Abstract

We developed a systematic method for optimizing the design of depth-graded multilayers for astronomical hard-x-ray and soft-γ-ray telescopes based on the instrument’s bandpass and the field of view. We apply these methods to the design of the conical-approximation Wolter I optics employed by the balloon-borne High Energy Focusing Telescope, using W/Si as the multilayer materials. In addition, we present optimized performance calculations of mirrors, using other material pairs that are capable of extending performance to photon energies above the W K-absorption edge (69.5 keV), including Pt/C, Ni/C, Cu/Si, and Mo/Si.

© 1999 Optical Society of America

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  1. K. Yamashita, P. J. Serlemitsos, J. Tueller, S. D. Barthelmy, L. M. Bartlett, K. W. Chan, A. Furuzawa, N. Gehrels, K. Haga, H. Kunieda, P. Kurczynski, G. Lodha, N. Nakajo, N. Nakamura, Y. Namba, Y. Ogasaka, T. Okajima, D. Palmer, A. Parsons, Y. Soong, S. M. Stahl, H. Takata, K. Tamura, Y. Tawara, B. J. Teegarden, “Supermirror hard-x-ray telescope,” Appl. Opt. 37, 8067–8073 (1998).
    [CrossRef]
  2. P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
    [CrossRef]
  3. C. J. Hailey, S. Abdali, F. E. Christensen, W. W. Craig, T. R. Decker, F. A. Harrison, M. Jimenez-Garate, “Substrates and mounting techniques for the High-Energy Focusing Telescope (HEFT),” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 535–543 (1997).
    [CrossRef]
  4. H. Tananbaum, N. White, P. Sullivan, eds., Proceedings of the High Throughput X-ray Spectroscopy Workshop (Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass, 1996).
  5. F. E. Christensen, A. Hornstrup, N. J. Westergaard, H. W. Schnopper, J. L. Wood, K. Parker, “A graded d-spacing multilayer telescope for high energy X-ray astronomy,” in Multilayer and Grazing Incidence X-ray/EUV Optics, R. B. Hoover, ed., Proc. SPIE1546, 160–167 (1992).
    [CrossRef]
  6. K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
    [CrossRef]
  7. K. D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Hoghoj, F. E. Christensen, “Design of grazing-incidence multilayer supermirrors for hard-X-ray reflectors,” Appl. Opt. 34, 7935–7944 (1995).
    [CrossRef] [PubMed]
  8. E. Spiller, Soft X-ray Optics (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1994).
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).
  10. L. Kissel, P. M. Bergstrom, “Anomalous scattering factors,” http://www-phys.llnl.gov/V_Div/scattering/asf.html .
  11. L. Névot, P. Croce, “Charactérisation des surfaces par refléxion rasante de rayons X. Application á l’étude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
    [CrossRef]
  12. F. Mezei, “Novel polarized neutron devices: supermirror and spin component amplifier,” Comment Phys. 1, 81–85 (1976).
  13. W. Gropp, E. Lusk, A. Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface (MIT Press, Cambridge, Mass., 1994).
  14. D. L. Windt, “Multilayer X-ray optics,” in Crystal and Multilayer Optics, A. T. Macrander, D. M. Mills, A. K. Freund, T. Ishikawa, eds., Proc. SPIE3448, 280–290 (1998).
    [CrossRef]
  15. D. L. Windt, “Cu/Si depth-graded multilayers for hard X-ray mirrors,” Appl. Phys. Lett. 74, 2890–2892 (1999).
    [CrossRef]
  16. J. H. Hubbell, S. M. Seltzer, “Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients,” , web version 1.02, National Institute of Standards and Technology http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html .
  17. K. Yamashita, K. Akiyama, K. Haga, H. Kunieda, G. S. Lodha, N. Nakajo, N. Nakamura, T. Okajima, K. Tamura, Y. Tawara, “Fabrication and characterization of multilayer supermirrors for hard X-ray optics,” J. Synchrotron Rad. 5, 711–713 (1998).
    [CrossRef]

1999 (1)

D. L. Windt, “Cu/Si depth-graded multilayers for hard X-ray mirrors,” Appl. Phys. Lett. 74, 2890–2892 (1999).
[CrossRef]

1998 (2)

1995 (1)

1980 (1)

L. Névot, P. Croce, “Charactérisation des surfaces par refléxion rasante de rayons X. Application á l’étude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
[CrossRef]

1976 (1)

F. Mezei, “Novel polarized neutron devices: supermirror and spin component amplifier,” Comment Phys. 1, 81–85 (1976).

Abdali, S.

