Abstract

We present a method to measure the surface profile of hard X-ray reflective optics with nanometer height accuracy and sub-millimetre lateral resolution. The technique uses X-ray near-field speckle, generated by a scattering membrane translated using a piezo motor, to infer the deflection of X-rays from the surface. The method provides a nano-radian order accuracy on the mirror slopes in both the tangential and sagittal directions. As a demonstration, a pair of focusing mirrors mounted in a Kirkpatrick-Baez (KB) configuration were characterized and the results were in good agreement with offline metrology data. It is hoped that the new technique will provide feedback to optic manufacturers to improve mirror fabrication and be useful for the online optimization of active, nano-focusing mirrors on modern synchrotron beamlines.

© 2014 Optical Society of America

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  1. S. Berujon, At-Wavelength Metrology of Hard X-Ray Synchrotron Beams and Optics (University of Grenoble, Online, 2013).
  2. S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 224–228 (2010).
    [CrossRef]
  3. K. Sawhney, H. Wang, J. Sutter, S. Alcock, S. Berujon, “At-wavelength metrology of X-ray optics at Diamond Light Source,” Synchrotron Radiat. News 26, 17–22 (2013).
    [CrossRef]
  4. K. Sawhney, S. Alcock, J. Sutter, S. Berujon, H. Wang, R. Signorato, “Characterisation of a novel super-polished bimorph mirror,” J. Phys: Conf. Ser. 425, 052026 (2013).
  5. J. Sutter, S. Alcock, K. Sawhney, “In situ beamline analysis and correction of active optics,” J. Synchrotron Radiat. 19, 960–968 (2012).
    [CrossRef] [PubMed]
  6. O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, T. W. Tonnessen, “Incoherent X-ray mirror surface metrology,” Proceedings of SPIE 3152, 188–199 (1997).
    [CrossRef]
  7. M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 162–171 (2010).
    [CrossRef]
  8. H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, K. Yamauchi, “At-wavelength figure metrology of hard X-ray focusing mirrors,” Rev. Sci. Instrum. 77, 063712 (2006).
    [CrossRef]
  9. S. Berujon, H. Wang, E. Ziegler, K. Sawhney, “Shearing interferometer spatial resolution for at-wavelength hard X-ray metrology,” AIP Conference Proceedings 1466, 217–222 (2012).
    [CrossRef]
  10. S. Rutishauser, A. Rack, T. Weitkamp, Y. Kayser, C. David, A. T. Macrander, “Heat bump on a monochromator crystal measured with X-ray grating interferometry,” J. Synchrotron Radiat. 20, 300–305 (2013).
    [CrossRef] [PubMed]
  11. 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, L. Assoufid, “Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data,” Opt. Express 18, 23420–23427 (2010).
    [CrossRef] [PubMed]
  12. S. Berujon, E. Ziegler, “Grating-based at-wavelength metrology of hard X-ray reflective optics,” Opt. Lett. 37, 4464–4466 (2012).
    [CrossRef] [PubMed]
  13. J. W. Goodman, Speckle Phenomena in Optics; Theory and Applications, 1st edition (Roberts & Company Publishers, Greenwood Village, 2006).
  14. R. S. Sirohi, Speckle Metrology, Optical Science and Engineering (Marcel Dekker, In., 1993).
  15. R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
    [CrossRef]
  16. S. Berujon, E. Ziegler, R. Cerbino, L. Peverini, “Two-dimensional X-ray beam phase sensing,” Phys. Rev. Lett. 108, 158102 (2012).
    [CrossRef] [PubMed]
  17. K. S. Morgan, D. M. Paganin, K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
    [CrossRef]
  18. J. Rizzi, T. Weitkamp, N. Gurineau, M. Idir, P. Mercre, G. Druart, G. Vincent, P. da Silva, J. Primot, “Quadri-wave lateral shearing interferometry in an achromatic and continuously self-imaging regime for future x-ray phase imaging,” Opt. Lett. 36, 1398–1400 (2011).
    [CrossRef] [PubMed]
  19. R. Cerbino, “Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem,” Phys. Rev. A. 75, 053815 (2007).
    [CrossRef]
  20. E. Born, E. Wolf, Principle Of Optics, 7th edition (Cambridge University, 2008).
  21. S. Berujon, H. Wang, K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 063813 (2012).
    [CrossRef]
  22. K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
    [CrossRef]
  23. B. Pan, K. Qian, H. Xie, A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
    [CrossRef]
  24. B. Pan, H.-m. Xie, B.-q. Xu, F.-l. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615 (2006).
    [CrossRef]
  25. K. A. Goldberg, J. Bokor, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40, 2886–2894 (2001).
    [CrossRef]

