Abstract

Normal incidence Talbot-Lau interferometers in x-ray applications have the drawbacks of low fringe visibility with polychromatic sources when the wave propagation distance is increased to achieve higher phase sensitivity, and when fabrication limits the attainable grating density. In contrast, reflective gratings illuminated at grazing angles have dramatically higher effective densities than their physical values. However, new designs are needed for far field interferometers using grazing angle geometry with incoherent light sources. We show that, with the appropriate design and choice of reflective phase gratings, there exist pairs of interfering pathways of exactly equal lengths independent of the incoming beam’s incidence angle and wavelength. With a visible light grazing angle Mach-Zehnder interferometer, we show the conditions for achieving near ideal fringe visibility and demonstrate both absolute and differential phase-contrast imaging. We also describe the design parameters of an x-ray interferometer and key factors for its implementation.

© 2010 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2010 (3)

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

D. Stutman, M. Finkenthal, and N. Moldovan, “Development of microperiodic mirrors for hard x-ray phase-contrast imaging,” Appl. Opt. 49(25), 4677–4686 (2010).
[CrossRef] [PubMed]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

2009 (3)

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[CrossRef] [PubMed]

2008 (3)

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of X-ray scattering--initial results,” IEEE Trans. Med. Imaging 27(8), 997–1002 (2008).
[CrossRef] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

D. Noda, M. Tanaka, K. Shimada, W. Yashiro, A. Momose, and T. Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–1315 (2008).
[CrossRef]

2005 (1)

2002 (1)

C. David, B. Nohammer, 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]

2000 (1)

1997 (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

1996 (1)

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

1994 (1)

J. F. Clauser and S. F. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994).
[CrossRef] [PubMed]

1991 (1)

D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, “An interferometer for atoms,” Phys. Rev. Lett. 66(21), 2693–2696 (1991).
[CrossRef] [PubMed]

1982 (1)

1975 (1)

Alferness, R.

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Baumann, J.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Bennett, E. E.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[CrossRef] [PubMed]

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of X-ray scattering--initial results,” IEEE Trans. Med. Imaging 27(8), 997–1002 (2008).
[CrossRef] [PubMed]

Bunk, O.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Carroll, S. C.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of X-ray scattering--initial results,” IEEE Trans. Med. Imaging 27(8), 997–1002 (2008).
[CrossRef] [PubMed]

Chang, B. J.

Chapman, D.

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Chilla, J. L. A.

Clauser, J. F.

J. F. Clauser and S. F. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994).
[CrossRef] [PubMed]

Cloetens, P.

Connor, D.

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

David, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[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]

C. David, B. Nohammer, 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]

Diaz, A.

Ekstrom, C. R.

D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, “An interferometer for atoms,” Phys. Rev. Lett. 66(21), 2693–2696 (1991).
[CrossRef] [PubMed]

Engelhardt, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Filevich, J.

Finkenthal, M.

Fogarty, D. P.

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

Gao, K.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Ge, X.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Gmür, N.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Handa, S.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Hattori, T.

D. Noda, M. Tanaka, K. Shimada, W. Yashiro, A. Momose, and T. Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–1315 (2008).
[CrossRef]

Hegedus, M. M.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[CrossRef] [PubMed]

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of X-ray scattering--initial results,” IEEE Trans. Med. Imaging 27(8), 997–1002 (2008).
[CrossRef] [PubMed]

Hirano, K.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

Hong, Y. L.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Huang, W. X.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Ina, H.

Inagaki, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Ishikawa, T.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Itai, Y.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

Johnston, R. E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Kanizay, K.

Keith, D. W.

D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, “An interferometer for atoms,” Phys. Rev. Lett. 66(21), 2693–2696 (1991).
[CrossRef] [PubMed]

Khelashvili, G.

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

Kimura, T.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Kobayashi, S.

Kottler, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Leith, E. N.

Li, J.

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

Li, S. F.