C. J. Hailey, S. Abdali, F. E. Christensen, W. W. Craig, T. R. Decker, F. A. Harrison, M. Jimenez-Garate, “Substrates and mounting techniques for the High-Energy Focusing Telescope (HEFT),” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 535–543 (1997).
[CrossRef]

Akiyama, K.

K. Yamashita, K. Akiyama, K. Haga, H. Kunieda, G. S. Lodha, N. Nakajo, N. Nakamura, T. Okajima, K. Tamura, Y. Tawara, “Fabrication and characterization of multilayer supermirrors for hard X-ray optics,” J. Synchrotron Rad. 5, 711–713 (1998).
[CrossRef]

Barthelmy, S. D.

Bartlett, L. M.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).

Broadway, D.

P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
[CrossRef]

Chan, K. W.

Christensen, F. E.

K. D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Hoghoj, F. E. Christensen, “Design of grazing-incidence multilayer supermirrors for hard-X-ray reflectors,” Appl. Opt. 34, 7935–7944 (1995).
[CrossRef] [PubMed]

F. E. Christensen, A. Hornstrup, N. J. Westergaard, H. W. Schnopper, J. L. Wood, K. Parker, “A graded d-spacing multilayer telescope for high energy X-ray astronomy,” in Multilayer and Grazing Incidence X-ray/EUV Optics, R. B. Hoover, ed., Proc. SPIE1546, 160–167 (1992).
[CrossRef]

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

C. J. Hailey, S. Abdali, F. E. Christensen, W. W. Craig, T. R. Decker, F. A. Harrison, M. Jimenez-Garate, “Substrates and mounting techniques for the High-Energy Focusing Telescope (HEFT),” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 535–543 (1997).
[CrossRef]

P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
[CrossRef]

Craig, W. W.

P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
[CrossRef]

C. J. Hailey, S. Abdali, F. E. Christensen, W. W. Craig, T. R. Decker, F. A. Harrison, M. Jimenez-Garate, “Substrates and mounting techniques for the High-Energy Focusing Telescope (HEFT),” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 535–543 (1997).
[CrossRef]

Croce, P.

L. Névot, P. Croce, “Charactérisation des surfaces par refléxion rasante de rayons X. Application á l’étude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
[CrossRef]

Decker, T. R.

C. J. Hailey, S. Abdali, F. E. Christensen, W. W. Craig, T. R. Decker, F. A. Harrison, M. Jimenez-Garate, “Substrates and mounting techniques for the High-Energy Focusing Telescope (HEFT),” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 535–543 (1997).
[CrossRef]

Degroot, B.

P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
[CrossRef]

Furuzawa, A.

Gehrels, N.

Gorenstein, P.

K. D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Hoghoj, F. E. Christensen, “Design of grazing-incidence multilayer supermirrors for hard-X-ray reflectors,” Appl. Opt. 34, 7935–7944 (1995).
[CrossRef] [PubMed]

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

Gropp, W.

W. Gropp, E. Lusk, A. Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface (MIT Press, Cambridge, Mass., 1994).

Haga, K.

Hailey, C. J.

P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
[CrossRef]

C. J. Hailey, S. Abdali, F. E. Christensen, W. W. Craig, T. R. Decker, F. A. Harrison, M. Jimenez-Garate, “Substrates and mounting techniques for the High-Energy Focusing Telescope (HEFT),” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 535–543 (1997).
[CrossRef]

Harrison, F. A.

C. J. Hailey, S. Abdali, F. E. Christensen, W. W. Craig, T. R. Decker, F. A. Harrison, M. Jimenez-Garate, “Substrates and mounting techniques for the High-Energy Focusing Telescope (HEFT),” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 535–543 (1997).
[CrossRef]

P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
[CrossRef]

Hoghoj, P.

