Abstract

The spatial resolution of a traditional imaging system is restricted by the Rayleigh diffraction limit. In this paper, two types of classical light sources are generated by modulating the amplitude distribution and wavefront of a laser beam randomly, and the generated light sources can exhibit the features of the superposition of two-photon Fock states and the incoherent mixture of two-photon Fock states, respectively. With the generated light sources, the two-fold coherent and incoherent imaging schemes can be achieved, which lead to spatial resolution enhancement, and exceed the Rayleigh diffraction limit in the imaging system.

© 2015 Optical Society of America

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References

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  1. G. Brooker, Modern Classical Optics (Oxford University, 2003).
  2. C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24(10), 1051–1073 (1977).
    [Crossref]
  3. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994).
    [Crossref] [PubMed]
  4. M. Tsang, “Quantum Imaging beyond the Diffraction Limit by Optical Centroid Measurements,” Phys. Rev. Lett. 102(25), 253601 (2009).
    [Crossref] [PubMed]
  5. H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum Spatial Superresolution by Optical Centroid Measurements,” Phys. Rev. Lett. 107(8), 083603 (2011).
    [Crossref] [PubMed]
  6. L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
    [Crossref] [PubMed]
  7. P. L. Zhang, W. L. Gong, X. Shen, D. J. Huang, and S. S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34(8), 1222–1224 (2009).
    [Crossref] [PubMed]
  8. J. E. Oh, Y. W. Cho, G. Scarelli, and Y. H. Kim, “Sub-Rayleigh imaging via speckle illumination,” Opt. Lett. 38(5), 682–684 (2013).
    [Crossref] [PubMed]
  9. A. D. Rodríguez, P. Clemente, E. Irles, E. Tajahuerce, and J. Lancis, “Resolution analysis in computational imaging with patterned illumination and bucket detection,” Opt. Lett. 39(13), 3888–3891 (2014).
    [Crossref] [PubMed]
  10. X. R. Yao, L. Z. Li, X. F. Liu, W. K. Yu, and G. J. Zhai, “Sub-Rayleigh limit imaging via intensity correlation measurements,” Chin. Phys. B 24(4), 044203 (2015).
    [Crossref]
  11. E. F. Zhang, W. T. Liu, and P. X. Chen, “High-resolution interference with programmable classical incoherent light,” J. Opt. Soc. Am. A 32(7), 1251–1255 (2015).
    [Crossref]
  12. E. F. Zhang, W. T. Liu, and P. X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
    [Crossref]
  13. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
    [Crossref] [PubMed]
  14. M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-Photon Diffraction and Quantum Lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
    [Crossref]
  15. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
    [Crossref]
  16. F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh Imaging via N-Photon Detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
    [Crossref]
  17. S. Mouradian, F. N. C. Wong, and J. H. Shapiro, “Achieving sub-Rayleigh resolution via thresholding,” Opt. Express 19(6), 5480–5488 (2011).
    [Crossref] [PubMed]
  18. D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
    [Crossref]
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1988).
  20. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
    [Crossref]
  21. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
    [Crossref]
  22. R. J. Glauber, “The Quantum Theory of Optical Coherence,” Phys. Rev. 130(6), 2529–2539 (1963).
    [Crossref]
  23. R. J. Glauber, “Coherent and Incoherent States of the Radiation Field,” Phys. Rev. 131, (6)2766–2788 (1963).
    [Crossref]
  24. S. Kosmeier, M. Mazilu, J. Baumgartl, and K. Dholakia, “Enhanced two-point resolution using optical eigenmode optimized pupil functions,” J. Opt. 13(10), 105707 (2011).
    [Crossref]
  25. R. Loudon, The Quantum Theory of Light (Clarendon, 1983).

