Abstract

Measurements of signal amplitude distributions with a FM-cw CO2 laser radar have various targets in both imaging and staring modes. Data show good agreement with theoretical distributions. From the measurements conclusions are drawn about the atmospheric- as well as target-induced effects. Beam wandering effects are shown to be of importance in the staring mode.

© 1986 Optical Society of America

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  1. J. H. Shapiro, “Target-Reflectivity Theory for Coherent Laser Radars,” Appl. Opt. 21, 3398 (1982).
    [CrossRef] [PubMed]
  2. J. C. Leader, “Analysis and Prediction of Laser Scattering from Rough-Surface Materials,” J. Opt. Soc. Am. 69, 610 (1979).
    [CrossRef]
  3. J. K. Jao, M. Elbaum, “Probability Distribution of Optical Amplitudes Scattered from a Rough Object Containing Multiple Glints,” J. Opt. Soc. Am. 67, 1266 (1977).
    [CrossRef]
  4. J. Y. Wang, “Statistical Properties of Multiple-Glint Targets Under Laser Illumination,” Appl. Opt. 23, 2950 (1984).
    [CrossRef] [PubMed]
  5. J. H. Shapiro, “Correlation Scales of Laser Speckle in Heterodyne Detection,” Appl. Opt. 24, 1883 (1985).
    [CrossRef] [PubMed]
  6. D. M. Papurt, J. H. Shapiro, “Atmospheric Propagation Effects on Coherent Laser Radars,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 86 (1982).
  7. V. S. R. Gudimetla, J. F. Holmes, “Probability Density Function of the Intensity for a Laser-Generated Speckle Field After Propagation Through the Turbulent Atmosphere,” J. Opt. Soc. Am. 72, 1213 (1982).
    [CrossRef]
  8. 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]
  9. J. Y. Wang, “Heterodyne Laser Radar SNR from a Diffuse Target Containing Multiple Glints,” Appl. Opt. 21, 464 (1982).
    [CrossRef] [PubMed]
  10. 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 (1982).
    [CrossRef]
  11. P. H. Flamant, R. T. Menzies, M. J. Kavaya, “Evidence for Speckle Effects on Pulsed CO2 Lidar Signal Returns from Remote Targets,” Appl. Opt. 23, 1412 (1984).
    [CrossRef] [PubMed]
  12. D. M. Papurt, J. H. Shapiro, S. T. Lau, “Measured Turbulence and Speckle Effects in Laser Radar Target Returns,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 166 (1983).
  13. 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).
  14. I. Renhorn, O. Steinvall, D. Letalick, K. Gullberg, T. Claesson, A. Widén, “Performance Study of a Coherent Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 39 (1983).
  15. J. Y. Wang, B. J. Bartholomew, M. L. Streiff, E. F. Starr, “Imaging CO2 Laser Radar Field Tests,” Appl. Opt. 23, 2565 (1984).
    [CrossRef] [PubMed]
  16. A. D. Whalen, Detection of Signals in Noise (Academic, New York, 1971), p. 105.
  17. J. W. Strohbehn, Laser Beam Propagation in the Atmosphere (Springer-Verlag, Berlin, 1978), pp. 98–101.
  18. J. R. Kerr, “Turbulence Effects on Target Illumination by Cases Transmitter: Unified Analysis and Experimental Verification,” AGARD Conf. Proc. 183, Lyngby, Denmark (Oct. 1975).
  19. J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, New York, 1975), Chap. 2.
    [CrossRef]
  20. See, e.g., R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669 (1975).
    [CrossRef]
  21. G. G. Van Damm, M. J. Amoruso, J. W. McGarvey, “Reflectivity Measurements with 10.6-μm Infrared Radiation,” Army Weapons Laboratory, Rock Island (1972), AD 746238.
  22. M. D. Blue, G. R. Loefer, “Active/Passive Long Wavelength Infrared Laser Guidance,” Battelle Columbus Laboratories (1979), AD-A 082509.
  23. D. G. Eanby, J. A. Smith, “Target Signature Analyses Center, Data Compilation,” Utah U. (1966), AD 489968.
  24. D. Letalick, I. Renhorn, O. Steinvall, “Target and Atmospheric Influence on Coherent CO2 Laser Radar Performance,” Appl. Opt. 25, 0000 (1986), this issue.

1986 (1)

D. Letalick, I. Renhorn, O. Steinvall, “Target and Atmospheric Influence on Coherent CO2 Laser Radar Performance,” Appl. Opt. 25, 0000 (1986), this issue.

1985 (1)

1984 (3)

1983 (2)

D. M. Papurt, J. H. Shapiro, S. T. Lau, “Measured Turbulence and Speckle Effects in Laser Radar Target Returns,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 166 (1983).