J. F. Clauser and S. F. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994).
[CrossRef] [PubMed]

Liu, X. S.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Marconi, M. C.

Matsuyama, S.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Menk, R.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Mimura, H.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Moldovan, N.

Momose, A.

D. Noda, M. Tanaka, K. Shimada, W. Yashiro, A. Momose, and T. Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–1315 (2008).
[CrossRef]

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

Muehleman, C.

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

Nesch, I.

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

Nishino, Y.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Noda, D.

D. Noda, M. Tanaka, K. Shimada, W. Yashiro, A. Momose, and T. Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–1315 (2008).
[CrossRef]

Nohammer, B.

C. David, B. Nohammer, 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]

Parham, C.

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

Pfeiffer, F.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[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]

Pisano, E.

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Pritchard, D. E.

D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, “An interferometer for atoms,” Phys. Rev. Lett. 66(21), 2693–2696 (1991).
[CrossRef] [PubMed]

Rapacchi, S.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[CrossRef] [PubMed]

Reinhart, B.

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

Rocca, J. J.

Sano, Y.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Sayers, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Schroer, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Schuster, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Shimada, K.

D. Noda, M. Tanaka, K. Shimada, W. Yashiro, A. Momose, and T. Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–1315 (2008).
[CrossRef]

Solak, H. H.

C. David, B. Nohammer, 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.

Stutman, D.

Takeda, M.

Takeda, T.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

Tamasaku, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Tanaka, M.

D. Noda, M. Tanaka, K. Shimada, W. Yashiro, A. Momose, and T. Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–1315 (2008).
[CrossRef]

Thomlinson, W.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Turchette, Q. A.

D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, “An interferometer for atoms,” Phys. Rev. Lett. 66(21), 2693–2696 (1991).
[CrossRef] [PubMed]

Tzvetkov, T.

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

Walus, A. C.

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

Wang, Z. L.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Washburn, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Weitkamp, T.

Wen, H.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[CrossRef] [PubMed]

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of X-ray scattering--initial results,” IEEE Trans. Med. Imaging 27(8), 997–1002 (2008).
[CrossRef] [PubMed]

Wu, Z. Y.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Yabashi, M.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Yamakawa, D.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Yamamura, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Yamauchi, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Yashiro, W.

D. Noda, M. Tanaka, K. Shimada, W. Yashiro, A. Momose, and T. Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–1315 (2008).
[CrossRef]

Yokoyama, H.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Yuan, Q. X.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Yumoto, H.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Zhang, H. T.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Zhang, K.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Zhong, Z.

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Zhu, P. P.

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Ziegler, E.

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]

C. David, B. Nohammer, 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]

Acad. Radiol. (1)

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

Anal. Bioanal. Chem. (1)

Z. L. Wang, P. P. Zhu, W. X. Huang, Q. X. Yuan, X. S. Liu, K. Zhang, Y. L. Hong, H. T. Zhang, X. Ge, K. Gao, and Z. Y. Wu, “Analysis of polychromaticity effects in X-ray Talbot interferometer,” Anal. Bioanal. Chem. 397(6), 2137–2141 (2010).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. David, B. Nohammer, 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]

IEEE Trans. Med. Imaging (1)

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of X-ray scattering--initial results,” IEEE Trans. Med. Imaging 27(8), 997–1002 (2008).
[CrossRef] [PubMed]

J. Microsc. (1)

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Microsyst. Technol. (1)

D. Noda, M. Tanaka, K. Shimada, W. Yashiro, A. Momose, and T. Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–1315 (2008).
[CrossRef]

Nat. Med. (1)

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

Nat. Phys. (1)

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard x-ray focusing,” Nat. Phys. 6(2), 57–60 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Med. Biol. (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Phys. Rev. A (1)

J. F. Clauser and S. F. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, “An interferometer for atoms,” Phys. Rev. Lett. 66(21), 2693–2696 (1991).
[CrossRef] [PubMed]

Radiology (1)