2015 (4)

X. R. Yao, L. Z. Li, X. F. Liu, W. K. Yu, and G. J. Zhai, “Sub-Rayleigh limit imaging via intensity correlation measurements,” Chin. Phys. B 24(4), 044203 (2015).
[Crossref]

E. F. Zhang, W. T. Liu, and P. X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
[Crossref]

E. F. Zhang, W. T. Liu, and P. X. Chen, “High-resolution interference with programmable classical incoherent light,” J. Opt. Soc. Am. A 32(7), 1251–1255 (2015).
[Crossref]

2014 (2)

A. D. Rodríguez, P. Clemente, E. Irles, E. Tajahuerce, and J. Lancis, “Resolution analysis in computational imaging with patterned illumination and bucket detection,” Opt. Lett. 39(13), 3888–3891 (2014).
[Crossref] [PubMed]

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
[Crossref] [PubMed]

2013 (1)

2011 (3)

S. Mouradian, F. N. C. Wong, and J. H. Shapiro, “Achieving sub-Rayleigh resolution via thresholding,” Opt. Express 19(6), 5480–5488 (2011).
[Crossref] [PubMed]

S. Kosmeier, M. Mazilu, J. Baumgartl, and K. Dholakia, “Enhanced two-point resolution using optical eigenmode optimized pupil functions,” J. Opt. 13(10), 105707 (2011).
[Crossref]

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum Spatial Superresolution by Optical Centroid Measurements,” Phys. Rev. Lett. 107(8), 083603 (2011).
[Crossref] [PubMed]

2010 (1)

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh Imaging via N-Photon Detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

2009 (3)

P. L. Zhang, W. L. Gong, X. Shen, D. J. Huang, and S. S. Han, “Improving resolution by the second-order correlation of light fields,” Opt. Lett. 34(8), 1222–1224 (2009).
[Crossref] [PubMed]

M. Tsang, “Quantum Imaging beyond the Diffraction Limit by Optical Centroid Measurements,” Phys. Rev. Lett. 102(25), 253601 (2009).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

2001 (1)

M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-Photon Diffraction and Quantum Lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[Crossref]

2000 (1)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref] [PubMed]

1994 (1)

1977 (1)

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24(10), 1051–1073 (1977).
[Crossref]

1963 (2)

R. J. Glauber, “The Quantum Theory of Optical Coherence,” Phys. Rev. 130(6), 2529–2539 (1963).
[Crossref]

R. J. Glauber, “Coherent and Incoherent States of the Radiation Field,” Phys. Rev. 131, (6)2766–2788 (1963).
[Crossref]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref] [PubMed]

Bateman, J. D.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
[Crossref] [PubMed]

Baumgartl, J.

S. Kosmeier, M. Mazilu, J. Baumgartl, and K. Dholakia, “Enhanced two-point resolution using optical eigenmode optimized pupil functions,” J. Opt. 13(10), 105707 (2011).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref] [PubMed]

Boyd, R. W.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum Spatial Superresolution by Optical Centroid Measurements,” Phys. Rev. Lett. 107(8), 083603 (2011).
[Crossref] [PubMed]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref] [PubMed]

Brooker, G.

G. Brooker, Modern Classical Optics (Oxford University, 2003).

Chan, K. W. C.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum Spatial Superresolution by Optical Centroid Measurements,” Phys. Rev. Lett. 107(8), 083603 (2011).
[Crossref] [PubMed]

Chang, H. J.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum Spatial Superresolution by Optical Centroid Measurements,” Phys. Rev. Lett. 107(8), 083603 (2011).
[Crossref] [PubMed]

Chekhova, M. V.

M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-Photon Diffraction and Quantum Lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[Crossref]

Chen, P. X.

E. F. Zhang, W. T. Liu, and P. X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

E. F. Zhang, W. T. Liu, and P. X. Chen, “High-resolution interference with programmable classical incoherent light,” J. Opt. Soc. Am. A 32(7), 1251–1255 (2015).
[Crossref]

Cho, Y. W.

Choudhury, A.

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24(10), 1051–1073 (1977).
[Crossref]

Clemente, P.

D’Angelo, M.

M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-Photon Diffraction and Quantum Lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[Crossref]

Dholakia, K.

S. Kosmeier, M. Mazilu, J. Baumgartl, and K. Dholakia, “Enhanced two-point resolution using optical eigenmode optimized pupil functions,” J. Opt. 13(10), 105707 (2011).
[Crossref]

Dowling, J. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref] [PubMed]

Feizpour, A.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
[Crossref] [PubMed]

Giovannetti, V.