2013

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

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

S. Rutishauser, A. Rack, T. Weitkamp, Y. Kayser, C. David, A. T. Macrander, “Heat bump on a monochromator crystal measured with X-ray grating interferometry,” J. Synchrotron Radiat. 20, 300–305 (2013).
[CrossRef] [PubMed]

2012

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

K. S. Morgan, D. M. Paganin, K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
[CrossRef]

S. Berujon, H. Wang, K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 063813 (2012).
[CrossRef]

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

S. Berujon, H. Wang, E. Ziegler, K. Sawhney, “Shearing interferometer spatial resolution for at-wavelength hard X-ray metrology,” AIP Conference Proceedings 1466, 217–222 (2012).
[CrossRef]

S. Berujon, E. Ziegler, “Grating-based at-wavelength metrology of hard X-ray reflective optics,” Opt. Lett. 37, 4464–4466 (2012).
[CrossRef] [PubMed]

2011

2010

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, L. Assoufid, “Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data,” Opt. Express 18, 23420–23427 (2010).
[CrossRef] [PubMed]

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

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

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
[CrossRef]

2009

B. Pan, K. Qian, H. Xie, A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

2008

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[CrossRef]

2007

R. Cerbino, “Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem,” Phys. Rev. A. 75, 053815 (2007).
[CrossRef]

2006

B. Pan, H.-m. Xie, B.-q. Xu, F.-l. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

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

2001

1997

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, T. W. Tonnessen, “Incoherent X-ray mirror surface metrology,” Proceedings of SPIE 3152, 188–199 (1997).
[CrossRef]

Alcock, S.

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

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

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

Alcock, S. G.

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

Alianelli, L.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
[CrossRef]

Assoufid, L.

Asundi, A.

B. Pan, K. Qian, H. Xie, A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

Benson, C.

Berujon, S.

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

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

S. Berujon, E. Ziegler, “Grating-based at-wavelength metrology of hard X-ray reflective optics,” Opt. Lett. 37, 4464–4466 (2012).
[CrossRef] [PubMed]

S. Berujon, H. Wang, K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 063813 (2012).
[CrossRef]

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

S. Berujon, H. Wang, E. Ziegler, K. Sawhney, “Shearing interferometer spatial resolution for at-wavelength hard X-ray metrology,” AIP Conference Proceedings 1466, 217–222 (2012).
[CrossRef]

S. Berujon, At-Wavelength Metrology of Hard X-Ray Synchrotron Beams and Optics (University of Grenoble, Online, 2013).

Bokor, J.

Born, E.

E. Born, E. Wolf, Principle Of Optics, 7th edition (Cambridge University, 2008).

Bosecke, P.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[CrossRef]

Bucourt, S.

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

Bunk, O.

Cerbino, R.

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

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[CrossRef]

R. Cerbino, “Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem,” Phys. Rev. A. 75, 053815 (2007).
[CrossRef]

Chinchio, E.

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, T. W. Tonnessen, “Incoherent X-ray mirror surface metrology,” Proceedings of SPIE 3152, 188–199 (1997).
[CrossRef]

da Silva, P.

Dai, F.-l.

