Abstract

We report an alternative approach to x-ray wave-front analysis that uses a refractive microlens array as a Shack–Hartmann sensor. The sensor was manufactured by self-assembly and electroplating techniques and is suitable for high-resolution wave-front analysis of medium to hard x rays. We demonstrate its effectiveness at an x-ray energy of 3 keV for analysis of x-ray wave-front perturbations caused by microscopic objects. The sensor has potential advantages over other methods for x-ray phase imaging and will also be useful for the characterization of x-ray beams and optics.

© 2004 Optical Society of America

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References

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  1. B. C. Platt and R. Shack, J. Refr. Surg. 17, S573 (2001).
  2. L. Thibos and X. Hong, Optom. Vis. Sci. 76, 817 (1999).
    [CrossRef] [PubMed]
  3. A. Glindemann, S. Hippler, T. Berkefeld, and W. Hackenberg, Exp. Astron. 10, 5 (2000).
    [CrossRef]
  4. S. Wilkins, “X-ray optics, especially for phase contrast imaging,” U.S. patent5,802,137 (September1, 1998).
  5. K. Baker, J. Brase, M. Kartz, S. S. Olivier, B. Sawvel, and J. Tucker, Opt. Lett. 28, 149 (2003).
    [CrossRef] [PubMed]
  6. S. Le Pape, P. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. Francois, Phys. Rev. Lett. 88, 183 (2002).
    [CrossRef]
  7. A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).
    [CrossRef]
  8. A. Momose, T. Takeda, and Y. Itai, Rev. Sci. Instrum. 66, 1434 (1995).
    [CrossRef]
  9. C. David, B. Nöhammer, H. Solak, and E. Ziegler, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 595–598.
  10. S. Wilkins, T. Gureyev, D. Gao, A. Popany, and A. Stevenson, Nature 384, 335 (1996).
    [CrossRef]
  11. P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
    [CrossRef]
  12. J. R. Palmer and G. R. Morrison, in Short-Wavelength Coherent Radiation: Generation and Applications, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 141.
  13. M. Feser, C. Jacobsen, P. Rehak, and G. DeGeronimo, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 529–534.
  14. S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
    [CrossRef] [PubMed]
  15. W. H. Southwell, J. Opt. Soc. Am. 70, 998 (1980).
  16. C. J. Solomon, S. Rios, E. Acosta, and S. Bará, Opt. Commun. 155, 251 (1998).
    [CrossRef]

2003 (1)

2002 (2)

S. Le Pape, P. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. Francois, Phys. Rev. Lett. 88, 183 (2002).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

2001 (1)

B. C. Platt and R. Shack, J. Refr. Surg. 17, S573 (2001).

2000 (1)

A. Glindemann, S. Hippler, T. Berkefeld, and W. Hackenberg, Exp. Astron. 10, 5 (2000).
[CrossRef]

1999 (2)

L. Thibos and X. Hong, Optom. Vis. Sci. 76, 817 (1999).
[CrossRef] [PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

1998 (1)

C. J. Solomon, S. Rios, E. Acosta, and S. Bará, Opt. Commun. 155, 251 (1998).
[CrossRef]

1996 (2)

S. Wilkins, T. Gureyev, D. Gao, A. Popany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).
[CrossRef]

1995 (1)

A. Momose, T. Takeda, and Y. Itai, Rev. Sci. Instrum. 66, 1434 (1995).
[CrossRef]

1980 (1)

Acosta, E.

C. J. Solomon, S. Rios, E. Acosta, and S. Bará, Opt. Commun. 155, 251 (1998).
[CrossRef]

Baker, K.

Bará, S.

C. J. Solomon, S. Rios, E. Acosta, and S. Bará, Opt. Commun. 155, 251 (1998).
[CrossRef]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

Berkefeld, T.

A. Glindemann, S. Hippler, T. Berkefeld, and W. Hackenberg, Exp. Astron. 10, 5 (2000).
[CrossRef]

Brase, J.

