Abstract

We present an analytical study to provide guide lines to design a block structure hard X-ray supermirror. The block structure supermirror is a kind of layered structure consisting of several “blocks” of multilayer of different d-spacing to obtain broad energy bandwidth response. This structure has been widely applied in X-ray telescopes because it is easy to fabricate. To examine the propagation of X-rays in a supermirror structure, further simplified approximation of Kozhevnikov’s theory has been developed. The supermirror structure is described by a structure function. The spectral function of the structure, which is the Laplace transformation of the structure function, turns out to be proportional to the reflectivity profile against X-ray energy. By analyzing the expression of the spectral function, we found the reflectivity of the supermirror could be smooth due to the box-car shaped spectral function if the d-spacing and layer number of each block is arranged with appropriate constraints.

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  2. M. C. Weisskopf, H. D. Tananbaum, L. P. Van Speybroeck, and S. L. O'Dell, “Chandra x-ray observatory (CXO): overview,” proc. SPIE4012, 2–16 (2000).
    [CrossRef]
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    [CrossRef]
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  5. S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE4012, 619–625 (2000).
    [CrossRef]
  6. F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  17. E. Spiller, Soft X-ray Optics (SPIE, 1994), Chap. 7.
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    [CrossRef]

2011 (1)

2010 (2)

I. V. Kozhevnikov and C. Montcalm, “Design of x-ray multilayer mirrors with maximal integral efficiency,” Nucl. Instrum. Methods Phys. Res. A624(1), 192–202 (2010).
[CrossRef]

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

2006 (1)

X. Cheng, Z. Wang, Z. Zhang, F. Wang, and L. Chen, “Design of X-ray super-mirrors using simulated annealing algorithm,” Opt. Commun.265(1), 197–206 (2006).
[CrossRef]

2005 (1)

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

2004 (1)

K. Yamashita, “Development of Pt/C multilayer supermirrors for hard x-ray optics,” Nucl. Instrum. Methods Phys. Res. A529(1-3), 59–62 (2004).
[CrossRef]

2002 (1)

C. Morawe, E. Ziegler, J. C. Peffen, and I. V. Kozhevnikov, “Design and fabrication of depth-graded x-ray multilayers,” Nucl. Instrum. Methods Phys. Res. A493(3), 189–198 (2002).
[CrossRef]

2001 (2)

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, “Design of X-ray supermirrors,” Nucl. Instrum. Methods Phys. Res. A460(2-3), 424–443 (2001).
[CrossRef]

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

2000 (2)

M. C. Weisskopf, H. D. Tananbaum, L. P. Van Speybroeck, and S. L. O'Dell, “Chandra x-ray observatory (CXO): overview,” proc. SPIE4012, 2–16 (2000).
[CrossRef]

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE4012, 619–625 (2000).
[CrossRef]

1999 (1)

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

1998 (2)

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

D. L. Windt, “IMD—software for modeling the optical properties of multilayer films,” Comput. Phys.12(4), 360–370 (1998).
[CrossRef]

1995 (1)

1994 (1)

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

1988 (1)

E. Spiller, “Characterization of multilayer coating by x-ray reflection,” Rev. Phys. Appl. (Paris)23(10), 1687–1700 (1988).
[CrossRef]

Altieri, B.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Awaki, H.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Baumgartner, W.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Berendse, F.

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE4012, 619–625 (2000).
[CrossRef]

Bloemen, H.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Boggs, S.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Chan, K. W.

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Chen, C. M. H.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Chen, L.

X. Cheng, Z. Wang, Z. Zhang, F. Wang, and L. Chen, “Design of X-ray super-mirrors using simulated annealing algorithm,” Opt. Commun.265(1), 197–206 (2006).
[CrossRef]

Cheng, X.

