Abstract

Achromatic combinations of a diffractive phase Fresnel lens and a refractive correcting element have been proposed for x-ray and gamma-ray astronomy and for microlithography, but considerations of absorption often dictate that the refractive component be given a stepped profile, resulting in a double Fresnel lens. The imaging performance of corrected Fresnel lenses, with and without stepping, is investigated, and the trade-off between resolution and useful bandwidth in different circumstances is discussed. Provided that the focal ratio is large, correction lenses made from low atomic number materials can be used with x rays in the range of approximately 10–100 keV without stepping. The use of stepping extends the possibility of correction to higher-aperture systems, to energies as low as a few kilo electron volts, and to gamma rays of mega electron volt energy.

© 2004 Optical Society of America

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2003 (2)

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

B. Nöhammer, J. Hoszowska, H.-P. Herzig, C. David, “Zoneplates for hard x-rays with ultra-high diffraction efficiencies,” J. Phys. IV 104, 193–196 (2003).

2002 (1)

G. K. Skinner, “Diffractive-refractive optics for high energy astronomy. II. Variations on the theme,” Astron. Astrophys. 383, 352–359 (2002).
[CrossRef]

2001 (2)

G. K. Skinner, “Diffractive-refractive optics for high energy astronomy. I. Gamma-ray phase Fresnel lenses,” Astron. Astrophys. 375, 691–700 (2001).
[CrossRef]

E. M. Dufresne, D. A. Arms, R. Clarke, N. R. Pereira, S. B. Dierker, D. Foster, “Lithium metal for x-ray refractive optics,” Appl. Phys. Lett. 79, 4085–4087 (2001).
[CrossRef]

2000 (1)

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

1999 (2)

E. Di Fabrizio, F. Romanato, M. Gentill, S. Cabrini, B. Kaulich, J. Susini, R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999).
[CrossRef]

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
[CrossRef]

1998 (1)

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84, 5855–5861 (1998).
[CrossRef]

1996 (1)

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

1989 (1)

D. Faklis, G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592–598 (1989).
[CrossRef]

1976 (1)

1961 (1)

Anderson, E. H.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Arms, D. A.

E. M. Dufresne, D. A. Arms, R. Clarke, N. R. Pereira, S. B. Dierker, D. Foster, “Lithium metal for x-ray refractive optics,” Appl. Phys. Lett. 79, 4085–4087 (2001).
[CrossRef]

Attwood, D.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Baron, R.

J. Early, R. Hyde, R. Baron, “Twenty meter space telescope based on diffractive lens,” in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio, S. L. O’Dell, eds., Proc. SPIE5168, 459–470 (2004).

Barrett, R.

E. Di Fabrizio, F. Romanato, M. Gentill, S. Cabrini, B. Kaulich, J. Susini, R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999).
[CrossRef]

Benner, B.

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Bennett, S. J.

Cabrini, S.

E. Di Fabrizio, F. Romanato, M. Gentill, S. Cabrini, B. Kaulich, J. Susini, R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999).
[CrossRef]

Cai, Z.

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
[CrossRef]

Cerrina, F.

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
[CrossRef]

Chao, W.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Chen, Z.

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
[CrossRef]

Clarke, R.

E. M. Dufresne, D. A. Arms, R. Clarke, N. R. Pereira, S. B. Dierker, D. Foster, “Lithium metal for x-ray refractive optics,” Appl. Phys. Lett. 79, 4085–4087 (2001).
[CrossRef]

David, C.

B. Nöhammer, J. Hoszowska, H.-P. Herzig, C. David, “Zoneplates for hard x-rays with ultra-high diffraction efficiencies,” J. Phys. IV 104, 193–196 (2003).

Denbeaux, G.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Di Fabrizio, E.

E. Di Fabrizio, F. Romanato, M. Gentill, S. Cabrini, B. Kaulich, J. Susini, R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999).
[CrossRef]

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
[CrossRef]

Dierker, S. B.