I. Renhorn, O. Steinvall, D. Letalick, K. Gullberg, T. Claesson, A. Widén, “Performance Study of a Coherent Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 39 (1983).

1982 (5)

1981 (2)

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]

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).

1979 (2)

J. C. Leader, “Analysis and Prediction of Laser Scattering from Rough-Surface Materials,” J. Opt. Soc. Am. 69, 610 (1979).
[CrossRef]

M. D. Blue, G. R. Loefer, “Active/Passive Long Wavelength Infrared Laser Guidance,” Battelle Columbus Laboratories (1979), AD-A 082509.

1977 (1)

1975 (1)

See, e.g., R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669 (1975).
[CrossRef]

Amoruso, M. J.

G. G. Van Damm, M. J. Amoruso, J. W. McGarvey, “Reflectivity Measurements with 10.6-μm Infrared Radiation,” Army Weapons Laboratory, Rock Island (1972), AD 746238.

Bartholomew, B. J.

Blue, M. D.

M. D. Blue, G. R. Loefer, “Active/Passive Long Wavelength Infrared Laser Guidance,” Battelle Columbus Laboratories (1979), AD-A 082509.

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.

Claesson, T.

I. Renhorn, O. Steinvall, D. Letalick, K. Gullberg, T. Claesson, A. Widén, “Performance Study of a Coherent Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 39 (1983).

DeFeo, W. E.

Eanby, D. G.

D. G. Eanby, J. A. Smith, “Target Signature Analyses Center, Data Compilation,” Utah U. (1966), AD 489968.

Elbaum, M.

Fante, R. L.

See, e.g., R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669 (1975).
[CrossRef]

Flamant, P. H.

Goodman, J. W.

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, New York, 1975), Chap. 2.
[CrossRef]

Gudimetla, V. S. R.

Gullberg, K.

I. Renhorn, O. Steinvall, D. Letalick, K. Gullberg, T. Claesson, A. Widén, “Performance Study of a Coherent Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 39 (1983).

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).

Harney, R. C.

Holmes, J. F.

Jao, J. K.

Kavaya, M. J.

Kerr, J. R.

J. R. Kerr, “Turbulence Effects on Target Illumination by Cases Transmitter: Unified Analysis and Experimental Verification,” AGARD Conf. Proc. 183, Lyngby, Denmark (Oct. 1975).

Killinger, D. K.

Lau, S. T.

D. M. Papurt, J. H. Shapiro, S. T. Lau, “Measured Turbulence and Speckle Effects in Laser Radar Target Returns,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 166 (1983).

Leader, J. C.

Letalick, D.

D. Letalick, I. Renhorn, O. Steinvall, “Target and Atmospheric Influence on Coherent CO2 Laser Radar Performance,” Appl. Opt. 25, 0000 (1986), this issue.

I. Renhorn, O. Steinvall, D. Letalick, K. Gullberg, T. Claesson, A. Widén, “Performance Study of a Coherent Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 39 (1983).

Loefer, G. R.

M. D. Blue, G. R. Loefer, “Active/Passive Long Wavelength Infrared Laser Guidance,” Battelle Columbus Laboratories (1979), AD-A 082509.

McGarvey, J. W.

G. G. Van Damm, M. J. Amoruso, J. W. McGarvey, “Reflectivity Measurements with 10.6-μm Infrared Radiation,” Army Weapons Laboratory, Rock Island (1972), AD 746238.

Menyuk, N.

Menzies, R. T.

Papurt, D. M.

D. M. Papurt, J. H. Shapiro, S. T. Lau, “Measured Turbulence and Speckle Effects in Laser Radar Target Returns,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 166 (1983).

D. M. Papurt, J. H. Shapiro, “Atmospheric Propagation Effects on Coherent Laser Radars,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 86 (1982).

Renhorn, I.

D. Letalick, I. Renhorn, O. Steinvall, “Target and Atmospheric Influence on Coherent CO2 Laser Radar Performance,” Appl. Opt. 25, 0000 (1986), this issue.

I. Renhorn, O. Steinvall, D. Letalick, K. Gullberg, T. Claesson, A. Widén, “Performance Study of a Coherent Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 39 (1983).

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).

Shapiro, J. H.

J. H. Shapiro, “Correlation Scales of Laser Speckle in Heterodyne Detection,” Appl. Opt. 24, 1883 (1985).
[CrossRef] [PubMed]

D. M. Papurt, J. H. Shapiro, S. T. Lau, “Measured Turbulence and Speckle Effects in Laser Radar Target Returns,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 166 (1983).

J. H. Shapiro, “Target-Reflectivity Theory for Coherent Laser Radars,” Appl. Opt. 21, 3398 (1982).
[CrossRef] [PubMed]

D. M. Papurt, J. H. Shapiro, “Atmospheric Propagation Effects on Coherent Laser Radars,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 86 (1982).