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

I. Nesch, D. P. Fogarty, T. Tzvetkov, B. Reinhart, A. C. Walus, G. Khelashvili, C. Muehleman, and D. Chapman, “The design and application of an in-laboratory diffraction-enhanced x-ray imaging instrument,” Rev. Sci. Instrum. 80(9), 093702 (2009).
[CrossRef] [PubMed]

Other (1)

L. A. Sayce, and A. Franks, “N.P.L. Gratings for X-Ray Spectroscopy,” Proc. R. Soc. London 282, 353- + (1964).

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Figures (9)

Fig. 1
Fig. 1

Setup of the dual phase grating grazing angle Mach-Zehnder interferometer (not to scale). White light from the flashlight is first reflected by a phase grating G1 of 1.0 mm period, then by another phase grating G2 of 0.5 mm period. The interference fringes at the image plane are recorded by a camera. The grating surfaces and the image plane are all parallel to the XY plane, while the image plane and grating G1 are coplanar. The grating lines are all parallel to the Y axis. Due to the grazing angle incidence, the effective grating period of G2 is approximately Psinθ. The two aperture slits are used to control the spread of the grazing angle and the width of the illuminated area on the grating G1.

Fig. 2
Fig. 2

Schematics of light diffraction in the dual-phase-grating grazing angle interferometer. The grazing angle θ shown here is much larger than the actual values for clear illustration. Inset: the reflective gratings are viewed as equivalent transmission gratings, such that the transmitted waves are exact mirror images of the actual reflected waves. The first grating G1 splits the incident beam into diffracted beams of orders m. Each is further split by the second grating according to diffraction orders n. It can be seen that the (m = −1,n = 1) and (m = 1,n = −1) pair of beams each have the exact same path length together forms a parallelogram. Equal pathway length and parallelogram formation is independent of the incidence angle and wavelength. The two beams interfere at the image plane to give fringes of 100% visibility, which is defined as (Imax-Imin)/(Imax + Imin). The positions of the interference zones (Im,n ) are dependent on the incidence angle. High fringe visibility is maintained if the I -1,1 zone does not substantially overlap with neighboring zones. For direct derivation of wave propagation see Eq. (1)(5).

Fig. 3
Fig. 3

Illustration of the overlap of interference zones of different orders with a spread of incidence angles. The various interference zones have phase-locked fringes but different levels of visibility. The central I -1,1 zone has the highest fringe visibility of 100%, and the peripheral zones have lower fringe contrast. A finite source can be viewed as producing beams of a range of incidence angles. They are incoherent to each other such that their intensity patterns on the image plane simply add to each other. Here two sets of diffracted beams from incidence angles θ 1 and θ 2 are shown in red and maroon. The central I -1,1 zone of the red beams overlap the I -3,-1 zone of the maroon beams, and vice versa.

Fig. 4
Fig. 4

The fabrication process of the phase gratings. An initial 1.0 µm of aluminum was deposited on a silica optical flat substrate. A grid pattern of photoresist was laid on the Al layer by photolithography. After etching away the unprotected Al, the photoresist was removed. An over layer of 0.1 µm Al was finally deposited to make the surface fully reflective. The height step d introduces the desired phase shift for a given incidence angle.

Fig. 5
Fig. 5

Measured intensity distribution of the diffraction pattern of a single phase grating. The incidence light was a collimated green beam. Ideally the zeroth order peak should have zero intensity. The measured area under the zeroth order peak is 10% of the + 1 and −1 peaks.

Fig. 6
Fig. 6

Placement of the imaged object for absolute phase delay and differential phase contrast imaging. The two diffracted beams drawn in orange and green are the (1, −1) and (−1, 1) diffractions from an incident beam of grazing angle θ. They interfere coherently at the image plane to produce fringes. In the absolute phase measurement setting, the maroon beam is used as the object beam and the green beam the reference beam. The sample is placed in object beam and as near as possible to the G2 grating so as not to intersect the reference beam. The resulting fringe shifts represent the absolute phase delay in the object relative to air. In the differential phase contrast setting, the object is placed in the intersecting zone of the two beams near the image plane, where the fringe shifts represent the local difference in phase delay between the two beams.

