Abstract

We report a novel method for in situ metrology of an X-ray bimorph mirror by using the speckle scanning technique. Both the focusing beam and the “tophat” defocussed beam have been generated by optimizing the bimorph mirror in a single iteration. Importantly, we have demonstrated that the angular sensitivity for measuring the slope error of an optical surface can reach accuracy in the range of two nanoradians. When compared with conventional ex-situ metrology techniques, the method enables a substantial increase of around two orders of magnitude in the angular sensitivity and opens the way to a previously inaccessible region of slope error measurement. Such a super precision metrology technique will be beneficial for both the manufacture of polished mirrors and the optimization of beam shaping.

© 2015 Optical Society of America

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References

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  1. D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam-shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A 710, 125–130 (2013).
    [Crossref]
  2. 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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
    [Crossref]
  3. K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, “Characterisation of a novel super-polished bimorph mirror,” J. Phys. Conf. Ser. 425(5), 052026 (2013).
    [Crossref]
  4. R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat. 5(3), 797–800 (1998).
    [Crossref] [PubMed]
  5. S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
    [Crossref]
  6. H. Wang, K. Sawhney, S. Berujon, E. Ziegler, S. Rutishauser, and C. David, “X-ray wavefront characterization using a rotating shearing interferometer technique,” Opt. Express 19(17), 16550–16559 (2011).
    [Crossref] [PubMed]
  7. K. Sawhney, H. Wang, J. Sutter, S. Alcock, and S. Berujon, “At-wavelength metrology of X-ray optics at Diamond Light Source,” Synchrotron Radiat. News 26(5), 17–22 (2013).
    [Crossref]
  8. S. Berujon, H. Wang, S. Alcock, and K. Sawhney, “At-wavelength metrology of hard X-ray mirror using near field speckle,” Opt. Express 22(6), 6438–6446 (2014).
    [Crossref] [PubMed]
  9. J. Sutter, S. Alcock, and K. Sawhney, “In situ beamline analysis and correction of active optics,” J. Synchrotron Radiat. 19(6), 960–968 (2012).
    [Crossref] [PubMed]
  10. M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
    [Crossref]
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    [Crossref]
  12. H. Wang, K. Sawhney, S. Berujon, J. Sutter, S. G. Alcock, U. Wagner, and C. Rau, “Fast optimization of a bimorph mirror using x-ray grating interferometry,” Opt. Lett. 39(8), 2518–2521 (2014).
    [Crossref] [PubMed]
  13. S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, “Two-dimensional X-ray beam phase sensing,” Phys. Rev. Lett. 108(15), 158102 (2012).
    [Crossref] [PubMed]
  14. S. Berujon, H. Wang, I. Pape, K. Sawhney, S. Rutishauser, and C. David, “X-ray submicrometer phase contrast imaging with a Fresnel zone plate and a two dimensional grating interferometer,” Opt. Lett. 37(10), 1622–1624 (2012).
    [Crossref] [PubMed]
  15. B. Pan, H.-M. Xie, B.-Q. Xu, and F.-L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17(6), 1615–1621 (2006).
    [Crossref]
  16. K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, “Figuring with subnanometer-level accuracy by numerically controlled elastic emission machining,” Rev. Sci. Instrum. 73(11), 4028–4033 (2002).
    [Crossref]
  17. K. J. S. Sawhney, S. G. Alcock, and R. Signorato, “A novel adaptive bimorph focusing mirror and wavefront corrector with sub-nanometre dynamical figure control,” Proc. SPIE 7803, 780303 (2010).
    [Crossref]
  18. F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27(7), 1223–1225 (1988).
    [Crossref] [PubMed]
  19. J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE 9208, 92080G (2014).
    [Crossref]

2014 (3)

2013 (3)

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam-shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A 710, 125–130 (2013).
[Crossref]

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, “Characterisation of a novel super-polished bimorph mirror,” J. Phys. Conf. Ser. 425(5), 052026 (2013).
[Crossref]

K. Sawhney, H. Wang, J. Sutter, S. Alcock, and S. Berujon, “At-wavelength metrology of X-ray optics at Diamond Light Source,” Synchrotron Radiat. News 26(5), 17–22 (2013).
[Crossref]

2012 (3)

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, “Two-dimensional X-ray beam phase sensing,” Phys. Rev. Lett. 108(15), 158102 (2012).
[Crossref] [PubMed]

S. Berujon, H. Wang, I. Pape, K. Sawhney, S. Rutishauser, and C. David, “X-ray submicrometer phase contrast imaging with a Fresnel zone plate and a two dimensional grating interferometer,” Opt. Lett. 37(10), 1622–1624 (2012).
[Crossref] [PubMed]