X. Cheng, Z. Wang, Z. Zhang, F. Wang, and L. Chen, “Design of X-ray super-mirrors using simulated annealing algorithm,” Opt. Commun.265(1), 197–206 (2006).
[CrossRef]

Chonko, J.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Christensen, F. E.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

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

Clavel, J.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Cook, W. R.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Craig, W.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Diehl, R.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Ehle, M.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Erd, C.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Furuzawa, A.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Gabriel, C.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Gondoin, P.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Gorenstein, P.

Gotou, A.

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Guainazzi, M.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Haba, Y.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Haga, K.

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Hailey, C.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Harrison, F. A.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Hermsen, W.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Hidaka, Y.

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Høghøj, P.

Ichimaru, S.

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Iizuka, R.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Ishibashi, K.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Iyudin, A. F.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Jansen, F.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Jiang, H.

Joensen, K. D.

Kitou, H.

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Koglin, J.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Kozhevnikov, I. V.

I. V. Kozhevnikov and C. Montcalm, “Design of x-ray multilayer mirrors with maximal integral efficiency,” Nucl. Instrum. Methods Phys. Res. A624(1), 192–202 (2010).
[CrossRef]

C. Morawe, E. Ziegler, J. C. Peffen, and I. V. Kozhevnikov, “Design and fabrication of depth-graded x-ray multilayers,” Nucl. Instrum. Methods Phys. Res. A493(3), 189–198 (2002).
[CrossRef]

Kunieda, H.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Li, D.

Lichti, G. G.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Lodha, G. S.

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Lumb, D.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Madsen, K. K.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Michette, A.

Miyaza, T.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Montcalm, C.

I. V. Kozhevnikov and C. Montcalm, “Design of x-ray multilayer mirrors with maximal integral efficiency,” Nucl. Instrum. Methods Phys. Res. A624(1), 192–202 (2010).
[CrossRef]

Morawe, C.

C. Morawe, E. Ziegler, J. C. Peffen, and I. V. Kozhevnikov, “Design and fabrication of depth-graded x-ray multilayers,” Nucl. Instrum. Methods Phys. Res. A493(3), 189–198 (2002).
[CrossRef]

Mori, H.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Morris, D.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Much, R.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Munoz, R.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

N. Bukreeva, I.

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, “Design of X-ray supermirrors,” Nucl. Instrum. Methods Phys. Res. A460(2-3), 424–443 (2001).
[CrossRef]

Nakajo, N.

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Namba, Y.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

O'Dell, S. L.

M. C. Weisskopf, H. D. Tananbaum, L. P. Van Speybroeck, and S. L. O'Dell, “Chandra x-ray observatory (CXO): overview,” proc. SPIE4012, 2–16 (2000).
[CrossRef]

Ogasaka, Y.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE4012, 619–625 (2000).
[CrossRef]

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Ogi, K.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Okajima, T.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE4012, 619–625 (2000).
[CrossRef]

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Owens, S. M.

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE4012, 619–625 (2000).
[CrossRef]

Peffen, J. C.

C. Morawe, E. Ziegler, J. C. Peffen, and I. V. Kozhevnikov, “Design and fabrication of depth-graded x-ray multilayers,” Nucl. Instrum. Methods Phys. Res. A493(3), 189–198 (2002).
[CrossRef]

Petre, R.

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Pfauntsch, S.

Pivavoroff, M.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Roll, J.

Ryan, J.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Santos, M.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Schartel, N.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Schonfelder, V.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Serlemitsos, P. J.

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE4012, 619–625 (2000).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Smith, D.

F. A. Harrison, F. E. Christensen, W. Craig, C. Hailey, W. Baumgartner, C. M. H. Chen, J. Chonko, W. R. Cook, J. Koglin, K. K. Madsen, M. Pivavoroff, S. Boggs, and D. Smith, “Development of the HEFT and NuSTAR focusing telescopes,” ExA20, 131–137 (2005).

Spiller, E.

E. Spiller, “Characterization of multilayer coating by x-ray reflection,” Rev. Phys. Appl. (Paris)23(10), 1687–1700 (1988).
[CrossRef]

Steinle, H.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Suzuki, Y.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Szentgyorgyi, A.

