Abstract

Remote detection of gaseous pollutants and other atmospheric constituents can be achieved with differential absorption lidar (DIAL) methods. The technique relies on the transmission of two or more laser wavelengths and exploits absorption features in the target gas by measuring the ratio of their detected powers to determine gas concentration. A common mode of operation is when the transmitter and receiver are collocated, and the absorption is measured over a return trip by a randomly scattering topographic target. Hence, in coherent DIAL, speckle fluctuation leads to a large uncertainty in the detected powers unless the signal is averaged over multiple correlation times, i.e., over many independent speckles. We examine a continuous-wave coherent DIAL system in which the laser wavelengths are transmitted and received by the same single-mode optical fibers. This ensures that the two wavelengths share a common spatial mode, which, for certain transmitter and target parameters, enables highly correlated speckle fluctuations to be readily achieved in practice. For a DIAL system, this gives the potential for improved accuracy in a given observation time. A theoretical analysis quantifies this benefit as a function of the degree of correlation between the two time series (which depends on wavelength separation and target depth). The results are compared with both a numerical simulation and a laboratory-based experiment.

© 2001 Optical Society of America

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References

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  1. R. M. Measures, ed., Laser Remote Chemical Analysis, Vol. 94 of Wiley InterScience Series on Chemical Analysis (Wiley, New York, 1988).
  2. D. K. Killinger, A. Mooradian, eds., Optical and Laser Remote Sensing, Vol. 39 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1983).
    [CrossRef]
  3. E. D. Hinkley, ed., Laser Monitoring of the Atmosphere, Vol. 14 of Topics in Applied Physics (Springer-Verlag, Berlin, 1976).
    [CrossRef]
  4. V. Wulfmeyer, J. Boesenberg, “Ground-based differential absorption lidar for water-vapor profiling: assessment of accuracy, resolution, and meteorological applications,” Appl. Opt. 37, 3825–3844 (1998).
    [CrossRef]
  5. A. Papayannis, G. Ancellet, J. Pelon, G. Megie, “Multiwavelength lidar for ozone measurement in the troposphere and the lower stratosphere,” Appl. Opt. 29, 467–478 (1990).
    [CrossRef] [PubMed]
  6. W. B. Grant, “Effect of differential spectral reflectance on DIAL measurements using topographic targets,” Appl. Opt. 21, 2390–2394 (1982).
    [CrossRef] [PubMed]
  7. W. B. Grant, “Differential absorption and Raman lidar for water vapour profile measurements: a review,” Opt. Eng. 30, 40–48 (1991).
    [CrossRef]
  8. E. R. Murray, D. D. Powell, J. E. van der Laan, “Measurement of average atmospheric temperature using a CO2 laser radar,” Appl. Opt. 19, 1794–1797 (1980).
    [CrossRef] [PubMed]
  9. B. J. Rye, “Differential absorption lidar system sensitivity with heterodyne reception,” Appl. Opt. 17, 3862–3864 (1978).
    [CrossRef] [PubMed]
  10. B. J. Rye, “Power ratio estimation in incoherent backscatter lidar: heterodyne receiver with square law detector,” J. Clim. Appl. Meteorol. 22, 1899–1913 (1983).
    [CrossRef]
  11. N. Menyuk, D. Killinger, C. R. Menyuk, “Error reduction in laser remote sensing: combined effects of cross correlation and signal averaging,” Appl. Opt. 24, 118–131 (1985).
    [CrossRef] [PubMed]
  12. R. M. Hardesty, “Coherent DIAL measurement of range-resolved water vapor concentration,” Appl. Opt. 23, 2545–2553 (1984).
    [CrossRef] [PubMed]
  13. P. Drobinski, P. H. Flamant, P. Salamitou, “Spectral diversity technique for heterodyne Doppler lidar that uses hard target returns,” Appl. Opt. 39, 376–385 (2000).
    [CrossRef]
  14. W. B. Grant, “HeNe and cw CO2 laser long-path systems for gas detection,” Appl. Opt. 25, 709–714 (1986).
    [CrossRef] [PubMed]
  15. R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, “Characteristics of coherent lidar returns from calibration targets and aerosols,” Appl. Opt. 20, 3763–3769 (1981).
    [CrossRef] [PubMed]
  16. M. Harris, G. N. Pearson, C. A. Hill, J. M. Vaughan, “Higher moments of scattered light fields by heterodyne analysis,” Appl. Opt. 33, 7226–7230 (1994).
    [CrossRef] [PubMed]
  17. M. J. T. Milton, P. T. Woods, “Pulse averaging methods for a laser remote monitoring system using atmospheric backscatter,” Appl. Opt. 26, 2598–2603 (1987).
    [CrossRef] [PubMed]
  18. L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).
  19. J. C. Marron, “Wavelength decorrelation of laser speckle from three-dimensional diffuse objects,” Opt. Commun. 88, 305–308 (1992).
    [CrossRef]
  20. S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).
    [CrossRef]
  21. A. Erdeyli, ed., Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1.
  22. H. Cramer, Mathematical Methods of Statistics (Princeton University, Princeton, N.J., 1946), Sect. 18.3.
  23. K. D. Ridley, E. Jakeman, “Incomplete phase conjugation through a random phase screen. II. Numerical simulations,” J. Opt. Soc. Am. A 13, 2393–2402 (1996).
    [CrossRef]
  24. M. Harris, “Intensity correlations in filtered phase-diffusing laser light,” Opt. Lett. 23, 519–521 (1998).
    [CrossRef]
  25. M. Harris, G. Constant, C. Ward, “Continuous-wave bistatic laser Doppler wind sensor,” Appl. Opt. 40, 1501–1506 (2001).
    [CrossRef]
  26. R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
    [CrossRef]