Fig. 7
Fig. 7

Interferograms with narrow and wide divergence of the incidence angle. (a) At 5 milliradian spread of the incidence angles, the interference zones of different beam pairs are separated. (b) Magnified view of the central zone shows high contrast fringes. The “waviness” of the fringes comes from the imperfect flatness of the image screen. (c) Intensity plot of the central fringes show a fringe visibility of 78%. (d) At 20 milliradian spread of the incidence angles, the interference zones merge into an area of relatively uniform brightness and fringe visibility. (e) Magnified view of the central region and (f) intensity plot show decreased fringe visibility relative to the narrow angle setting.

Fig. 8
Fig. 8

(a) A patch of oil between two glass slides was placed in one of the two interfering beams to produce this interferogram. The fringes within the oil patch appear to be uniformly shifted to the right relative to the fringes outside the patch. (b) Absolute phase shift map obtained through Fourier fringe analysis quantifies the amount of fringe shift in the oil film, and shows the corresponding phase delay of the transmitted light. (c) A differential phase-contrast image of a clear acrylic layer on a glass slide shows fringe distortions due to gradients of phase shifts, which come from thickness variations of the layer. (d) Another way to show the uneven thickness of the acrylic layer is this photo of a grid pattern taken under normal room lighting. The glass slide with the acrylic layer was positioned at 2 cm in front of the grid. The acrylic layer is highlighted by the red line. Light refraction due to the uneven thickness causes the visible bending of the grid lines, which corroborates the inteferogram of (c).

Fig. 9
Fig. 9

Calculated grating phase shift and visibility of the interference fringes for a range of grazing angles and x-ray energy. The left graph is a contour plot superimposed on a gray scale representation of the phase shift induced by the height step in the grating. The right graph shows the corresponding fringe visibility. The fringe visibility is expected to be between 60% and 100% for x-ray energy between 25 keV and 40 keV.

Tables (1)

Tables Icon

Table 1 Design parameters of the x-ray grazing angle interferometer

Equations (11)

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T 1 = m = odd integers B m exp [ i π P m x ] , T 2 = n = odd integers C n exp [ i 2 π P n x ] ,
A ( x ) = m , n A 0 B m C n exp { i [ k cos θ + m π P + 2 π n P ) ] x } exp [ i ϕ Z ( m , n ) ] ,
ϕ Z ( m , n ) = { k 2 ( k cos θ + m π P ) 2 + k 2 ( k cos θ + m π P + 2 π n P ) 2 } h .
ϕ Z ( m 1 , 1 ) = ϕ Z ( m + 1 , 1 ) .
I m 1 , m + 1 = A m 1 , 1 A * m + 1 , 1 + A * m 1 , 1 A m + 1 , 1 + A m 1 , 1 A * m 1 , 1 + A m + 1 , 1 A * m + 1 , 1 = A 0 2 [ B m 1 C 1 B * m + 1 C * 1 exp ( i 2 π P x ) + B * m 1 C * 1 B m + 1 C 1 exp ( i 2 π P x ) + | B m 1 C 1 | 2 + | B m + 1 C 1 | 2 ] .
I 1 , 1 = A 0 2 32 π 4 [ 1 + cos ( 2 π P x ) ] ,
Δ θ S 2 cos ( θ ) / ( L S 2 L S 1 ) ;
Δ L 1 S 1 cos ( θ ) ( 1 L S 1 / L S 2 ) / θ + L S 1 Δ θ / θ .
d = λ / ( 4  sin θ ) ,
Δ X ( x ' , y ' ) P = 1 λ Light  path  in  object [ n ( x , y , z ) 1 ] d x ,
Δ X ( x ' , y ' ) P = 2 D θ P Light  path  in  object z n ( x , y , z ) d x ,

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