Abstract

A fast and accurate method to characterize the X-ray wavefront by rotating one of the two gratings of an X-ray shearing interferometer is described and investigated step by step. Such a shearing interferometer consists of a phase grating mounted on a rotation stage, and an absorption grating used as a transmission mask. The mathematical relations for X-ray Moiré fringe analysis when using this device are derived and discussed in the context of the previous literature assumptions. X-ray beam wavefronts without and after X-ray reflective optical elements have been characterized at beamline B16 at Diamond Light Source (DLS) using the presented X-ray rotating shearing interferometer (RSI) technique. It has been demonstrated that this improved method allows accurate calculation of the wavefront radius of curvature and the wavefront distortion, even when one has no previous information on the grating projection pattern period, magnification ratio and the initial grating orientation. As the RSI technique does not require any a priori knowledge of the beam features, it is suitable for routine characterization of wavefronts of a wide range of radii of curvature.

© 2011 OSA

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  1. E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, “On-line mirror surfacing monitored by X-ray shearing interferometry and X-ray scattering,” AIP Conf. Proc. 879, 778–781 (2007).
    [CrossRef]
  2. C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
    [CrossRef]
  3. T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101–054103 (2005).
    [CrossRef]
  4. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
    [CrossRef]
  5. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
    [CrossRef]
  6. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
    [CrossRef] [PubMed]
  7. F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
    [CrossRef] [PubMed]
  8. T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
    [CrossRef]
  9. A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
    [CrossRef] [PubMed]
  10. J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synchrotron Radiat. 11(6), 476–482 (2004).
    [CrossRef] [PubMed]
  11. M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1993).
  12. K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
    [CrossRef]
  13. C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
    [CrossRef]
  14. I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
    [CrossRef] [PubMed]
  15. H. Itoh, K. Nagai, G. Sato, K. Yamaguchi, T. Nakamura, T. Kondoh, C. Ouchi, T. Teshima, Y. Setomoto, and T. Den, “Two-dimensional grating-based X-ray phase-contrast imaging using Fourier transform phase retrieval,” Opt. Express 19(4), 3339–3346 (2011).
    [CrossRef] [PubMed]

2011 (1)

2010 (3)

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

2007 (2)

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, “On-line mirror surfacing monitored by X-ray shearing interferometry and X-ray scattering,” AIP Conf. Proc. 879, 778–781 (2007).
[CrossRef]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

2005 (3)

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101–054103 (2005).
[CrossRef]

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

2004 (2)

T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
[CrossRef]

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synchrotron Radiat. 11(6), 476–482 (2004).
[CrossRef] [PubMed]

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

2002 (1)

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Bauer, G.

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

Bruder, J.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Bunk, O.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

Cloetens, P.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synchrotron Radiat. 11(6), 476–482 (2004).
[CrossRef] [PubMed]

David, C.

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, “On-line mirror surfacing monitored by X-ray shearing interferometry and X-ray scattering,” AIP Conf. Proc. 879, 778–781 (2007).
[CrossRef]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101–054103 (2005).
[CrossRef]

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
[CrossRef]

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synchrotron Radiat. 11(6), 476–482 (2004).
[CrossRef] [PubMed]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

Den, T.

Diaz, A.

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101–054103 (2005).
[CrossRef]

T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
[CrossRef]

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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Donath, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

Garrett, R.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Gentle, I.

K. J. S. Sawhney, I. P. Dolbnya, M. K. Tiwari, L. Alianelli, S. M. Scott, G. M. Preece, U. K. Pedersen, R. D. Walton, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Grünzweig, C.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Guigay, J.-P.

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synchrotron Radiat. 11(6), 476–482 (2004).
[CrossRef] [PubMed]

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Itoh, H.

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Keplinger, M.

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

Kondoh, T.

Kottler, C.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Kozhevnikov, I. V.

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, “On-line mirror surfacing monitored by X-ray shearing interferometry and X-ray scattering,” AIP Conf. Proc. 879, 778–781 (2007).
[CrossRef]

Metzger, T. H.

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

Mocuta, C.

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

Mokso, R.

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synchrotron Radiat. 11(6), 476–482 (2004).
[CrossRef] [PubMed]

Momose, A.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Nagai, K.

Nakamura, T.

Nöhammer, B.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101–054103 (2005).
[CrossRef]

T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
[CrossRef]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

Nugent, 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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Ouchi, C.

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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Peverini, L.

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, “On-line mirror surfacing monitored by X-ray shearing interferometry and X-ray scattering,” AIP Conf. Proc. 879, 778–781 (2007).
[CrossRef]

Pfeiffer, F.

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
[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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Robinson, I. K.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

Rohbeck, T.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Rutishauser, S.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

Sato, G.

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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Schlenker, M.

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synchrotron Radiat. 11(6), 476–482 (2004).
[CrossRef] [PubMed]

Schulze-Briese, C.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Setomoto, Y.

Solak, H. H.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

Stampanoni, M.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
[CrossRef]

Stangl, J.

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Teshima, T.

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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

van der Veen, J. F.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

Vartanyants, I.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Weitkamp, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, “On-line mirror surfacing monitored by X-ray shearing interferometry and X-ray scattering,” AIP Conf. Proc. 879, 778–781 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101–054103 (2005).
[CrossRef]

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
[CrossRef]

Wilkins, 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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Yamaguchi, K.