K. D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Hoghoj, F. E. Christensen, “Design of grazing-incidence multilayer supermirrors for hard-X-ray reflectors,” Appl. Opt. 34, 7935–7944 (1995).
[CrossRef] [PubMed]

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

Hornstrup, A.

F. E. Christensen, A. Hornstrup, N. J. Westergaard, H. W. Schnopper, J. L. Wood, K. Parker, “A graded d-spacing multilayer telescope for high energy X-ray astronomy,” in Multilayer and Grazing Incidence X-ray/EUV Optics, R. B. Hoover, ed., Proc. SPIE1546, 160–167 (1992).
[CrossRef]

Hubbell, J. H.

J. H. Hubbell, S. M. Seltzer, “Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients,” , web version 1.02, National Institute of Standards and Technology http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html .

Hustache, R.

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

Jimenez-Garate, M.

C. J. Hailey, S. Abdali, F. E. Christensen, W. W. Craig, T. R. Decker, F. A. Harrison, M. Jimenez-Garate, “Substrates and mounting techniques for the High-Energy Focusing Telescope (HEFT),” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 535–543 (1997).
[CrossRef]

Joensen, K. D.

K. D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Hoghoj, F. E. Christensen, “Design of grazing-incidence multilayer supermirrors for hard-X-ray reflectors,” Appl. Opt. 34, 7935–7944 (1995).
[CrossRef] [PubMed]

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

Kunieda, H.

Kurczynski, P.

Lodha, G.

Lodha, G. S.

K. Yamashita, K. Akiyama, K. Haga, H. Kunieda, G. S. Lodha, N. Nakajo, N. Nakamura, T. Okajima, K. Tamura, Y. Tawara, “Fabrication and characterization of multilayer supermirrors for hard X-ray optics,” J. Synchrotron Rad. 5, 711–713 (1998).
[CrossRef]

Lusk, E.

W. Gropp, E. Lusk, A. Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface (MIT Press, Cambridge, Mass., 1994).

Mao, P. H.

P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
[CrossRef]

Mezei, F.

F. Mezei, “Novel polarized neutron devices: supermirror and spin component amplifier,” Comment Phys. 1, 81–85 (1976).

Nakajo, N.

Nakamura, N.

Namba, Y.

Névot, L.

L. Névot, P. Croce, “Charactérisation des surfaces par refléxion rasante de rayons X. Application á l’étude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
[CrossRef]

Ogasaka, Y.

Okajima, T.

Palmer, D.

Parker, K.

F. E. Christensen, A. Hornstrup, N. J. Westergaard, H. W. Schnopper, J. L. Wood, K. Parker, “A graded d-spacing multilayer telescope for high energy X-ray astronomy,” in Multilayer and Grazing Incidence X-ray/EUV Optics, R. B. Hoover, ed., Proc. SPIE1546, 160–167 (1992).
[CrossRef]

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

Parsons, A.

Platonov, Y. Y.

P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
[CrossRef]

Roll, J.

Schnopper, H. W.

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

F. E. Christensen, A. Hornstrup, N. J. Westergaard, H. W. Schnopper, J. L. Wood, K. Parker, “A graded d-spacing multilayer telescope for high energy X-ray astronomy,” in Multilayer and Grazing Incidence X-ray/EUV Optics, R. B. Hoover, ed., Proc. SPIE1546, 160–167 (1992).
[CrossRef]

Seltzer, S. M.

J. H. Hubbell, S. M. Seltzer, “Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients,” , web version 1.02, National Institute of Standards and Technology http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html .

Serlemitsos, P. J.

Skjellum, A.

W. Gropp, E. Lusk, A. Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface (MIT Press, Cambridge, Mass., 1994).

Soong, Y.

Spiller, E.

E. Spiller, Soft X-ray Optics (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1994).
[CrossRef]

Stahl, S. M.

Susini, J.

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

Szentgyorgyi, A.

Takata, H.

Tamura, K.

Tawara, Y.

Teegarden, B. J.

Tueller, J.

Voutov, P.

Westergaard, N. J.

