleventh Proceedings of the U.S. National Conference, P. Pianetta, J. Arthur, S. Brennan, eds. (American Institute of Physics, New York, 2000), Vol. 521, pp. 258–266.

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. Feinstein, “Compound x-ray refractive lenses made of polyimide,” in Advances in Laboratory-based X-Ray Sources and Optics, C. A. MacDonald, A. M. Khounsary, eds., Proc. SPIE4144, 155–164 (2000).
[CrossRef]

Khounsary, A. M.

R. K. Smither, A. M. Khounsary, S. Xu, “Potential of a beryllium x-ray lens,” in High Heat Flux and Synchrotron Radiation Beamlines, A. T. Macrander, A. M. Khounsary, eds., Proc. SPIE3151, 150–163 (1997).
[CrossRef]

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]

Lengeler, B.

B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
[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]

Pantell, R. H.

R. H. Pantell, J. Feinstein, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, “The effect of unit lens alignment and surface quality on compound refractive lens performance,” Rev. Sci. Instrum. 72, 48–52 (2001).
[CrossRef]

M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, R. H. Pantell, “Two-dimensional x-ray focusing from compound lenses made of plastic,” Rev. Sci. Instrum. 71, 4375–4379 (2000).
[CrossRef]

J. T. Cremer, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, R. H. Pantell, R. Tatchyn, “Cylindrical compound refractive x-ray lenses using plastic substrates,” Rev. Sci. Instrum. 70, 3545–3548 (1999).
[CrossRef]

H. R. Beguiristain, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. T. Cremer, “Development of compound refractive lenses for x-rays,” in Synchrotron Radiation Instrumentation: Eleventh Proceedings of the U.S. National Conference, P. Pianetta, J. Arthur, S. Brennan, eds. (American Institute of Physics, New York, 2000), Vol. 521, pp. 258–266.

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. Feinstein, “Compound x-ray refractive lenses made of polyimide,” in Advances in Laboratory-based X-Ray Sources and Optics, C. A. MacDonald, A. M. Khounsary, eds., Proc. SPIE4144, 155–164 (2000).
[CrossRef]

M. A. Piestrup, R. H. Pantell, J. T. Cremer, H. R. Beguiristain, “Compound refractive lens,” U.S. patent6,269,145 (31July2001).

Piestrup, M. A.

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, C. K. Gary, “X-ray focusing with compound lenses made from beryllium,” Opt. Lett. 27, 778–780 (2002).
[CrossRef]

R. H. Pantell, J. Feinstein, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, “The effect of unit lens alignment and surface quality on compound refractive lens performance,” Rev. Sci. Instrum. 72, 48–52 (2001).
[CrossRef]

M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, R. H. Pantell, “Two-dimensional x-ray focusing from compound lenses made of plastic,” Rev. Sci. Instrum. 71, 4375–4379 (2000).
[CrossRef]

J. T. Cremer, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, R. H. Pantell, R. Tatchyn, “Cylindrical compound refractive x-ray lenses using plastic substrates,” Rev. Sci. Instrum. 70, 3545–3548 (1999).
[CrossRef]

H. R. Beguiristain, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. T. Cremer, “Development of compound refractive lenses for x-rays,” in Synchrotron Radiation Instrumentation: Eleventh Proceedings of the U.S. National Conference, P. Pianetta, J. Arthur, S. Brennan, eds. (American Institute of Physics, New York, 2000), Vol. 521, pp. 258–266.

M. A. Piestrup, R. H. Pantell, J. T. Cremer, H. R. Beguiristain, “Compound refractive lens,” U.S. patent6,269,145 (31July2001).

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. Feinstein, “Compound x-ray refractive lenses made of polyimide,” in Advances in Laboratory-based X-Ray Sources and Optics, C. A. MacDonald, A. M. Khounsary, eds., Proc. SPIE4144, 155–164 (2000).
[CrossRef]

Protopopov, V. V.

V. V. Protopopov, K. A. Valiev, “Theory of an ideal compound x-ray lens,” Opt. Commun. 151, 297–312 (1998).
[CrossRef]

Richwin, M.

B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
[CrossRef]

Schroer, C. G.

B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
[CrossRef]

Smither, R. K.

R. K. Smither, A. M. Khounsary, S. Xu, “Potential of a beryllium x-ray lens,” in High Heat Flux and Synchrotron Radiation Beamlines, A. T. Macrander, A. M. Khounsary, eds., Proc. SPIE3151, 150–163 (1997).
[CrossRef]

Snigirev, A.

B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
[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]

Snigireva, I.

B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
[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]

Tatchyn, R.

J. T. Cremer, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, R. H. Pantell, R. Tatchyn, “Cylindrical compound refractive x-ray lenses using plastic substrates,” Rev. Sci. Instrum. 70, 3545–3548 (1999).
[CrossRef]

Tomie, T.

T. Tomie, “X-ray lens,” Japan patent6-045288 (18February1994).

T. Tomie, “X-ray lens,” U.S. patent5,594,773 (14January1997).

T. Tomie, “X-ray lens,” U.S. patent5,684,852 (4November1997).

Tümmler, J.

B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
[CrossRef]

Valiev, K. A.

V. V. Protopopov, K. A. Valiev, “Theory of an ideal compound x-ray lens,” Opt. Commun. 151, 297–312 (1998).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), p. 171 ff.

Xu, S.

R. K. Smither, A. M. Khounsary, S. Xu, “Potential of a beryllium x-ray lens,” in High Heat Flux and Synchrotron Radiation Beamlines, A. T. Macrander, A. M. Khounsary, eds., Proc. SPIE3151, 150–163 (1997).
[CrossRef]

Yang, B. X.

