Abstract

The theoretical proposal for an improved Talbot imaging technique has been analyzed in a periodic object illuminated by a pseudo-thermal light source and detected only by two detectors in two imaging schemes. The improved effect of lensless grating ghost image and Talbot image quality (fringe resolution and visibility) can be attributed to the higher correlation orders N. While at a certain order N, the spatial resolution of Talbot carpet patterns is determined by two-photon bunching effect, which depends on the positions of the periodic object and two detectors and different detection methods. Moreover, the sub wavelength of spatial correlation peaks and Talbot images obtained, when we use two asynchronous scanning detectors or an accelerated scanning detector. The present imaging schemes have the characteristic of the controllable image visibility and resolution, which has a potential application in periodic image reconstructions, sub wavelength resolution microscopy and sub wavelength atom lithography.

© 2017 Optical Society of America

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References

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  1. H. Talbot, “Facts relating to optical science: No IV,” Philos. Mag. 9, 401–407 (1836).
  2. L. Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
    [Crossref]
  3. M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot Effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
    [Crossref]
  4. X. Song, J. Xiong, X. Zhang, and K. Wang, “Second-order Talbot self-imaging with pseudothermal light,” Phys. Rev. A 82(3), 033823 (2010).
    [Crossref]
  5. K. Luo, X. Chen, Q. Liu, and L. A. Wu, “Nonlocal Talbot self-imaging with incoherent light,” Phys. Rev. A 82(3), 033803 (2010).
    [Crossref]
  6. Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
    [Crossref] [PubMed]
  7. K. Luo, J. Wen, X. Chen, Q. Liu, M. Xiao, and L. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80(4), 043820 (2009).
    [Crossref]
  8. X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011).
    [Crossref] [PubMed]
  9. J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
    [Crossref]
  10. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
    [Crossref] [PubMed]
  11. X. Shi, W. Yang, H. Xing, and X. Chen, “Discrete plasmonic Talbot effect in finite metal waveguide arrays,” Opt. Lett. 40(8), 1635–1638 (2015).
    [Crossref] [PubMed]
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    [Crossref]
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  20. J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
    [Crossref] [PubMed]

2016 (2)

J. A. Salas, K. Varga, J. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93(10), 104305 (2016).
[Crossref]

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

2015 (3)

N. Bender, H. Li, F. M. Ellis, and T. Kottos, “Wave-packet self-imaging and giant recombinations via stable Bloch-Zener oscillations in photonic lattices with local PT symmetry,” Phys. Rev. A 92(4), 041803 (2015).
[Crossref]

Y. Lumer, L. Drori, Y. Hazan, and M. Segev, “Accelerating Self-Imaging: The Airy-Talbot Effect,” Phys. Rev. Lett. 115(1), 013901 (2015).
[Crossref] [PubMed]

X. Shi, W. Yang, H. Xing, and X. Chen, “Discrete plasmonic Talbot effect in finite metal waveguide arrays,” Opt. Lett. 40(8), 1635–1638 (2015).
[Crossref] [PubMed]

2013 (1)

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

2011 (1)

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011).
[Crossref] [PubMed]

2010 (3)

X. Song, J. Xiong, X. Zhang, and K. Wang, “Second-order Talbot self-imaging with pseudothermal light,” Phys. Rev. A 82(3), 033823 (2010).
[Crossref]

K. Luo, X. Chen, Q. Liu, and L. A. Wu, “Nonlocal Talbot self-imaging with incoherent light,” Phys. Rev. A 82(3), 033803 (2010).
[Crossref]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

2009 (2)

K. Luo, J. Wen, X. Chen, Q. Liu, M. Xiao, and L. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80(4), 043820 (2009).
[Crossref]

J. Liu and Y. Shih, “Nth-order coherence of thermal light,” Phys. Rev. A 79(2), 023819 (2009).
[Crossref]

2008 (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

2007 (1)

Y. Bai and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76(4), 043828 (2007).
[Crossref]

2006 (1)

2004 (1)

J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref] [PubMed]

1996 (1)

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot Effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

1881 (1)

L. Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
[Crossref]

1836 (1)

H. Talbot, “Facts relating to optical science: No IV,” Philos. Mag. 9, 401–407 (1836).

Ahmed, I.

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

Bai, Y.

Y. Bai and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76(4), 043828 (2007).
[Crossref]

Bech, M.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Bender, N.