B. Pan, H.-m. Xie, B.-q. Xu, F.-l. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

David, C.

S. Rutishauser, A. Rack, T. Weitkamp, Y. Kayser, C. David, A. T. Macrander, “Heat bump on a monochromator crystal measured with X-ray grating interferometry,” J. Synchrotron Radiat. 20, 300–305 (2013).
[CrossRef] [PubMed]

Dolbnya, I. P.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
[CrossRef]

Dovillaire, G.

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

Druart, G.

Escolano, L.

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

Fienup, J. R.

Freund, A. K.

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, T. W. Tonnessen, “Incoherent X-ray mirror surface metrology,” Proceedings of SPIE 3152, 188–199 (1997).
[CrossRef]

Giglio, M.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[CrossRef]

Goldberg, K. A.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics; Theory and Applications, 1st edition (Roberts & Company Publishers, Greenwood Village, 2006).

Guizar-Sicairos, M.

Gurineau, N.

Handa, S.

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

Hignette, O.

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, T. W. Tonnessen, “Incoherent X-ray mirror surface metrology,” Proceedings of SPIE 3152, 188–199 (1997).
[CrossRef]

Idir, M.

J. Rizzi, T. Weitkamp, N. Gurineau, M. Idir, P. Mercre, G. Druart, G. Vincent, P. da Silva, J. Primot, “Quadri-wave lateral shearing interferometry in an achromatic and continuously self-imaging regime for future x-ray phase imaging,” Opt. Lett. 36, 1398–1400 (2011).
[CrossRef] [PubMed]

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

Ishikawa, T.

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

Kayser, Y.

S. Rutishauser, A. Rack, T. Weitkamp, Y. Kayser, C. David, A. T. Macrander, “Heat bump on a monochromator crystal measured with X-ray grating interferometry,” J. Synchrotron Radiat. 20, 300–305 (2013).
[CrossRef] [PubMed]

Kewish, C. M.

Khounsary, A. M.

Lammert, H.

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

Levecq, X.

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

Liu, C.

Macrander, A. T.

Matsuyama, S.

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

Mercere, P.

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

Mercre, P.

Mimura, H.

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

Modi, M. H.

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

Morgan, K. S.

K. S. Morgan, D. M. Paganin, K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
[CrossRef]

Nishino, Y.

H. Yumoto, H. Mimura, S. Matsuyama, S. Handa, Y. Sano, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, K. Yamauchi, “At-wavelength figure metrology of hard X-ray focusing mirrors,” Rev. Sci. Instrum. 77, 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, H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 224–228 (2010).
[CrossRef]

Paganin, D. M.

K. S. Morgan, D. M. Paganin, K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
[CrossRef]

Pan, B.

B. Pan, K. Qian, H. Xie, A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

B. Pan, H.-m. Xie, B.-q. Xu, F.-l. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

Pedersen, U.

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

Pedersen, U. K.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
[CrossRef]

Peverini, L.

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

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[CrossRef]

Potenza, M. A. C.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[CrossRef]

Preece, G. M.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
[CrossRef]

Primot, J.

Qian, J.

Qian, K.

B. Pan, K. Qian, H. Xie, A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

Rack, A.

S. Rutishauser, A. Rack, T. Weitkamp, Y. Kayser, C. David, A. T. Macrander, “Heat bump on a monochromator crystal measured with X-ray grating interferometry,” J. Synchrotron Radiat. 20, 300–305 (2013).
[CrossRef] [PubMed]

Rizzi, J.

Robert, A.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[CrossRef]

Rutishauser, S.

S. Rutishauser, A. Rack, T. Weitkamp, Y. Kayser, C. David, A. T. Macrander, “Heat bump on a monochromator crystal measured with X-ray grating interferometry,” J. Synchrotron Radiat. 20, 300–305 (2013).
[CrossRef] [PubMed]

Sano, Y.

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

Sauvageot, P.

