Abstract

A novel thermal-light-based ranging scheme utilizing second-order coherence in the time domain is proposed and studied. Such a scheme allows ultrahigh accuracy to be achieved for absolute range measurement. Besides, the scheme has the advantages of high immunity to noise and no measuring dead zone. A proof-of-principle experiment has been done, and the result shows a ±10cm accuracy at a distance of 1 km, which is currently limited by our detectors. The accuracy can be greatly improved to the nanometer scale by using state-of-the-art detectors with an appropriate data processing algorithm.

© 2012 Optical Society of America

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References

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  1. E. Bergstrand, “The geodimeter system: a short discussion of its principal function and future development,” J. Geophys. Res. 65, 404–409 (1960).
    [CrossRef]
  2. S. Pellegrin, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11, 712–716 (2000).
    [CrossRef]
  3. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernandez, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48, 6241–6251 (2009).
    [CrossRef]
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    [CrossRef]
  5. R. Pierce, J. Leitch, M. Stephens, P. Bender, and R. Nerem, “Intersatellite range monitoring using optical interferometry,” Appl. Opt. 47, 5007–5019 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29, 1153–1155(2004).
    [CrossRef]
  9. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270(2009).
    [CrossRef]
  18. F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).
    [CrossRef]
  19. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  20. J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Supplementary information for experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425, 268–271 (2003).
    [CrossRef]
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    [CrossRef]
  22. G. Present and D. B. Scarl, “Two-photon correlations in a mixture of Gaussian and laser light,” Appl. Opt. 11, 120–124 (1972).
    [CrossRef]

2009 (3)

A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernandez, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48, 6241–6251 (2009).
[CrossRef]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270(2009).
[CrossRef]

2008 (3)

Y. C. Wang and A. B. Wang, “A novel high resolution chaotic lidar with optical injection to chaotic laser diode,” Proc. SPIE 6824, 68241l (2008).
[CrossRef]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
[CrossRef]

R. Pierce, J. Leitch, M. Stephens, P. Bender, and R. Nerem, “Intersatellite range monitoring using optical interferometry,” Appl. Opt. 47, 5007–5019 (2008).
[CrossRef]

2007 (1)

2005 (2)

G. Li, T. C. Zhang, Y. Li, and J. M. Wang, “Correction of photon statistics of quantum states in single photon detection,” Proc. SPIE 5631, 134–142 (2005).
[CrossRef]

H. J. Yang, J. Deibel, S. Nyberg, and K. Riles, “High-precision absolute distance and vibration measurement with frequency scanned interferometry,” Appl. Opt. 44, 3937–3944 (2005).
[CrossRef]

2004 (2)

J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29, 1153–1155(2004).
[CrossRef]

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40, 815–820 (2004).
[CrossRef]

2003 (1)

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Supplementary information for experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425, 268–271 (2003).
[CrossRef]

2000 (1)

S. Pellegrin, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11, 712–716 (2000).
[CrossRef]

1993 (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
[CrossRef]

1988 (1)

1972 (1)

1965 (1)

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).
[CrossRef]

1963 (1)

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

1960 (1)

E. Bergstrand, “The geodimeter system: a short discussion of its principal function and future development,” J. Geophys. Res. 65, 404–409 (1960).
[CrossRef]

1956 (1)

R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).
[CrossRef]

Bender, P.

Bergstrand, E.

E. Bergstrand, “The geodimeter system: a short discussion of its principal function and future development,” J. Geophys. Res. 65, 404–409 (1960).
[CrossRef]

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
[CrossRef]

Boca, A.

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Supplementary information for experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425, 268–271 (2003).
[CrossRef]

Boitier, F.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270(2009).
[CrossRef]

Boozer, A. D.

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Supplementary information for experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425, 268–271 (2003).
[CrossRef]

Buck, J. R.

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Supplementary information for experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425, 268–271 (2003).
[CrossRef]

Buller, G. S.

A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernandez, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48, 6241–6251 (2009).
[CrossRef]

S. Pellegrin, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11, 712–716 (2000).
[CrossRef]

Coddington, I.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Collins, R. J.

Cova, S.

S. Pellegrin, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11, 712–716 (2000).
[CrossRef]

Dadliker, R.

Deibel, J.

Fabre, C.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270(2009).
[CrossRef]

Fernandez, V.

Gisin, N.

Glauber, R. J.

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

Godard, A.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270(2009).
[CrossRef]

Hanbury-Brown, R.

R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[CrossRef]

He, H. C.

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
[CrossRef]

Kimble, H. J.

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Supplementary information for experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425, 268–271 (2003).
[CrossRef]

Krichel, N. J.

Legre, M.

Leitch, J.

Li, G.

G. Li, T. C. Zhang, Y. Li, and J. M. Wang, “Correction of photon statistics of quantum states in single photon detection,” Proc. SPIE 5631, 134–142 (2005).
[CrossRef]

Li, Y.

G. Li, T. C. Zhang, Y. Li, and J. M. Wang, “Correction of photon statistics of quantum states in single photon detection,” Proc. SPIE 5631, 134–142 (2005).
[CrossRef]

Lin, F. Y.

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40, 815–820 (2004).
[CrossRef]

Liu, J. M.

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40, 815–820 (2004).
[CrossRef]

Mandel, L.

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

McCarthy, A.

McKeever, J.

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Supplementary information for experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425, 268–271 (2003).
[CrossRef]

Milburn, F. J.

D. F. Walls and F. J. Milburn, Quantum Optics (Springer-Verlag, 1995).

Nenadovic, L.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Nerem, R.

Newbury, N. R.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Nyberg, S.

Pellegrin, S.

S. Pellegrin, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11, 712–716 (2000).
[CrossRef]

Pierce, R.

Present, G.

