Abstract

When lidar pulses travel through a short path that includes a relatively high concentration of aerosols, scattering phenomena can alter the power and temporal properties of the pulses significantly, causing undesirable effects in the received pulse. In many applications the design of the lidar transmitter and receiver must consider adverse environmental aerosol conditions to ensure the desired performance. We present an analytical model of lidar system operation when the optical path includes aerosols for use in support of instrument design, simulations, and system evaluation. The model considers an optical path terminated with a solid object, although it can also be applied, with minor modifications, to cases where the expected backscatter occurs from nonsolid objects. The optical path aerosols are characterized by their attenuation and backscatter coefficients derived by the Mie theory from the concentration and particle size distribution of the aerosol. Other inputs include the lidar system parameters and instrument response function, and the model output is the time-resolved received pulse. The model is demonstrated and experimentally validated with military fog oil smoke for short ranges (several meters). The results are obtained with a lidar system operating at a wavelength of 0.905μm within and outside the aerosol. The model goodness of fit is evaluated using the statistical coefficient of determination whose value ranged from 0.88 to 0.99 in this study.

© 2008 Optical Society of America

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References

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  1. R. W. Byren, “Laser rangefinders,” in The Infrared and Electro-Optical Systems Handbook, C.S.Fox, ed. (SPIE Optical Engineering, 1993), Vol. 6, Chap. 2, pp. 77-114.
  2. M. Kleiman and N. Shiloah, “The effect of dense atmospheric environment on the performances of laser radar sensors used for collision avoidance,” Proc. SPIE 3707, 624-635 (1999).
    [CrossRef]
  3. R. M. Measures, Laser Remote Sensing (John Wiley, 1984).
  4. H. N. Burns, C. G. Christodoulou, and G. D. Boreman, “System design of a pulsed laser rangefinder,” Opt. Eng. 30, 323-329(1991).
    [CrossRef]
  5. G. W. Kamerman, “Laser radar,” in The Infrared and Electro-Optical Systems Handbook, C. S. Fox, ed. (SPIE Optical Engineering, 1993), Vol. 6, Chap. 1, pp. 3-76.
  6. W. C. Hinds, Aerosol Technology (Wiley, 1999).
  7. K. Willeke and P. A. Baron, Aerosol Measurement (Wiley, 1993).
  8. H. R. Carlon, D. H. Anderson, M. E. Milham, T. L. Tarnove, R. H. Frickel, and I. Sindoni, “Infrared extinction spectra of some common liquid aerosols,” Appl. Opt. 16, 1598-1605(1977).
    [CrossRef] [PubMed]
  9. M. E. Thomas and D. D. Duncan, “Atmospheric transmission,” in The Infrared and Electro-Optical Systems Handbook, F. G. Smith, ed. (SPIE Optical Engineering, 1993), Vol. 2, Chap. 1, pp. 1-156.
  10. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).
  11. C. S. Zender, “Particle size distributions: theory and application to aerosols, clouds, and soils,” (2008), http://dust.ess.uci.edu/facts/psd/psd.pdf.
  12. D. H. Anderson, Soldier Biological Chemical Command (SBCCOM), Edgewood, Maryland 21010 (personal communication, 2001).
  13. Joint Technical Coordinating Group for Munitions Effectiveness, Smoke and Aerosol Working Group, “Smoke and natural aerosol parameters (SNAP) manual,” Report No. 61JTCG/ME-85-2 (1985), p. 5-1.
  14. V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004).
    [CrossRef]
  15. R. G. Knollenberg, “Techniques for probing cloud microstructure,” in Clouds Their Formation, Optical Properties, and Effects, P. V. Hobbs and A. Deepak, eds. (Academic, 1981), pp. 15-91.
  16. R. E. Walker and J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. 38, 2384-2397(1999).
    [CrossRef]

2008 (1)

C. S. Zender, “Particle size distributions: theory and application to aerosols, clouds, and soils,” (2008), http://dust.ess.uci.edu/facts/psd/psd.pdf.