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

Sawhney, K.

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

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

S. Berujon, H. Wang, E. Ziegler, K. Sawhney, “Shearing interferometer spatial resolution for at-wavelength hard X-ray metrology,” AIP Conference Proceedings 1466, 217–222 (2012).
[CrossRef]

S. Berujon, H. Wang, K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 063813 (2012).
[CrossRef]

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

Sawhney, K. J. S.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
[CrossRef]

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

Scott, S. M.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (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, H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 224–228 (2010).
[CrossRef]

Shi, B.

Siewert, F.

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

Signorato, R.

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

Sirohi, R. S.

R. S. Sirohi, Speckle Metrology, Optical Science and Engineering (Marcel Dekker, In., 1993).

Siu, K. K. W.

K. S. Morgan, D. M. Paganin, K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
[CrossRef]

Sutter, J.

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

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

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

Takacs, P. Z.

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, T. W. Tonnessen, “Incoherent X-ray mirror surface metrology,” Proceedings of SPIE 3152, 188–199 (1997).
[CrossRef]

Tamasaku, K.

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

Tiwari, M. K.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
[CrossRef]

Tonnessen, T. W.

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, T. W. Tonnessen, “Incoherent X-ray mirror surface metrology,” Proceedings of SPIE 3152, 188–199 (1997).
[CrossRef]

Vila-Comamala, J.

Vincent, G.

Walton, R.

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

Walton, R. D.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
[CrossRef]

Wang, H.

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

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

S. Berujon, H. Wang, E. Ziegler, K. Sawhney, “Shearing interferometer spatial resolution for at-wavelength hard X-ray metrology,” AIP Conference Proceedings 1466, 217–222 (2012).
[CrossRef]

S. Berujon, H. Wang, K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 063813 (2012).
[CrossRef]

Weitkamp, T.

S. Rutishauser, A. Rack, T. Weitkamp, Y. Kayser, C. David, A. T. Macrander, “Heat bump on a monochromator crystal measured with X-ray grating interferometry,” J. Synchrotron Radiat. 20, 300–305 (2013).
[CrossRef] [PubMed]

J. Rizzi, T. Weitkamp, N. Gurineau, M. Idir, P. Mercre, G. Druart, G. Vincent, P. da Silva, J. Primot, “Quadri-wave lateral shearing interferometry in an achromatic and continuously self-imaging regime for future x-ray phase imaging,” Opt. Lett. 36, 1398–1400 (2011).
[CrossRef] [PubMed]

Wolf, E.

E. Born, E. Wolf, Principle Of Optics, 7th edition (Cambridge University, 2008).

Xie, H.

B. Pan, K. Qian, H. Xie, A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

Xie, H.-m.

B. Pan, H.-m. Xie, B.-q. Xu, F.-l. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

Xu, B.-q.

B. Pan, H.-m. Xie, B.-q. Xu, F.-l. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

Yabashi, M.

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

Zeschke, T.

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

Ziegler, E.

S. Berujon, H. Wang, E. Ziegler, K. Sawhney, “Shearing interferometer spatial resolution for at-wavelength hard X-ray metrology,” AIP Conference Proceedings 1466, 217–222 (2012).
[CrossRef]

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

S. Berujon, E. Ziegler, “Grating-based at-wavelength metrology of hard X-ray reflective optics,” Opt. Lett. 37, 4464–4466 (2012).
[CrossRef] [PubMed]

AIP Conference Proceedings

S. Berujon, H. Wang, E. Ziegler, K. Sawhney, “Shearing interferometer spatial resolution for at-wavelength hard X-ray metrology,” AIP Conference Proceedings 1466, 217–222 (2012).
[CrossRef]

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, “A test beamline on Diamond Light Source,” AIP Conference Proceedings 1234, 387–390 (2010).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

K. S. Morgan, D. M. Paganin, K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
[CrossRef]

J. Phys: Conf. Ser.

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

J. Synchrotron Radiat.

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

S. Rutishauser, A. Rack, T. Weitkamp, Y. Kayser, C. David, A. T. Macrander, “Heat bump on a monochromator crystal measured with X-ray grating interferometry,” J. Synchrotron Radiat. 20, 300–305 (2013).
[CrossRef] [PubMed]

Meas. Sci. Technol.