Prongue, D.

Riles, K.

Rosencher, E.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270(2009).
[CrossRef]

Scarl, D. B.

Smith, J. M.

S. Pellegrin, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11, 712–716 (2000).
[CrossRef]

Stephens, M.

Swann, W. C.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Thalmann, R.

Thew, R.

Twiss, R. Q.

R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[CrossRef]

Wallace, A. M.

A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernandez, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48, 6241–6251 (2009).
[CrossRef]

S. Pellegrin, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11, 712–716 (2000).
[CrossRef]

Walls, D. F.

D. F. Walls and F. J. Milburn, Quantum Optics (Springer-Verlag, 1995).

Wang, A. B.

Y. C. Wang and A. B. Wang, “A novel high resolution chaotic lidar with optical injection to chaotic laser diode,” Proc. SPIE 6824, 68241l (2008).
[CrossRef]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
[CrossRef]

Wang, J. M.

G. Li, T. C. Zhang, Y. Li, and J. M. Wang, “Correction of photon statistics of quantum states in single photon detection,” Proc. SPIE 5631, 134–142 (2005).
[CrossRef]

Wang, Y. C.

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
[CrossRef]

Y. C. Wang and A. B. Wang, “A novel high resolution chaotic lidar with optical injection to chaotic laser diode,” Proc. SPIE 6824, 68241l (2008).
[CrossRef]

Wolf, E.

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

Yang, H. J.

Ye, J.

Zbinden, H.

Zhang, T. C.

G. Li, T. C. Zhang, Y. Li, and J. M. Wang, “Correction of photon statistics of quantum states in single photon detection,” Proc. SPIE 5631, 134–142 (2005).
[CrossRef]

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40, 815–820 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
[CrossRef]

J. Geophys. Res. (1)

E. Bergstrand, “The geodimeter system: a short discussion of its principal function and future development,” J. Geophys. Res. 65, 404–409 (1960).
[CrossRef]

Meas. Sci. Technol. (2)

S. Pellegrin, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11, 712–716 (2000).
[CrossRef]

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
[CrossRef]

Nat. Photon. (1)

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photon. 3, 351–356 (2009).
[CrossRef]

Nat. Phys. (1)

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270(2009).
[CrossRef]

Nature (2)

R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[CrossRef]

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, “Supplementary information for experimental realization of a one-atom laser in the regime of strong coupling,” Nature 425, 268–271 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

Phys. Rev. Lett. (1)

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).
[CrossRef]

Proc. SPIE (2)

Y. C. Wang and A. B. Wang, “A novel high resolution chaotic lidar with optical injection to chaotic laser diode,” Proc. SPIE 6824, 68241l (2008).
[CrossRef]

G. Li, T. C. Zhang, Y. Li, and J. M. Wang, “Correction of photon statistics of quantum states in single photon detection,” Proc. SPIE 5631, 134–142 (2005).
[CrossRef]

Other (2)

D. F. Walls and F. J. Milburn, Quantum Optics (Springer-Verlag, 1995).

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

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the principal modules of the positioning scheme.

Fig. 2.
Fig. 2.

Experiment setup for the protocol of one-dimensional positioning with a pseudothermal source.

Fig. 3.
Fig. 3.

Normalized second-order coherence function g(2) versus delay time τ. Distribution function on the left: with the 1 km optical fiber. Distribution function on the right: without the 1 km optical fiber. The solid lines are theoretical fitting curves of g(2) considering the mixture of Gaussian and coherence light.

Fig. 4.
Fig. 4.

Normalized second-order coherence function g(2). Distribution function in blue points: with environment noise. Distribution function in red circles: without environment noise.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

g(2)(t1,t2)=E()(t1)E()(t2)E(+)(t2)E(+)(t1)E()(t1)E(+)(t1)E()(t2)E(+)(t2),
g(2)(t1,t2)=1+|g(1)(t1,t2)|2=1+|Tr[ρE()(t1)E(+)(t2)]|2Tr[ρE()(t1)E(+)(t1)]Tr[ρE()(t2)E(+)(t2)],
ρ={nk}{nk}{nk}k(n¯k)nk(1+n¯k)nk+1,
g(2)(τ)=1+|g(1)(τ)|2=1+|exp(iω0τ12δ2τ2)|2=1+exp(δ2τ2),
Ł=ct22=c(t1+Δt)2.
g(2)(t1,t2)=Er()(t1)[Em()(t2)+En()(t2)][Em(+)(t2)+En(+)(t2)]Er(+)(t1)Er()(t1)Er(+)(t1)[Em()(t2)+En()(t2)][Em(+)(t2)+En(+)(t2)],
g(2)(t1,t2)=Er()(t1)Em()(t2)Em(+)(t2)Er(+)(t1)+Er()(t1)Er(+)(t1)En()(t2)En(+)(t2)Er()(t1)Er(+)(t1)(Em()(t2)Em(+)(t2)+En()(t2)En(+)(t2))=IrIm+IrInIrIm+IrIn.
n(τ)=Tδ(R1+γ1)(R2+γ2)[1+g(2)(τ)1(1+γ1/R1)(1+γ2/R2)].
g(2)(τ)=n(τ)Tδ(R1+γ1)(R2+γ2)+TδR1R2TδR1R2.
g(2)(τ)=n(τ)TδR1R2.
gptl(2)(τ)=1+(m1+m)2exp[(τp)2/q12]+2m(1+m)2exp[(τp)2/q22],
L=vgΔτ=cngΔτ=1091.44±0.1m.
γ1=9.15×1051.01×105=8.14×105c/s,
SNR=PSPNR1γ1=1.01×1058.14×105=9dB.
g(2)(τ)=n(τ)Tδγ1R2TδR1R2,
PSL=1.0511.691=11.4dB,

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