Abstract

Point sources in the atmosphere are surrounded by aureoles because of atmospheric scattering. The properties of an aureole were calculated by use of a Monte Carlo approach and an iterative method for an isotropic source and an axially symmetric emission source inside an infinite homogeneous atmosphere. The influence of single-scattering albedo, optical depth between source and observer, and source intensity anisotropy were studied from both approaches. For each situation, the limits and advantages of the Monte Carlo technique and the iterative method are described.

© 1999 Optical Society of America

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References

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  1. A. S. Zachor, “Aureole radiance field about a source in a scattering–absorbing medium,” Appl. Opt. 17, 1911–1922 (1978).
    [Crossref] [PubMed]
  2. L. C. Bissonette, “Multiscattering model for propagation of narrow light beams in aerosol media,” Appl. Opt. 27, 2478–2484 (1988).
    [Crossref]
  3. W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert Law. 1. Open detector,” Appl. Opt. 21, 2405–2412 (1982).
    [Crossref] [PubMed]
  4. W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert law. 2. Detector with a variable field of view,” Appl. Opt. 21, 2412–2420 (1982).
    [Crossref]
  5. P. H. Paul, S. A. Self, “Method for spectroradiometric temperature measurements in two phase flows. 1. Theory,” Appl. Opt. 28, 2143–2149 (1989).
    [Crossref] [PubMed]
  6. P. H. Paul, S. A. Self, “Method for spectroradiometric temperature measurements in two phase flows. 2. Experimental verification,” Appl. Opt. 28, 2150–2155 (1989).
    [Crossref] [PubMed]
  7. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  8. P. Bruscaglioni, G. Zaccanti, Q. Wei, “Transmission of a pulsed polarized light beam through thick turbid media: numerical results,” Appl. Opt. 32, 6142–6150 (1993).
    [Crossref] [PubMed]
  9. F. Riewe, A. E. S. Green, “Ultraviolet aureole arounda source at a finite distance,” Appl. Opt. 17, 1923–1929(1978).
    [Crossref] [PubMed]
  10. R. R. Meier, J. S. Lee, D. E. Anderson, “Atmospheric scattering of middle UV radiation from an internal source,” Appl. Opt. 17, 3216–3225 (1978).
    [Crossref] [PubMed]
  11. G. Zaccanti, “Monte Carlo study of light propagation in optically thick media: point source case,” Appl. Opt. 30, 2031–2041 (1991).
    [Crossref] [PubMed]
  12. K. N. Liou, Y. Takano, S. C. Ou, A. Heymsfield, W. Kreiss, “Infrared transmission through cirrus clouds: a radiative model for target detection,” Appl. Opt. 29, 1886–1896 (1990).
    [Crossref] [PubMed]
  13. J. P. Briton, “Simulations numériques de la diffusion de la lumière par une méthode de Monte Carlo et applications,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1989).
  14. J. P. Briton, B. Maheu, G. Gréhan, G. Gouesbet, “Monte Carlo simulation of multiple scattering in arbitrary 3-D geometry,” Part. Part. Syst. Charact. 9, 52–58 (1992).
    [Crossref]
  15. C. Rozé, B. Maheu, G. Gréhan, “Evaluations of the distance of visibility in a foggy atmosphere by Monte Carlo simulation,” Atmos. Environ. 28, 769–775 (1994).
    [Crossref]
  16. T. Girasole, C. Rozé, B. Maheu, G. Gréhan, J. Ménard, “Visibility distances in a foggy atmosphere: comparison between lighting installations by means of Monte Carlo simulation,” Int. J. Lighting Res. Technol. 30, 23–36 (1998).
  17. T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).
  18. W. H. Press, B. P. Flannery, S. A. Teukolski, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), pp. 196–197.

