Abstract

Experimentally verified signal amplitude distributions from a coherent CO2 laser radar have been used to derive radar performance for atmospheric remote sensing and hard target detection. Different target types include man-made diffuse, semirough, and glint targets as well as terrain backgrounds. The results, given as accuracy and probability of detection, respectively, show the importance of including beam gas concentration wandering especially for glint targets. It is shown how Doppler sensing and range gating improve target detection against terrain background.

© 1986 Optical Society of America

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References

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  1. D. Letalick, I. Renhorn, O. Steinvall, “Measured Signal Amplitude Distributions for a Coherent FM-cw CO2 Laser Radar,” Appl. Opt. 25, 3927 (1986).
    [CrossRef] [PubMed]
  2. R. M. Hardesty, “Coherent DIAL Measurement of Range-Resolved Water Vapor Concentration,” Appl. Opt. 23, 2545 (1984).
    [CrossRef] [PubMed]
  3. T. Fukuda, Y. Matsuura, T. Mori, “Sensitivity of Coherent Range-Resolved Differential Absorption Lidar,” Appl. Opt. 23, 2026 (1984).
    [CrossRef] [PubMed]
  4. D. K. Killinger, N. Menuyuk, W. E. DeFeo, “Experimental Comparison of Heterodyne and Direct Detection for Pulsed Differential Absorption CO2 Lidar,” Appl. Opt. 22, 682 (1983).
    [CrossRef] [PubMed]
  5. R. C. Harney, “Laser prf Considerations in Differential Absorption Lidar Applications,” Appl. Opt. 22, 3747 (1983).
    [CrossRef] [PubMed]
  6. 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]
  7. W. B. Grant, “Effect of Differential Spectral Reflectance on DIAL Measurements Using Topographic Targets,” Appl. Opt. 21, 2390 (1982).
    [CrossRef] [PubMed]
  8. K. Asai, T. Igarashi, “Interference from Differential Reflectance of Moist Topographic Targets in CO2 DIAL Ozone Measurement,” Appl. Opt. 23, 734 (1984).
    [CrossRef] [PubMed]
  9. See, e.g., A. D. Whalen, Detection of Signals in Noise (Academic, New York, 1971).
  10. M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1962).
  11. O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widén, “Experimental Studies with a Coherent CO2 Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).
  12. H. Ahlberg, S. Lundquist, D. Letalick, I. Renhorn, O. Steinvall, “Design and Evaluation of an Imaging Q-Switched CO2-Laser Radar with Heterodyne Detection,” Appl. Opt. 25, 2891 (1986).
    [CrossRef] [PubMed]

1986 (2)

1984 (3)

1983 (2)

1982 (1)

1981 (2)

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widén, “Experimental Studies with a Coherent CO2 Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

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]

Ahlberg, H.

Asai, K.

Bolander, G.

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widén, “Experimental Studies with a Coherent CO2 Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Capron, B. A.

DeFeo, W. E.

Fukuda, T.

Grant, W. B.

Gullberg, K.

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widén, “Experimental Studies with a Coherent CO2 Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Hardesty, R. M.

Harney, R. C.

Igarashi, T.

Killinger, D. K.

Letalick, D.

Lundquist, S.

Matsuura, Y.

Menuyuk, N.

Mori, T.

Renhorn, I.

Shapiro, J. H.

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1962).

Steinvall, O.

Widén, A.