2004 (1)

V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004).
[CrossRef]

2001 (1)

D. H. Anderson, Soldier Biological Chemical Command (SBCCOM), Edgewood, Maryland 21010 (personal communication, 2001).

1999 (3)

R. E. Walker and J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. 38, 2384-2397(1999).
[CrossRef]

M. Kleiman and N. Shiloah, “The effect of dense atmospheric environment on the performances of laser radar sensors used for collision avoidance,” Proc. SPIE 3707, 624-635 (1999).
[CrossRef]

W. C. Hinds, Aerosol Technology (Wiley, 1999).

1993 (4)

K. Willeke and P. A. Baron, Aerosol Measurement (Wiley, 1993).

M. E. Thomas and D. D. Duncan, “Atmospheric transmission,” in The Infrared and Electro-Optical Systems Handbook, F. G. Smith, ed. (SPIE Optical Engineering, 1993), Vol. 2, Chap. 1, pp. 1-156.

R. W. Byren, “Laser rangefinders,” in The Infrared and Electro-Optical Systems Handbook, C.S.Fox, ed. (SPIE Optical Engineering, 1993), Vol. 6, Chap. 2, pp. 77-114.

G. W. Kamerman, “Laser radar,” in The Infrared and Electro-Optical Systems Handbook, C. S. Fox, ed. (SPIE Optical Engineering, 1993), Vol. 6, Chap. 1, pp. 3-76.

1991 (1)

H. N. Burns, C. G. Christodoulou, and G. D. Boreman, “System design of a pulsed laser rangefinder,” Opt. Eng. 30, 323-329(1991).
[CrossRef]

1985 (1)

Joint Technical Coordinating Group for Munitions Effectiveness, Smoke and Aerosol Working Group, “Smoke and natural aerosol parameters (SNAP) manual,” Report No. 61JTCG/ME-85-2 (1985), p. 5-1.

1984 (1)

R. M. Measures, Laser Remote Sensing (John Wiley, 1984).

1981 (1)

R. G. Knollenberg, “Techniques for probing cloud microstructure,” in Clouds Their Formation, Optical Properties, and Effects, P. V. Hobbs and A. Deepak, eds. (Academic, 1981), pp. 15-91.

1977 (1)

1969 (1)

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).

Anderson, D. H.

Baron, P. A.

K. Willeke and P. A. Baron, Aerosol Measurement (Wiley, 1993).

Boreman, G. D.

H. N. Burns, C. G. Christodoulou, and G. D. Boreman, “System design of a pulsed laser rangefinder,” Opt. Eng. 30, 323-329(1991).
[CrossRef]

Burns, H. N.

H. N. Burns, C. G. Christodoulou, and G. D. Boreman, “System design of a pulsed laser rangefinder,” Opt. Eng. 30, 323-329(1991).
[CrossRef]

Byren, R. W.

R. W. Byren, “Laser rangefinders,” in The Infrared and Electro-Optical Systems Handbook, C.S.Fox, ed. (SPIE Optical Engineering, 1993), Vol. 6, Chap. 2, pp. 77-114.

Carlon, H. R.

Christodoulou, C. G.

H. N. Burns, C. G. Christodoulou, and G. D. Boreman, “System design of a pulsed laser rangefinder,” Opt. Eng. 30, 323-329(1991).
[CrossRef]

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).

Duncan, D. D.

M. E. Thomas and D. D. Duncan, “Atmospheric transmission,” in The Infrared and Electro-Optical Systems Handbook, F. G. Smith, ed. (SPIE Optical Engineering, 1993), Vol. 2, Chap. 1, pp. 1-156.

Eichinger, W. E.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004).
[CrossRef]

Frickel, R. H.

Hinds, W. C.

W. C. Hinds, Aerosol Technology (Wiley, 1999).

Kamerman, G. W.

G. W. Kamerman, “Laser radar,” in The Infrared and Electro-Optical Systems Handbook, C. S. Fox, ed. (SPIE Optical Engineering, 1993), Vol. 6, Chap. 1, pp. 3-76.

Kleiman, M.

M. Kleiman and N. Shiloah, “The effect of dense atmospheric environment on the performances of laser radar sensors used for collision avoidance,” Proc. SPIE 3707, 624-635 (1999).
[CrossRef]

Knollenberg, R. G.