1998 (1)

T. Girasole, C. Rozé, B. Maheu, G. Gréhan, J. Ménard, “Visibility distances in a foggy atmosphere: comparison between lighting installations by means of Monte Carlo simulation,” Int. J. Lighting Res. Technol. 30, 23–36 (1998).

1997 (1)

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

1994 (1)

C. Rozé, B. Maheu, G. Gréhan, “Evaluations of the distance of visibility in a foggy atmosphere by Monte Carlo simulation,” Atmos. Environ. 28, 769–775 (1994).
[Crossref]

1993 (1)

1992 (1)

J. P. Briton, B. Maheu, G. Gréhan, G. Gouesbet, “Monte Carlo simulation of multiple scattering in arbitrary 3-D geometry,” Part. Part. Syst. Charact. 9, 52–58 (1992).
[Crossref]

1991 (1)

1990 (1)

1989 (2)

1988 (1)

1982 (2)

W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert Law. 1. Open detector,” Appl. Opt. 21, 2405–2412 (1982).
[Crossref] [PubMed]

W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert law. 2. Detector with a variable field of view,” Appl. Opt. 21, 2412–2420 (1982).
[Crossref]

1978 (3)

Anderson, D. E.

Bissonette, L. C.

Briton, J. P.

J. P. Briton, B. Maheu, G. Gréhan, G. Gouesbet, “Monte Carlo simulation of multiple scattering in arbitrary 3-D geometry,” Part. Part. Syst. Charact. 9, 52–58 (1992).
[Crossref]

J. P. Briton, “Simulations numériques de la diffusion de la lumière par une méthode de Monte Carlo et applications,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1989).

Bruscaglioni, P.

Bultynck, H.

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolski, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), pp. 196–197.

Girasole, T.

T. Girasole, C. Rozé, B. Maheu, G. Gréhan, J. Ménard, “Visibility distances in a foggy atmosphere: comparison between lighting installations by means of Monte Carlo simulation,” Int. J. Lighting Res. Technol. 30, 23–36 (1998).

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

Gouesbet, G.

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

J. P. Briton, B. Maheu, G. Gréhan, G. Gouesbet, “Monte Carlo simulation of multiple scattering in arbitrary 3-D geometry,” Part. Part. Syst. Charact. 9, 52–58 (1992).
[Crossref]

Green, A. E. S.

Gréhan, G.

T. Girasole, C. Rozé, B. Maheu, G. Gréhan, J. Ménard, “Visibility distances in a foggy atmosphere: comparison between lighting installations by means of Monte Carlo simulation,” Int. J. Lighting Res. Technol. 30, 23–36 (1998).

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

C. Rozé, B. Maheu, G. Gréhan, “Evaluations of the distance of visibility in a foggy atmosphere by Monte Carlo simulation,” Atmos. Environ. 28, 769–775 (1994).
[Crossref]

J. P. Briton, B. Maheu, G. Gréhan, G. Gouesbet, “Monte Carlo simulation of multiple scattering in arbitrary 3-D geometry,” Part. Part. Syst. Charact. 9, 52–58 (1992).
[Crossref]

Heymsfield, A.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

Kreiss, W.

Le Meur, F.

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

Le Toulouzan, J. N.

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

Lee, J. S.

Liou, K. N.

Maheu, B.

T. Girasole, C. Rozé, B. Maheu, G. Gréhan, J. Ménard, “Visibility distances in a foggy atmosphere: comparison between lighting installations by means of Monte Carlo simulation,” Int. J. Lighting Res. Technol. 30, 23–36 (1998).

C. Rozé, B. Maheu, G. Gréhan, “Evaluations of the distance of visibility in a foggy atmosphere by Monte Carlo simulation,” Atmos. Environ. 28, 769–775 (1994).
[Crossref]

J. P. Briton, B. Maheu, G. Gréhan, G. Gouesbet, “Monte Carlo simulation of multiple scattering in arbitrary 3-D geometry,” Part. Part. Syst. Charact. 9, 52–58 (1992).
[Crossref]

Meier, R. R.