N. Bender, H. Li, F. M. Ellis, and T. Kottos, “Wave-packet self-imaging and giant recombinations via stable Bloch-Zener oscillations in photonic lattices with local PT symmetry,” Phys. Rev. A 92(4), 041803 (2015).
[Crossref]

Berry, M. V.

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot Effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

Bevan, K. H.

J. A. Salas, K. Varga, J. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93(10), 104305 (2016).
[Crossref]

Brönnimann, Ch.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Bunk, O.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Chen, X.

X. Shi, W. Yang, H. Xing, and X. Chen, “Discrete plasmonic Talbot effect in finite metal waveguide arrays,” Opt. Lett. 40(8), 1635–1638 (2015).
[Crossref] [PubMed]

K. Luo, X. Chen, Q. Liu, and L. A. Wu, “Nonlocal Talbot self-imaging with incoherent light,” Phys. Rev. A 82(3), 033803 (2010).
[Crossref]

K. Luo, J. Wen, X. Chen, Q. Liu, M. Xiao, and L. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80(4), 043820 (2009).
[Crossref]

Cheng, J.

J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref] [PubMed]

Chuang, Y. C.

David, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Drori, L.

Y. Lumer, L. Drori, Y. Hazan, and M. Segev, “Accelerating Self-Imaging: The Airy-Talbot Effect,” Phys. Rev. Lett. 115(1), 013901 (2015).
[Crossref] [PubMed]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Ellis, F. M.

N. Bender, H. Li, F. M. Ellis, and T. Kottos, “Wave-packet self-imaging and giant recombinations via stable Bloch-Zener oscillations in photonic lattices with local PT symmetry,” Phys. Rev. A 92(4), 041803 (2015).
[Crossref]

Gao, H.

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Han, S.

Y. Bai and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76(4), 043828 (2007).
[Crossref]

J. Cheng and S. Han, “Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref] [PubMed]

Hazan, Y.

Y. Lumer, L. Drori, Y. Hazan, and M. Segev, “Accelerating Self-Imaging: The Airy-Talbot Effect,” Phys. Rev. Lett. 115(1), 013901 (2015).
[Crossref] [PubMed]

Klein, S.

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot Effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

Kottos, T.

N. Bender, H. Li, F. M. Ellis, and T. Kottos, “Wave-packet self-imaging and giant recombinations via stable Bloch-Zener oscillations in photonic lattices with local PT symmetry,” Phys. Rev. A 92(4), 041803 (2015).
[Crossref]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Li, H.

N. Bender, H. Li, F. M. Ellis, and T. Kottos, “Wave-packet self-imaging and giant recombinations via stable Bloch-Zener oscillations in photonic lattices with local PT symmetry,” Phys. Rev. A 92(4), 041803 (2015).
[Crossref]

Li, Z.

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

Liu, J.

J. Liu and Y. Shih, “Nth-order coherence of thermal light,” Phys. Rev. A 79(2), 023819 (2009).
[Crossref]

Liu, Q.

K. Luo, X. Chen, Q. Liu, and L. A. Wu, “Nonlocal Talbot self-imaging with incoherent light,” Phys. Rev. A 82(3), 033803 (2010).
[Crossref]

K. Luo, J. Wen, X. Chen, Q. Liu, M. Xiao, and L. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80(4), 043820 (2009).
[Crossref]

Liu, Z.

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

Lumer, Y.

Y. Lumer, L. Drori, Y. Hazan, and M. Segev, “Accelerating Self-Imaging: The Airy-Talbot Effect,” Phys. Rev. Lett. 115(1), 013901 (2015).
[Crossref] [PubMed]

Luo, K.

K. Luo, X. Chen, Q. Liu, and L. A. Wu, “Nonlocal Talbot self-imaging with incoherent light,” Phys. Rev. A 82(3), 033803 (2010).
[Crossref]

K. Luo, J. Wen, X. Chen, Q. Liu, M. Xiao, and L. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80(4), 043820 (2009).
[Crossref]

Luo, K. H.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011).
[Crossref] [PubMed]

Pfeiffer, F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Rayleigh, L.

L. Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
[Crossref]

Salas, J. A.

J. A. Salas, K. Varga, J. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93(10), 104305 (2016).
[Crossref]

Segev, M.