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Glauber, R. J.

R. J. Glauber, “The Quantum Theory of Optical Coherence,” Phys. Rev. 130(6), 2529–2539 (1963).
[Crossref]

R. J. Glauber, “Coherent and Incoherent States of the Radiation Field,” Phys. Rev. 131, (6)2766–2788 (1963).
[Crossref]

Gong, W. L.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1988).

Guerrieri, F.

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh Imaging via N-Photon Detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

Han, S. S.

Hayat, A.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
[Crossref] [PubMed]

Hell, S. W.

Huang, D. J.

Irles, E.

Kim, Y. H.

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref] [PubMed]

Kosmeier, S.

S. Kosmeier, M. Mazilu, J. Baumgartl, and K. Dholakia, “Enhanced two-point resolution using optical eigenmode optimized pupil functions,” J. Opt. 13(10), 105707 (2011).
[Crossref]

Lancis, J.

Li, H. G.

D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
[Crossref]

Li, L. Z.

X. R. Yao, L. Z. Li, X. F. Liu, W. K. Yu, and G. J. Zhai, “Sub-Rayleigh limit imaging via intensity correlation measurements,” Chin. Phys. B 24(4), 044203 (2015).
[Crossref]

Liu, W. T.

E. F. Zhang, W. T. Liu, and P. X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

E. F. Zhang, W. T. Liu, and P. X. Chen, “High-resolution interference with programmable classical incoherent light,” J. Opt. Soc. Am. A 32(7), 1251–1255 (2015).
[Crossref]

Liu, X. F.

X. R. Yao, L. Z. Li, X. F. Liu, W. K. Yu, and G. J. Zhai, “Sub-Rayleigh limit imaging via intensity correlation measurements,” Chin. Phys. B 24(4), 044203 (2015).
[Crossref]

Lloyd, S.

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Clarendon, 1983).

Maccone, L.

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh Imaging via N-Photon Detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Mahler, D. H.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
[Crossref] [PubMed]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[Crossref]

Mazilu, M.

S. Kosmeier, M. Mazilu, J. Baumgartl, and K. Dholakia, “Enhanced two-point resolution using optical eigenmode optimized pupil functions,” J. Opt. 13(10), 105707 (2011).
[Crossref]

Mouradian, S.

Oh, J. E.

Okamoto, R.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
[Crossref] [PubMed]

Rodríguez, A. D.

Rozema, L. A.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
[Crossref] [PubMed]

Scarelli, G.

Shapiro, J. H.

S. Mouradian, F. N. C. Wong, and J. H. Shapiro, “Achieving sub-Rayleigh resolution via thresholding,” Opt. Express 19(6), 5480–5488 (2011).
[Crossref] [PubMed]

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh Imaging via N-Photon Detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Shen, X.

Sheppard, C. J. R.

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24(10), 1051–1073 (1977).
[Crossref]

Shih, Y. H.

M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-Photon Diffraction and Quantum Lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[Crossref]

Shin, H.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum Spatial Superresolution by Optical Centroid Measurements,” Phys. Rev. Lett. 107(8), 083603 (2011).
[Crossref] [PubMed]

Song, X. B.

D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
[Crossref]

Steinberg, A. M.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
[Crossref] [PubMed]

Tajahuerce, E.

Tisa, S.

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh Imaging via N-Photon Detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

Tsang, M.

M. Tsang, “Quantum Imaging beyond the Diffraction Limit by Optical Centroid Measurements,” Phys. Rev. Lett. 102(25), 253601 (2009).
[Crossref] [PubMed]

Wang, H. B.

D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
[Crossref]

Wang, K. G.

D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
[Crossref]

Wichmann, J.

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref] [PubMed]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[Crossref]

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Wong, F. N. C.

S. Mouradian, F. N. C. Wong, and J. H. Shapiro, “Achieving sub-Rayleigh resolution via thresholding,” Opt. Express 19(6), 5480–5488 (2011).
[Crossref] [PubMed]

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh Imaging via N-Photon Detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

Xiong, J.

