Abstract

We present our design and fabrication scheme of a supermirror for hard x-ray telescopes to improve the performance of reflection. Supermirrors are designed to achieve target reflectivity profiles with small ripples in the interesting energy range with a limited number of layer pairs. Starting from conventional design methods, we optimized the thickness distribution of the structure using a numerical approach with the merit function established for this application. As an example, a platinum–carbon supermirror structure of 123 layer pairs with a varying d-space of 2–6 nm was designed to enhance the reflectivity in the energy range from 11 to 55 keV with a flat top at a grazing angle of 0.28 deg. The multilayer thus designed was deposited on a float glass by our DC magnetron sputtering system. The reflectivity profile was successfully measured to be 20% with little oscillation in all energy band of interest.

© 2013 Optical Society of America

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  1. S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE 4012, 619–625 (2000).
    [CrossRef]
  2. 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,” Exp. Astron. 20, 131–137 (2005).
    [CrossRef]
  3. K. Yamashita, “Development of Pt/C multilayer supermirrors for hard x-ray optics,” Nucl. Instrum. Methods Phys. Res. A 529, 59–62 (2004).
    [CrossRef]
  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. SPIE 3766, 327–335 (1999).
    [CrossRef]
  5. 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. SPIE 7732, 773214 (2010).
    [CrossRef]
  6. K. D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Hoghoj, and F. E. Christensen, “Design of grazing-incidence multilayer supermirrors for hard x-ray reflectors,” Appl. Opt. 34, 7935–7944 (1995).
    [CrossRef]
  7. Y. Yao, H. Kunieda, and Z. Wang, “The theoretical analysis of the hard X-ray block-structure supermirror,” Opt. Express 21, 008638 (2013).
    [CrossRef]
  8. I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, “Design of X-ray supermirrors,” Nucl. Instrum. Methods Phys. Res. A 460, 424–443 (2001).
    [CrossRef]
  9. X. Cheng, Z. Wang, Z. Zhang, F. Wang, and L. Chen, “Design of X-ray super-mirrors using simulated annealing algorithm,” Opt. Commun. 265, 197–206 (2006).
    [CrossRef]
  10. 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. A 493, 189–198 (2002).
    [CrossRef]
  11. H. Maury, F. Bridou, P. Troussel, E. Meltchakov, and F. Delmotte, “Design and fabrication of supermirrors for (2–10 keV) high resolution X-ray plasmas diagnostic imaging,” Nucl. Instrum. Methods Phys. Res. A 621, 242–246 (2010).
    [CrossRef]
  12. F. Bridou, F. Delmotte, P. Troussel, and B. Villette, “Design and fabrication of X-ray non-periodic multilayer mirrors: apodization and shaping of their spectral response,” Nucl. Instrum. Methods Phys. Res. A 680, 69–74 (2012).
    [CrossRef]
  13. K. Yamashita, “Multilayer X-ray optical systems for future X-ray astronomy missions,” in Workshop Proceedings: The Next Generation of X-Ray Observatories, Special Report , M. J. Turner and M. G. Watson, eds. (Leicester X-ray Astronomy Group, 1997), pp. 115–121.
  14. Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
    [CrossRef]
  15. K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
    [CrossRef]
  16. D. L. Windt, “IMD—software for modeling the optical properties of multilayer films,” Comput. Phys. 12, 360–370 (1998).
  17. X.-S. Yang, Introduction to Mathematical Optimization (Cambridge International Science, 2008).

2013

Y. Yao, H. Kunieda, and Z. Wang, “The theoretical analysis of the hard X-ray block-structure supermirror,” Opt. Express 21, 008638 (2013).
[CrossRef]

2012

F. Bridou, F. Delmotte, P. Troussel, and B. Villette, “Design and fabrication of X-ray non-periodic multilayer mirrors: apodization and shaping of their spectral response,” Nucl. Instrum. Methods Phys. Res. A 680, 69–74 (2012).
[CrossRef]

2010

H. Maury, F. Bridou, P. Troussel, E. Meltchakov, and F. Delmotte, “Design and fabrication of supermirrors for (2–10 keV) high resolution X-ray plasmas diagnostic imaging,” Nucl. Instrum. Methods Phys. Res. A 621, 242–246 (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. SPIE 7732, 773214 (2010).
[CrossRef]

2006

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

2005

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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

2004

K. Yamashita, “Development of Pt/C multilayer supermirrors for hard x-ray optics,” Nucl. Instrum. Methods Phys. Res. A 529, 59–62 (2004).
[CrossRef]

2002

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. A 493, 189–198 (2002).
[CrossRef]

2001

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, “Design of X-ray supermirrors,” Nucl. Instrum. Methods Phys. Res. A 460, 424–443 (2001).
[CrossRef]

2000

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE 4012, 619–625 (2000).
[CrossRef]

1999

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. SPIE 3766, 327–335 (1999).
[CrossRef]

1998

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

1997

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

1996

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[CrossRef]

1995

Akiyama, K.