Y. Lumer, L. Drori, Y. Hazan, and M. Segev, “Accelerating Self-Imaging: The Airy-Talbot Effect,” Phys. Rev. Lett. 115(1), 013901 (2015).
[Crossref] [PubMed]

Shi, X.

Shih, Y.

J. Liu and Y. Shih, “Nth-order coherence of thermal light,” Phys. Rev. A 79(2), 023819 (2009).
[Crossref]

Song, X.

X. Song, J. Xiong, X. Zhang, and K. Wang, “Second-order Talbot self-imaging with pseudothermal light,” Phys. Rev. A 82(3), 033823 (2010).
[Crossref]

Song, X. B.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011).
[Crossref] [PubMed]

Suleski, T. J.

Talbot, H.

H. Talbot, “Facts relating to optical science: No IV,” Philos. Mag. 9, 401–407 (1836).

Testorf, M.

Varga, K.

J. A. Salas, K. Varga, J. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93(10), 104305 (2016).
[Crossref]

Wang, H.

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

Wang, H. B.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011).
[Crossref] [PubMed]

Wang, K.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011).
[Crossref] [PubMed]

X. Song, J. Xiong, X. Zhang, and K. Wang, “Second-order Talbot self-imaging with pseudothermal light,” Phys. Rev. A 82(3), 033823 (2010).
[Crossref]

Wen, F.

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

Wen, J.

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

K. Luo, J. Wen, X. Chen, Q. Liu, M. Xiao, and L. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80(4), 043820 (2009).
[Crossref]

Wu, L.

K. Luo, J. Wen, X. Chen, Q. Liu, M. Xiao, and L. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80(4), 043820 (2009).
[Crossref]

Wu, L. A.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011).
[Crossref] [PubMed]

K. Luo, X. Chen, Q. Liu, and L. A. Wu, “Nonlocal Talbot self-imaging with incoherent light,” Phys. Rev. A 82(3), 033803 (2010).
[Crossref]

Xiao, M.

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

K. Luo, J. Wen, X. Chen, Q. Liu, M. Xiao, and L. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80(4), 043820 (2009).
[Crossref]

Xing, H.

Xiong, J.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011).
[Crossref] [PubMed]

X. Song, J. Xiong, X. Zhang, and K. Wang, “Second-order Talbot self-imaging with pseudothermal light,” Phys. Rev. A 82(3), 033823 (2010).
[Crossref]

Yan, J.

J. A. Salas, K. Varga, J. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93(10), 104305 (2016).
[Crossref]

Yang, W.

Zhang, X.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011).
[Crossref] [PubMed]

X. Song, J. Xiong, X. Zhang, and K. Wang, “Second-order Talbot self-imaging with pseudothermal light,” Phys. Rev. A 82(3), 033823 (2010).
[Crossref]

Zhang, Y.

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

Zhang, Z.

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

Zhu, S. N.

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

J. Mod. Opt. (1)

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot Effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

Laser Phys. Lett. (1)

F. Wen, Z. Zhang, I. Ahmed, Z. Li, H. Wang, Z. Liu, H. Gao, and Y. Zhang, “Second-order self-imaging with parametric amplification four-wave mixing,” Laser Phys. Lett. 13(7), 075403 (2016).
[Crossref]

Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Philos. Mag. (2)

H. Talbot, “Facts relating to optical science: No IV,” Philos. Mag. 9, 401–407 (1836).

L. Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
[Crossref]

Phys. Rev. A (6)

K. Luo, J. Wen, X. Chen, Q. Liu, M. Xiao, and L. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80(4), 043820 (2009).
[Crossref]

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Phys. Rev. B (1)

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Figures (5)