D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
[Crossref]

Xu, D. Q.

D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
[Crossref]

Yao, X. R.

X. R. Yao, L. Z. Li, X. F. Liu, W. K. Yu, and G. J. Zhai, “Sub-Rayleigh limit imaging via intensity correlation measurements,” Chin. Phys. B 24(4), 044203 (2015).
[Crossref]

Yu, W. K.

X. R. Yao, L. Z. Li, X. F. Liu, W. K. Yu, and G. J. Zhai, “Sub-Rayleigh limit imaging via intensity correlation measurements,” Chin. Phys. B 24(4), 044203 (2015).
[Crossref]

Zappa, F.

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh Imaging via N-Photon Detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

Zhai, G. J.

X. R. Yao, L. Z. Li, X. F. Liu, W. K. Yu, and G. J. Zhai, “Sub-Rayleigh limit imaging via intensity correlation measurements,” Chin. Phys. B 24(4), 044203 (2015).
[Crossref]

Zhang, D. J.

D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
[Crossref]

Zhang, E. F.

E. F. Zhang, W. T. Liu, and P. X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

E. F. Zhang, W. T. Liu, and P. X. Chen, “High-resolution interference with programmable classical incoherent light,” J. Opt. Soc. Am. A 32(7), 1251–1255 (2015).
[Crossref]

Zhang, P. L.

Appl. Phys. Lett. (1)

D. Q. Xu, X. B. Song, H. G. Li, D. J. Zhang, H. B. Wang, J. Xiong, and K. G. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
[Crossref]

Chin. Phys. B (1)

X. R. Yao, L. Z. Li, X. F. Liu, W. K. Yu, and G. J. Zhai, “Sub-Rayleigh limit imaging via intensity correlation measurements,” Chin. Phys. B 24(4), 044203 (2015).
[Crossref]

J. Opt. (2)

E. F. Zhang, W. T. Liu, and P. X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

S. Kosmeier, M. Mazilu, J. Baumgartl, and K. Dholakia, “Enhanced two-point resolution using optical eigenmode optimized pupil functions,” J. Opt. 13(10), 105707 (2011).
[Crossref]

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

Opt. Acta (1)

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24(10), 1051–1073 (1977).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. (2)

R. J. Glauber, “The Quantum Theory of Optical Coherence,” Phys. Rev. 130(6), 2529–2539 (1963).
[Crossref]

R. J. Glauber, “Coherent and Incoherent States of the Radiation Field,” Phys. Rev. 131, (6)2766–2788 (1963).
[Crossref]

Phys. Rev. A (1)

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Phys. Rev. Lett. (6)

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh Imaging via N-Photon Detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[Crossref] [PubMed]

M. D’Angelo, M. V. Chekhova, and Y. H. Shih, “Two-Photon Diffraction and Quantum Lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[Crossref]

M. Tsang, “Quantum Imaging beyond the Diffraction Limit by Optical Centroid Measurements,” Phys. Rev. Lett. 102(25), 253601 (2009).
[Crossref] [PubMed]

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum Spatial Superresolution by Optical Centroid Measurements,” Phys. Rev. Lett. 107(8), 083603 (2011).
[Crossref] [PubMed]

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable Spatial Superresolution Using Entangled Photons,” Phys. Rev. Lett. 112(22), 223602 (2014).
[Crossref] [PubMed]

Other (5)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1988).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[Crossref]

G. Brooker, Modern Classical Optics (Oxford University, 2003).

R. Loudon, The Quantum Theory of Light (Clarendon, 1983).

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Figures (3)

Fig. 1
Fig. 1 The schematic for sub-Rayleigh imaging via modulating classical light.
Fig. 2
Fig. 2 The proof-of-principle experimental setup of the modulator.
Fig. 3
Fig. 3 The simulated results reconstructed by the four different imaging schemes.

