Abstract

We propose a model based on the properties of cascading lenses modulation transfer function (MTF) to reproduce the irradiance of a screen illuminated through a dense aerosol cloud. In this model, the aerosol cloud is broken into multiple thin layers considered as individual lenses. The screen irradiance generated by these individual layers is equivalent to the point-spread function (PSF) of each aerosol lens. Taking the Fourier transform of the PSF as a MTF, we cascade the lenses MTF to find the cloud MTF. The screen irradiance is found with the Fourier transform of this MTF. We show the derivation of the model and we compare the results with the Undique Monte Carlo simulator for four aerosols at three optical depths. The model is in agreement with the Monte Carlo for all the cases tested.

© 2011 Optical Society of America

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References

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  1. E. P. Silaeva and V. P. Kandidov, Atmos. Oceanic Opt. 22, 26 (2009).
    [CrossRef]
  2. V. O. Militsin, E. P. Kachan, and V. P. Kandidov, Quantum Electron. 36, 1032 (2006).
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    [CrossRef]
  6. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw Hill, 1986).
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    [CrossRef]
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    [CrossRef]
  9. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1983).

2010

G. Tremblay, X. Cao, and G. Roy, Proc. SPIE 7828, 78280C (2010).
[CrossRef]

2009

E. P. Silaeva and V. P. Kandidov, Atmos. Oceanic Opt. 22, 26 (2009).
[CrossRef]

2006

V. O. Militsin, E. P. Kachan, and V. P. Kandidov, Quantum Electron. 36, 1032 (2006).
[CrossRef]

1992

L. R. Bissonnette, Opt. Eng. 31, 1045 (1992).
[CrossRef]

1974

R. E. Swing, Proc. SPIE 46, 104 (1974).

1967

Bissonnette, L. R.

L. R. Bissonnette, Opt. Eng. 31, 1045 (1992).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1983).

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw Hill, 1986).

Cao, X.

G. Tremblay, X. Cao, and G. Roy, Proc. SPIE 7828, 78280C (2010).
[CrossRef]

DeVelis, J. B.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1983).

Kachan, E. P.

V. O. Militsin, E. P. Kachan, and V. P. Kandidov, Quantum Electron. 36, 1032 (2006).
[CrossRef]

Kandidov, V. P.

E. P. Silaeva and V. P. Kandidov, Atmos. Oceanic Opt. 22, 26 (2009).
[CrossRef]

V. O. Militsin, E. P. Kachan, and V. P. Kandidov, Quantum Electron. 36, 1032 (2006).
[CrossRef]

Militsin, V. O.

V. O. Militsin, E. P. Kachan, and V. P. Kandidov, Quantum Electron. 36, 1032 (2006).
[CrossRef]

Parrent, G. B.

Roy, G.

G. Tremblay, X. Cao, and G. Roy, Proc. SPIE 7828, 78280C (2010).
[CrossRef]

Schroeder, D. J.

D. J. Schroeder, Astronomical Optics (Academic, 1987).

Silaeva, E. P.

E. P. Silaeva and V. P. Kandidov, Atmos. Oceanic Opt. 22, 26 (2009).
[CrossRef]

Swing, R. E.

R. E. Swing, Proc. SPIE 46, 104 (1974).

Tremblay, G.

G. Tremblay, X. Cao, and G. Roy, Proc. SPIE 7828, 78280C (2010).
[CrossRef]

Atmos. Oceanic Opt.

E. P. Silaeva and V. P. Kandidov, Atmos. Oceanic Opt. 22, 26 (2009).
[CrossRef]

J. Opt. Soc. Am.

Opt. Eng.

L. R. Bissonnette, Opt. Eng. 31, 1045 (1992).
[CrossRef]

Proc. SPIE

G. Tremblay, X. Cao, and G. Roy, Proc. SPIE 7828, 78280C (2010).
[CrossRef]

R. E. Swing, Proc. SPIE 46, 104 (1974).

Quantum Electron.

V. O. Militsin, E. P. Kachan, and V. P. Kandidov, Quantum Electron. 36, 1032 (2006).
[CrossRef]

Other

D. J. Schroeder, Astronomical Optics (Academic, 1987).

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw Hill, 1986).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1983).

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Figures (4)

Fig. 1
Fig. 1

Conversion from a system propagating a narrow light beam through aerosols (top) to a stratified model made of a succession of “aerosol lenses” (bottom).

Fig. 2
Fig. 2

Image formation by a thin layer of aerosols dominated by order one forward scattering.

Fig. 3
Fig. 3

Comparison between the stratified model and the Undique Imaging Monte Carlo simulator. In the usual order, the results for water droplets 100 μm , 10 μm , 1 μm , and 0.1 μm in diameter. Red lines are the UNDIQUE results. Dark lines are the aerosol lenses model results.

Fig. 4
Fig. 4

Scattered signal irradiance on the screen by scattering order for water droplets 100 μm , 10 μm , 1 μm , and 0.1 μm in diameter at τ = 2 . Red lines are the UNDIQUE results. Dark lines are the aerosol lenses model results.

Equations (13)

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P 0 = ( P U + P S ) n .
I S i ( r ) = P 0 Φ ( θ ( r ) , φ ) d i 2 cos ( θ ( r ) ) ,
I u ( r ) = P 0 area δ ( r ) π | r | .
I i ( r ) = α i I s i ( r ) I s i ( 0 ) + β i I u ( r ) I u ( 0 ) .
H i ( k ) = P s i H s i ( k ) + P u i H u ( k ) P u i + P s i ,
P u i = P 0 exp ( τ i ) P s i = P 0 ( 1 exp ( τ i ) ) * E s ( θ ) ,
E S ( θ ) = φ = 0 2 π θ = 0 θ Φ ( θ , φ ) sin θ d θ d φ .
I ( r ) = F ( i = 1 n [ P s i H S i ( k ) + P u i H u ( k ) P u i + P s i ] ) .
I ( r ) = F ( [ P s H s ( k ) + P u H u ( k ) ] n ) .
I 0 th = F [ i = 1 n ( P u i H u i P s i + P u i ) ] ,
I 1 st = F [ j = 1 n [ H s j H u j P s j P u j i = 1 n ( P u i H u i P s i + P u i ) ] ] ,
I 2 nd = F [ j = 1 n 1 k = j + 1 n [ H s j H s k P s j P s k H u j H u k P u j P u k i = 1 n ( P u i H u i P s i + P u i ) ] ] ,
I n th = F [ i = 1 n ( P u i H u i P s i + P u i ) ] .

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