R. G. Knollenberg, “Techniques for probing cloud microstructure,” in Clouds Their Formation, Optical Properties, and Effects, P. V. Hobbs and A. Deepak, eds. (Academic, 1981), pp. 15-91.

Kovalev, V. A.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004).
[CrossRef]

McLean, J. W.

Measures, R. M.

R. M. Measures, Laser Remote Sensing (John Wiley, 1984).

Milham, M. E.

Shiloah, N.

M. Kleiman and N. Shiloah, “The effect of dense atmospheric environment on the performances of laser radar sensors used for collision avoidance,” Proc. SPIE 3707, 624-635 (1999).
[CrossRef]

Sindoni, I.

Tarnove, T. L.

Thomas, M. E.

M. E. Thomas and D. D. Duncan, “Atmospheric transmission,” in The Infrared and Electro-Optical Systems Handbook, F. G. Smith, ed. (SPIE Optical Engineering, 1993), Vol. 2, Chap. 1, pp. 1-156.

Walker, R. E.

Willeke, K.

K. Willeke and P. A. Baron, Aerosol Measurement (Wiley, 1993).

Zender, C. S.

C. S. Zender, “Particle size distributions: theory and application to aerosols, clouds, and soils,” (2008), http://dust.ess.uci.edu/facts/psd/psd.pdf.

Appl. Opt. (2)

Opt. Eng. (1)

H. N. Burns, C. G. Christodoulou, and G. D. Boreman, “System design of a pulsed laser rangefinder,” Opt. Eng. 30, 323-329(1991).
[CrossRef]

Proc. SPIE (1)

M. Kleiman and N. Shiloah, “The effect of dense atmospheric environment on the performances of laser radar sensors used for collision avoidance,” Proc. SPIE 3707, 624-635 (1999).
[CrossRef]

Other (12)

R. M. Measures, Laser Remote Sensing (John Wiley, 1984).

R. W. Byren, “Laser rangefinders,” in The Infrared and Electro-Optical Systems Handbook, C.S.Fox, ed. (SPIE Optical Engineering, 1993), Vol. 6, Chap. 2, pp. 77-114.

G. W. Kamerman, “Laser radar,” in The Infrared and Electro-Optical Systems Handbook, C. S. Fox, ed. (SPIE Optical Engineering, 1993), Vol. 6, Chap. 1, pp. 3-76.

W. C. Hinds, Aerosol Technology (Wiley, 1999).

K. Willeke and P. A. Baron, Aerosol Measurement (Wiley, 1993).

M. E. Thomas and D. D. Duncan, “Atmospheric transmission,” in The Infrared and Electro-Optical Systems Handbook, F. G. Smith, ed. (SPIE Optical Engineering, 1993), Vol. 2, Chap. 1, pp. 1-156.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).

C. S. Zender, “Particle size distributions: theory and application to aerosols, clouds, and soils,” (2008), http://dust.ess.uci.edu/facts/psd/psd.pdf.

D. H. Anderson, Soldier Biological Chemical Command (SBCCOM), Edgewood, Maryland 21010 (personal communication, 2001).

Joint Technical Coordinating Group for Munitions Effectiveness, Smoke and Aerosol Working Group, “Smoke and natural aerosol parameters (SNAP) manual,” Report No. 61JTCG/ME-85-2 (1985), p. 5-1.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004).
[CrossRef]

R. G. Knollenberg, “Techniques for probing cloud microstructure,” in Clouds Their Formation, Optical Properties, and Effects, P. V. Hobbs and A. Deepak, eds. (Academic, 1981), pp. 15-91.

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Figures (9)

Fig. 1
Fig. 1

Configuration for the sensor located outside the obscurant.

Fig. 2
Fig. 2

Instrument response function for the short-range lidar.

Fig. 3
Fig. 3

Fog oil smoke chamber. The sensor and motorized track assembly can also be placed inside the smoke chamber.

Fig. 4
Fig. 4

Particle density versus particle radius for a lognormal distribution with MMD = 1.26 μm , r g = 0.45 μm , and σ g = 1.4 and the measured distribution. The horizontal bars show bin width ( 0.25 μm radius).

Fig. 5
Fig. 5

Mass extinction coefficient versus wavelength for various mass median fog oil smoke diameter particles for a lognormal distribution.