J. Sutter, S. Alcock, and K. Sawhney, “In situ beamline analysis and correction of active optics,” J. Synchrotron Radiat. 19(6), 960–968 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (3)

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

K. J. S. Sawhney, S. G. Alcock, and R. Signorato, “A novel adaptive bimorph focusing mirror and wavefront corrector with sub-nanometre dynamical figure control,” Proc. SPIE 7803, 780303 (2010).
[Crossref]

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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

2006 (2)

B. Pan, H.-M. Xie, B.-Q. Xu, and F.-L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17(6), 1615–1621 (2006).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

2002 (1)

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, “Figuring with subnanometer-level accuracy by numerically controlled elastic emission machining,” Rev. Sci. Instrum. 73(11), 4028–4033 (2002).
[Crossref]

1998 (1)

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat. 5(3), 797–800 (1998).
[Crossref] [PubMed]

1988 (1)

Alcock, S.

S. Berujon, H. Wang, S. Alcock, and K. Sawhney, “At-wavelength metrology of hard X-ray mirror using near field speckle,” Opt. Express 22(6), 6438–6446 (2014).
[Crossref] [PubMed]

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, “Characterisation of a novel super-polished bimorph mirror,” J. Phys. Conf. Ser. 425(5), 052026 (2013).
[Crossref]

K. Sawhney, H. Wang, J. Sutter, S. Alcock, and S. Berujon, “At-wavelength metrology of X-ray optics at Diamond Light Source,” Synchrotron Radiat. News 26(5), 17–22 (2013).
[Crossref]

J. Sutter, S. Alcock, and K. Sawhney, “In situ beamline analysis and correction of active optics,” J. Synchrotron Radiat. 19(6), 960–968 (2012).
[Crossref] [PubMed]

Alcock, S. G.

H. Wang, K. Sawhney, S. Berujon, J. Sutter, S. G. Alcock, U. Wagner, and C. Rau, “Fast optimization of a bimorph mirror using x-ray grating interferometry,” Opt. Lett. 39(8), 2518–2521 (2014).
[Crossref] [PubMed]

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE 9208, 92080G (2014).
[Crossref]

K. J. S. Sawhney, S. G. Alcock, and R. Signorato, “A novel adaptive bimorph focusing mirror and wavefront corrector with sub-nanometre dynamical figure control,” Proc. SPIE 7803, 780303 (2010).
[Crossref]

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Berujon, S.

Bérujon, S.

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, “Two-dimensional X-ray beam phase sensing,” Phys. Rev. Lett. 108(15), 158102 (2012).
[Crossref] [PubMed]

Bucourt, S.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

Cerbino, R.

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, “Two-dimensional X-ray beam phase sensing,” Phys. Rev. Lett. 108(15), 158102 (2012).
[Crossref] [PubMed]

Dai, F.-L.

B. Pan, H.-M. Xie, B.-Q. Xu, and F.-L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17(6), 1615–1621 (2006).
[Crossref]

David, C.

Dovillaire, G.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

Escolano, L.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

Goulon, J.

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat. 5(3), 797–800 (1998).
[Crossref] [PubMed]

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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

Hignette, O.

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat. 5(3), 797–800 (1998).
[Crossref] [PubMed]

Idir, M.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, “Figuring with subnanometer-level accuracy by numerically controlled elastic emission machining,” Rev. Sci. Instrum. 73(11), 4028–4033 (2002).
[Crossref]

Ishikawa, 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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

Lammert, H.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Levecq, X.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

Matsuyama, 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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

Mercere, P.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, “Figuring with subnanometer-level accuracy by numerically controlled elastic emission machining,” Rev. Sci. Instrum. 73(11), 4028–4033 (2002).
[Crossref]

Modi, M. H.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

Mori, Y.

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, “Figuring with subnanometer-level accuracy by numerically controlled elastic emission machining,” Rev. Sci. Instrum. 73(11), 4028–4033 (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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

Noll, T.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Pan, B.

B. Pan, H.-M. Xie, B.-Q. Xu, and F.-L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17(6), 1615–1621 (2006).
[Crossref]

Pape, I.

Pedersen, U.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Peverini, L.

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, “Two-dimensional X-ray beam phase sensing,” Phys. Rev. Lett. 108(15), 158102 (2012).
[Crossref] [PubMed]

Raimondi, L.

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam-shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A 710, 125–130 (2013).
[Crossref]

Rau, C.

Roddier, F.

Rust, F.

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE 9208, 92080G (2014).
[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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

Sauvageot, P.

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

Sawhney, K.