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]

Smith, J. A.

D. G. Eanby, J. A. Smith, “Target Signature Analyses Center, Data Compilation,” Utah U. (1966), AD 489968.

Starr, E. F.

Steinvall, O.

D. Letalick, I. Renhorn, O. Steinvall, “Target and Atmospheric Influence on Coherent CO2 Laser Radar Performance,” Appl. Opt. 25, 0000 (1986), this issue.

I. Renhorn, O. Steinvall, D. Letalick, K. Gullberg, T. Claesson, A. Widén, “Performance Study of a Coherent Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 39 (1983).

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).

Streiff, M. L.

Strohbehn, J. W.

J. W. Strohbehn, Laser Beam Propagation in the Atmosphere (Springer-Verlag, Berlin, 1978), pp. 98–101.

Van Damm, G. G.

G. G. Van Damm, M. J. Amoruso, J. W. McGarvey, “Reflectivity Measurements with 10.6-μm Infrared Radiation,” Army Weapons Laboratory, Rock Island (1972), AD 746238.

Wang, J. Y.

Whalen, A. D.

A. D. Whalen, Detection of Signals in Noise (Academic, New York, 1971), p. 105.

Widén, A.

I. Renhorn, O. Steinvall, D. Letalick, K. Gullberg, T. Claesson, A. Widén, “Performance Study of a Coherent Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 39 (1983).

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)

Battelle Columbus Laboratories (1)

M. D. Blue, G. R. Loefer, “Active/Passive Long Wavelength Infrared Laser Guidance,” Battelle Columbus Laboratories (1979), AD-A 082509.

J. Opt. Soc. Am. (3)

Proc. IEEE (1)

See, e.g., R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE 63, 1669 (1975).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

D. M. Papurt, J. H. Shapiro, S. T. Lau, “Measured Turbulence and Speckle Effects in Laser Radar Target Returns,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 166 (1983).

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).

I. Renhorn, O. Steinvall, D. Letalick, K. Gullberg, T. Claesson, A. Widén, “Performance Study of a Coherent Laser Radar,” Proc. Soc. Photo-Opt. Instrum. Eng. 415, 39 (1983).

D. M. Papurt, J. H. Shapiro, “Atmospheric Propagation Effects on Coherent Laser Radars,” Proc. Soc. Photo-Opt. Instrum. Eng. 300, 86 (1982).

Other (6)

G. G. Van Damm, M. J. Amoruso, J. W. McGarvey, “Reflectivity Measurements with 10.6-μm Infrared Radiation,” Army Weapons Laboratory, Rock Island (1972), AD 746238.

D. G. Eanby, J. A. Smith, “Target Signature Analyses Center, Data Compilation,” Utah U. (1966), AD 489968.

A. D. Whalen, Detection of Signals in Noise (Academic, New York, 1971), p. 105.

J. W. Strohbehn, Laser Beam Propagation in the Atmosphere (Springer-Verlag, Berlin, 1978), pp. 98–101.

J. R. Kerr, “Turbulence Effects on Target Illumination by Cases Transmitter: Unified Analysis and Experimental Verification,” AGARD Conf. Proc. 183, Lyngby, Denmark (Oct. 1975).

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, New York, 1975), Chap. 2.
[CrossRef]

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Figures (18)

Fig. 1
Fig. 1

System overview of the FM-cw CO2 laser radar.

Fig. 2
Fig. 2

Illustration of the measurement scenario.

Fig. 3
Fig. 3

Example of measured signal amplitude distributions for the beam centered on the glint target. The fitted curves follow lognormal distributions from which values of σ z and C n can be deduced. In the above examples σ z = 0.08 and 0.17 for the 200- and 2000-m cases. The corresponding values of C n were 1.3 × 10−13 and 8.9 × 10−15 m−2/3, respectively.

Fig. 4
Fig. 4

Examples of measured signal amplitude distribution for the beam centered off the glint target. From the curve fits the normalized off-center distance (x0/w0) and the beam wandering (σ bw /w0) can be estimated. For the 200-m example, x0/w0 = 1.63 and σ bw /w0 = 0.15 are obtained and for 2000 m, x0/w0 = 1.35 and σ bw /w0 = 0.15. The prechosen misalignments were x0/w0 = 1.51 and 1.14, respectively (w0 = beam waist).

Fig. 5
Fig. 5

Time series from the glint target at 200-m range showing the time constants for scintillation (τ sci ≃ 30–40 ms) and beam wandering (τ bw ~ 200 ms).

Fig. 6
Fig. 6

Autocorrelation functions for the signal fluctuations from a glint target. The graphs are exponential fits to ten series of measured data. The increased influence of beam wander is reflected by the broadened curves for misaligned beams.