Buffiere, J. Y.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

Cloetens, P.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

David, C.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 595–598.

Davis, T. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

DeGeronimo, G.

M. Feser, C. Jacobsen, P. Rehak, and G. DeGeronimo, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 529–534.

Dhez, P.

S. Le Pape, P. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. Francois, Phys. Rev. Lett. 88, 183 (2002).
[CrossRef]

Feser, M.

M. Feser, C. Jacobsen, P. Rehak, and G. DeGeronimo, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 529–534.

Francois, M.

S. Le Pape, P. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. Francois, Phys. Rev. Lett. 88, 183 (2002).
[CrossRef]

Gao, D.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

S. Wilkins, T. Gureyev, D. Gao, A. Popany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Glindemann, A.

A. Glindemann, S. Hippler, T. Berkefeld, and W. Hackenberg, Exp. Astron. 10, 5 (2000).
[CrossRef]

Guigay, J. P.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

Gureyev, T.

S. Wilkins, T. Gureyev, D. Gao, A. Popany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Gureyev, T. E.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

Hackenberg, W.

A. Glindemann, S. Hippler, T. Berkefeld, and W. Hackenberg, Exp. Astron. 10, 5 (2000).
[CrossRef]

Hippler, S.

A. Glindemann, S. Hippler, T. Berkefeld, and W. Hackenberg, Exp. Astron. 10, 5 (2000).
[CrossRef]

Hong, X.

L. Thibos and X. Hong, Optom. Vis. Sci. 76, 817 (1999).
[CrossRef] [PubMed]

Idir, M.

S. Le Pape, P. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. Francois, Phys. Rev. Lett. 88, 183 (2002).
[CrossRef]

Itai, Y.

A. Momose, T. Takeda, and Y. Itai, Rev. Sci. Instrum. 66, 1434 (1995).
[CrossRef]

Jacobsen, C.

M. Feser, C. Jacobsen, P. Rehak, and G. DeGeronimo, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 529–534.

Kartz, M.

Kohn, V.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).
[CrossRef]

Le Pape, S.

S. Le Pape, P. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. Francois, Phys. Rev. Lett. 88, 183 (2002).
[CrossRef]

Lengeler, B.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).
[CrossRef]

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

Maire, E.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

Mayo, S. C.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

Miller, P. R.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

Momose, A.

A. Momose, T. Takeda, and Y. Itai, Rev. Sci. Instrum. 66, 1434 (1995).
[CrossRef]

Morrison, G. R.

J. R. Palmer and G. R. Morrison, in Short-Wavelength Coherent Radiation: Generation and Applications, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 141.

Nöhammer, B.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 595–598.

Olivier, S. S.

Paganin, D.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

Palmer, J. R.

J. R. Palmer and G. R. Morrison, in Short-Wavelength Coherent Radiation: Generation and Applications, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 141.

Parry, D. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

Peix, G.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

Pernot-Rejmankova, P.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

Platt, B. C.

B. C. Platt and R. Shack, J. Refr. Surg. 17, S573 (2001).

Pogany, A.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

Popany, A.

S. Wilkins, T. Gureyev, D. Gao, A. Popany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Rehak, P.

M. Feser, C. Jacobsen, P. Rehak, and G. DeGeronimo, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 529–534.

Rios, S.

C. J. Solomon, S. Rios, E. Acosta, and S. Bará, Opt. Commun. 155, 251 (1998).
[CrossRef]

Rocca, J. J.

S. Le Pape, P. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. Francois, Phys. Rev. Lett. 88, 183 (2002).
[CrossRef]

Salome-Pateyron, M.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

Sawvel, B.

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

Shack, R.

B. C. Platt and R. Shack, J. Refr. Surg. 17, S573 (2001).

Snigirev, A.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).
[CrossRef]

Snigireva, I.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).
[CrossRef]

Solak, H.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 595–598.

Solomon, C. J.