2001 (1)

2000 (1)

1998 (2)

1996 (1)

1994 (1)

1992 (2)

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

J. C. Marron, “Wavelength decorrelation of laser speckle from three-dimensional diffuse objects,” Opt. Commun. 88, 305–308 (1992).
[CrossRef]

1991 (1)

W. B. Grant, “Differential absorption and Raman lidar for water vapour profile measurements: a review,” Opt. Eng. 30, 40–48 (1991).
[CrossRef]

1990 (1)

1987 (1)

1986 (1)

1985 (1)

1984 (1)

1983 (1)

B. J. Rye, “Power ratio estimation in incoherent backscatter lidar: heterodyne receiver with square law detector,” J. Clim. Appl. Meteorol. 22, 1899–1913 (1983).
[CrossRef]

1982 (1)

1981 (1)

1980 (1)

1978 (1)

1975 (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

1948 (1)

S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).
[CrossRef]

Ancellet, G.

Ariel, E. D.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Boesenberg, J.

Constant, G.

Cramer, H.

H. Cramer, Mathematical Methods of Statistics (Princeton University, Princeton, N.J., 1946), Sect. 18.3.

Drobinski, P.

Fante, R. L.

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

Flamant, P. H.

Grant, W. B.

Hallerman, G. R.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Hardesty, R. M.

Harris, M.

Hill, C. A.

Jakeman, E.

Keeler, R. J.

Killinger, D.

Marron, J. C.

J. C. Marron, “Wavelength decorrelation of laser speckle from three-dimensional diffuse objects,” Opt. Commun. 88, 305–308 (1992).
[CrossRef]

Megie, G.

Menyuk, C. R.

Menyuk, N.

Milton, M. J. T.

Murray, E. R.

Papayannis, A.

Payson, H. C.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Pearson, G. N.

Pelon, J.

Post, M. J.

Powell, D. D.

Rice, S. O.

S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).
[CrossRef]

Richter, R. A.

Ridley, K. D.

Rye, B. J.