E. M. Dufresne, D. A. Arms, R. Clarke, N. R. Pereira, S. B. Dierker, D. Foster, “Lithium metal for x-ray refractive optics,” Appl. Phys. Lett. 79, 4085–4087 (2001).
[CrossRef]

Dufresne, E. M.

E. M. Dufresne, D. A. Arms, R. Clarke, N. R. Pereira, S. B. Dierker, D. Foster, “Lithium metal for x-ray refractive optics,” Appl. Phys. Lett. 79, 4085–4087 (2001).
[CrossRef]

Early, J.

J. Early, R. Hyde, R. Baron, “Twenty meter space telescope based on diffractive lens,” in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio, S. L. O’Dell, eds., Proc. SPIE5168, 459–470 (2004).

Faklis, D.

D. Faklis, G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592–598 (1989).
[CrossRef]

Foster, D.

E. M. Dufresne, D. A. Arms, R. Clarke, N. R. Pereira, S. B. Dierker, D. Foster, “Lithium metal for x-ray refractive optics,” Appl. Phys. Lett. 79, 4085–4087 (2001).
[CrossRef]

Gentill, M.

E. Di Fabrizio, F. Romanato, M. Gentill, S. Cabrini, B. Kaulich, J. Susini, R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999).
[CrossRef]

Gentilli, M.

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
[CrossRef]

Gluskin, E.

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
[CrossRef]

Gorenstein, P.

P. Gorenstein, “Role of diffractive and refractive optics in x-ray astronomy,” in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio, S. L. O’Dell, eds., Proc. SPIE5168, 411–419 (2004).
[CrossRef]

P. Gorenstein, “Concepts: x-ray telescopes with high-angular resolution and high throughput,” in X-Ray and Gamma-Ray Telescopes for Astronomy, J. E. Truemper, H. D. Tananbaum, eds., Proc. SPIE4851, 599–606 (2003).
[CrossRef]

Günzler, T. F.

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Harteneck, B.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Herzig, H.-P.

B. Nöhammer, J. Hoszowska, H.-P. Herzig, C. David, “Zoneplates for hard x-rays with ultra-high diffraction efficiencies,” J. Phys. IV 104, 193–196 (2003).

Hoszowska, J.

B. Nöhammer, J. Hoszowska, H.-P. Herzig, C. David, “Zoneplates for hard x-rays with ultra-high diffraction efficiencies,” J. Phys. IV 104, 193–196 (2003).

Hyde, R.

J. Early, R. Hyde, R. Baron, “Twenty meter space telescope based on diffractive lens,” in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio, S. L. O’Dell, eds., Proc. SPIE5168, 459–470 (2004).

Jacobsen, C.

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

Johnson, L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Kaulich, B.

E. Di Fabrizio, F. Romanato, M. Gentill, S. Cabrini, B. Kaulich, J. Susini, R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999).
[CrossRef]

Kohn, V.

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

Krasnoperova, A. A.

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
[CrossRef]

Kuhlmann, M.

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Kurapova, O.

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Lai, B.

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
[CrossRef]

Lengeler, B.

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84, 5855–5861 (1998).
[CrossRef]

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

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Lucero, A.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Miyamoto, K.

Morris, G. M.

D. Faklis, G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592–598 (1989).
[CrossRef]

Nöhammer, B.

B. Nöhammer, J. Hoszowska, H.-P. Herzig, C. David, “Zoneplates for hard x-rays with ultra-high diffraction efficiencies,” J. Phys. IV 104, 193–196 (2003).

Olynick, D. L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Pereira, N. R.

E. M. Dufresne, D. A. Arms, R. Clarke, N. R. Pereira, S. B. Dierker, D. Foster, “Lithium metal for x-ray refractive optics,” Appl. Phys. Lett. 79, 4085–4087 (2001).
[CrossRef]

Rau, C.

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Raven, C.