Takahashi, S.

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Takata, H.

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Takeda, S.

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Tamura, K.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Tananbaum, H. D.

M. C. Weisskopf, H. D. Tananbaum, L. P. Van Speybroeck, and S. L. O'Dell, “Chandra x-ray observatory (CXO): overview,” proc. SPIE4012, 2–16 (2000).
[CrossRef]

Tawara, Y.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Texier, D.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Tsusaka, Y.

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Tueller, J.

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Uesugi, K.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

V. Kozhevnikov, I.

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, “Design of X-ray supermirrors,” Nucl. Instrum. Methods Phys. Res. A460(2-3), 424–443 (2001).
[CrossRef]

Vacanti, G.

F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
[CrossRef]

Van Speybroeck, L. P.

M. C. Weisskopf, H. D. Tananbaum, L. P. Van Speybroeck, and S. L. O'Dell, “Chandra x-ray observatory (CXO): overview,” proc. SPIE4012, 2–16 (2000).
[CrossRef]

Varendorff, M.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Voutov, P.

Vries, C.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Wang, F.

X. Cheng, Z. Wang, Z. Zhang, F. Wang, and L. Chen, “Design of X-ray super-mirrors using simulated annealing algorithm,” Opt. Commun.265(1), 197–206 (2006).
[CrossRef]

Wang, Z.

Weisskopf, M. C.

M. C. Weisskopf, H. D. Tananbaum, L. P. Van Speybroeck, and S. L. O'Dell, “Chandra x-ray observatory (CXO): overview,” proc. SPIE4012, 2–16 (2000).
[CrossRef]

Windt, D. L.

D. L. Windt, “IMD—software for modeling the optical properties of multilayer films,” Comput. Phys.12(4), 360–370 (1998).
[CrossRef]

Winkler, C.

A. F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G. G. Lichti, D. Morris, J. Ryan, V. Schonfelder, H. Steinle, M. Varendorff, C. Vries, and C. Winkler, “COMPTEL observations of 44Ti gamma-ray line emission from Cas A,” Astron. Astrophys.284, L1–L4 (1994).

Yamashita, K.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

K. Yamashita, “Development of Pt/C multilayer supermirrors for hard x-ray optics,” Nucl. Instrum. Methods Phys. Res. A529(1-3), 59–62 (2004).
[CrossRef]

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Yamauchi, S.

H. Kunieda, H. Awaki, A. Furuzawa, Y. Haba, R. Iizuka, K. Ishibashi, T. Miyaza, H. Mori, Y. Namba, Y. Ogasaka, K. Ogi, T. Okajima, Y. Suzuki, K. Tamura, Y. Tawara, K. Uesugi, K. Yamashita, and S. Yamauchi, “Hard X-ray Telescope to be onboard ASTRO-H,” Proc. SPIE7732, 773214, 773214-12 (2010).
[CrossRef]

Yang, S.

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

Yokoyama, K.

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Yu, J.

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
[CrossRef]

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X. Cheng, Z. Wang, Z. Zhang, F. Wang, and L. Chen, “Design of X-ray super-mirrors using simulated annealing algorithm,” Opt. Commun.265(1), 197–206 (2006).
[CrossRef]

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C. Morawe, E. Ziegler, J. C. Peffen, and I. V. Kozhevnikov, “Design and fabrication of depth-graded x-ray multilayers,” Nucl. Instrum. Methods Phys. Res. A493(3), 189–198 (2002).
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Appl. Opt. (1)

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F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-Newton observatory,” Astron. Astrophys.365(1), L1–L6 (2001).
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Comput. Phys. (1)

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Nucl. Instrum. Methods Phys. Res. A (4)

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[CrossRef]

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Opt. Commun. (1)

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[CrossRef]

Opt. Express (1)

Proc. SPIE (4)

