Abstract

A propagation model that describes the characteristics of multiscatter radiation in atmosphere is presented. The model is based on the Monte Carlo method; each scattering process is set as an event of probability. LOWTRAN7 is used to calculate the atmospheric coefficients, and Mie theory is used to calculate the scattering characteristics of the particles. It is shown that the multiscatter model matches the single-scatter model perfectly when the scattering count is 1, and the formula for the single-scatter approximation is modified for the non-line-of-sight (NLOS) problem. It is also shown that the duration of the impulse response is about 8μs, the proportion of single-scatter irradiance is very small, and the average scattering count is 3.85 instead of 1 when the range is close to 1 km (weather conditions, field of view, and elevation angle are given). All these characteristics are presented for what is, to our knowledge, the first time. This model is wavelength-independent; 0.254μm is chosen as the wavelength of simulation.

© 2009 Optical Society of America

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References

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  1. M. Z. Jacobson, Fundamentals of Atmospheric Modeling (Cambridge Univ. Press, 2005).
  2. C. N. Hewitt and A. V. Jackson, Handbook of Atmospheric Science: Principles and Applications (Blackwell, 2003).
    [CrossRef]
  3. E. J. McCartney, Optics of the Atmosphere: Scattering by Molecules and Particles (Wiley, 1976).
  4. M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A 8, 1964-1972 (1991).
    [CrossRef]
  5. M. H. Kalos and P. A. Whitlock, Monte Carlo Methods (Wiley-VCH, 2004).
  6. F. X. Kneizys, E. P. Shettle, and L. W. Abreu, The MODTRAN 2/3 Report and LOWTRAN 7 MODEL (Ontar, 1996).
  7. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  8. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
    [CrossRef]
  9. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge Univ. Press, 2005).
  10. G. Mie, “A contribution to the optics of turbid media, especially colloidal metallica suspensions,” Ann. Phys. 25, 377-445 (1908), in German.
    [CrossRef]

1991 (1)

1908 (1)

G. Mie, “A contribution to the optics of turbid media, especially colloidal metallica suspensions,” Ann. Phys. 25, 377-445 (1908), in German.
[CrossRef]

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, and L. W. Abreu, The MODTRAN 2/3 Report and LOWTRAN 7 MODEL (Ontar, 1996).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Hewitt, C. N.

C. N. Hewitt and A. V. Jackson, Handbook of Atmospheric Science: Principles and Applications (Blackwell, 2003).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Jackson, A. V.

C. N. Hewitt and A. V. Jackson, Handbook of Atmospheric Science: Principles and Applications (Blackwell, 2003).
[CrossRef]

Jacobson, M. Z.

M. Z. Jacobson, Fundamentals of Atmospheric Modeling (Cambridge Univ. Press, 2005).

Kalos, M. H.

M. H. Kalos and P. A. Whitlock, Monte Carlo Methods (Wiley-VCH, 2004).

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, and L. W. Abreu, The MODTRAN 2/3 Report and LOWTRAN 7 MODEL (Ontar, 1996).

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge Univ. Press, 2005).

Luettgen, M. R.

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere: Scattering by Molecules and Particles (Wiley, 1976).

Mie, G.

G. Mie, “A contribution to the optics of turbid media, especially colloidal metallica suspensions,” Ann. Phys. 25, 377-445 (1908), in German.
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge Univ. Press, 2005).

Reilly, D. M.

Shapiro, J. H.

Shettle, E. P.

F. X. Kneizys, E. P. Shettle, and L. W. Abreu, The MODTRAN 2/3 Report and LOWTRAN 7 MODEL (Ontar, 1996).

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge Univ. Press, 2005).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Whitlock, P. A.

M. H. Kalos and P. A. Whitlock, Monte Carlo Methods (Wiley-VCH, 2004).

Ann. Phys. (1)

G. Mie, “A contribution to the optics of turbid media, especially colloidal metallica suspensions,” Ann. Phys. 25, 377-445 (1908), in German.
[CrossRef]

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

Other (8)

M. Z. Jacobson, Fundamentals of Atmospheric Modeling (Cambridge Univ. Press, 2005).

C. N. Hewitt and A. V. Jackson, Handbook of Atmospheric Science: Principles and Applications (Blackwell, 2003).
[CrossRef]

E. J. McCartney, Optics of the Atmosphere: Scattering by Molecules and Particles (Wiley, 1976).

M. H. Kalos and P. A. Whitlock, Monte Carlo Methods (Wiley-VCH, 2004).

F. X. Kneizys, E. P. Shettle, and L. W. Abreu, The MODTRAN 2/3 Report and LOWTRAN 7 MODEL (Ontar, 1996).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge Univ. Press, 2005).

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Figures (7)

Fig. 1
Fig. 1

Vertical distribution of atmospheric coefficients.

Fig. 2
Fig. 2

Multiscatter propagation link.

Fig. 3
Fig. 3

Impulse responses of single-scatter and multiscatter models.

Fig. 4
Fig. 4

Energy density versus scattering count.

Fig. 5
Fig. 5

Single-scatter approximation.

Fig. 6
Fig. 6

Energy density and time (duration) of impulse response versus range.

Fig. 7
Fig. 7

Proportion of single-scatter energy and average scattering count versus range.

Equations (10)

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( I Q U V ) = ( 1 0 0 0 0 cos 2 ψ sin 2 ψ 0 0 sin 2 ψ cos 2 ψ 0 0 0 0 1 ) ( I Q U V ) .
( I s Q s U s V s ) = ( S 11 S 12 0 0 S 12 S 11 0 0 0 0 S 33 S 34 0 0 S 34 S 33 ) ( I Q U V ) .
k ext = Q ext ( a ) π a 2 n ( a ) d a ,
k sca = Q sca ( a ) π a 2 n ( a ) d a ,
k abs = Q abs ( a ) π a 2 n ( a ) d a .
z 0 z 0 + l z d ( x d 2 + y d 2 + z d 2 ) 1 2 k ext ( z ) d z = L z d ( x d 2 + y d 2 + z d 2 ) 1 2 .
P e ( γ ) = P ( γ , a ) Q sca ( a ) π a 2 n ( a ) d a Q sca ( a ) π a 2 n ( a ) d a .
τ < 0.1 ( h + ( h 2 1 ) 1 2 ) ,
h = 1 + cos ( β T θ T ) cos ( β R θ R ) cos ( β T θ T ) + cos ( β R θ R ) ,
0 < ( β R θ R ) + ( β T θ T ) < 180 ° .

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