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widén, “Experimental Studies with a Coherent CO2 Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Appl. Opt. (9)

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]

W. B. Grant, “Effect of Differential Spectral Reflectance on DIAL Measurements Using Topographic Targets,” Appl. Opt. 21, 2390 (1982).
[CrossRef] [PubMed]

D. K. Killinger, N. Menuyuk, W. E. DeFeo, “Experimental Comparison of Heterodyne and Direct Detection for Pulsed Differential Absorption CO2 Lidar,” Appl. Opt. 22, 682 (1983).
[CrossRef] [PubMed]

R. C. Harney, “Laser prf Considerations in Differential Absorption Lidar Applications,” Appl. Opt. 22, 3747 (1983).
[CrossRef] [PubMed]

K. Asai, T. Igarashi, “Interference from Differential Reflectance of Moist Topographic Targets in CO2 DIAL Ozone Measurement,” Appl. Opt. 23, 734 (1984).
[CrossRef] [PubMed]

T. Fukuda, Y. Matsuura, T. Mori, “Sensitivity of Coherent Range-Resolved Differential Absorption Lidar,” Appl. Opt. 23, 2026 (1984).
[CrossRef] [PubMed]

R. M. Hardesty, “Coherent DIAL Measurement of Range-Resolved Water Vapor Concentration,” Appl. Opt. 23, 2545 (1984).
[CrossRef] [PubMed]

H. Ahlberg, S. Lundquist, D. Letalick, I. Renhorn, O. Steinvall, “Design and Evaluation of an Imaging Q-Switched CO2-Laser Radar with Heterodyne Detection,” Appl. Opt. 25, 2891 (1986).
[CrossRef] [PubMed]

D. Letalick, I. Renhorn, O. Steinvall, “Measured Signal Amplitude Distributions for a Coherent FM-cw CO2 Laser Radar,” Appl. Opt. 25, 3927 (1986).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

O. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, A. Widén, “Experimental Studies with a Coherent CO2 Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).

Other (2)

See, e.g., A. D. Whalen, Detection of Signals in Noise (Academic, New York, 1971).

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1962).

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Figures (8)

Fig. 1
Fig. 1

Accuracy in mean concentration, σ< c >, in a path-averaged DIAL system using a coherent CO2 laser system. Idealized glint and diffuse targets are assumed. For discussion of the results, see text.

Fig. 2
Fig. 2

Maximum normalized beam angle jitter (σ bw /w0) for beam jitter fluctuations to be less than turbulence-induced scintillations. Levels of turbulence are indicated strong ( C n 2 = 5 × 10 13 m - 2 / 3 ) , ( C n 2 = 10 - 14 m - 2 / 3 ) , and weak ( C n 2 10 - 16 m - 2 / 3 ). For a misaligned beam (x0/w0 = 1) the jitter fluctuations exceed the scintillation level at much smaller values of σ bw /w0.

Fig. 3
Fig. 3

Probability of glint target detection vs CNR for pure scintillation and pure beam wandering fluctuations. For the same value of log-variance ( σ χ 2 ), the beam jitter gives a substantially lower performance. The values of σ χbw = 0.05 and 0.5 correspond to a misalignment of σ bw /w0 = 0.22 and 0.61, respectively. False alarm probability P F = 10−5.

Fig. 4
Fig. 4

P D vs CNR for a pure speckle (a) and a semirough target (b). The semirough target has a glint-to-diffuse power ratio (A2/2σ2 = 5) corresponding to a smooth painted metal surface. At low turbulence levels there is a great difference in performance between the two types of target. This difference disappears at high turbulence levels.

Fig. 5
Fig. 5

Improvement in detection probability by pixel integration. The averaging filter which compares the sum of m pixels with a certain threshold is better than the single-pixel threshold. For the incoherent integration a P F of 10−5 was used. The P F for the single-pixel processor are given by P F (4) = 4 × 10−5 and P F (16) = 1.6 × 10−5 for P F (1) = 10−5.

Fig. 6
Fig. 6

Probability of detection for a target in terrain background (grass) with a = 1.08 and c = 1.65 in the Weibull distribution [Eq. (23)]. Note the high target-to-clutter ratio that is needed to obtain a high P D value. The difference between different types of target and turbulence level is not dramatic.

Fig. 7
Fig. 7

Geometrical parameters in a simple range gating scenario.