Ménard, J.

T. Girasole, C. Rozé, B. Maheu, G. Gréhan, J. Ménard, “Visibility distances in a foggy atmosphere: comparison between lighting installations by means of Monte Carlo simulation,” Int. J. Lighting Res. Technol. 30, 23–36 (1998).

Mroczka, J.

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

Ou, S. C.

Paul, P. H.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolski, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), pp. 196–197.

Ren, K. F.

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

Riewe, F.

Rozé, C.

T. Girasole, C. Rozé, B. Maheu, G. Gréhan, J. Ménard, “Visibility distances in a foggy atmosphere: comparison between lighting installations by means of Monte Carlo simulation,” Int. J. Lighting Res. Technol. 30, 23–36 (1998).

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

C. Rozé, B. Maheu, G. Gréhan, “Evaluations of the distance of visibility in a foggy atmosphere by Monte Carlo simulation,” Atmos. Environ. 28, 769–775 (1994).
[Crossref]

Self, S. A.

Takano, Y.

Tam, W. G.

W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert Law. 1. Open detector,” Appl. Opt. 21, 2405–2412 (1982).
[Crossref] [PubMed]

W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert law. 2. Detector with a variable field of view,” Appl. Opt. 21, 2412–2420 (1982).
[Crossref]

Teukolski, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolski, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), pp. 196–197.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolski, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), pp. 196–197.

Wei, Q.

Wysoczanski, D.

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

Zaccanti, G.

Zachor, A. S.

Zardecki, A.

W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert law. 2. Detector with a variable field of view,” Appl. Opt. 21, 2412–2420 (1982).
[Crossref]

W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert Law. 1. Open detector,” Appl. Opt. 21, 2405–2412 (1982).
[Crossref] [PubMed]

Appl. Opt. (11)

A. S. Zachor, “Aureole radiance field about a source in a scattering–absorbing medium,” Appl. Opt. 17, 1911–1922 (1978).
[Crossref] [PubMed]

L. C. Bissonette, “Multiscattering model for propagation of narrow light beams in aerosol media,” Appl. Opt. 27, 2478–2484 (1988).
[Crossref]

W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert Law. 1. Open detector,” Appl. Opt. 21, 2405–2412 (1982).
[Crossref] [PubMed]

W. G. Tam, A. Zardecki, “Multiple scattering corrections to the Beer–Lambert law. 2. Detector with a variable field of view,” Appl. Opt. 21, 2412–2420 (1982).
[Crossref]

P. H. Paul, S. A. Self, “Method for spectroradiometric temperature measurements in two phase flows. 1. Theory,” Appl. Opt. 28, 2143–2149 (1989).
[Crossref] [PubMed]

P. H. Paul, S. A. Self, “Method for spectroradiometric temperature measurements in two phase flows. 2. Experimental verification,” Appl. Opt. 28, 2150–2155 (1989).
[Crossref] [PubMed]

P. Bruscaglioni, G. Zaccanti, Q. Wei, “Transmission of a pulsed polarized light beam through thick turbid media: numerical results,” Appl. Opt. 32, 6142–6150 (1993).
[Crossref] [PubMed]

F. Riewe, A. E. S. Green, “Ultraviolet aureole arounda source at a finite distance,” Appl. Opt. 17, 1923–1929(1978).
[Crossref] [PubMed]

R. R. Meier, J. S. Lee, D. E. Anderson, “Atmospheric scattering of middle UV radiation from an internal source,” Appl. Opt. 17, 3216–3225 (1978).
[Crossref] [PubMed]

G. Zaccanti, “Monte Carlo study of light propagation in optically thick media: point source case,” Appl. Opt. 30, 2031–2041 (1991).
[Crossref] [PubMed]