K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Gotou, H. Kitou, T. Okajima, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard x-ray optics,” Proc. SPIE3766, 327–335 (1999).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Tamura, A. Furuzawa, K. Haga, N. Nakajo, T. Okajima, H. Takata, P. J. Serlemitsos, J. Tueller, R. Petre, S. Yang, K. W. Chan, G. S. Lodha, Y. Namba, and J. Yu, “Development of a multilayer supermirror for hard x-ray telescopes,” Proc. SPIE3444, 569–575 (1998).
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A. R. S. Bahai, B. R. Saltzber, and M. Ergen, Multi-Carrier Digital Communications Theory and Applications of OFDM (Sprigner, 2004), Chap. 1.

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E. Spiller, Soft X-ray Optics (SPIE, 1994), Chap. 4.

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Figures (10)

Fig. 1
Fig. 1

Physical model of a multilayer structure introduced from ref. 9. (a) Cross section of multilayer structure. The structure consists of two kinds of materials with different dielectric constants ε1 and ε2. (b) Layer number function y(z). Although the layer number is a discrete number, in the case of periodic multilayer, the layer number function should be extended to linear function. (c) Step-like function U(y(z),Г). The meaning of U(y(z),Г) is to select the dielectric constant. (d) Dielectric constant function.

Fig. 2
Fig. 2

Reflectivity profile against X-ray energy of a block-structure supermirror. The red solid line is the reflectivity of the supermirror while the dashed lines are the reflectivity of individual blocks. The basic idea of this design method is to broaden the response by several periodic multilayer blocks with different d-spacing.

Fig. 3
Fig. 3

The spectral function of a block which start from zero point. k0 is the inverse lattice of Block0. Since the thickness of Block0 is L0, the spectral function of the structure can be expressed as the subtraction between the image function (original function defined from 0 to infinity) and delayed image function (original function defined from L0 to infinity).

Fig. 4
Fig. 4

Calculation of the spectral function of each block in supermirror structure. Normal component of the X-ray wave vector propagate from left to the right side. The spectral function of each block is affected by the thickness, the lattice and the position. The starting point of the later block must be the end point of the former block. Thus, the spectral function of the block structure can be obtained.

Fig. 5
Fig. 5

An example structure to demonstrate the validity of the “vector model” assumption. In this example, the thickness of each block is equal and set as 32nm. The layer number of each block increases incrementally from 12 to 16.

Fig. 6
Fig. 6

Calculated reflectivity of the example structure mentioned in Fig. 5. The red line is the reflectivity calculated by exact method [20] and the blue line calculated by Eqs. (21) and (22). The oscillation of these lines is very similar, which suggests that “vector model” approach is enough to analyze the interference behavior of the X-ray propagating in block mirror.

Fig. 7
Fig. 7

The structure that will provide smooth reflectivity. Here L0, N0 and n are arbitrary parameters which means the thickness of the blocks, the layer number of the first block, and the total number of the blocks . In our experience, whatever they are, the oscillation of the response profile is low (in high energy band~30keV).

Fig. 8
Fig. 8

Power spectrum of the structure function. The structure follows the design rule mentioned in Fig. 7. This example consists of 8 blocks. The red line is the absolute value of the final spectral amplitude of the designed structure as is mention in Eq. (23). The red line slightly declines with the energy because of the absorption. However, the profile is box-car type, relatively smooth and very suitable to be applied in a supermirror.

Fig. 9
Fig. 9

Designed results of the power law structure and block structure. (a) The red line is the thickness distribution of the block structure supermirror, the blue line corresponds to the power law structure. Upper lines correspond to carbon and lower lines correspond to platinum. (b) The evolution of the Merit function of the optimization process of power law structure.

Fig. 10
Fig. 10

Comparison of the calculated reflectivity. The red line is the reflectivity of block structure calculated by exact method. The blue line is the reflectivity of the power law structure calculated by exact method. Both structures have the same number of layers. The green line is the block structure reflectivity calculated by Eqs. (21) and (22).