C. J. Solomon, S. Rios, E. Acosta, and S. Bará, Opt. Commun. 155, 251 (1998).
[CrossRef]

Southwell, W. H.

Stevenson, A.

S. Wilkins, T. Gureyev, D. Gao, A. Popany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Stevenson, A. W.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

Takeda, T.

A. Momose, T. Takeda, and Y. Itai, Rev. Sci. Instrum. 66, 1434 (1995).
[CrossRef]

Thibos, L.

L. Thibos and X. Hong, Optom. Vis. Sci. 76, 817 (1999).
[CrossRef] [PubMed]

Tucker, J.

Wilkins, S.

S. Wilkins, T. Gureyev, D. Gao, A. Popany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

S. Wilkins, “X-ray optics, especially for phase contrast imaging,” U.S. patent5,802,137 (September1, 1998).

Wilkins, S. W.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

Zeitoun, P.

S. Le Pape, P. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. Francois, Phys. Rev. Lett. 88, 183 (2002).
[CrossRef]

Ziegler, E.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 595–598.

Exp. Astron. (1)

A. Glindemann, S. Hippler, T. Berkefeld, and W. Hackenberg, Exp. Astron. 10, 5 (2000).
[CrossRef]

J. Microsc. (1)

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, J. Microsc. 207, 79 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Phys. D (1)

P. Cloetens, W. Ludwig, J. Baruchel, J. P. Guigay, P. Pernot-Rejmankova, M. Salome-Pateyron, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, J. Phys. D 32, 145 (1999).
[CrossRef]

J. Refr. Surg. (1)

B. C. Platt and R. Shack, J. Refr. Surg. 17, S573 (2001).

Nature (2)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).
[CrossRef]

S. Wilkins, T. Gureyev, D. Gao, A. Popany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Opt. Commun. (1)

C. J. Solomon, S. Rios, E. Acosta, and S. Bará, Opt. Commun. 155, 251 (1998).
[CrossRef]

Opt. Lett. (1)

Optom. Vis. Sci. (1)

L. Thibos and X. Hong, Optom. Vis. Sci. 76, 817 (1999).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

S. Le Pape, P. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. Francois, Phys. Rev. Lett. 88, 183 (2002).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Momose, T. Takeda, and Y. Itai, Rev. Sci. Instrum. 66, 1434 (1995).
[CrossRef]

Other (4)

C. David, B. Nöhammer, H. Solak, and E. Ziegler, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 595–598.

S. Wilkins, “X-ray optics, especially for phase contrast imaging,” U.S. patent5,802,137 (September1, 1998).

J. R. Palmer and G. R. Morrison, in Short-Wavelength Coherent Radiation: Generation and Applications, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), p. 141.

M. Feser, C. Jacobsen, P. Rehak, and G. DeGeronimo, in Proceedings of the 7th International Conference on X-Ray Microscopy 2002, J. Susini, D. Joyeux, and F. Polack, eds. (EDS Sciences, Le Ulis, France, 2003) pp. 529–534.

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Figures (3)

Fig. 1
Fig. 1

a, Imaging geometry of the x-ray microscope. Magnification of the sample at the detector is given by R+D/R. b, Shift in lenslet focal-spot position Δr when the incident wave-front gradient is modified by a sample immediately in front of (upper) or behind (lower) the array. Provided that dD,θ, the change in wave-front gradient caused by the sample is θ=Δr/D for both cases.

Fig. 2
Fig. 2

a, Array region with no object. b, The same region with a human hair running approximately horizontally across it. c, Difference image in which displaced spots show up as asymmetric spots that are dark on one side and bright on the other (the edges of the hair can be seen on either side of the array as a result of phase-contrast edge enhancement). d, Three-dimensional plot of the reconstructed wave front (arbitrary z scale).

Fig. 3
Fig. 3

a, Second array region with no object; b, the same region with a polyglycolic acid fiber running approximately horizontally across it; c, a difference image; and d, a three-dimensional plot of the reconstructed wave front (arbitrary z scale).

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