Abstract

By using a dynamically phase-controlled screen proposed in [Opt. Express 25, 22789 (2017)], we demonstrated experimentally a correlation imaging scheme with its spatial resolution reaching the fundamental Heisenberg limit. In the experiments, the dynamically phase-controlled screen was realized through a commercial spatial light modulator by dynamically loading computer generated phase patterns, and the scanning-focused-beam illumination mode was employed to achieve the Heisenberg-resolution imaging with classical light such as laser and pseudo-thermal light.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  2. Y. Shih, An Introduction to Quantum Optics (CRC press, 2011).
  3. F. R. S. Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” The London, Edinburgh, Dublin Philos. Mag. J. Sci. 8(49), 261–274 (1879).
  4. D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106(17), 171104 (2015).
  5. T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. United States Am. 106(52), 22287–22292 (2009).
  6. J.-E. Oh, Y.-W. Cho, G. Scarcelli, and Y.-H. Kim, “Sub-Rayleigh imaging via speckle illumination,” Opt. Lett. 38(5), 682–684 (2013).
  7. D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
  8. E. Zhang, H. Lin, W. Liu, Q. Li, and P. Chen, “Sub-Rayleigh-diffraction imaging via modulating classical light,” Opt. Express 23(26), 33506–33513 (2015).
  9. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
  10. 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).
  11. S. Mouradian, F. N. C. Wong, and J. H. Shapiro, “Achieving sub-Rayleigh resolution via thresholding,” Opt. Express 19(6), 5480–5488 (2011).
  12. P. Hong and G. Zhang, “Heisenberg-resolution imaging through a phase-controlled screen,” Opt. Express 25(19), 22789–22796 (2017).
  13. M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, “Super-resolution quantum imaging at the Heisenberg limit,” arXiv preprint arXiv:1712.02200 (2018).
  14. M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102(25), 253601 (2009).
  15. W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919–926 (1964).

2017 (1)

2015 (2)

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

E. Zhang, H. Lin, W. Liu, Q. Li, and P. Chen, “Sub-Rayleigh-diffraction imaging via modulating classical light,” Opt. Express 23(26), 33506–33513 (2015).

2014 (1)

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

2013 (1)

2011 (1)

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).

2009 (3)

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

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. United States Am. 106(52), 22287–22292 (2009).

M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102(25), 253601 (2009).

1964 (1)

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919–926 (1964).

1879 (1)

F. R. S. Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” The London, Edinburgh, Dublin Philos. Mag. J. Sci. 8(49), 261–274 (1879).

Bessire, B.

M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, “Super-resolution quantum imaging at the Heisenberg limit,” arXiv preprint arXiv:1712.02200 (2018).

Born, M.

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

Brida, G.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

Chen, P.

Cho, Y.-W.

Colyer, R.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. United States Am. 106(52), 22287–22292 (2009).

Degiovanni, I. P.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

Dertinger, T.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. United States Am. 106(52), 22287–22292 (2009).

Enderlein, J.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. United States Am. 106(52), 22287–22292 (2009).

Forneris, J.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

Gasparini, L.

M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, “Super-resolution quantum imaging at the Heisenberg limit,” arXiv preprint arXiv:1712.02200 (2018).

Gatto Monticone, D.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

Genovese, M.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

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).

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).

Hong, P.

Iyer, G.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. United States Am. 106(52), 22287–22292 (2009).

Katamadze, K.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

Kim, Y.-H.

Li, H.-G.

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

Li, Q.

Lin, H.

Liu, W.

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).

Lord Rayleigh, F. R. S.

F. R. S. Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” The London, Edinburgh, Dublin Philos. Mag. J. Sci. 8(49), 261–274 (1879).

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).

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

Martienssen, W.

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919–926 (1964).

Moreva, E.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

Mouradian, S.

Oh, J.-E.

Olivero, P.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

Perenzoni, M.

M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, “Super-resolution quantum imaging at the Heisenberg limit,” arXiv preprint arXiv:1712.02200 (2018).

