Abstract

Diffraction from a finite-diameter entrance pupil imposes the Rayleigh bound on the spatial resolution achievable by a conventional imaging system. We demonstrate resolution beyond this limit through unstructured scanning of a focused laser beam across an object together with dynamic application of a threshold N less than the maximum count level Nmax. Experimental results show sub-Rayleigh resolution enhancement by a factor of [ln(Nmax/N)]1/2.

© 2011 Optical Society of America

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  1. L. Rayleigh, “Investigations in optics with special reference to the spectroscope,” Philos. Mag. 8, 261–274 (1879).
  2. C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J. 44, 76–86 (1916).
    [CrossRef]
  3. 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, 2733–2736 (2000).
    [CrossRef] [PubMed]
  4. J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N States,” Contemp. Phys. 49, 125–143 (2008).
    [CrossRef]
  5. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).
    [CrossRef]
  6. M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102, 253601 (2009).
    [CrossRef] [PubMed]
  7. K. Wang and D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70,041801(R) (2004).
    [CrossRef]
  8. P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96, 163603 (2006).
    [CrossRef] [PubMed]
  9. S. J. Bently and R. W. Boyd, “Nonlinear optical lithography with ultra-high sub-Rayleigh resolution,” Opt. Express 12, 5735–5740 (2004).
    [CrossRef]
  10. S. W. Hell, J. Soukka, and P. E. Hänninen, “Two- and multiphoton detection as an imaging mode and means of increasing the resolution in far-field light microscopy: A study based on photon-optics,” Bioimaging 3, 64–69 (1995).
    [CrossRef]
  11. A. J. Pearlman, A. Ling, E. A. Goldschmidt, C. F. Wildfeuer, J. Fan, and A. Migdall, “Enhancing image contrast using coherent states and photon number resolving detectors,” Opt. Express 18, 6033–6039 (2010).
    [CrossRef] [PubMed]
  12. D. Semwogerere and E. R. Weeks, “Confocal microscopy,” in Encyclopedia of Biomaterials and Biomedical Engineering, G. E. Wnek and G. L. Bowlin, eds. (Taylor & Francis, 2005), pp. 705–714.
  13. A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466, 647–651 (2010).
    [CrossRef] [PubMed]
  14. 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, 163602 (2010).
    [CrossRef]

2010 (3)

A. J. Pearlman, A. Ling, E. A. Goldschmidt, C. F. Wildfeuer, J. Fan, and A. Migdall, “Enhancing image contrast using coherent states and photon number resolving detectors,” Opt. Express 18, 6033–6039 (2010).
[CrossRef] [PubMed]

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466, 647–651 (2010).
[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, 163602 (2010).
[CrossRef]

2009 (2)

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

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

2008 (1)

J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N States,” Contemp. Phys. 49, 125–143 (2008).
[CrossRef]

2006 (1)

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

2004 (2)

S. J. Bently and R. W. Boyd, “Nonlinear optical lithography with ultra-high sub-Rayleigh resolution,” Opt. Express 12, 5735–5740 (2004).
[CrossRef]

K. Wang and D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70,041801(R) (2004).
[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, 2733–2736 (2000).
[CrossRef] [PubMed]

1995 (1)

S. W. Hell, J. Soukka, and P. E. Hänninen, “Two- and multiphoton detection as an imaging mode and means of increasing the resolution in far-field light microscopy: A study based on photon-optics,” Bioimaging 3, 64–69 (1995).
[CrossRef]

1916 (1)

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J. 44, 76–86 (1916).
[CrossRef]

1879 (1)

L. Rayleigh, “Investigations in optics with special reference to the spectroscope,” Philos. Mag. 8, 261–274 (1879).

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, 2733–2736 (2000).
[CrossRef] [PubMed]

Bently, S. J.

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, 2733–2736 (2000).
[CrossRef] [PubMed]

Boyd, R. W.

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, 2733–2736 (2000).
[CrossRef] [PubMed]

Cao, D.-Z.

K. Wang and D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70,041801(R) (2004).
[CrossRef]

Chu, S.

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466, 647–651 (2010).
[CrossRef] [PubMed]

Dowling, J. P.

J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N States,” Contemp. Phys. 49, 125–143 (2008).
[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, 2733–2736 (2000).
[CrossRef] [PubMed]

Fan, J.

Giovannetti, V.

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

Goldschmidt, E. A.

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, 163602 (2010).
[CrossRef]

Hänninen, P. E.

S. W. Hell, J. Soukka, and P. E. Hänninen, “Two- and multiphoton detection as an imaging mode and means of increasing the resolution in far-field light microscopy: A study based on photon-optics,” Bioimaging 3, 64–69 (1995).
[CrossRef]

Hell, S. W.