B. J. Rye, “Power ratio estimation in incoherent backscatter lidar: heterodyne receiver with square law detector,” J. Clim. Appl. Meteorol. 22, 1899–1913 (1983).
[CrossRef]

B. J. Rye, “Differential absorption lidar system sensitivity with heterodyne reception,” Appl. Opt. 17, 3862–3864 (1978).
[CrossRef] [PubMed]

Salamitou, P.

Shirley, L. G.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

van der Laan, J. E.

Vaughan, J. M.

Vivilecchia, J. R.

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Ward, C.

Woods, P. T.

Wulfmeyer, V.

Appl. Opt. (13)

V. Wulfmeyer, J. Boesenberg, “Ground-based differential absorption lidar for water-vapor profiling: assessment of accuracy, resolution, and meteorological applications,” Appl. Opt. 37, 3825–3844 (1998).
[CrossRef]

A. Papayannis, G. Ancellet, J. Pelon, G. Megie, “Multiwavelength lidar for ozone measurement in the troposphere and the lower stratosphere,” Appl. Opt. 29, 467–478 (1990).
[CrossRef] [PubMed]

W. B. Grant, “Effect of differential spectral reflectance on DIAL measurements using topographic targets,” Appl. Opt. 21, 2390–2394 (1982).
[CrossRef] [PubMed]

E. R. Murray, D. D. Powell, J. E. van der Laan, “Measurement of average atmospheric temperature using a CO2 laser radar,” Appl. Opt. 19, 1794–1797 (1980).
[CrossRef] [PubMed]

B. J. Rye, “Differential absorption lidar system sensitivity with heterodyne reception,” Appl. Opt. 17, 3862–3864 (1978).
[CrossRef] [PubMed]

N. Menyuk, D. Killinger, C. R. Menyuk, “Error reduction in laser remote sensing: combined effects of cross correlation and signal averaging,” Appl. Opt. 24, 118–131 (1985).
[CrossRef] [PubMed]

R. M. Hardesty, “Coherent DIAL measurement of range-resolved water vapor concentration,” Appl. Opt. 23, 2545–2553 (1984).
[CrossRef] [PubMed]

P. Drobinski, P. H. Flamant, P. Salamitou, “Spectral diversity technique for heterodyne Doppler lidar that uses hard target returns,” Appl. Opt. 39, 376–385 (2000).
[CrossRef]

W. B. Grant, “HeNe and cw CO2 laser long-path systems for gas detection,” Appl. Opt. 25, 709–714 (1986).
[CrossRef] [PubMed]

R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, “Characteristics of coherent lidar returns from calibration targets and aerosols,” Appl. Opt. 20, 3763–3769 (1981).
[CrossRef] [PubMed]

M. Harris, G. N. Pearson, C. A. Hill, J. M. Vaughan, “Higher moments of scattered light fields by heterodyne analysis,” Appl. Opt. 33, 7226–7230 (1994).
[CrossRef] [PubMed]

M. J. T. Milton, P. T. Woods, “Pulse averaging methods for a laser remote monitoring system using atmospheric backscatter,” Appl. Opt. 26, 2598–2603 (1987).
[CrossRef] [PubMed]

M. Harris, G. Constant, C. Ward, “Continuous-wave bistatic laser Doppler wind sensor,” Appl. Opt. 40, 1501–1506 (2001).
[CrossRef]

Bell Syst. Tech. J. (1)

S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).
[CrossRef]

J. Clim. Appl. Meteorol. (1)

B. J. Rye, “Power ratio estimation in incoherent backscatter lidar: heterodyne receiver with square law detector,” J. Clim. Appl. Meteorol. 22, 1899–1913 (1983).
[CrossRef]

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

Lincoln Lab. J. (1)

L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, J. R. Vivilecchia, “Advanced techniques for target discrimination using laser speckle,” Lincoln Lab. J. 5, 367–440 (1992).