Equations (16)

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E ( x i ) = d x o E ( x o ) T ( x o ) h ( x i , x o ) ,
h ( x i , x o ) e i θ somb ( 2 π R | x o + x i / m | λ D o ) ,
I c o h ( x i ) | d x o T ( x o ) h ( x i , x o ) | 2 , I i n c o h ( x i ) d x o | T ( x o ) | 2 | h ( x i , x o ) | 2 ,
a ( x o ) = a 1 ( x o ) | cos [ φ 1 ( x o ) ] | , φ ( x o ) = π Π [ φ 1 ( x o ) ] ,
Π ( x ) = { 0 , x [ 0 , π / 2 ) or [ 3 π / 2 , 2 π ) , 1 , x [ π / 2 , 3 π / 2 ) .
E o * ( x o 1 ) E o * ( x o 2 ) E o ( x o 3 ) E o ( x o 4 ) = a ( x o 1 ) a ( x o 2 ) a ( x o 3 ) a ( x o 4 ) e i [ φ ( x o 1 ) + φ ( x o 2 ) φ ( x o 3 ) φ ( x o 4 ) ] = a 1 2 2 4 [ δ ( x o 1 x o 2 ) δ ( x o 3 x o 4 ) + δ ( x o 1 x o 3 ) δ ( x o 2 x o 4 ) + δ ( x o 1 x o 4 ) δ ( x o 2 x o 3 ) ] .
E o * ( x o 1 ) E o ( x o 2 ) = a 1 2 2 δ ( x o 1 x o 2 ) .
I 2 ( x i ) = [ E i * ( x i ) E i ( x i ) ] 2 = a 1 2 2 4 [ | d x o T 2 ( x o ) h 2 ( x i , x o ) | 2 + 2 ( d x o | T ( x o ) | 2 | h ( x i , x o ) | 2 ) 2 ] , I ( x i ) = E i * ( x i ) E i ( x i ) = a 1 2 2 d x o | T ( x o ) | 2 | h ( x i , x o ) | 2 .
Δ G 1 ( x i ) I 2 ( x i ) 2 I ( x i ) 2 | d x o T 2 ( x o ) h 2 ( x 1 , x o ) | 2 ,
a ( x o ) = a 1 ( x o ) a 2 ( x o ) | cos [ φ 1 ( x o ) ] | , φ ( x o ) = mod { π Π [ φ 1 ( x o ) ] + φ 2 ( x o ) , 2 π } ,
E o * ( x o 1 ) E o * ( x o 2 ) E o ( x o 3 ) E o ( x o 4 ) = a 1 2 2 a 2 2 2 4 [ 4 δ ( x o 1 x o 2 ) δ ( x o 1 x o 3 ) δ ( x o 1 x o 4 ) + δ ( x o 1 x o 3 ) δ ( x o 2 x o 4 ) + δ ( x o 1 x o 4 ) δ ( x o 2 x o 3 ) ] , E o * ( x o 1 ) E o ( x o 2 ) = a 1 2 a 2 2 2 δ ( x o 1 x o 2 ) .
Δ G 2 ( x i ) I 2 ( x i ) 2 I ( x i ) 2 d x o | T 2 ( x o ) | 2 | h 2 ( x i , x o ) | 2 .
Δ G ( x i ) = ( I i ( x i ) I i ( x i ) ) 2 ( d x o | T ( x o ) | 2 | h ( x i , x o ) | 2 ) 2 ,
ρ ( 1 ) = a 1 2 2 d x o | 1 x o 1 x o | , ρ ( 2 ) = a 1 2 4 ( 2 d x o 1 | 1 x o 1 1 x o 1 | d x o 2 | 1 x o 2 1 x o 2 | + d x o 1 | 2 x o 1 d x o 2 2 x o 2 | ) .
Δ G 1 ( x i ) Tr { ρ ( 2 ) [ E ( ) ( x i ) ] 2 [ E ( + ) ( x i ) ] 2 } 2 { Tr [ ρ ( 1 ) E ( ) ( x i ) E ( + ) ( x i ) ] } 2 Tr { d x o 1 | 2 x o 1 d x o 2 2 x o 2 | [ E ( ) ( x i ) ] 2 [ E ( + ) ( x i ) ] 2 } ,
E ( + ) ( x i ) = d x o a ( x o ) T ( x o ) h ( x i , x o ) .

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