Abstract

Phase contrast x-ray imaging (PCXI) is a promising imaging modality, capable of sensitively differentiating soft tissue structures at high spatial resolution. However, high sensitivity often comes at the cost of a long exposure time or multiple exposures per image, limiting the imaging speed and possibly increasing the radiation dose. Here, we demonstrate a PCXI method that uses a single short exposure to sensitively capture sample phase information, permitting high speed x-ray movies and live animal imaging. The method illuminates a checkerboard phase grid to produce a fine grid-like intensity reference pattern at the detector, then spatially maps sample-induced distortions of this pattern to recover differential phase images of the sample. The use of a phase grid is an improvement on our previous absorption grid work in two ways. There is minimal loss in x-ray flux, permitting faster imaging, and, a very fine pattern is produced for homogenous high spatial resolution. We describe how this pattern permits retrieval of five images from a single exposure; the sample phase gradient images in the horizontal and vertical directions, a projected phase depth image, an edge-enhanced image, and a type of scattering image. Finally, we describe how the reconstruction technique can achieve subpixel distortion retrieval and study the behavior of the technique in regard to analysis technique, Talbot distance, and exposure time.

© 2013 Optical Society of America

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  1. T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
    [CrossRef]
  2. C. David, B. Nohammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
    [CrossRef]
  3. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
    [CrossRef]
  4. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, Jpn. J. Appl. Phys. 45, 5254 (2006).
    [CrossRef]
  5. P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, J. Phys. D 29, 133 (1996).
    [CrossRef]
  6. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, Rev. Sci. Instrum. 66, 5486 (1995).
    [CrossRef]
  7. E. E. Bennet, R. Kopace, A. F. Stein, and H. Wen, Med. Phys. 37, 6047 (2010).
    [CrossRef]
  8. K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Opt. Lett. 36, 55 (2011).
    [CrossRef]
  9. H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, Opt. Lett. 35, 1932 (2010).
    [CrossRef]
  10. K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Opt. Express 19, 19781 (2011).
    [CrossRef]
  11. M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. A 72, 156 (1982).
    [CrossRef]
  12. J. Rizzi, P. Mercère, M. Idir, P. Da Silva, G. Vincent, and J. Primot, Opt. Express 21, 17340 (2013).
    [CrossRef]
  13. M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, Phys. Med. Biol. 49, 4335 (2004).
    [CrossRef]
  14. K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Appl. Phys. Lett. 100, 124102 (2012).
    [CrossRef]
  15. S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, Phys. Rev. Lett. 108, 158102 (2012).
    [CrossRef]
  16. S. C. Mayo and B. Sexton, Opt. Lett. 29, 866 (2004).
    [CrossRef]
  17. A. A. Michelson, Studies in Optics, (University of Chicago, 1995).
  18. I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, Phys. Rev. Lett. 105, 248102 (2010).
    [CrossRef]
  19. K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).
  20. S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkammp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013).
    [CrossRef]
  21. C. Kottler, C. David, F. Pfeiffer, and O. Bunk, Opt. Express 15, 1175 (2007).
    [CrossRef]
  22. P. Bon, S. Monneret, and B. Wattellier, Appl. Opt. 51, 5698 (2012).
    [CrossRef]
  23. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
    [CrossRef]
  24. P. Modregger, B. R. Pinzer, T. Thüring, S. Rutishauser, C. David, and M. Stampanoni, Opt. Express 19, 18324 (2011).
    [CrossRef]

2013 (3)

J. Rizzi, P. Mercère, M. Idir, P. Da Silva, G. Vincent, and J. Primot, Opt. Express 21, 17340 (2013).
[CrossRef]

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkammp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013).
[CrossRef]

2012 (3)

P. Bon, S. Monneret, and B. Wattellier, Appl. Opt. 51, 5698 (2012).
[CrossRef]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Appl. Phys. Lett. 100, 124102 (2012).
[CrossRef]

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, Phys. Rev. Lett. 108, 158102 (2012).
[CrossRef]

2011 (3)

2010 (3)

H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, Opt. Lett. 35, 1932 (2010).
[CrossRef]

E. E. Bennet, R. Kopace, A. F. Stein, and H. Wen, Med. Phys. 37, 6047 (2010).
[CrossRef]

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

2007 (1)

2006 (2)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
[CrossRef]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, Jpn. J. Appl. Phys. 45, 5254 (2006).
[CrossRef]

2004 (2)

S. C. Mayo and B. Sexton, Opt. Lett. 29, 866 (2004).
[CrossRef]

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, Phys. Med. Biol. 49, 4335 (2004).
[CrossRef]

2002 (2)

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef]

1996 (1)

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, J. Phys. D 29, 133 (1996).
[CrossRef]

1995 (2)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[CrossRef]

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. A 72, 156 (1982).
[CrossRef]

Barrett, R.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, J. Phys. D 29, 133 (1996).
[CrossRef]

Baruchel, J.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, J. Phys. D 29, 133 (1996).
[CrossRef]

Bednarzik, M.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkammp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013).
[CrossRef]

Bennet, E. E.

