Abstract

A mean of characterizing the tangential shape of a hard x-ray mirror is presented. Derived from a group of methods operating under visible light, its application in the x-ray domain using an x-ray absorption grating allows recovery of the mirror shape with nanometer accuracy and submillimeter spatial resolution. The method works with incoherent light, does not require any a priori information about the mirror characteristics and allows shape reconstruction of x-ray reflective optics under thermal and mechanical working conditions.

© 2012 Optical Society of America

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References

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2010 (1)

A. V. Rommeveaux, B. Lantelme, and R. Barrett, Proc. SPIE 7801, 780107 (2010).
[CrossRef]

2008 (1)

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, Microsyst. Technol. 14, 1683 (2008).
[CrossRef]

2007 (1)

P. Revesz, A. Kazimirov, and I. Bazarov, Nucl. Instrum. Methods Phys. Res. Sect. A 582, 142 (2007).
[CrossRef]

2006 (1)

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

2005 (2)

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, Appl. Phys. Lett. 86, 054101 (2005).
[CrossRef]

S. Mirza and C. Shakher, Opt. Eng. 44, 013601 (2005).
[CrossRef]

2001 (1)

1997 (2)

O. Hignette, A. K. Freund, and E. Chinchio, Proc. SPIE 3152, 188 (1997).
[CrossRef]

R. Signorato and M. S. del Rio, Proc. SPIE 3152, 136 (1997).

1994 (1)

1991 (1)

1988 (1)

I. Glatt and O. Kafri, Opt. Lasers Eng. 8, 277 (1988).
[CrossRef]

1981 (1)

1980 (1)

Asundi, A.

Barrett, R.

A. V. Rommeveaux, B. Lantelme, and R. Barrett, Proc. SPIE 7801, 780107 (2010).
[CrossRef]

Bazarov, I.

P. Revesz, A. Kazimirov, and I. Bazarov, Nucl. Instrum. Methods Phys. Res. Sect. A 582, 142 (2007).
[CrossRef]

Boerner, M.

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, Microsyst. Technol. 14, 1683 (2008).
[CrossRef]

Bokor, J.

Chinchio, E.

O. Hignette, A. K. Freund, and E. Chinchio, Proc. SPIE 3152, 188 (1997).
[CrossRef]

David, C.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, Appl. Phys. Lett. 86, 054101 (2005).
[CrossRef]

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, in AIP Conference Proceedings (2007), Vol. 879, p. 778.
[CrossRef]

del Rio, M. S.

R. Signorato and M. S. del Rio, Proc. SPIE 3152, 136 (1997).

Diaz, A.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, Appl. Phys. Lett. 86, 054101 (2005).
[CrossRef]

Dorsch, R. G.

Freund, A. K.

O. Hignette, A. K. Freund, and E. Chinchio, Proc. SPIE 3152, 188 (1997).
[CrossRef]

Glatt, I.

I. Glatt and O. Kafri, Opt. Lasers Eng. 8, 277 (1988).
[CrossRef]

Goldberg, K. A.

Handa, S.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Hignette, O.

O. Hignette, A. K. Freund, and E. Chinchio, Proc. SPIE 3152, 188 (1997).
[CrossRef]

Hoffman, J. D.

J. D. Hoffman, Numerical Methods for Engineers and Scientists, 2nd ed. (Marcel Dekker, 2001).

Ishikawa, T.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Jakobs, P.-J.

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, Microsyst. Technol. 14, 1683 (2008).
[CrossRef]

Kafri, O.

Kazimirov, A.

P. Revesz, A. Kazimirov, and I. Bazarov, Nucl. Instrum. Methods Phys. Res. Sect. A 582, 142 (2007).
[CrossRef]

Kozhevnikov, I. V.

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, in AIP Conference Proceedings (2007), Vol. 879, p. 778.
[CrossRef]

Lantelme, B.

A. V. Rommeveaux, B. Lantelme, and R. Barrett, Proc. SPIE 7801, 780107 (2010).
[CrossRef]

Livnat, A.

Matsuyama, S.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Mimura, H.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Mirza, S.