F. E. Christensen, A. Hornstrup, N. J. Westergaard, H. W. Schnopper, J. L. Wood, K. Parker, “A graded d-spacing multilayer telescope for high energy X-ray astronomy,” in Multilayer and Grazing Incidence X-ray/EUV Optics, R. B. Hoover, ed., Proc. SPIE1546, 160–167 (1992).
[CrossRef]

Windt, D. L.

D. L. Windt, “Cu/Si depth-graded multilayers for hard X-ray mirrors,” Appl. Phys. Lett. 74, 2890–2892 (1999).
[CrossRef]

D. L. Windt, “Multilayer X-ray optics,” in Crystal and Multilayer Optics, A. T. Macrander, D. M. Mills, A. K. Freund, T. Ishikawa, eds., Proc. SPIE3448, 280–290 (1998).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).

Wood, J. L.

F. E. Christensen, A. Hornstrup, N. J. Westergaard, H. W. Schnopper, J. L. Wood, K. Parker, “A graded d-spacing multilayer telescope for high energy X-ray astronomy,” in Multilayer and Grazing Incidence X-ray/EUV Optics, R. B. Hoover, ed., Proc. SPIE1546, 160–167 (1992).
[CrossRef]

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

Yamashita, K.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. L. Windt, “Cu/Si depth-graded multilayers for hard X-ray mirrors,” Appl. Phys. Lett. 74, 2890–2892 (1999).
[CrossRef]

Comment Phys. (1)

F. Mezei, “Novel polarized neutron devices: supermirror and spin component amplifier,” Comment Phys. 1, 81–85 (1976).

J. Synchrotron Rad. (1)

K. Yamashita, K. Akiyama, K. Haga, H. Kunieda, G. S. Lodha, N. Nakajo, N. Nakamura, T. Okajima, K. Tamura, Y. Tawara, “Fabrication and characterization of multilayer supermirrors for hard X-ray optics,” J. Synchrotron Rad. 5, 711–713 (1998).
[CrossRef]

Rev. Phys. Appl. (1)

L. Névot, P. Croce, “Charactérisation des surfaces par refléxion rasante de rayons X. Application á l’étude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 (1980).
[CrossRef]

Other (11)

W. Gropp, E. Lusk, A. Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface (MIT Press, Cambridge, Mass., 1994).

D. L. Windt, “Multilayer X-ray optics,” in Crystal and Multilayer Optics, A. T. Macrander, D. M. Mills, A. K. Freund, T. Ishikawa, eds., Proc. SPIE3448, 280–290 (1998).
[CrossRef]

J. H. Hubbell, S. M. Seltzer, “Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients,” , web version 1.02, National Institute of Standards and Technology http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html .

E. Spiller, Soft X-ray Optics (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1994).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).

L. Kissel, P. M. Bergstrom, “Anomalous scattering factors,” http://www-phys.llnl.gov/V_Div/scattering/asf.html .

P. H. Mao, F. A. Harrison, Y. Y. Platonov, D. Broadway, B. Degroot, F. E. Christensen, W. W. Craig, C. J. Hailey, “Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 526–534 (1997).
[CrossRef]

C. J. Hailey, S. Abdali, F. E. Christensen, W. W. Craig, T. R. Decker, F. A. Harrison, M. Jimenez-Garate, “Substrates and mounting techniques for the High-Energy Focusing Telescope (HEFT),” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII, O. H. Siegmund, M. A. Gummin, eds., Proc. SPIE3114, 535–543 (1997).
[CrossRef]

H. Tananbaum, N. White, P. Sullivan, eds., Proceedings of the High Throughput X-ray Spectroscopy Workshop (Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass, 1996).

F. E. Christensen, A. Hornstrup, N. J. Westergaard, H. W. Schnopper, J. L. Wood, K. Parker, “A graded d-spacing multilayer telescope for high energy X-ray astronomy,” in Multilayer and Grazing Incidence X-ray/EUV Optics, R. B. Hoover, ed., Proc. SPIE1546, 160–167 (1992).
[CrossRef]

K. D. Joensen, F. E. Christensen, H. W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J. L. Wood, K. Parker, “Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers,” in X-Ray Detector Physics and Applications, R. B. Hoover, ed., Proc. SPIE1736, 239–248 (1993).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

On- and off-axis reflection geometry for a conical approximation to the Wolter I design. On-axis photons reflect at the same angle off the primary and the secondary mirrors. Off-axis photons that reflect at α + ϕ′ off the primary mirror and whose directions of travel intersect the optical axis reflect at α - ϕ′ off the secondary mirror. Off-axis photons that do not intersect the optical axis and reflect at α + ϕ′ off the primary mirror reflect at angles within 2.5% of α - ϕ′ off the secondary mirror.