Zabler, S.

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synchrotron Radiat. 11(6), 476–482 (2004).
[CrossRef] [PubMed]

Zanette, I.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

Ziegler, E.

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, “On-line mirror surfacing monitored by X-ray shearing interferometry and X-ray scattering,” AIP Conf. Proc. 879, 778–781 (2007).
[CrossRef]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101–054103 (2005).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
[CrossRef]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

AIP Conf. Proc. (2)

E. Ziegler, L. Peverini, I. V. Kozhevnikov, T. Weitkamp, and C. David, “On-line mirror surfacing monitored by X-ray shearing interferometry and X-ray scattering,” AIP Conf. Proc. 879, 778–781 (2007).
[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, R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, “A test beamline on diamond light source,” AIP Conf. Proc. 1234, 387–390 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101–054103 (2005).
[CrossRef]

J. Synchrotron Radiat. (2)

A. Diaz, C. Mocuta, J. Stangl, M. Keplinger, T. Weitkamp, F. Pfeiffer, C. David, T. H. Metzger, and G. Bauer, “Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry,” J. Synchrotron Radiat. 17(3), 299–307 (2010).
[CrossRef] [PubMed]

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Synchrotron Radiat. 11(6), 476–482 (2004).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys. (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Microelectron. Eng. (1)

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Nat. Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

Opt. Express (2)

Phys. Rev. Lett. (2)

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. F. van der Veen, I. Vartanyants, and I. K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 164801 (2005).
[CrossRef] [PubMed]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

Proc. SPIE (1)

T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, M. Stampanoni, E. Ziegler, and C. David, “Moire interferometry formulas for hard x-ray wavefront sensing,” Proc. SPIE 5533, 140–144 (2004).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1993).

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Figures (7)

Fig. 1
Fig. 1

Moiré fringes formation. The Moiré fringes will have an inclination angle θ with respect to the vertical axis when the two gratings are tilted from the horizontal axis by angles β and α, respectively

Fig. 2
Fig. 2

A schematic of the rotating shearing interferometer at B16 beamline.

Fig. 3
Fig. 3

Interferograms recorded at four different angles: (a) β = 0.019 rad, (b) β = 0.025 rad, (c) β = 0.041 rad, (d) β = 0.048 rad.

Fig. 4
Fig. 4

Experimental data and fitted model from Eq. (16) for γ y as function of γ x at the 3rd, 9th, 15th and 21st order Talbot distances. The points corresponding to the four images shown in Fig. 2 are circled.

Fig. 5
Fig. 5

Linear regression of the κ factors calculated at the different Talbot orders. The 3rd, 9th, 15th and 21st Talbot orders are circled.

Fig. 6
Fig. 6

Data extracted from the images presented in Fig. 3: (1) Radius of curvature as function of y, (2) Wavefront slope error obtained after subtraction of the linear fit. Different line types correspond to calculated data from different images (a-d) of Fig. 3.

Fig. 7
Fig. 7

Experimental data and its fitting to Eq. (16): γ y as function of γ x at the 3rd Talbot order distance (L = 93 mm) for a wavefront reflected from a focusing mirror.

Tables (1)

Tables Icon

Table 1 Radius of Curvature of DCM direct beam at B16 with RSI

Equations (20)

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

η = d 0 d 2
L m = m d 0 2 8 λ
L m * = R R L m L m
M = L m * + R R
d 1 = η d 2 2 M = d 2 κ
κ = 2 R ( L m * + R ) η
{ I 1 ( x , y ) = cos 2 [ π d 1 ( y cos β x sin β ) ] cos 2 B I 2 ( x , y ) = cos 2 [ π d 2 ( y cos α x sin α ) ] cos 2 A
I ( x , y ) = I 1 ( x , y ) × I 2 ( x , y ) = cos 2 B × cos 2 A = 1 8 [ cos ( 2 B + 2 A ) + cos ( 2 B 2 A ) I m ( x , y ) + 4 cos 2 B I 1 ( x , y ) + 4 cos 2 A I 2 ( x , y ) 2 ]
I m ( x , y ) = cos [ 2 π d 1 ( y cos β x sin β ) 2 π d 2 ( y cos α x sin α ) ]
I m ( x , y ) = cos [ 2 π d 2 ( sin α κ sin β ) x 2 π d 2 ( cos α κ cos β ) y ]
tan θ = cos α κ cos β sin α κ sin β
{ d x = d 2 sin α κ sin β d 2 γ x d y = d 2 cos α κ cos β d 2 γ y
{ γ x = sin α κ sin β γ y = cos α κ cos β
I j ( x ) = a 0 + b 0 cos ( 2 π d x x + φ )
2 π d x x + φ = c
tan θ = x y = d x 2 π φ y
γ y = cos α κ 2 ( γ x sin α ) 2
κ ( y ) = ( γ y ( y ) cos α ) 2 + ( γ x ( y ) sin α ) 2
R ( y ) = L m * η κ ( y ) 2 η κ ( y )
S y = 0 y R ( y ) 1 d y

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