Abstract

Calculations are presented of the effect of pulse-pair correlation on the detection statistics of alarm systems using differential absorption lidar (DIAL) for the remote sensing of toxic gases. This experimentally observed correlation is found to have a significant beneficial effect on the performance of such systems. The calculations are performed for both coherent- and direct-detection DIAL systems using a statistical detection model that assumes a bivariate normal distribution for the on- and off-resonance returns.

© 1985 Optical Society of America

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References

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  1. R. C. Harney, “Laser prf Considerations in Differential Absorption Lidar Applications,” Appl. Opt. 22, 3747 (1983).
    [CrossRef] [PubMed]
  2. P. Brockman, R. V. Hess, C. H. Bair, “CO2 DIAL Sensitivity Studies for Measurements of Atmospheric Trace Gases,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, New York, 1983).
  3. R. M. Schotland, “Errors in the Lidar Measurement of Atmospheric Gases by Differential Absorption,” J. Appl. Meteorol. 13, 71 (1974).
    [CrossRef]
  4. D. K. Killinger, N. Menyuk, W. E. DeFeo, “Experimental Comparison of Heterodyne and Direct Detection for Pulsed Differential Absorption CO2 Lidar,” Appl. Opt. 22, 682 (1983).
    [CrossRef] [PubMed]
  5. J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and Target Detection with a Heterodyne-Reception Optical Radar,” Appl. Opt. 20, 3292 (1981).
    [CrossRef] [PubMed]
  6. Equation (6) assumes the on- and off-resonance signal-to-noise ratios are approximately equal as they would be for weak toxic gas absorption and equal atmospheric extinction. It also neglects pulse correlation which would introduce an additional factor 1−μ.
  7. In Eq. (7) it is intended that the N-pulse averaging takes place before ratioing or taking the logarithm. Computer simulations have shown that averaging the ratios of the individual pulses produces a biased estimator for CL while averaging the differences of the logarithms increases the variance in the estimator.
  8. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965).

1983 (2)

1981 (1)

1974 (1)

R. M. Schotland, “Errors in the Lidar Measurement of Atmospheric Gases by Differential Absorption,” J. Appl. Meteorol. 13, 71 (1974).
[CrossRef]

Bair, C. H.

P. Brockman, R. V. Hess, C. H. Bair, “CO2 DIAL Sensitivity Studies for Measurements of Atmospheric Trace Gases,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, New York, 1983).

Brockman, P.

P. Brockman, R. V. Hess, C. H. Bair, “CO2 DIAL Sensitivity Studies for Measurements of Atmospheric Trace Gases,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, New York, 1983).

Capron, B. A.

DeFeo, W. E.

Harney, R. C.

Hess, R. V.

P. Brockman, R. V. Hess, C. H. Bair, “CO2 DIAL Sensitivity Studies for Measurements of Atmospheric Trace Gases,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, New York, 1983).

Killinger, D. K.

Menyuk, N.

Schotland, R. M.

R. M. Schotland, “Errors in the Lidar Measurement of Atmospheric Gases by Differential Absorption,” J. Appl. Meteorol. 13, 71 (1974).
[CrossRef]

Shapiro, J. H.

Appl. Opt. (3)

J. Appl. Meteorol. (1)

R. M. Schotland, “Errors in the Lidar Measurement of Atmospheric Gases by Differential Absorption,” J. Appl. Meteorol. 13, 71 (1974).
[CrossRef]

Other (4)

Equation (6) assumes the on- and off-resonance signal-to-noise ratios are approximately equal as they would be for weak toxic gas absorption and equal atmospheric extinction. It also neglects pulse correlation which would introduce an additional factor 1−μ.

In Eq. (7) it is intended that the N-pulse averaging takes place before ratioing or taking the logarithm. Computer simulations have shown that averaging the ratios of the individual pulses produces a biased estimator for CL while averaging the differences of the logarithms increases the variance in the estimator.

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965).

P. Brockman, R. V. Hess, C. H. Bair, “CO2 DIAL Sensitivity Studies for Measurements of Atmospheric Trace Gases,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, Eds. (Springer, New York, 1983).

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Figures (3)

Fig. 1
Fig. 1

Signal-to-noise ratio dependence on range for direct- and coherent-detection systems.

Fig. 2
Fig. 2

Minimum detectable CL vs range for direct detection.

Fig. 3
Fig. 3

Minimum detectable CL vs range for coherent detection.

Tables (1)

Tables Icon

Table I Parameters used in Direct/Coherent Detection Comparison

Equations (26)

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SNR D = [ N CNR D 1 + CNR D / SNR sat 2 ] 1 / 2 ,
CNR D = ( ε P av prf ) 2 D * 2 A D τ ( D 2 4 L 2 ) 2 r 2 exp [ 4 k L ] ,
SNR sat D / D T ,
SNR H = [ N CNR H / 2 1 + CNR H / 2 SNR sat 2 + 1 / 2 CNR H ] 1 / 2 ,
CNR H = η eff ε P av h v prf D 2 4 L 2 r exp ( 2 k L )
σ CL = 1 2 Δ ρ SNR ,
CL = 1 2 Δ ρ ln ( p off p on ) .
probability that CL CL 0 prob { CL CL 0 } = prob { T T 0 } ,
T 0 exp ( 2 Δ ρ CL 0 ) .
prob { p on p ˆ on and p off p ˆ off } = p ˆ o n d p on p ˆ o f d p off P ( p on , p off ) .
prob { T T 0 } = 0 d p on p on T 0 d p off P ( p on , p off ) .
P ( p on , p off ) = 1 2 π σ 2 1 μ 2 exp [ { ( p on p on ) 2 2 μ ( p on p on ) ( p off p off ) + ( p off p off ) 2 } / 2 ( 1 μ 2 ) σ 2 ] .
prob { T > T 0 } = 1 / 2 [ 1 erf ( T 0 SNR on SNR off 2 T 0 2 2 T 0 μ + 1 ) ]
P FA = 1 / 2 [ 1 erf ( ( T 0 1 ) SNR off 2 T 0 2 2 T 0 μ + 1 ) ] .
SNR on = exp ( 2 Δ ρ CL min ) SNR off .
T 0 = 1 + 1 2 δ 2 + δ [ 1 + 1 4 δ 2 ] 1 / 2 ,
δ [ 2 β ( 1 μ ) 1 β ] 1 / 2 , β [ Q 1 ( P FA ) SNR off ] 2
Q ( x ) 1 2 π x d t exp ( t 2 / 2 ) .
CL min = 1 2 Δ ρ ln [ T 0 1 + ( T 0 1 ) Q 1 ( P D ) / Q 1 ( P FA ) ] .
prob { T T 0 } = 1 π 1 μ 2 d x exp ( x 2 ) y 0 d y × exp [ ( y μ x ) 2 / ( 1 μ 2 ) ] ,
y 0 = T 0 ( x + p on / 2 σ ) p off / 2 σ .
prob { T T 0 } = 1 π d x exp ( x 2 ) A x + B d t exp ( t 2 ) ,
A = ( T 0 μ ) / 1 μ 2 , B = ( T 0 p on p off ) / 2 σ 1 μ 2 .
prob { T T 0 } = 1 π 0 π d ϕ s / sin ϕ d ρ ρ exp ( ρ 2 ) 1 π 0 π / 2 d ϕ exp ( s 2 / sin 2 ϕ ) ,
s = B 1 + A 2 = T 0 p on p off 2 σ T 0 2 2 T 0 μ + 1 .
prob { T T 0 } = 1 / 2 [ 1 erfs ] ,

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