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[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. SPIE 7732, 773214 (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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

Berendse, F.

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE 4012, 619–625 (2000).
[CrossRef]

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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

Bridou, F.

F. Bridou, F. Delmotte, P. Troussel, and B. Villette, “Design and fabrication of X-ray non-periodic multilayer mirrors: apodization and shaping of their spectral response,” Nucl. Instrum. Methods Phys. Res. A 680, 69–74 (2012).
[CrossRef]

H. Maury, F. Bridou, P. Troussel, E. Meltchakov, and F. Delmotte, “Design and fabrication of supermirrors for (2–10 keV) high resolution X-ray plasmas diagnostic imaging,” Nucl. Instrum. Methods Phys. Res. A 621, 242–246 (2010).
[CrossRef]

Bukreeva, I. N.

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, “Design of X-ray supermirrors,” Nucl. Instrum. Methods Phys. Res. A 460, 424–443 (2001).
[CrossRef]

Chan, K. W.

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

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, 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, 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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

K. D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Hoghoj, and F. E. Christensen, “Design of grazing-incidence multilayer supermirrors for hard x-ray reflectors,” Appl. Opt. 34, 7935–7944 (1995).
[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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

Delmotte, F.

F. Bridou, F. Delmotte, P. Troussel, and B. Villette, “Design and fabrication of X-ray non-periodic multilayer mirrors: apodization and shaping of their spectral response,” Nucl. Instrum. Methods Phys. Res. A 680, 69–74 (2012).
[CrossRef]

H. Maury, F. Bridou, P. Troussel, E. Meltchakov, and F. Delmotte, “Design and fabrication of supermirrors for (2–10 keV) high resolution X-ray plasmas diagnostic imaging,” Nucl. Instrum. Methods Phys. Res. A 621, 242–246 (2010).
[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. SPIE 7732, 773214 (2010).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[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. SPIE 3766, 327–335 (1999).
[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. SPIE 7732, 773214 (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. SPIE 3766, 327–335 (1999).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

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. SPIE 3766, 327–335 (1999).
[CrossRef]

Hoghoj, 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. SPIE 3766, 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. SPIE 7732, 773214 (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. SPIE 7732, 773214 (2010).
[CrossRef]

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. SPIE 3766, 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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

Kozhevnikov, I. V.

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. A 493, 189–198 (2002).
[CrossRef]

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, “Design of X-ray supermirrors,” Nucl. Instrum. Methods Phys. Res. A 460, 424–443 (2001).
[CrossRef]

Kunieda, H.

Y. Yao, H. Kunieda, and Z. Wang, “The theoretical analysis of the hard X-ray block-structure supermirror,” Opt. Express 21, 008638 (2013).
[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. SPIE 7732, 773214 (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. SPIE 3766, 327–335 (1999).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[CrossRef]

Lodha, G.

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

Maury, H.

H. Maury, F. Bridou, P. Troussel, E. Meltchakov, and F. Delmotte, “Design and fabrication of supermirrors for (2–10 keV) high resolution X-ray plasmas diagnostic imaging,” Nucl. Instrum. Methods Phys. Res. A 621, 242–246 (2010).
[CrossRef]

Meltchakov, E.

H. Maury, F. Bridou, P. Troussel, E. Meltchakov, and F. Delmotte, “Design and fabrication of supermirrors for (2–10 keV) high resolution X-ray plasmas diagnostic imaging,” Nucl. Instrum. Methods Phys. Res. A 621, 242–246 (2010).
[CrossRef]

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. SPIE 7732, 773214 (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. A 493, 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. SPIE 7732, 773214 (2010).
[CrossRef]

Nakajo, N.

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

Nakamura, N.

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[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. SPIE 7732, 773214 (2010).
[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. SPIE 7732, 773214 (2010).
[CrossRef]

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE 4012, 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. SPIE 3766, 327–335 (1999).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[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. SPIE 7732, 773214 (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. SPIE 7732, 773214 (2010).
[CrossRef]

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE 4012, 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. SPIE 3766, 327–335 (1999).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[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. SPIE 4012, 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. A 493, 189–198 (2002).
[CrossRef]

Petre, R.

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

Roll, J.

Serlemitsos, P. J.

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE 4012, 619–625 (2000).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

Soong, Y.