Fig. 1
Fig. 1 The setup of scheme I (a) and II (b) for high-order Talbot imaging with pseudo-thermal light. GG: ground glass; BE: beam expander; Dp: diaphragm; M1, M2: mirrors; BS: beam splitter.
Fig. 2
Fig. 2 Theoretical results of the grating N-order ghost interference for N = 2, 4, 10 in scheme I, with n = 1 in (a), n = 3 in (b) and n = 5 in (c), respectively. (b) and (c) are density-plots. All curves are normalized by their maximum values.
Fig. 3
Fig. 3 Schematics diagram of the asynchronous scanning method (a1) and the accelerated scanning method (a2). (b1) Measuring g(4)(u1, u2) with u1 = 0 (solid) and u1 = -u2 (dash), respectively, (b2) measuring g(4)(u1, 0) with the scanning speed of D1 is v (solid), 2v (dash) and 3v (dot), respectively.
Fig. 4
Fig. 4 Tenth-order Talbot imaging carpet patterns of scheme I obtained by scanning Di in the transverse x direction and through z1(0~2zT) along the longitudinal z direction. At z2 = 1.5zT and z0 = 0.5zT, (a1) measuring g(10)(u1, 0), (a2) measuring g(10)(0, u2); At z2 = 0.2zT and z0 = 2.5zT, (b1) measuring g(10)(u1, 0), (b2) measuring g(10)(u1 = u2); (c1) and (c2) are same as (b1) except the scanning speed of D1 is increased twice and fourfold, respectively. The color bar denotes the normalized intensity value of the tenth-order correlation function.
Fig. 5
Fig. 5 Tenth-order Talbot lithography carpets of scheme II obtained by scanning Di in the transverse x direction and through z1 (0 to 2zT) along the longitudinal z direction and satisfies the constraint relations z2 = 1/2z1. (a1) Measuring g(10)(u1, 0); (a2) Measuring g(10)(0, u2); (b1) Measuring g(10)(u2,-u2); (b2) is same as (a1) except the scanning speed of D1 is increased fourfold, respectively. The color bar denotes the normalized intensity value of the tenth-order correlation function.

Equations (13)

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C= 1 T d t 1 d t 2 d t N G (N) ( t 1 , u 1 ; t 2 , u 2 ;; t N , u N ) ,
G (N) ( u 1 , u 2 ,, u N )= I( u 1 )I( u 2 )I( u N ) = E () ( u 1 ) E () ( u 2 ) E () ( u N ) E (+) ( u N ) E (+) ( u 2 ) E (+) ( u 1 ) .
g (N) ( u 1 , u 2 ,, u N )= I 1 ( u 1 ) I 2 ( u 2 ) I N ( u N ) I 1 ( u 1 ) I 2 ( u 2 ) I N ( u N ) .
g (N) ( u 1 , u 2 )= I 1 ( u 1 ) I 2 N1 ( u 2 ) I 1 ( u 1 ) I 2 ( u 2 ) N1 =(N1)!+(N1)!(N1) | g (1) ( u 1 , u 2 ) | 2 .
g (1) ( u 1 , u 2 )= d x 1 d x 2 E () ( x 1 ) E (+) ( x 2 ) h 1 + ( x 1 , u 1 )  h 2 ( x 2 , u 2 ) / I 1 ( u 1 ) I 2 ( u 2 ) ,
h 1 ( x 1 , u 1 , z 1 )= dx e ik z 0 iλ z 0 exp[ iπ λ z 0 ( x 1 x) 2 ] T(x) e ik z 1 iλ z 1 exp[ iπ λ z 1 ( u 1 x) 2 ],
h 2 ( x 2 , u 2 , z 2 )= e ik z 2 iλ z 2 exp[ iπ λ z 2 ( x 2 u 2 ) 2 ].
g (1) ( u 1 , u 2 )sinc[ Δθ λ ( u 1 u 2 )].
g (1) ( u 1 , u 2 ,z , 1 z ) 2 = dx I 0 e ik( z 0 z 2 ) iλ( z 0 z 2 ) exp[ iπ λ( z 0 z 2 ) ( u 2 x) 2 ]T(x) e ik z 1 iλ z 1 exp[ iπ λ z 1 ( u 1 x) 2 ].
T(x)= b n exp[i 2πnx a ] ,
g (1) ( u 1 , u 2 ,z , 1 z ) 2 = C 0 n= b n exp[i 2πn a z 1 u 2 +( z 0 z ) 2 u 1 z 1 + z 0 z 2 ] exp[iπλ n 2 a 2 z 1 ( z 0 z ) 2 z 1 + z 0 z 2 ].
h i ( u i , z i )= e ik z i iλ z i dxT(x) exp[ iπ λ z i (x u i ) 2 ](i=1,2).
g (1) ( u 1 , u 2 , z 1 , z 2 )= B 0 b n exp[i2π n a ( u 1 z 2 u 2 z 1 z 1 z 2 )]  exp[iλπ n 2 a 2 ( z 1 z 2 z 1 z 2 )].

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