E. E. Bennet, R. Kopace, A. F. Stein, and H. Wen, Med. Phys. 37, 6047 (2010).
[CrossRef]

Bennett, E. E.

Bérujon, S.

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, Phys. Rev. Lett. 108, 158102 (2012).
[CrossRef]

Bon, P.

Börner, M.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkammp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013).
[CrossRef]

Boucher, R. C.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

Bunk, O.

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, Opt. Express 15, 1175 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
[CrossRef]

Cerbino, R.

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, Phys. Rev. Lett. 108, 158102 (2012).
[CrossRef]

Cloetens, P.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, J. Phys. D 29, 133 (1996).
[CrossRef]

Da Silva, P.

David, C.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkammp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013).
[CrossRef]

P. Modregger, B. R. Pinzer, T. Thüring, S. Rutishauser, C. David, and M. Stampanoni, Opt. Express 19, 18324 (2011).
[CrossRef]

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

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, Opt. Express 15, 1175 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
[CrossRef]

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

Davis, T. J.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[CrossRef]

Donath, T.

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

Donnelley, M.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

Fouras, A.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

Gao, D.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[CrossRef]

Guigay, J. P.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, J. Phys. D 29, 133 (1996).
[CrossRef]

Gureyev, T. E.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[CrossRef]

Hattori, T.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, Jpn. J. Appl. Phys. 45, 5254 (2006).
[CrossRef]

Idir, M.

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. A 72, 156 (1982).
[CrossRef]

Kitchen, M. J.

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, Phys. Med. Biol. 49, 4335 (2004).
[CrossRef]

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. A 72, 156 (1982).
[CrossRef]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Kopace, R.

E. E. Bennet, R. Kopace, A. F. Stein, and H. Wen, Med. Phys. 37, 6047 (2010).
[CrossRef]

H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, Opt. Lett. 35, 1932 (2010).
[CrossRef]

Kottler, C.

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Lewis, R. A.

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, Phys. Med. Biol. 49, 4335 (2004).
[CrossRef]

Mayo, S. C.

S. C. Mayo and B. Sexton, Opt. Lett. 29, 866 (2004).
[CrossRef]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef]

Mercère, P.

Michelson, A. A.

A. A. Michelson, Studies in Optics, (University of Chicago, 1995).

Miller, P. R.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef]

Modregger, P.

Mohr, J.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkammp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013).
[CrossRef]

Momose, A.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, Jpn. J. Appl. Phys. 45, 5254 (2006).
[CrossRef]

Monneret, S.

Morgan, K. S.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Appl. Phys. Lett. 100, 124102 (2012).
[CrossRef]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Opt. Express 19, 19781 (2011).
[CrossRef]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Opt. Lett. 36, 55 (2011).
[CrossRef]

Mudie, S. T.

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, Phys. Med. Biol. 49, 4335 (2004).
[CrossRef]

Nohammer, B.

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

Paganin, D.

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, Phys. Med. Biol. 49, 4335 (2004).
[CrossRef]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef]

Paganin, D. M.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Appl. Phys. Lett. 100, 124102 (2012).
[CrossRef]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Opt. Express 19, 19781 (2011).
[CrossRef]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Opt. Lett. 36, 55 (2011).
[CrossRef]

Pai, V.

Parsons, D. W.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

Peverini, L.

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, Phys. Rev. Lett. 108, 158102 (2012).
[CrossRef]

Pfeiffer, F.

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, Opt. Express 15, 1175 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
[CrossRef]

Pinzer, B. R.

Primot, J.

Rizzi, J.

Rutishauser, S.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkammp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013).
[CrossRef]

P. Modregger, B. R. Pinzer, T. Thüring, S. Rutishauser, C. David, and M. Stampanoni, Opt. Express 19, 18324 (2011).
[CrossRef]

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

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Schlenker, M.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, J. Phys. D 29, 133 (1996).
[CrossRef]

Sexton, B.

Siu, K. K. W.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Appl. Phys. Lett. 100, 124102 (2012).
[CrossRef]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Opt. Express 19, 19781 (2011).
[CrossRef]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, Opt. Lett. 36, 55 (2011).
[CrossRef]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Solak, H. H.