Equations (23)

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ε(z)= ε 2 +( ε 1 ε 2 )U(y(z),Γ), z[0,L]
U(y(z),Γ)={ 0, 1, my<m+Γ m+Γy<m+1
y(z)= 0 z q(z')dz', q(z)>0
ε(z)=μ+ n=1 B n cos(2πny(z)+πnΓ) μ=Γ ε 1 +(1Γ) ε 2 , B n =2( ε 1 ε 2 ) sin(πnΓ) πn
E''(z)+ k 2 (ε(z) cos 2 (θ))E(z)=0, k= 2π λ
U + (z)=1+ j k 2 4κ n=1 B n exp(jnπΓ) 0 z U (z')exp[j2πny(z')2jκz']dz' + S + (z)
U (z)= j k 2 4κ n=1 B n exp(jnπΓ) z L U + (z')exp[j2πny(z')+2jκz']dz' + S (z)
r= U (0)= j k 2 4κ n=1 B n exp(jπnΓ) 0 L exp[2πjny(z')]exp(j2κz')dz' + S (0)
r(κ)= j k 2 4κ n=1 B n exp(jπnΓ)L[exp(j2πy(z)) | 0 L ] + S (0)
r(κ)= [ ε 1 (k) cos 2 (θ)][ ε 2 (k) cos 2 (θ)] Γ[ ε 1 (k) cos 2 (θ)]+(1Γ)[ ε 2 (k) cos 2 (θ)] sin(πΓ) 2π {κL[exp(j2πy(z))]}+ S (0)
r(κ)= [ ε 1 (k) cos 2 (θ)][ ε 2 (k) cos 2 (θ)] [ ε 1 (k) cos 2 (θ)]+[ ε 2 (k) cos 2 (θ)] 1 π {κL[exp(j2πy(z))]}+ S (0)
R(κ)=| [ ε 1 cos 2 (θ)][ ε 2 cos 2 (θ)] [ ε 1 cos 2 (θ)]+[ ε 2 cos 2 (θ)] | 2 1 π 2 κ 2 L L * +(terms including S (0))
L(A+B) L (A+B)=L(A) L (A)+L(B) L * (B)+L(A) L (B)+ L (A)L(B)
r(κ)= [ ε 1 (k) cos 2 (θ)][ ε 2 (k) cos 2 (θ)] [ ε 1 (k) cos 2 (θ)]+[ ε 2 (k) cos 2 (θ)] 1 π κ m=1 N L m + S (0)
exp[j2πy(z)] | 0 L 0 =exp(j k 0 z) | 0 L 0
L[exp(j k 0 z) | 0 ]L[exp(j k 0 z)u(z)]= 1 j(2κ k 0 )
L[BLOC K n ]= 1 j(2κ k 0 ) [1exp( L 0 2κj)]
U (z)= j k 2 2κ n=1 B n z L U + (z') cos[2πny(z')+πnΓ]exp(j2κz')dz'
r= j k 2 2κ n=1 B n 0 L cos[2πny(z')+πnΓ]exp(j2κz')dz'
r(κ)= j k 2 4κ n=1 B n exp(jπnΓ)L[exp(j2πy(z)) | 0 L ] + S (0) S (0)= j k 2 4κ n=1 B n exp(jπnΓ)L[exp(j2πy(z)) | 0 L ]
r(κ)= [ ε 1 (k) cos 2 (θ)][ ε 2 (k) cos 2 (θ)] [ ε 1 (k) cos 2 (θ)]+[ ε 2 (k) cos 2 (θ)] 1 π κ m=1 N L m
n=0 N L [Block n ] = n=0 N { 1 j(2κ k n ) [1exp( L n 2κj)] exp( i=0 n L i1 2κj )}
n=1 N L [Block n ] = n=1 N 1exp(2κj L 0 ) 2κ k 0 2π(n1) L 0 exp(2jκ(n1) L 0 )

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