S. Berujon, H. Wang, S. Alcock, and K. Sawhney, “At-wavelength metrology of hard X-ray mirror using near field speckle,” Opt. Express 22(6), 6438–6446 (2014).
[Crossref] [PubMed]

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE 9208, 92080G (2014).
[Crossref]

H. Wang, K. Sawhney, S. Berujon, J. Sutter, S. G. Alcock, U. Wagner, and C. Rau, “Fast optimization of a bimorph mirror using x-ray grating interferometry,” Opt. Lett. 39(8), 2518–2521 (2014).
[Crossref] [PubMed]

K. Sawhney, H. Wang, J. Sutter, S. Alcock, and S. Berujon, “At-wavelength metrology of X-ray optics at Diamond Light Source,” Synchrotron Radiat. News 26(5), 17–22 (2013).
[Crossref]

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, “Characterisation of a novel super-polished bimorph mirror,” J. Phys. Conf. Ser. 425(5), 052026 (2013).
[Crossref]

J. Sutter, S. Alcock, and K. Sawhney, “In situ beamline analysis and correction of active optics,” J. Synchrotron Radiat. 19(6), 960–968 (2012).
[Crossref] [PubMed]

S. Berujon, H. Wang, I. Pape, K. Sawhney, S. Rutishauser, and C. David, “X-ray submicrometer phase contrast imaging with a Fresnel zone plate and a two dimensional grating interferometer,” Opt. Lett. 37(10), 1622–1624 (2012).
[Crossref] [PubMed]

H. Wang, K. Sawhney, S. Berujon, E. Ziegler, S. Rutishauser, and C. David, “X-ray wavefront characterization using a rotating shearing interferometer technique,” Opt. Express 19(17), 16550–16559 (2011).
[Crossref] [PubMed]

Sawhney, K. J. S.

K. J. S. Sawhney, S. G. Alcock, and R. Signorato, “A novel adaptive bimorph focusing mirror and wavefront corrector with sub-nanometre dynamical figure control,” Proc. SPIE 7803, 780303 (2010).
[Crossref]

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Scott, S.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Senf, F.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Siewert, F.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Signorato, R.

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, “Characterisation of a novel super-polished bimorph mirror,” J. Phys. Conf. Ser. 425(5), 052026 (2013).
[Crossref]

K. J. S. Sawhney, S. G. Alcock, and R. Signorato, “A novel adaptive bimorph focusing mirror and wavefront corrector with sub-nanometre dynamical figure control,” Proc. SPIE 7803, 780303 (2010).
[Crossref]

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat. 5(3), 797–800 (1998).
[Crossref] [PubMed]

Spiga, D.

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam-shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A 710, 125–130 (2013).
[Crossref]

Sutter, J.

H. Wang, K. Sawhney, S. Berujon, J. Sutter, S. G. Alcock, U. Wagner, and C. Rau, “Fast optimization of a bimorph mirror using x-ray grating interferometry,” Opt. Lett. 39(8), 2518–2521 (2014).
[Crossref] [PubMed]

K. Sawhney, H. Wang, J. Sutter, S. Alcock, and S. Berujon, “At-wavelength metrology of X-ray optics at Diamond Light Source,” Synchrotron Radiat. News 26(5), 17–22 (2013).
[Crossref]

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, “Characterisation of a novel super-polished bimorph mirror,” J. Phys. Conf. Ser. 425(5), 052026 (2013).
[Crossref]

J. Sutter, S. Alcock, and K. Sawhney, “In situ beamline analysis and correction of active optics,” J. Synchrotron Radiat. 19(6), 960–968 (2012).
[Crossref] [PubMed]

Sutter, J. P.

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE 9208, 92080G (2014).
[Crossref]

Svetina, C.

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam-shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A 710, 125–130 (2013).
[Crossref]

Tamasaku, 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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

Wagner, U.

Walton, R.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Wang, H.

Xie, H.-M.

B. Pan, H.-M. Xie, B.-Q. Xu, and F.-L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17(6), 1615–1621 (2006).
[Crossref]

Xu, B.-Q.

B. Pan, H.-M. Xie, B.-Q. Xu, and F.-L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17(6), 1615–1621 (2006).
[Crossref]

Yabashi, M.

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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

Yamauchi, 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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, “Figuring with subnanometer-level accuracy by numerically controlled elastic emission machining,” Rev. Sci. Instrum. 73(11), 4028–4033 (2002).
[Crossref]

Yokoyama, 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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

Zangrando, M.

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam-shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A 710, 125–130 (2013).
[Crossref]

Zeschke, T.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

Ziegler, E.

