Abstract

An x-ray grating interferometer was employed for in situ optimization of an x-ray bimorph mirror. Unlike many other at-wavelength techniques, only a single interferogram image, captured out of the focal plane, is required, enabling the optical surface to be quickly optimized. Moiré fringe analysis was used to calculate the wavefront slope error, which is proportional to the mirror’s slope error. Using feedback from grating interferometry, the slope error of a bimorph mirror was reduced to <200nrad (rms) in only two iterations. This technique has the potential to create photon beams with spatially homogeneous intensities for use in synchrotron and free electron laser beam lines.

© 2014 Optical Society of America

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2014 (1)

2013 (2)

H. Wang, S. Berujon, I. Pape, S. Rutishauser, C. David, and K. Sawhney, Opt. Lett. 38, 827 (2013).
[CrossRef]

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, J. Phys. Conf. Ser. 425, 052026 (2013).
[CrossRef]

2012 (4)

2011 (1)

2010 (3)

C. M. Kewish, M. Guizar-Sicairos, C. Liu, J. Qian, B. Shi, C. Benson, A. M. Khounsary, J. Vila-Comamala, O. Bunk, J. R. Fienup, A. T. Macrander, and L. Assoufid, Opt. Express 18, 23420 (2010).
[CrossRef]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, Nucl. Instrum. Meth. A 616, 162 (2010).

2009 (1)

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

2007 (1)

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, Microelectron. Eng. 84, 1172 (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 (1)

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

2002 (2)

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002).
[CrossRef]

1998 (1)

R. Signorato, O. Hignette, and J. Goulon, J. Synchrotron Rad. 5, 797 (1998).

1997 (1)

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, and T. W. Tonnessen, Proc. SPIE 3152, 188 (1997).

Alcock, S.

S. Berujon, H. Wang, S. Alcock, and K. Sawhney, Opt. Express 22, 6438 (2014).
[CrossRef]

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, J. Phys. Conf. Ser. 425, 052026 (2013).
[CrossRef]

J. Sutter, S. Alcock, and K. Sawhney, J. Synchrotron Rad. 19, 960 (2012).

Assoufid, L.

Benson, C.

Berujon, S.

Bruder, J.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, Microelectron. Eng. 84, 1172 (2007).
[CrossRef]

Bucourt, S.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, Nucl. Instrum. Meth. A 616, 162 (2010).

Bunk, O.

Chinchio, E.

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, and T. W. Tonnessen, Proc. SPIE 3152, 188 (1997).

David, C.

H. Wang, S. Berujon, I. Pape, S. Rutishauser, C. David, and K. Sawhney, Opt. Lett. 38, 827 (2013).
[CrossRef]

S. Berujon, H. Wang, I. Pape, K. Sawhney, S. Rutishauser, and C. David, Opt. Lett. 37, 1622 (2012).
[CrossRef]

H. Wang, K. Sawhney, S. Berujon, E. Ziegler, S. Rutishauser, and C. David, Opt. Express 19, 16550 (2011).
[CrossRef]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, Microelectron. Eng. 84, 1172 (2007).
[CrossRef]

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

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

Diaz, A.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, Microelectron. Eng. 84, 1172 (2007).
[CrossRef]

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

Donath, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

Dovillaire, G.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, Nucl. Instrum. Meth. A 616, 162 (2010).

Escolano, L.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, Nucl. Instrum. Meth. A 616, 162 (2010).

Fienup, J. R.

Freund, A. K.

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, and T. W. Tonnessen, Proc. SPIE 3152, 188 (1997).

Fukui, R.

Goulon, J.

R. Signorato, O. Hignette, and J. Goulon, J. Synchrotron Rad. 5, 797 (1998).

Grünzweig, C.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, Microelectron. Eng. 84, 1172 (2007).
[CrossRef]

Guizar-Sicairos, M.

Handa, S.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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.

R. Signorato, O. Hignette, and J. Goulon, J. Synchrotron Rad. 5, 797 (1998).

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, and T. W. Tonnessen, Proc. SPIE 3152, 188 (1997).

Idir, M.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, Nucl. Instrum. Meth. A 616, 162 (2010).

Inagaki, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002).
[CrossRef]

Ishikawa, T.

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, Opt. Express 20, 24977 (2012).
[CrossRef]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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]

Kewish, C. M.