Opt. Commun. (1)

J. C. Marron, “Wavelength decorrelation of laser speckle from three-dimensional diffuse objects,” Opt. Commun. 88, 305–308 (1992).
[CrossRef]

Opt. Eng. (1)

W. B. Grant, “Differential absorption and Raman lidar for water vapour profile measurements: a review,” Opt. Eng. 30, 40–48 (1991).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

R. L. Fante, “Electromagnetic beam propagation in turbulent media,” Proc. IEEE 63, 1669–1692 (1975).
[CrossRef]

Other (5)

A. Erdeyli, ed., Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 1.

H. Cramer, Mathematical Methods of Statistics (Princeton University, Princeton, N.J., 1946), Sect. 18.3.

R. M. Measures, ed., Laser Remote Chemical Analysis, Vol. 94 of Wiley InterScience Series on Chemical Analysis (Wiley, New York, 1988).

D. K. Killinger, A. Mooradian, eds., Optical and Laser Remote Sensing, Vol. 39 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1983).
[CrossRef]

E. D. Hinkley, ed., Laser Monitoring of the Atmosphere, Vol. 14 of Topics in Applied Physics (Springer-Verlag, Berlin, 1976).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Probability density of the intensity ratio u for a correlation coefficient of s = 0.9 and four different values of the number of samples N = 1, 4, 16, and 64.

Fig. 2
Fig. 2

Standard deviation in the intensity ratio (I/ I′) as a function of smoothing time. Simulation, solid curves; theory, dashed curves; correlation parameter s 2 = 0, uppermost curve; 0.5, 0.9, 0.99, lowermost curve. Symbols show experimental data.

Fig. 3
Fig. 3

Probability density of the logarithm of the intensity ratio α for a correlation coefficient of s = 0.9 and three different values of the number of samples N = 1, 4, and 16.

Fig. 4
Fig. 4

Results for the standard deviation of the logarithm of the intensity ratio as a function of the number of samples N. The solid symbols are the exact results, found by numerical integration (circles, s = 0; triangles, s 2 = 0.9), and the solid curves are the results of Eq. (10).

Fig. 5
Fig. 5

Experimental arrangement, showing the modular nature of the system with standard components connected by single-mode optical fiber. OI, optical isolator; AOM, acousto-optic modulator; FPC, fiber polarization controller; 1 × 2 and 2 × 2, fiber couplers; L.O., local oscillator; BPLO, backpropagated local oscillator; O/P, output signal intensity.

Fig. 6
Fig. 6

Experimental intensity time series obtained with dual-wavelength lidar. Upper trace, highly correlated speckle at small wavelength separation. Lower trace, uncorrelated speckle for large separation.

Equations (22)

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

u=NINI.
s2=IIII-1.
PI, I=11-s2 I02s1-s2IIexp-I+I1-s2,
Cp, p=11-s2pp+p+p+1.
PM, M=11-s2N-1!MMs2N-12×exp-M+M1-s2IN-12s1-s2MM
M=N I,  M=N I,
PM, u=MNexp-M1-s21-s2sN-1N-1! uN-12×exp-uM1-s2IN-12Ms1-s2u,
Pu=1-s2N2N-1!N-1!2uN-11+u1+u2-4s2uN+1/2.
u=N-s2N-1, u2=NN+1-4s2N+1+6s4N-1N-2.
σ2=1-s2N-12N-2s24-5N+2N-1N.
σ221-s2N.
EtE*t+τ=exp-τ2/τc2.
Px=1-s2N2N-1!N-1!2bN+2xN-1b+xb+x2-4s2bxN+1/2.
Eλ  - Dzexpiϕexpi 4πzλdz,
E*λEλ+Δλ  - D2zexp-i 4πzΔλλdz,
Dz=exp-z22L2,
ρEΔλ=exp-2πLΔλλ22.
2πLΔλλ2=1,
0 u2j+N-12exp-uM1-s2IN-12Ms1-s2udu.
-1jddxjaN-12expaxxN,
aN-12expaxxN-2jk=0jjCkaj-kN+j-1!N+j-1-k! xk,
uj=1N-1!k=0jjCk1-s2ks2j-k×N-k-1!N+j-1!N+j-k-1!,

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