Appl. Opt. (1)

J. Phys. Conf. Ser. (1)

K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, and R. Signorato, “Characterisation of a novel super-polished bimorph mirror,” J. Phys. Conf. Ser. 425(5), 052026 (2013).
[Crossref]

J. Synchrotron Radiat. (2)

R. Signorato, O. Hignette, and J. Goulon, “Multi-segmented piezoelectric mirrors as active/adaptive optics components,” J. Synchrotron Radiat. 5(3), 797–800 (1998).
[Crossref] [PubMed]

J. Sutter, S. Alcock, and K. Sawhney, “In situ beamline analysis and correction of active optics,” J. Synchrotron Radiat. 19(6), 960–968 (2012).
[Crossref] [PubMed]

Meas. Sci. Technol. (1)

B. Pan, H.-M. Xie, B.-Q. Xu, and F.-L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17(6), 1615–1621 (2006).
[Crossref]

Nat. Phys. (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, “Breaking the 10nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009).
[Crossref]

Nucl. Instrum. Methods Phys. Res. A (3)

D. Spiga, L. Raimondi, C. Svetina, and M. Zangrando, “X-ray beam-shaping via deformable mirrors: Analytical computation of the required mirror profile,” Nucl. Instrum. Methods Phys. Res. A 710, 125–130 (2013).
[Crossref]

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: a non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 224–228 (2010).
[Crossref]

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, and P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res. A 616(2-3), 162–171 (2010).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, “Two-dimensional X-ray beam phase sensing,” Phys. Rev. Lett. 108(15), 158102 (2012).
[Crossref] [PubMed]

Proc. SPIE (2)

K. J. S. Sawhney, S. G. Alcock, and R. Signorato, “A novel adaptive bimorph focusing mirror and wavefront corrector with sub-nanometre dynamical figure control,” Proc. SPIE 7803, 780303 (2010).
[Crossref]

J. P. Sutter, S. G. Alcock, F. Rust, H. Wang, and K. Sawhney, “Structure in defocused beams of x-ray mirrors: causes and possible solutions,” Proc. SPIE 9208, 92080G (2014).
[Crossref]

Rev. Sci. Instrum. (2)

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, “Figuring with subnanometer-level accuracy by numerically controlled elastic emission machining,” Rev. Sci. Instrum. 73(11), 4028–4033 (2002).
[Crossref]

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “At-wavelength figure metrology of hard x-ray focusing mirrors,” Rev. Sci. Instrum. 77(6), 063712 (2006).
[Crossref]

Synchrotron Radiat. News (1)

K. Sawhney, H. Wang, J. Sutter, S. Alcock, and S. Berujon, “At-wavelength metrology of X-ray optics at Diamond Light Source,” Synchrotron Radiat. News 26(5), 17–22 (2013).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Optical layout of the in situ optimization of a bimorph mirror for two cases (a) zero volts (without correction), (b) corrected to focus the beam at F. (c) is a speckle image recorded by the detector at a particular position ym of the membrane. (d) is the image assembled from the ith row of pixels of all speckle images in the membrane scan. (e) is the same as (d) but is assembled from the jth row. (f) is the correlation map from (d) and (e). The offset of the correlation peak is 0 if i = j and εμ otherwise.
Fig. 2
Fig. 2 Piezo response function in term of local wavefront curvature of the bimorph mirror. Local wavefront curvature change induced by applying a fixed voltage to each piezo actuator from first to eighth in sequence. Here line 1-0 means the slope response of the 1st electrode calculated by subtracting the 0th scan (no voltages applied) from the 1st scan (voltage applied only to first electrode).
Fig. 3
Fig. 3 Wavefront radius of curvature at detector versus corresponding position on mirror and the corresponding intensity profiles as a function of distance z in mm from the bimorph mirror for the four cases, (a) bimorph voltages at 0 V, (b) bimorph voltages for focused operation after 1st iteration, (c) first optimization for bimorph defocused, (d) second optimization for bimorph defocused. The yellow dotted lines mark the focal planes.
Fig. 4
Fig. 4 The first derivative of the transmission signal from a gold wire scan in the focal plane of the bimorph mirror for case (b) bimorph voltages for focused operation after 1st iteration, (c) first optimization for bimorph defocused (d) second optimization for bimorph defocused.
Fig. 5
Fig. 5 The repeatability measurement for the mirror slope error after the focus optimization case (b).

Tables (1)

Tables Icon

Table 1 Summary of the focus and defocus optimization

Equations (10)

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

R 1 = λ 2π d 2 Ψ d y 2 = dφ dy
Rd R = ε ij μ (ji)p
R 1 = (ji)p ε ij μ (ji)pd
η= ε ij (ji)
dφ dy ( y )= 1 d [ 1 η(y)μ p ]
φ( y 2 )φ( y 1 )= y 2 y 1 d μ pd y 1 y 2 η(y)dy
| Φ( y 2 )Φ( y 1 ) |= μ pd | y 1 y 2 η(y)dy |
| Φ( y 1 +p)Φ( y 1 ) |= μ d | η( y 1 ) |
M ik =( R 1 ik R 1 i,k1 )/v
R 1 o =( R 1 t R 1 i )

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