Fig. 8
Fig. 8

Probability of detection using range gating instead of intensity only (see Fig. 6) for a target in terrain background corresponding to Fig. 7. Range interval is half of the target size. The number of target pixels (m t ) corresponds to ~1/4 and 1/100 of the total frame of 1282 pixels. The number of background pixels (m b ) corresponds to inclination angles of 25 and 100 mrad. Rayleigh statistics has been used for both target and background with P Db = 0.3 corresponding to P F = 10−5 for CNR b = 10 dB.

Equations (29)

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σ < c > = ( 2 α d · L · SNR · N ) - 1 ,
SNR = < r ¯ 2 - n ¯ 2 > var ( r ¯ 2 ) ,
CNR = < z ¯ 2 > < n ¯ 2 >
SNR SNR sat < z ¯ 2 > var ( z ¯ 2 ) .
G l i n t :             SNR = ( { exp [ 4 x 0 2 σ b w 2 ( w 0 2 + 8 σ b w 2 ) ( w 0 2 + 4 σ b w 2 ) ] × ( w 0 2 + 4 σ b w 2 ) 2 w 0 2 ( w 0 2 + 8 σ b w 2 ) · exp ( 16 σ χ sci 2 ) } - 1 ) - 1
D i f f u s e s t a r i n g :             SNR sat = 1 + α 2 ( 1 + α 2 / 2 ) 2 + 2 [ exp ( 16 σ χ sci 2 - 1 ) ] · ξ ;
D i f f u s e i m a g i n g :             SNR sat = 1 + 2 [ exp ( 16 σ χ sci 2 - 1 ) ] · ξ ;
P D ( z = z ) = P r ( z ¯ + n ¯ 2 > - ln P F ) ,
P D = 0 P D ( z = z ) · P z ( z ) d z ,
P D ( z = z ) = Q [ 2 1 / 2 · z , ( - 2 ln P F ) 1 / 2 ] ,
Q ( α , β ) = β u exp - [ ( u 2 + α 2 ) / 2 ] · I 0 ( α u ) d u
P D = - P ( χ tot ) Q [ 2 · CNR g · exp 2 χ tot , ( - 2 ln P F ) 1 / 2 ] d χ ,
P χ tot = 0 P sci ( χ tot - χ b w ) · P b w ( χ b w ) d x b w .
P sci ( χ ) = ( 2 π σ χ sci 2 ) - 1 / 2 · exp [ - ( χ sci + σ sci 2 ) 2 / 2 σ χ sci 2 ]
P b w ( χ b w ) = w 0 2 2 σ b w 2 · exp { - 1 2 σ b w 2 [ w 0 2 ( - χ b w ) + x 0 2 ] } · I 0 ( w 0 x 0 - χ b w σ b w 2 ) ,
P z ( z ) = P t ( z z ¯ = z ) · P sci ( z ) d z ,
P t ( z ) = z / σ · exp ( - z 2 + A 2 2 σ 2 ) · I 0 ( A · z σ 2 )
P D ( m ) = 1 - ( 1 - P D ) m ,
S = i = 1 m z i 2 ,
P D incoh ( m ) = 1 - 0 S T / 2 ( 1 + CNR ) x m - 1 · exp ( - x ) Γ ( m ) d x .
P D = i T P t ( r ) d r z T P t ( z ) d z .
P F = i T P b ( r ) d r z T P b ( z ) d z ,
P b ( z ) = c · z c - 1 a c · exp - ( z / α ) c
( z T / a ) c = - ln P F .
q + CNR t / CNR b ,
S t ( b ) = P t ( b ) ( ω ) · h ( ω - ω c ω 1 / 2 ) d ω ,
P F = x = x T m b ( m b x ) P D b x ( 1 ) · [ 1 - P D b ( 1 ) ] m b - x
P D = x = x T m b ( m t x ) · P D t x ( 1 ) · [ 1 - P D t ( 1 ) ] m t - x .
P D = P F 1 / 1 + CNR t

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