Fig. 7
Fig. 7

Example of signal amplitude distribution from a laser radar image using a diffuse target (sandblasted aluminum) at 2-km range. The distribution is well described by a Rayleigh distribution. Number of samples is 6400.

Fig. 8
Fig. 8

Signal amplitude distribution for a short exposure time of 2.4 s against a diffuse target (sulfur flowers). Number of samples is 1024. This distribution clearly deviates from the Rayleigh distribution.

Fig. 9
Fig. 9

Same as for Fig. 8 but with longer exposure time (12 s). Number of samples is 1024.

Fig. 10
Fig. 10

(a)–(d) A series of amplitude spectra from the laser in a staring mode against a diffuse target of sulfur flowers. The spectra with short exposure (2.4 s) from 200 and 600 m clearly deviates from a Rayleigh distribution and are well fitted with a Rician distribution with a high signal-to-noise power ratio A2/2σ2. At longer ranges or longer exposure times the distributions are close to the Rayleigh type.

Fig. 11
Fig. 11

Time series of fluctuations from a diffuse target with the laser in the staring mode. The different dominating time constants are attributed to target vibration (τ1), beam wandering (τ2), and scintillation (τ3), respectively.

Fig. 12
Fig. 12

Surface profiles of painted surfaces on smooth (target I) and rough (target II) metal, respectively.

Fig. 13
Fig. 13

Angular scattering functions G(θ,0) measured with an incoherent laser reflectometer at 10.6 and 1.06 μm. Curves with ρ = 1 and ρ = 10−2 indicate Lambertian reflection with 100 and 1% reflectivities. Same targets as in Fig. 12 were used.

Fig. 14
Fig. 14

Signal amplitude distributions from a semirough surface: (a) gives the result from 1024 pixels across the whole cylinder shaped surface, and (b) gives the distribution along the center line giving glints.

Fig. 15
Fig. 15

Example of semirough target imaging showing the glintlike Doppler image from a ferry at 7-km range.

Fig. 16
Fig. 16

Example of signal distributions from natural targets. The curves represent fitted Weibull distributions for A, trees; B, grass; and C, rocks.

Fig. 17
Fig. 17

Example of background measurements showing a stone pier against water: range 1.7 km; angle of incidence against water ~40 mrad.

Fig. 18
Fig. 18

Laser radar image and photo of a sandblasted Al plate (1.5 × 1.5 m2) against grass and tree background; range 2 km.

Tables (3)

Tables Icon

Table I Measured and Evaluated Parameters for the Glint Target PDF

Tables Icon

Table II Measured Characteristics of Terrain Backgrounds at 10.6 μm

Tables Icon

Table III Weibull Distribution Constants and Reflectance Values for Different Types of Terrain; the Constants a and c Refer to Eq.(17) for Best Curve Fit

Equations (17)

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Z = Z s c i · Z b w = exp ( χ f s c i + χ b s c i ) · exp χ b w ,
σ ln Z s c i 2 = 4 · σ χ s c i 2 = 4 · min ( 0 . 124 · C ¯ n 2 · ( 2 π λ ) 7 / 6 · L 11 / 6 ; 0.5 ) ,
σ lnZ 2 = 4 σ χ s c i 2 + σ χ s c i 2 + σ χ b w 2 .
P ( r , θ ) = 1 2 π σ b w 2 · exp - [ ( r cos θ - x ) 2 + r 2 · sin 2 θ ] / 2 σ b w 2 .
Z = E / E 0 = exp - r 2 w 0 2 ,
χ = ln Z = - r 2 w 0 2 .
P ( χ ) = 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 [ x 0 ω 0 ( - χ ) 1 / 2 σ b w 2 ] ,
w 0 2 ( - χ b w ) n = n ! ( 1 2 σ b w 2 ) n F 1 1 [ - n ; 1 ; x 0 2 2 σ b w 2 ] ,
σ χ b w 2 = 4 · ( σ b w w 0 ) 2 · ( x 0 w 0 ) 2 + ( σ b w w 0 ) 4 ] .
p ( z ) = z / σ 2 · exp - ( z 2 + A 2 ) 2 σ 2 · I 0 [ A z σ 2 ] .
A 2 2 σ 2 = γ 1 · γ t 1 - γ 1 γ t .
γ 1 = exp - 2 · ( Δ θ Δ θ coh ) 2 ;             Δ θ coh = 2 / k · w 0 ,
Δ ψ coh = w 0 L ( 1 + k 2 w 0 4 / 4 L 2 ) 1 / 2 ,
Q = E g / 2 σ 2 .
P ( z ) = z σ 2 · exp - ( z 2 2 σ 2 + Q ) · I 0 ( Q · 2 · z σ ) ,
Q p = Q c · A beam A coh Q c · π w 0 2 λ R c · L ,
P w ( Z ) = c ( z ) c - 1 a c · exp - ( z a ) c ,

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