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

Stampanoni, M.

Stein, A. F.

E. E. Bennet, R. Kopace, A. F. Stein, and H. Wen, Med. Phys. 37, 6047 (2010).
[CrossRef]

H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, Opt. Lett. 35, 1932 (2010).
[CrossRef]

Stevenson, A. W.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[CrossRef]

Suzuki, Y.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, Jpn. J. Appl. Phys. 45, 5254 (2006).
[CrossRef]

Takeda, M.

M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. A 72, 156 (1982).
[CrossRef]

Takeda, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, Jpn. J. Appl. Phys. 45, 5254 (2006).
[CrossRef]

Takeuchi, A.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

Thüring, T.

Uesugi, K.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, Phys. Med. Biol. 49, 4335 (2004).
[CrossRef]

Vincent, G.

Wattellier, B.

Weitkammp, T.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkammp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013).
[CrossRef]

Weitkamp, T.

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

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
[CrossRef]

Wen, H.

E. E. Bennet, R. Kopace, A. F. Stein, and H. Wen, Med. Phys. 37, 6047 (2010).
[CrossRef]

Wen, H. H.

Wilkins, S. W.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. 206, 33 (2002).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[CrossRef]

Yagi, N.

K. S. Morgan, M. Donnelley, D. M. Paganin, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Boucher, D. W. Parsons, and K. K. W. Siu, PLOS ONE 8, e55822 (2013).

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, Phys. Med. Biol. 49, 4335 (2004).
[CrossRef]

Yashiro, W.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, Jpn. J. Appl. Phys. 45, 5254 (2006).
[CrossRef]

Zanette, I.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkammp, M. Börner, J. Mohr, and C. David, Microelectron. Eng. 101, 12 (2013).
[CrossRef]

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

Ziegler, E.

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, Phys. Rev. Lett. 108, 158102 (2012).
[CrossRef]

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, Appl. Phys. Lett. 81, 3287 (2002).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup (not to scale).

Fig. 2.
Fig. 2.

Single-phase-grid PCXI images of an ant head, with 2.7 μm period grid pattern, 0.36 μm effective pixel size, 25 keV. The (a) grating-only image, (b) grating and sample image are all that is required to reconstruct (c) horizontal, (d) vertical phase gradients, (e) projected phase depth, (f) edge-enhanced attenuation image (like propagation-based PCXI), and (g) cross-correlation amplitude for scattering properties. For comparison to (e), (h) is the projected phase depth reconstructed from (f). In (a),(b), a larger Moiré grid may be seen depending on printer/viewer sampling.

Fig. 3.
Fig. 3.

Fourier analysis [9,11] in Fig. 2(b) shows (a) horizontal gradients and (b) horizontal sample-only gradients, with nonsample gradients removed by subtracting the result of a Fourier analysis on the grid-only image [Fig. 2(a)] from Fig. 3(a).

Fig. 4.
Fig. 4.

Magnification of Fig. 2(d), the phase gradient, by (a) the spatial mapping method; (b) by the Fourier method, cropping around the peak; and (c) by Fourier, bandpass filtering the peak (both with a window equal in width to the frequency of the grid).

Fig. 5.
Fig. 5.

(a) Signal to noise ratio (SNR) in the flat area of the reconstructed differential phase image, shown as a function of exposure time. The images use (b) the Fourier method with 10 ms exposure (mean 700 raw counts) and (c) with 700 ms exposure (mean 47,000 raw counts), and use the spatial mapping method with (d) 700 ms exposure, (e) 10 ms exposure, and (f) 10 ms exposure with “salt and pepper” noise [inset of (e)] removed. The sample is a 1.5 mm diameter PMMA sphere and a 50 μm thin scrap of polyethylene (top of image), propagation 22 cm. To magnify noise detail, (b)–(f) show just 20% of the full field of view.

Fig. 6.
Fig. 6.

(a) Grid pattern visibility as a function of grid-detector distance, and corresponding SNR along the profile shown in horizontal gradient images captured at (b) D=22cm and (c) D=80cm (long exp). This part of the image shows a 1.5 mm PMMA sphere (upper right corner of the image) and a 0.25 mm PMMA cylinder (left side of the image); short exposure=30ms, long=600ms. Points are fitted with a third-order spline to guide the eye.

Equations (3)

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

Dn=nT2/(8λ),
S=(aia0)+(ai1ai+1)/(2ai14ai+2ai+1),
Z<T/2tan(1kdφdx)

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