S. Mirza and C. Shakher, Opt. Eng. 44, 013601 (2005).
[CrossRef]

Mohr, J.

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, Microsyst. Technol. 14, 1683 (2008).
[CrossRef]

Nazmov, V.

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, Microsyst. Technol. 14, 1683 (2008).
[CrossRef]

Nishino, Y.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Nöhammer, B.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, Appl. Phys. Lett. 86, 054101 (2005).
[CrossRef]

Oreb, B. F.

Peverini, L.

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, in AIP Conference Proceedings (2007), Vol. 879, p. 778.
[CrossRef]

Revesz, P.

P. Revesz, A. Kazimirov, and I. Bazarov, Nucl. Instrum. Methods Phys. Res. Sect. A 582, 142 (2007).
[CrossRef]

Reznikova, E.

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, Microsyst. Technol. 14, 1683 (2008).
[CrossRef]

Rommeveaux, A. V.

A. V. Rommeveaux, B. Lantelme, and R. Barrett, Proc. SPIE 7801, 780107 (2010).
[CrossRef]

Sano, Y.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Shakher, C.

S. Mirza and C. Shakher, Opt. Eng. 44, 013601 (2005).
[CrossRef]

Signorato, R.

R. Signorato and M. S. del Rio, Proc. SPIE 3152, 136 (1997).

Tamasaku, K.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Weitkamp, T.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, Appl. Phys. Lett. 86, 054101 (2005).
[CrossRef]

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, in AIP Conference Proceedings (2007), Vol. 879, p. 778.
[CrossRef]

Yabashi, M.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Yamauchi, K.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Yumoto, H.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Yung, K. H.

Ziegler, E.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, Appl. Phys. Lett. 86, 054101 (2005).
[CrossRef]

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, in AIP Conference Proceedings (2007), Vol. 879, p. 778.
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, Appl. Phys. Lett. 86, 054101 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

Microsyst. Technol. (1)

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, Microsyst. Technol. 14, 1683 (2008).
[CrossRef]

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

P. Revesz, A. Kazimirov, and I. Bazarov, Nucl. Instrum. Methods Phys. Res. Sect. A 582, 142 (2007).
[CrossRef]

Opt. Eng. (1)

S. Mirza and C. Shakher, Opt. Eng. 44, 013601 (2005).
[CrossRef]

Opt. Lasers Eng. (1)

I. Glatt and O. Kafri, Opt. Lasers Eng. 8, 277 (1988).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (3)

A. V. Rommeveaux, B. Lantelme, and R. Barrett, Proc. SPIE 7801, 780107 (2010).
[CrossRef]

R. Signorato and M. S. del Rio, Proc. SPIE 3152, 136 (1997).

O. Hignette, A. K. Freund, and E. Chinchio, Proc. SPIE 3152, 188 (1997).
[CrossRef]

Rev. Sci. Instrum. (1)

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 77, 063712 (2006).
[CrossRef]

Other (3)

ESRF, ed., Purple Book: Science and Technology Programme 2008–2017 (2007).

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, in AIP Conference Proceedings (2007), Vol. 879, p. 778.
[CrossRef]

J. D. Hoffman, Numerical Methods for Engineers and Scientists, 2nd ed. (Marcel Dekker, 2001).

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Figures (3)

Fig. 1.
Fig. 1.

Sketch of the experiment. An absorption grating is placed at a short distance a from the mirror while an imaging detector is placed upstream at d 0 L . An example image of the structured light produced by the grating after reflection on a mirror is also displayed.

Fig. 2.
Fig. 2.

Geometrical considerations.

Fig. 3.
Fig. 3.

Mirror slope error measured with LTP and x-ray grating profilometry for different incidence angles.

Equations (4)

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

y j = Φ ( j ) 2 π p and x j 0 = Φ ( j ) 2 π p tan ( Θ inc ) .
S l 0 ( x j 0 ) = 1 2 Y j det y j d 0 x j 0 ,
S l n + 1 ( x j n + 1 ) = 1 2 Y j det y j ( d 0 x j n + 1 ) ,
h n + 1 ( x ) = 0 x S l n ( X ) d X x j n + 1 = h n + 1 1 ( y j ) .

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