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84, 5855–5861 (1998).
[CrossRef]

Romanato, F.

E. Di Fabrizio, F. Romanato, M. Gentill, S. Cabrini, B. Kaulich, J. Susini, R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999).
[CrossRef]

Schroer, C. G.

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Schupmann, L.

L. Schupmann, Die Medial Fernrohre: Eine neue Konstrucktion für grosse astronomische Instrumente (Tuebner, Leipzig, Germany, 1899).

Simionovici, A. S.

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Skinner, G. K.

G. K. Skinner, “Diffractive-refractive optics for high energy astronomy. II. Variations on the theme,” Astron. Astrophys. 383, 352–359 (2002).
[CrossRef]

G. K. Skinner, “Diffractive-refractive optics for high energy astronomy. I. Gamma-ray phase Fresnel lenses,” Astron. Astrophys. 375, 691–700 (2001).
[CrossRef]

G. K. Skinner, “Fresnel lenses for Xray and gammaray astronomy,” in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio, S. L. O’Dell, eds., Proc. SPIE5168, 459–470 (2004).
[CrossRef]

Snigirev, A.

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84, 5855–5861 (1998).
[CrossRef]

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

Snigirev, A. A.

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Snigireva, I.

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84, 5855–5861 (1998).
[CrossRef]

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

C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
[CrossRef]

Susini, J.

E. Di Fabrizio, F. Romanato, M. Gentill, S. Cabrini, B. Kaulich, J. Susini, R. Barrett, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–898 (1999).
[CrossRef]

Tümmler, J.

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84, 5855–5861 (1998).
[CrossRef]

Veklerov, E.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
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[CrossRef] [PubMed]

Yun, W.

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

W. Yun, B. Lai, A. A. Krasnoperova, E. Di Fabrizio, Z. Cai, F. Cerrina, Z. Chen, M. Gentilli, E. Gluskin, “Development of zone plates with a blazed profile for hard x-ray applications,” Rev. Sci. Instrum. 70, 3537–3541 (1999).
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Appl. Opt. (1)

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G. K. Skinner, “Diffractive-refractive optics for high energy astronomy. I. Gamma-ray phase Fresnel lenses,” Astron. Astrophys. 375, 691–700 (2001).
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G. K. Skinner, “Diffractive-refractive optics for high energy astronomy. II. Variations on the theme,” Astron. Astrophys. 383, 352–359 (2002).
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J. Appl. Phys. (1)

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84, 5855–5861 (1998).
[CrossRef]

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B. Nöhammer, J. Hoszowska, H.-P. Herzig, C. David, “Zoneplates for hard x-rays with ultra-high diffraction efficiencies,” J. Phys. IV 104, 193–196 (2003).

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Other (10)

Mixing energy and wavelength notation seems inevitable here; the former is more generally recognisable in the x-ray and gamma-ray domain, but the present study depends heavily on the wavelike nature of the radiation.

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C. G. Schroer, M. Kuhlmann, B. Lengeler, T. F. Günzler, O. Kurapova, B. Benner, C. Rau, A. S. Simionovici, A. A. Snigirev, I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” in Microfabrication of Novel X-Ray Optics, D. C. Mancini, ed., Proc. SPIE4783, 10–18 (2002).
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NASA, Fresnel Lens Gamma-Ray Mission (7–10 January 2002) and Fresnel Lens Pathfinder (28–29 January 2002) integrated mission design center studies (NASA Goddard Space Flight Center, Greenbelt, Md., 2002).

G. K. Skinner, “Fresnel lenses for Xray and gammaray astronomy,” in Optics for EUV, X-Ray, and Gamma-Ray Astronomy, O. Citterio, S. L. O’Dell, eds., Proc. SPIE5168, 459–470 (2004).
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Figures (11)

Fig. 1
Fig. 1

Use of a refractive lens to compensate for the chromatic effects in a PFL. (a) First-order correction, (b) second-order correction.