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

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. SPIE 7732, 773214 (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. SPIE 3766, 327–335 (1999).
[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. SPIE 3766, 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. SPIE 7732, 773214 (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. SPIE 3766, 327–335 (1999).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[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. SPIE 7732, 773214 (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. SPIE 3766, 327–335 (1999).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[CrossRef]

Terashima, Y.

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[CrossRef]

Troussel, P.

F. Bridou, F. Delmotte, P. Troussel, and B. Villette, “Design and fabrication of X-ray non-periodic multilayer mirrors: apodization and shaping of their spectral response,” Nucl. Instrum. Methods Phys. Res. A 680, 69–74 (2012).
[CrossRef]

H. Maury, F. Bridou, P. Troussel, E. Meltchakov, and F. Delmotte, “Design and fabrication of supermirrors for (2–10 keV) high resolution X-ray plasmas diagnostic imaging,” Nucl. Instrum. Methods Phys. Res. A 621, 242–246 (2010).
[CrossRef]

Tsuda, O.

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[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. SPIE 3766, 327–335 (1999).
[CrossRef]

Tueller, J.

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[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. SPIE 7732, 773214 (2010).
[CrossRef]

Villette, B.

F. Bridou, F. Delmotte, P. Troussel, and B. Villette, “Design and fabrication of X-ray non-periodic multilayer mirrors: apodization and shaping of their spectral response,” Nucl. Instrum. Methods Phys. Res. A 680, 69–74 (2012).
[CrossRef]

Voutov, P.

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, 197–206 (2006).
[CrossRef]

Wang, Z.

Y. Yao, H. Kunieda, and Z. Wang, “The theoretical analysis of the hard X-ray block-structure supermirror,” Opt. Express 21, 008638 (2013).
[CrossRef]

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

Windt, D. L.

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

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. SPIE 7732, 773214 (2010).
[CrossRef]

K. Yamashita, “Development of Pt/C multilayer supermirrors for hard x-ray optics,” Nucl. Instrum. Methods Phys. Res. A 529, 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. SPIE 3766, 327–335 (1999).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[CrossRef]

K. Yamashita, “Multilayer X-ray optical systems for future X-ray astronomy missions,” in Workshop Proceedings: The Next Generation of X-Ray Observatories, Special Report , M. J. Turner and M. G. Watson, eds. (Leicester X-ray Astronomy Group, 1997), pp. 115–121.

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. SPIE 7732, 773214 (2010).
[CrossRef]

Yang, X.-S.

X.-S. Yang, Introduction to Mathematical Optimization (Cambridge International Science, 2008).

Yao, Y.

Y. Yao, H. Kunieda, and Z. Wang, “The theoretical analysis of the hard X-ray block-structure supermirror,” Opt. Express 21, 008638 (2013).
[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. SPIE 3766, 327–335 (1999).
[CrossRef]

Zhang, Z.

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

Ziegler, E.

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. A 493, 189–198 (2002).
[CrossRef]

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, “Design of X-ray supermirrors,” Nucl. Instrum. Methods Phys. Res. A 460, 424–443 (2001).
[CrossRef]

Appl. Opt.

Comput. Phys.

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

Exp. Astron.

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,” Exp. Astron. 20, 131–137 (2005).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A

K. Yamashita, “Development of Pt/C multilayer supermirrors for hard x-ray optics,” Nucl. Instrum. Methods Phys. Res. A 529, 59–62 (2004).
[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. A 493, 189–198 (2002).
[CrossRef]

H. Maury, F. Bridou, P. Troussel, E. Meltchakov, and F. Delmotte, “Design and fabrication of supermirrors for (2–10 keV) high resolution X-ray plasmas diagnostic imaging,” Nucl. Instrum. Methods Phys. Res. A 621, 242–246 (2010).
[CrossRef]

F. Bridou, F. Delmotte, P. Troussel, and B. Villette, “Design and fabrication of X-ray non-periodic multilayer mirrors: apodization and shaping of their spectral response,” Nucl. Instrum. Methods Phys. Res. A 680, 69–74 (2012).
[CrossRef]

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, “Design of X-ray supermirrors,” Nucl. Instrum. Methods Phys. Res. A 460, 424–443 (2001).
[CrossRef]

Opt. Commun.