S. W. Hell, J. Soukka, and P. E. Hänninen, “Two- and multiphoton detection as an imaging mode and means of increasing the resolution in far-field light microscopy: A study based on photon-optics,” Bioimaging 3, 64–69 (1995).
[CrossRef]

Hemmer, P. R.

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

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, 2733–2736 (2000).
[CrossRef] [PubMed]

Ling, A.

Lloyd, S.

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

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, 163602 (2010).
[CrossRef]

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

Migdall, A.

Muthukrishnan, A.

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

Pearlman, A. J.

Pertsinidis, A.

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466, 647–651 (2010).
[CrossRef] [PubMed]

Rayleigh, L.

L. Rayleigh, “Investigations in optics with special reference to the spectroscope,” Philos. Mag. 8, 261–274 (1879).

Scully, M. O.

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

Shapiro, J. H.

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, 163602 (2010).
[CrossRef]

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

Soukka, J.

S. W. Hell, J. Soukka, and P. E. Hänninen, “Two- and multiphoton detection as an imaging mode and means of increasing the resolution in far-field light microscopy: A study based on photon-optics,” Bioimaging 3, 64–69 (1995).
[CrossRef]

Sparrow, C. M.

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J. 44, 76–86 (1916).
[CrossRef]

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, 163602 (2010).
[CrossRef]

Tsang, M.

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

Wang, K.

K. Wang and D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70,041801(R) (2004).
[CrossRef]

Wildfeuer, C. F.

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, 2733–2736 (2000).
[CrossRef] [PubMed]

Wong, F. N. C.

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, 163602 (2010).
[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, 163602 (2010).
[CrossRef]

Zhang, Y.

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466, 647–651 (2010).
[CrossRef] [PubMed]

Zubairy, M. S.

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

Astrophys. J. (1)

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J. 44, 76–86 (1916).
[CrossRef]

Bioimaging (1)

S. W. Hell, J. Soukka, and P. E. Hänninen, “Two- and multiphoton detection as an imaging mode and means of increasing the resolution in far-field light microscopy: A study based on photon-optics,” Bioimaging 3, 64–69 (1995).
[CrossRef]

Contemp. Phys. (1)

J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N States,” Contemp. Phys. 49, 125–143 (2008).
[CrossRef]

Nature (1)

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466, 647–651 (2010).
[CrossRef] [PubMed]

Opt. Express (2)

Philos. Mag. (1)

L. Rayleigh, “Investigations in optics with special reference to the spectroscope,” Philos. Mag. 8, 261–274 (1879).

Phys. Rev. A (2)

K. Wang and D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70,041801(R) (2004).
[CrossRef]

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

Phys. Rev. Lett. (4)

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

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, 2733–2736 (2000).
[CrossRef] [PubMed]

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96, 163603 (2006).
[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, 163602 (2010).
[CrossRef]

Other (1)

D. Semwogerere and E. R. Weeks, “Confocal microscopy,” in Encyclopedia of Biomaterials and Biomedical Engineering, G. E. Wnek and G. L. Bowlin, eds. (Taylor & Francis, 2005), pp. 705–714.

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Figures (5)

Fig. 3
Fig. 3

(a) Cross section through the center of a diffraction-limited image (black curve) of a point source. The dashed lines indicate two threshold values, N = 800 (red) and N = 1000 (blue), that yield reduced widths—after sub-threshold pixel values are set to zero—which are bounded by the two corresponding vertical lines. (b) Plot of half-widths σN (in pixels) as a function of the threshold value N for the image in (a).

Fig. 1
Fig. 1

Experimental setup for CCD-based sub-Rayleigh imaging system.

Fig. 2
Fig. 2

(a) USAF resolution target: red arrow indicates area of interest in Group 2, Element 2, with stripe width of 111 μm. (b) Section of an ISO-21550 dynamic range film target for gray-scale imaging, with specified transmissivities of 77.6%, 40.4%, 20.9%, 1.56% for regions 3, 5, 6, and 9, respectively.

Fig. 4
Fig. 4

Images of USAF resolution target using different methods (and incident powers). (a) Conventional full-object illumination with no aperture (30 μW). (b) Diffraction-limited conventional imaging with 1-mm-radius aperture (150 μW). (c) Sub-Rayleigh imaging with focused scanning and thresholding at high power (30 μW). (d) Sub-Rayleigh imaging with focused scanning and thresholding at low power (3.5 μW).

Fig. 5
Fig. 5

Gray-scale target imaged with (a) conventional full-object illumination without aperture, and (b) focused scanning with a 1-mm-radius aperture and thresholding.

Equations (3)

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R = 0.61 λ D 0 R A M ,
N ( x ) = N max e x 2 / σ 2 ,
σ N = σ ln ( N max N ) ,

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