B. Pan, K. Qian, H. Xie, A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

B. Pan, H.-m. Xie, B.-q. Xu, F.-l. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615 (2006).
[CrossRef]

Nat. Phys.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[CrossRef]

Nucl. Instrum. Methods Phys. Res., Sect. A

M. Idir, P. Mercere, M. H. Modi, G. Dovillaire, X. Levecq, S. Bucourt, L. Escolano, P. Sauvageot, “X-ray active mirror coupled with a Hartmann wavefront sensor,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 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, H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 224–228 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

S. Berujon, H. Wang, K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 063813 (2012).
[CrossRef]

Phys. Rev. A.

R. Cerbino, “Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem,” Phys. Rev. A. 75, 053815 (2007).
[CrossRef]

Phys. Rev. Lett.

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

Proceedings of SPIE

O. Hignette, A. K. Freund, E. Chinchio, P. Z. Takacs, T. W. Tonnessen, “Incoherent X-ray mirror surface metrology,” Proceedings of SPIE 3152, 188–199 (1997).
[CrossRef]

Rev. Sci. Instrum.

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

Synchrotron Radiat. News

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

Other

J. W. Goodman, Speckle Phenomena in Optics; Theory and Applications, 1st edition (Roberts & Company Publishers, Greenwood Village, 2006).

R. S. Sirohi, Speckle Metrology, Optical Science and Engineering (Marcel Dekker, In., 1993).

E. Born, E. Wolf, Principle Of Optics, 7th edition (Cambridge University, 2008).

S. Berujon, At-Wavelength Metrology of Hard X-Ray Synchrotron Beams and Optics (University of Grenoble, Online, 2013).

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Figures (4)

Fig. 1
Fig. 1

(a) Geometry considerations. (b) Speckle patterns acquired in two consecutive rows of the detector. (c) Cross-correlation map of the two patterns shown in (b).

Fig. 2
Fig. 2

(a) Sketch of the experimental setup with zh = 3015 mm, zv = 3125 mm and d ≈ 400 mm. (b–c) Single reflected beams from respectively the vertical and horizontally focusing mirrors.

Fig. 3
Fig. 3

Slope errors of the (a) vertical mirror and (b) horizontal mirror measured online and with the Diamond-NOM.

Fig. 4
Fig. 4

Sagittal measurements of the VFM: green, blue and red lines show line profiles across the width of the mirror in Fig. 2. (a) Mid-spatial frequency slope errors. (b) Corresponding figure errors.

Equations (13)

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

I cor = I rec I dark I flat I dark
w i ( y δ y , τ ) = w i ( y , τ + δ y )
w i ( P k 1 , τ ) = w o ( N k 1 , τ ) w i ( P k , τ ) = w o ( N k , τ )
w o ( N k 1 , τ ) = w o ( N k , τ + δ τ k )
w i ( P k 1 , τ ) = w i ( P k , τ + δ τ k )
δ y = P k 1 P k ¯ = δ τ k
δ τ k = arg max t ( w o ( P k , τ ) w o ( P k 1 , τ ) )
y ( P k ) = k δ τ k + cst
M k = N k 1 N k ¯ P k 1 P k ¯ = p δ τ k
1 R k 2 W ( z t , y ) y 2 = 1 δ τ p z t
y k 0 = y ( P k ) , x k 0 = y ( P k ) tan ( Θ inc ) , y ( N k ) = Y k = p k + 2 z tan Θ
Sl k 0 1 2 Y k y k 0 z x k 0
α min = σ ( α ) σ ( δ τ ) z

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