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

Appl. Phys. Lett. (1)

B. Lengeler, C. G. Schroer, M. Richwin, J. Tümmler, M. Drakopolulos, A. Snigirev, I. Snigireva, “A microscope for hard x rays based on parabolic compound refractive lenses,” Appl. Phys. Lett. 74, 3924–3926 (1999).
[CrossRef]

J. Synchrotron Radiat. (1)

P. Ellaume, “Two-plane focusing of 30 keV undulator radiation,” J. Synchrotron Radiat. 5, 1–5 (1998).
[CrossRef]

Nature (London) (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]

Nucl. Instrum. Methods Phys. Res. A (1)

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

Opt. Commun. (1)

V. V. Protopopov, K. A. Valiev, “Theory of an ideal compound x-ray lens,” Opt. Commun. 151, 297–312 (1998).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (3)

R. H. Pantell, J. Feinstein, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, “The effect of unit lens alignment and surface quality on compound refractive lens performance,” Rev. Sci. Instrum. 72, 48–52 (2001).
[CrossRef]

M. A. Piestrup, H. R. Beguiristain, C. K. Gary, J. T. Cremer, R. H. Pantell, “Two-dimensional x-ray focusing from compound lenses made of plastic,” Rev. Sci. Instrum. 71, 4375–4379 (2000).
[CrossRef]

J. T. Cremer, M. A. Piestrup, H. R. Beguiristain, C. K. Gary, R. H. Pantell, R. Tatchyn, “Cylindrical compound refractive x-ray lenses using plastic substrates,” Rev. Sci. Instrum. 70, 3545–3548 (1999).
[CrossRef]

Other (8)

H. R. Beguiristain, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. T. Cremer, “Development of compound refractive lenses for x-rays,” in Synchrotron Radiation Instrumentation: Eleventh Proceedings of the U.S. National Conference, P. Pianetta, J. Arthur, S. Brennan, eds. (American Institute of Physics, New York, 2000), Vol. 521, pp. 258–266.

H. R. Beguiristain, J. T. Cremer, M. A. Piestrup, R. H. Pantell, C. K. Gary, J. Feinstein, “Compound x-ray refractive lenses made of polyimide,” in Advances in Laboratory-based X-Ray Sources and Optics, C. A. MacDonald, A. M. Khounsary, eds., Proc. SPIE4144, 155–164 (2000).
[CrossRef]

M. A. Piestrup, R. H. Pantell, J. T. Cremer, H. R. Beguiristain, “Compound refractive lens,” U.S. patent6,269,145 (31July2001).

R. K. Smither, A. M. Khounsary, S. Xu, “Potential of a beryllium x-ray lens,” in High Heat Flux and Synchrotron Radiation Beamlines, A. T. Macrander, A. M. Khounsary, eds., Proc. SPIE3151, 150–163 (1997).
[CrossRef]

T. Tomie, “X-ray lens,” Japan patent6-045288 (18February1994).

T. Tomie, “X-ray lens,” U.S. patent5,594,773 (14January1997).

T. Tomie, “X-ray lens,” U.S. patent5,684,852 (4November1997).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999), p. 171 ff.

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Figures (10)

Fig. 1
Fig. 1

Multiple-lens elements are placed together to form a compound refractive lens.

Fig. 2
Fig. 2

Required lens thickness t, normalized to f 0, for the x-ray CRL as a function of f 0, where f 0 is the focal length for the thin CRL [see Eq. (1)]. For short focal lengths or high photon energies, t/ f 0 can be comparable to or greater than unity, which means that a thick-lens analysis is appropriate.

Fig. 3
Fig. 3

Required lens thickness versus f 0 in different materials for a thermal neutron CRL. A thick-lens analysis is necessary for focal lengths of a few meters or less.

Fig. 4
Fig. 4

Principal plane location for a thick optical lens.

Fig. 5
Fig. 5

Relevant parameters for a thick x-ray CRL. The ray trajectory is curved, in contrast with the straight-line trajectory in a thick optical lens.

Fig. 6
Fig. 6

Principal plane locations for a symmetrical thick lens. With focal length and image and source distances measured from the principal planes, the matrix representation for the thick lens becomes the matrix for a thin lens.

Fig. 7
Fig. 7

Focal length as a function of lens thickness for the optical lens and the CRL.

Fig. 8
Fig. 8

Principal plane position versus lens thickness. Because d/ t > 0.5, the principal planes are located as illustrated in Fig. 6.

Fig. 9
Fig. 9

Maximum source distance for the image plane to lie outside of the lens as a function of lens thickness.

Fig. 10
Fig. 10

Aperture for a thick CRL as a function of lens thickness.

Equations (20)

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f0=R2Nδ.
tf0=Rp2δf02,
f=f01-t4f0,
1f=1r0+1ri.
dΘ=hf0tdz,
dh=-Θdz.
h1Θ1=Mh0Θ0,
M=costf01/2-f0t1/2 sintf01/21f0t1/2sintf01/2costf01/2.
101f1.
1d01,
1d01M1d01=101f1.
ff0=tf01/2sintf01/2,
d=f1-costf01/2.
fd=11-costf01/2
3π2>tf01/2-2πm>π2,
r0fMAX=1-sectf01/2.
G=TAσr0f,
A0=4f0δμ1/2,
A0A0=h00tdzt h2z1/2,
hz=h0coszf0t1/2+f0t1/2ρ0sinzf0t1/2-sf0t1/2ρ0sinzf0t1/2,

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