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

Opt. Express

Y. Yao, H. Kunieda, and Z. Wang, “The theoretical analysis of the hard X-ray block-structure supermirror,” Opt. Express 21, 008638 (2013).
[CrossRef]

Proc. SPIE

S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J. Serlemitsos, “Multilayer coated thin foil mirrors for InFOCuS,” Proc. SPIE 4012, 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. SPIE 3766, 327–335 (1999).
[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. SPIE 7732, 773214 (2010).
[CrossRef]

Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama, A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayer supermirror coating for hard-x-ray telescope,” Proc. SPIE 2805, 236–243 (1996).
[CrossRef]

K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Furuzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Okajima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y. Ogasaka, Y. Soong, and K. W. Chan, “Development of ballon borne hard-x-ray telescopes using a multilayer supermirror,” Proc. SPIE 3113, 285–292 (1997).
[CrossRef]

Other

K. Yamashita, “Multilayer X-ray optical systems for future X-ray astronomy missions,” in Workshop Proceedings: The Next Generation of X-Ray Observatories, Special Report , M. J. Turner and M. G. Watson, eds. (Leicester X-ray Astronomy Group, 1997), pp. 115–121.

X.-S. Yang, Introduction to Mathematical Optimization (Cambridge International Science, 2008).

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Figures (13)

Fig. 1.
Fig. 1.

(a) Optimized response profiles of power law structure for different numbers of layer pairs. Rou means the interfacial roughness, which is considered as the Debye–Waller factor. (b) Integrated reflectivity (11–55 keV) of optimized power law structures versus number of layer pairs. The grazing angle is set at 0.28 deg.

Fig. 2.
Fig. 2.

(a) Local optimized reflectivity profiles for different target reflectivities. (b) Evolution of the corresponding MF along with the number of iterations.

Fig. 3.
Fig. 3.

(a) Thickness distribution of supermirror structure. Dashed lines show the initial smooth thickness distribution following the power law. The blue triangles show the optimized thickness distribution of carbon. Red open circles show those of platinum. (b) Energy response profiles of the initial power law structure (blue) and optimized structure (red). The orange-dotted line shows the target reflectivity level at 20% between 11 and 55 keV.

Fig. 4.
Fig. 4.

Optimization result of a sloped response profile. The reflectivity profile of the red line is optimized from a supermirror design for HXT of ASTRO-H (green line) with the sloped target profile shown with the red-dashed line. The blue data show the same profile as the red data in Fig. 3 with the flat target profile shown with the blue-dashed line.

Fig. 5.
Fig. 5.

Robustness check for grazing angles. Reflectivity profiles of the supermirror structure optimized at 0.28 deg are calculated with five different grazing angles ranging from 0.24 to 0.32 deg.

Fig. 6.
Fig. 6.

Standard deviation of reflectivity response versus the randomization amplitude of individual layer thicknesses. Error bars are given by the scatter of the standard deviation of reflectivity response of 100 sets.

Fig. 7.
Fig. 7.

(a) Layer thickness plotted against the layer number counted from the top. The open circles show the thickness distribution optimized by the power law method. The crosses depict the thickness distribution optimized by the Hook–Jeeves algorithm. (b) Measured reflectivity (red line) and calculated model (blue line) as a function of grazing angle. The best fit of interfacial roughness is 0.34 nm. In the target angular range (1.0–1.5 deg), the standard deviation of measured data from calculated data is 0.76%. The measured data below 0.1 deg is low, because the incident beam cannot be covered by the 7 cm long mirror sample at these grazing angles.

Fig. 8.
Fig. 8.

Relationship between the standard deviation of reflectivity response and the randomization amplitude of individual layer thicknesses. The standard deviation of reflectivity response of the measured sample is 0.76%, which suggests the thickness-controlling precision of our deposition system can be as good as 0.02 nm, at least when the number of layer pairs is smaller than 30.

Fig. 9.
Fig. 9.

Reflectivity versus grazing angle at 8.05 keV. The red line is the measured profile, and the blue line is the calculated model with best fitting roughness of 0.4 nm.

Fig. 10.
Fig. 10.

Reflectivity against x-ray energy at 0.28 deg grazing angle. The red line shows measured reflectivity. The blue line corresponds to the expected profile, which is the convolution of the designed profile with the detector response.

Fig. 11.
Fig. 11.

(a) Thickness distribution of supermirror structure. Open circles show the designed structure, and solid marks present the fitted structure with 5% higher Pt density. (b) Calculated thickness error (designed thickness—reconstructed one). (c) Fitting result of angular response at 8.05 keV. (d) Fitting result of energy response at 0.28 deg grazing angle.

Fig. 12.
Fig. 12.

Relationship between the normalized standard deviation of angular response and the randomization amplitude of individual layer thicknesses. Note that the vertical axis is not the deviation of actual reflectivity, but is the relative one normalized by the reflectivity at each angle.

Fig. 13.
Fig. 13.

Fitting result of angular response at 8.05 keV with 5% higher density.

Equations (2)

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MF=1mi=1m[R(Ei)Rtarget(Ei)]2,
dj=a(b+j)c,

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