Fig. 2
Fig. 2

Thickness t necessary to produce a phase shift of 2π for several materials (P-C, polycarbonate).

Fig. 3
Fig. 3

Absorption length divided by t for the materials in Fig. 2.

Fig. 4
Fig. 4

On-axis response of lenses for a nominal design energy of 78.4 keV and with the parameters given in Table 1. Dotted curves show the response in the absence of absorption. Curves are normalized such that the peak values are proportional to the effective areas. The peak response of the separated pair is lower than that of the contact pair because the absorption considerations discussed in Section 2 require a smaller diameter. Variations in image brightness linked to changes of the diffraction-limited resolution with energy have been removed.

Fig. 5
Fig. 5

Profile of a diffractive lens and a stepped compensating refractive component. The example shown corresponds to N d = 1, N r = 4. (a) Two distinct components in contact, (b) a single component with the same thickness profile.

Fig. 6
Fig. 6

Same as Fig. 5 but for N d = 1 and N r = 1. (b) The combined profile is identical to that of a simple PFL, so clearly in this limit no compensation is achieved.

Fig. 7
Fig. 7

On-axis responses of achromatic contact pairs with different degrees of stepping of the refractive component, characterized by N r , where the thickness is reduced modulo N r t . Focal length and diameter are kept constant. See Table 2 for detailed parameter values. Dashed curves, the response if there were no absorption. It can be seen that large values of N r give a response that is more nearly continuous as a function of energy but with absorption losses that become increasingly more serious. The energies indicated by B–E are those for which the point-source response functions are shown in Fig. 10 below.

Fig. 8
Fig. 8

Same as Fig. 7 but showing the effects of different focal lengths for a specific value of N r (=64). Shorter focal lengths require a more powerful correction lens, which, for a given N r , is divided into a larger number of zones, resulting in narrower individual peaks in the energy response. In the central plot showing the reference design, which would otherwise be a repeat of the corresponding plot in Fig. 7, the dashed curve indicates how the response differs when it is seen by a detector integrating over a 5-mm radius.

Fig. 9
Fig. 9

Total on-axis response to a point source integrated over energy for the lens in Fig. 7, and the corresponding peak response, shown for different degrees of stepping. The dashed curves again show the results in the absence of absorption. Points for the separated pair described in Subsection 4.C are also shown.

Fig. 10
Fig. 10

(a) Point-source response function of the lens in Fig. 7, averaged over energies 450–550 keV. (A, thickest curve) and at selected energies (B, 500.0 keV; C, 503.8 keV; D, 505.1 keV; E, 539.0 keV). Data have been normalized to the central peak, except for 503.8 keV, where there is none. (b) Corresponding fractional encircled power as a function of radius. Absorption is taken into account.

Fig. 11
Fig. 11

On-axis response of a separated achromatic pair (top) compared with that of a contact pair. Parameters are given in Table 2.

Tables (4)

Tables Icon

Table 1 Example of a Lens Using Unstepped Refractive Correcting Elements for an Astronomical Applicationa

Tables Icon

Table 2 Example of a Lens Using Unstepped Refractive Correcting Elements Similar to That in Table 1 but for a Laboratory Applicationa

Tables Icon

Table 3 Parameters for the Example Gamma-Ray Lenses for Astronomical Applications for Which the Performance is Shown in Figs. 79a

Tables Icon

Table 4 Widths of Point-Source Response Functions of the Lenses Listed in Table 3 and Shown in Fig. 7

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

ABCD,
A=1-εf0f1+ε2f0f2-f0S-εf1S+S2ε3f1f2, B=f0-S f0-Sε2f2, C=-εf1+ε2f2-Sε3f1f2, D=1-Sε2f2,
S=f0/9, fd=f0/3, fr=-8/27f0.
0r2 J0y sλf0exp-tsΛ+iπ tst2πλ-s+y2f0λds.
-tsΛ+iπtst2πλ01ε-s+y2f0λ0 ε+ϕs.

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