Khounsary, A. M.

Kimura, T.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

Kohmura, Y.

Kottler, C.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, Microelectron. Eng. 84, 1172 (2007).
[CrossRef]

Levecq, X.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, Nucl. Instrum. Meth. A 616, 162 (2010).

Liu, C.

Macrander, A. T.

Matsuyama, S.

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, Opt. Express 20, 24977 (2012).
[CrossRef]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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]

Mercere, P.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, Nucl. Instrum. Meth. A 616, 162 (2010).

Mimura, H.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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]

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002).
[CrossRef]

Modi, M. H.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, Nucl. Instrum. Meth. A 616, 162 (2010).

Momose, A.

Mori, Y.

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002).
[CrossRef]

Nishino, Y.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

Pape, I.

Pfeiffer, F.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, Microelectron. Eng. 84, 1172 (2007).
[CrossRef]

Qian, J.

Rohbeck, T.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, Microelectron. Eng. 84, 1172 (2007).
[CrossRef]

Rutishauser, S.

Sano, Y.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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]

Sauvageot, P.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, Nucl. Instrum. Meth. A 616, 162 (2010).

Sawhney, K.

Shi, B.

Signorato, R.

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, J. Phys. Conf. Ser. 425, 052026 (2013).
[CrossRef]

R. Signorato, O. Hignette, and J. Goulon, J. Synchrotron Rad. 5, 797 (1998).

Solak, H. H.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

Sutter, J.

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, J. Phys. Conf. Ser. 425, 052026 (2013).
[CrossRef]

J. Sutter, S. Alcock, and K. Sawhney, J. Synchrotron Rad. 19, 960 (2012).

Takacs, P. Z.

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, and T. W. Tonnessen, Proc. SPIE 3152, 188 (1997).

Tamasaku, K.

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, Opt. Express 20, 24977 (2012).
[CrossRef]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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]

Tonnessen, T. W.

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, and T. W. Tonnessen, Proc. SPIE 3152, 188 (1997).

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 3rd ed. (CRC Press, 2010).

Vila-Comamala, J.

Wang, H.

Weitkamp, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

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

Yabashi, M.

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, Opt. Express 20, 24977 (2012).
[CrossRef]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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]

Yamakawa, D.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

Yamamura, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

Yamauchi, K.

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, Opt. Express 20, 24977 (2012).
[CrossRef]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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]

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002).
[CrossRef]

Yashiro, W.

Yokoyama, H.

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, Opt. Express 20, 24977 (2012).
[CrossRef]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

Yumoto, H.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, Nat. Phys. 6, 122 (2009).
[CrossRef]

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]

Zanette, I.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

Ziegler, E.

H. Wang, K. Sawhney, S. Berujon, E. Ziegler, S. Rutishauser, and C. David, Opt. Express 19, 16550 (2011).
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Figures (5)

Fig. 1.
Fig. 1.

Optical layout of the in situ optimization of a bimorph mirror with 8 piezo actuators A1, A2,,A8 using a GI. The phase grating is noted G1 and the absorption grating G2.

Fig. 2.
Fig. 2.

Experimental data and fitted model for γy as a function of γx. Moiré fringe periods dx and dy along the x and y directions are also shown in the inset image.

Fig. 3.
Fig. 3.

Piezo response function of the bimorph mirror: (Top) the slope and (bottom) height changes induced by applying a fixed voltage to each piezo actuator from A1 to A8, in sequence. Here, line 1–0 means the slope response of the 1st electrode by subtracting the 0th image (no voltages applied) from the 1st image (only apply voltage for 1st electrode). The height change caused by each piezo actuator was calculated by numerical integration of the slope change.

Fig. 4.
Fig. 4.

Wavefront slope error at zero volts (without correction), and the 1st and 2nd iteration corrections.

Fig. 5.
Fig. 5.

Transmission signal from a gold wire scan (blue squares) in the focal plane of the bimorph mirror. A Gaussian fit (red line) of the derivative of the raw data (black dots) indicates a FWHM of 0.34 μm.

Equations (4)

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

γx=d2dx,γy=d2dy.
Mij=(Si,j+1Si,j)/v,
[V1V2V8]=[M11M12M18M21M22M28Mn1Mn2Mn8]1[ΔS1ΔS2ΔSn].
M+=(MTM)1MT.

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