Ruo-Berchera, I.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

Scarcelli, 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).

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).

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

Shih, Y.

Y. Shih, An Introduction to Quantum Optics (CRC press, 2011).

Song, X.-B.

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

Spiller, E.

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919–926 (1964).

Stefanov, A.

M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, “Super-resolution quantum imaging at the Heisenberg limit,” arXiv preprint arXiv:1712.02200 (2018).

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).

Traina, P.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

Tsang, M.

M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102(25), 253601 (2009).

Unternährer, M.

M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, “Super-resolution quantum imaging at the Heisenberg limit,” arXiv preprint arXiv:1712.02200 (2018).

Wang, H.-B.

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

Wang, K.

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

Weiss, S.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. United States Am. 106(52), 22287–22292 (2009).

Wolf, E.

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

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).

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).

Xiong, J.

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

Xu, D.-Q.

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

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).

Zhang, D.-J.

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

Zhang, E.

Zhang, G.

Am. J. Phys. (1)

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919–926 (1964).

Appl. Phys. Lett. (1)

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

Opt. Express (3)

Opt. Lett. (1)

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).

Phys. Rev. Lett. (3)

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).

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).

M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102(25), 253601 (2009).

Proc. Natl. Acad. Sci. United States Am. (1)

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Natl. Acad. Sci. United States Am. 106(52), 22287–22292 (2009).

The London, Edinburgh, Dublin Philos. Mag. J. Sci. (1)

F. R. S. Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” The London, Edinburgh, Dublin Philos. Mag. J. Sci. 8(49), 261–274 (1879).

Other (3)

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

Y. Shih, An Introduction to Quantum Optics (CRC press, 2011).

M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, “Super-resolution quantum imaging at the Heisenberg limit,” arXiv preprint arXiv:1712.02200 (2018).

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Figures (5)

Fig. 1
Fig. 1 The schematics of the Heisenberg-resolution imaging scheme by replacing the conventional imaging lens with a PCS.
Fig. 2
Fig. 2 Schematic diagram of the experimental setup for the Heisenberg-resolution imaging scheme. The inset at the left-bottom corner shows the standard resolution target in which four vertical stripes indicated by the red arrows were selected as the objects used in the experiments. L1, L2, L3: lenses; BS: beam splitter. See text for explanation of other elements.
Fig. 3
Fig. 3 The PSF of both the Heisenberg-resolution imaging scheme (a) and the conventional lens-assisted imaging scheme (b). Here, the empty black circles are the experimental data in both cases, and the red solid curves are the theoretical fits using Eq. (2) in (a) by setting A(x0) = δ(x0) and Eq. (1) in (b), respectively.
Fig. 4
Fig. 4 Images of the stripe objects with RN = 2.5 (a), 3.6 (b), 5.0 (c) and 6.3 (d), respectively, in the conventional lens-assisted and the Heisenberg-resolution imaging schemes. The blue empty circles and dashed curves are the experimental data and the theoretical fits in the conventional lens-assisted imaging scheme, while the red empty squares and solid curves are those in the Heisenberg-resolution imaging scheme, respectively. The gray blocks at the bottom represent the opaque stripes in the corresponding objects.
Fig. 5
Fig. 5 The PSF (a) and images of the stripe objects with RN = 3.6 (b), 4.5 (c) and 5.0 (d) in the Heisenberg-resolution imaging scheme with a pseudo-thermal light. Here the spatial resolution of the stripe object with RN = 4.5 is 222 µm. The circles are the experimental data, and the red solid curves are the theoretical fits using Eq. (2). The gray blocks at the bottom of (b)-(d) represent the opaque stripes in the objects.

Equations (2)

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I ( x ) somb 2 ( k NA | x o + x m | ) ,
g ( 2 ) ( x ) | A ( x o ) | 4 ( 1 + 1 2 somb 2 ( 2 k NA | x o + x m | ) ) d x o ,

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