Fig. 6
Fig. 6

Model and experimental waveforms for sensor (a) 2.4, (b) 3.0, (c) 3.7, and (d)  4.3 m from target. The target and the sensor are immersed in medium smoke. The solid curves are model calculations, and the dashed curves are experimental.

Fig. 7
Fig. 7

Model and experimental waveforms for sensor (a) 2.7, (b) 3.0, (c) 3.7, and (d)  4.3 m from target. The target and the sensor are immersed in light smoke. The solid curves are model calculations, and the dashed curves are experimental.

Fig. 8
Fig. 8

Model and experimental waveforms for sensor (a) 2.4, (b) 3.0, (c) 3.7, and (d)  4.3 m from target. The target and the sensor are immersed in heavy smoke. The solid curves are model calculations, and the dashed curves are experimental.

Fig. 9
Fig. 9

Model and experimental waveforms for sensor (a) 0, (b) 0.3, (c) 0.6, and (d)  1.2 m from medium smoke interface. The 4% reflectance target is located 7.3 m from the smoke interface. The solid curves are model calculations, and the dashed curves are experimental.

Tables (3)

Tables Icon

Table 1 Fog Oil Smoke Parameters Calculated from the Mie Theory

Tables Icon

Table 2 Sensor System Parameters

Tables Icon

Table 3 Parameter Comparison for Modeled and Experimental Waveforms a

Equations (17)

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P aerosol ( z ) := { P pk η O ( z ) π ( β aerosol ( π ) + β clear_air ( π ) ) c τ int D 2 exp [ 2 [ α clear_air z cos ( θ s ) + α ext ( z H + S ) cos ( θ s ) ] ] 8 ( z cos ( θ s ) ) ( z cos ( θ s ) c τ int 2 ) , if     H > z ( H S ) [ z   is in obscurant ] ; P pk η O ( z ) ρ cos ( θ s ) D 2 exp [ 2 ( α clear_air H cos ( θ s ) + α ext S cos ( θ s ) ) ] 4 ( H cos ( θ s ) ) 2 , if   z = H [ z   is at target ] ; P pk η O ( z ) π β clear_air ( π ) c τ int D 2 exp [ 2 ( α clear_air z cos ( θ s ) ) ] 8 ( z cos ( θ s ) ) ( z cos ( θ s ) c τ int 2 ) , otherwise     [ z   is before obscurant ] ,
P aerosol ( z ) := { P pk η O ( z ) π ( β aerosol ( π ) + β clear_air ( π ) ) c τ int D 2 exp [ 2 [ α clear_air z cos ( θ s ) + α ext z cos ( θ s ) ] ] 8 ( z cos ( θ s ) ) ( z cos ( θ s ) c τ int 2 ) , if     H > z > 0 [ z   is in obscurant ] ; P pk η O ( z ) ρ cos ( θ s ) D 2 exp [ 2 ( α clear_air H cos ( θ s ) + α ext H cos ( θ s ) ) ] 4 ( H cos ( θ s ) ) 2 , if     z = H [ z   is at target ] .
F ( t ) = F ( t ) R G ,
f ( t ) = 0 t = t I ( t ) F ( t t ) d t = I ( t ) * F ( t ) ,
n ( r ) = d N d r = [ N r 2 π ln σ g ] exp { ( ln r / r g ) 2 2 ( ln σ g ) 2 } ,
ln ( MMD ) = ln 2 r g + 3 ( ln σ g ) 2 .
α ext = 0 C ext ( r ) n ( r ) d r ,
α ext = κ ext C ,
C = 4 3 π r g 3 exp [ 9 2 ( ln σ g ) 2 ] ρ N .
α sca = 0 C sca ( r ) n ( r ) d r ,
α sca = κ sca C ,
P ( θ ) = N 4 π S 11 ( θ ) k 2 α sca ,
k = 2 π / λ ,
β aerosol ( π ) = P ( π ) 4 π α sca = P ( π ) 4 π κ sca C ,
τ OD = 0 Z α ext ( z ) d z .
T = exp ( κ ext C L ) ,
R 2 = 1 RSS / TSS ,

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