Abstract

We present in this Letter a type of quadriwave lateral shearing interferometer for x-ray phase imaging. This device is based on a phase chessboard, and we take advantage of the large spectrum of the source to produce interferograms with a propagation-invariant contrast. Such a grating has been created for hard x-ray interferometry and experimentally tested on a synchrotron beamline at Soleil.

© 2011 Optical Society of America

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  1. R. Fitzgerald, Phys. Today 53 (7), 23 (2000).
    [CrossRef]
  2. A. Momose, Opt. Express 11, 2303 (2003).
    [CrossRef] [PubMed]
  3. A. Momose, Jpn. J. Appl. Phys. 44, 6355 (2005).
    [CrossRef]
  4. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, Opt. Express 13, 6296 (2005).
    [CrossRef] [PubMed]
  5. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
    [CrossRef] [PubMed]
  6. J. M. Kim, I. H. Cho, S. Y. Lee, H. C. Kang, R. Conley, C. Liu, A. T. Macrander, and D. Y. Noh, Opt. Express 18, 24975 (2010).
    [CrossRef] [PubMed]
  7. G. Nomarski, J. Phys. Radium 16, S88 (1955).
  8. J. Primot and L. Sogno, J. Opt. Soc. Am. A 12, 2679(1995).
    [CrossRef]
  9. P. Bon, G. Maucort, B. Wattelier, and S. Monneret, Opt. Express 17, 13080 (2009).
    [CrossRef] [PubMed]
  10. J. Primot and N. Guérineau, Appl. Opt. 39, 5715 (2000).
    [CrossRef]
  11. H. F. Talbot, Philos. Mag. 9, 401 (1836).
  12. I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, Phys. Rev. Lett. 105, 248102 (2010).
    [CrossRef]
  13. N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, Opt. Lett. 7 (2001).
  14. N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180 (2000).
    [CrossRef]

2010 (2)

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

J. M. Kim, I. H. Cho, S. Y. Lee, H. C. Kang, R. Conley, C. Liu, A. T. Macrander, and D. Y. Noh, Opt. Express 18, 24975 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

2005 (2)

2003 (1)

2001 (1)

N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, Opt. Lett. 7 (2001).

2000 (3)

N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180 (2000).
[CrossRef]

R. Fitzgerald, Phys. Today 53 (7), 23 (2000).
[CrossRef]

J. Primot and N. Guérineau, Appl. Opt. 39, 5715 (2000).
[CrossRef]

1995 (1)

1955 (1)

G. Nomarski, J. Phys. Radium 16, S88 (1955).

1836 (1)

H. F. Talbot, Philos. Mag. 9, 401 (1836).

Bech, M.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

Bon, P.

Brönnimann, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

Bunk, O.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

Cho, I. H.

Cloetens, P.

Conley, R.

David, C.

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

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, Opt. Express 13, 6296 (2005).
[CrossRef] [PubMed]

Diaz, A.

Donath, T.

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

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

Fitzgerald, R.

R. Fitzgerald, Phys. Today 53 (7), 23 (2000).
[CrossRef]

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

Guérineau, N.

N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, Opt. Lett. 7 (2001).

N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180 (2000).
[CrossRef]

J. Primot and N. Guérineau, Appl. Opt. 39, 5715 (2000).
[CrossRef]

Harchaoui, B.

N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, Opt. Lett. 7 (2001).

N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180 (2000).
[CrossRef]

Heggarty, K.

N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, Opt. Lett. 7 (2001).

Kang, H. C.

Kim, J. M.

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

Lee, S. Y.

Liu, C.

Macrander, A. T.

Maucort, G.

Momose, A.

A. Momose, Jpn. J. Appl. Phys. 44, 6355 (2005).
[CrossRef]

A. Momose, Opt. Express 11, 2303 (2003).
[CrossRef] [PubMed]

Monneret, S.

Noh, D. Y.

Nomarski, G.

G. Nomarski, J. Phys. Radium 16, S88 (1955).

Pfeiffer, F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, Opt. Express 13, 6296 (2005).
[CrossRef] [PubMed]

Primot, J.

N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, Opt. Lett. 7 (2001).

N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180 (2000).
[CrossRef]

J. Primot and N. Guérineau, Appl. Opt. 39, 5715 (2000).
[CrossRef]

J. Primot and L. Sogno, J. Opt. Soc. Am. A 12, 2679(1995).
[CrossRef]

Rutishauser, S.

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

Sogno, L.

Stampanoni, M.

Talbot, H. F.

H. F. Talbot, Philos. Mag. 9, 401 (1836).

Wattelier, B.

Weitkamp, T.

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, Opt. Express 13, 6296 (2005).
[CrossRef] [PubMed]

Zanette, I.

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

Ziegler, E.

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

J. Phys. Radium (1)

G. Nomarski, J. Phys. Radium 16, S88 (1955).

Jpn. J. Appl. Phys. (1)

A. Momose, Jpn. J. Appl. Phys. 44, 6355 (2005).
[CrossRef]

Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Nat. Mater. 7, 134 (2008).
[CrossRef] [PubMed]

Opt. Commun. (1)

N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, Opt. Lett. 7 (2001).

Philos. Mag. (1)

H. F. Talbot, Philos. Mag. 9, 401 (1836).

Phys. Rev. Lett. (1)

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

Phys. Today (1)

R. Fitzgerald, Phys. Today 53 (7), 23 (2000).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Ideal device: an amplitude mask superposed on a phase chessboard, (b) realized device: a π-shifting phase chessboard only.

Fig. 2
Fig. 2

Simulations of propagated beams after a phase chessboard alone. (a) Simulation of propagation of a monochromatic beam with λ = 0.07 nm . Here the z T used corresponds to n = 1 in Eq. (1). (b) Simulation of propagation of a polychromatic beam with λ = 0.07 nm and Δ λ = 0.04 nm .

Fig. 3
Fig. 3

Estimated x-ray spectrum in the experiment. Dashed lines: spectral photon flux density. The thin dashed line corresponds to the source spectrum; the thick dashed line, to the spectrum after attenuation by vacuum window, grating substrate, and air path. Solid filled curve: spectral density of energy deposited in the scintillator.

Fig. 4
Fig. 4

Experimental setup: a simple interferometer for x-ray phase contrast imagery, using just one (phase) grating.

Fig. 5
Fig. 5

(a) One of the 20 interferograms recorded, taken at distance z = 49 cm . (b) Fourier spectrum of the image in (a). We also see other parasiting orders. (c) Evolution with the distance z of the energy in four main orders. The energy is normalized by the energy of the order 0.

Equations (3)

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z T = n 2 p 2 λ ( n = 1 , 2 , ) .
z f T = ( n 1 2 ) p 2 λ ( n = 1 , 2 , ) .
z ach = p 2 Δ λ .

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