Fig. 2
Fig. 2

Calculated reflectivity versus photon energy at 1.75 mrad of a graded W/Si multilayer and a Cu–Si multilayer with the exact same specifications (bilayer thickness distribution and interface width). The Cu/Si reflectivity demonstrates that the range in bilayer thicknesses for this mirror would allow for reflectivity at 1.75 mrad from 20 to 100 keV, but the jump in absorption at the W/K edge (69.5 keV) drastically reduces reflectivity of the W/Si multilayer above the absorption edge.

Fig. 3
Fig. 3

Angular weighting function (W α i ) for a uniform distribution of off-axis photons between 0 and 3 mrad on the innermost (α = 1.67 mrad) and the outermost (α = 5.0 mrad) mirrors of the HEFT design.

Fig. 4
Fig. 4

Mirror group 1 FOM calculations for W/Si with d min = 33.3 Å, d max = 297.6 Å, and σ = 3.5 Å. The FOM is calculated over the energy range 20–70 keV with ρatm = 3.5 g/cm2. Under these conditions the optimal design is 1.06 µm thick with N = 250, c = 0.20, and Γ = 0.35. (a) FOM versus c for N = 150 to N = 300 with Γ = 0.35. (b) FOM versus Γ for N = 150 to N = 300 with c = 0.20.

Fig. 5
Fig. 5

FOM(N) versus N for mirror group 1 designs with d min = 33.3 Å and d max = 297.6 Å. The weighting functions are as described in the text. W/Si is optimized over the energy range 20–70 keV. The other materials are optimized over the energy range 20–100 keV. Each marker indicates the optimum FOM (allowing for c and Γ to vary) for a multilayer with the given number of bilayers. The bold markers indicate the optimum designs.

Fig. 6
Fig. 6

Average effective area versus energy calculations of the optimum (solid curve) and near-optimum (dotted–dashed curve) W/Si multilayer designs for mirror group 1. For parameters see Table 2. Also shown is the performance of the optimum Pt/C multilayer (dashed curve) with the same bilayer thickness range but optimized for 20–80 keV. The parameters of the Pt/C design are c = 0.20 and Γ = 0.30.

Fig. 7
Fig. 7

Calculated effective area of the optimum (solid curves) and near-optimum (dashed curves) HEFT multilayer mirror designs for an on-axis point source and for point sources at 1.0, 2.0, and 3.0 mrad off axis.

Fig. 8
Fig. 8

Comparison of A(E, ρatm = 3.5 g/cm2) of the best N = 500 Ni/C, Cu/Si, and Mo/Si multilayers designed for mirror group 1. The coating thicknesses of these designs are all between 2.10 and 2.25 µm.

Tables (3)

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Table 1 HEFT Design: Mirror Shell Groups and Bilayer Thickness Ranges

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Table 2 HEFT Design Parameters for W–Si

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Table 3 Comparison of the Physical Properties of a Few Multilayer Material Combinationsa

Equations (8)

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mλ=2d sin θ1-2Γ1δ1+Γ2δ2sin2 θ1/2,
dmin=hc2Emax sinθmax1-2Γ1δ1+Γ2δ2sin2 θ-1/2,
dmax=hc2Emin sinθmin1-2Γ1δ1+Γ2δ2sin2 θ-1/2.
θmin=α-ϕα-ϕ>θcritθcritα-ϕ<θcrit,
θmax=α+ϕϕ<α2αϕ>α,
FOM=αiEminEmaxdE -ϕmaxϕmaxdϕTatmE, ρatmRE, αi+ϕRE, αi-ϕWαi,ϕαi, ϕWEEWEEmax-Emin,
AE, ρatm=TatmE, ρatmαi-ϕmaxϕmaxdϕWαi,ϕαi, ϕ×RE, αi+ϕRE, αi-ϕ.
di=a/b+ic,

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