K. N. Liou, Y. Takano, S. C. Ou, A. Heymsfield, W. Kreiss, “Infrared transmission through cirrus clouds: a radiative model for target detection,” Appl. Opt. 29, 1886–1896 (1990).
[Crossref] [PubMed]

Atmos. Environ. (1)

C. Rozé, B. Maheu, G. Gréhan, “Evaluations of the distance of visibility in a foggy atmosphere by Monte Carlo simulation,” Atmos. Environ. 28, 769–775 (1994).
[Crossref]

Int. J. Lighting Res. Technol. (1)

T. Girasole, C. Rozé, B. Maheu, G. Gréhan, J. Ménard, “Visibility distances in a foggy atmosphere: comparison between lighting installations by means of Monte Carlo simulation,” Int. J. Lighting Res. Technol. 30, 23–36 (1998).

Part. Part. Syst. Charact. (2)

T. Girasole, H. Bultynck, G. Gouesbet, G. Gréhan, F. Le Meur, J. N. Le Toulouzan, J. Mroczka, K. F. Ren, C. Rozé, D. Wysoczanski, “Cylindrical fibre orientation analysis by light scattering. 1. Numerical aspects,” Part. Part. Syst. Charact. 14, 163–174 (1997).

J. P. Briton, B. Maheu, G. Gréhan, G. Gouesbet, “Monte Carlo simulation of multiple scattering in arbitrary 3-D geometry,” Part. Part. Syst. Charact. 9, 52–58 (1992).
[Crossref]

Other (3)

W. H. Press, B. P. Flannery, S. A. Teukolski, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), pp. 196–197.

J. P. Briton, “Simulations numériques de la diffusion de la lumière par une méthode de Monte Carlo et applications,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1989).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

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Figures (12)

Fig. 1
Fig. 1

Geometry used for the iterative approach in the case of axially symmetric source intensity.

Fig. 2
Fig. 2

Schematic representation of first-order scattering in the case of axially symmetric source intensity.

Fig. 3
Fig. 3

Schematic representation of n-order scattering (n ≥ 1) in the case of axially symmetric source intensity.

Fig. 4
Fig. 4

Elementary detector arrangement for Monte Carlo calculations in the case of axially symmetric source intensity.

Fig. 5
Fig. 5

Comparisons of (a) the apparent radiance and (b) the FOV transmittance from Monte Carlo calculations and the iterative method for different optical thicknesses τ in the isotropic case (α s = 1) at λ = 260 nm.

Fig. 6
Fig. 6

Comparison of (a) the apparent radiance and (b) the FOV transmittance from Monte Carlo calculations and the iterative method for different optical thicknesses τ in the isotropic case (α s = 1) at λ = 280 nm.

Fig. 7
Fig. 7

Comparison of (a) the apparent radiance and (b) the FOV transmittance from Monte Carlo calculations and the iterative method for different optical thicknesses τ in the isotropic case (α s = 1) at λ = 300 nm.

Fig. 8
Fig. 8

Comparison of the FOV transmittance from Monte Carlo calculations and the iterative method for four optical thicknesses τ for an axially symmetric source intensity α s (peaked source). The four detectors are located on the source symmetry axis (θ0 = 0°).

Fig. 9
Fig. 9

Comparison of the FOV transmittance from Monte Carlo calculations with the iterative method for four optical thicknesses τ for an axially symmetric source intensity α s (shaded source). The four detectors are located on the source symmetry axis(θ0 = 0°).

Fig. 10
Fig. 10

Comparison of the apparent radiance calculated with the iterative method for the three types of source (shaded source, α s = 100; isotropic source, α s = 1; peaked source, α s = 0.01) for an optical thickness τ = 2. The detector is located on the source symmetry axis (θ0 = 0°).

Fig. 11
Fig. 11

Comparison of the FOV transmittance calculated with the iterative method for the three types of source (shaded source, α s = 100; isotropic source, α s = 1; peaked source, α s = 0.01) for an optical thickness τ = 2. The detector is located on the symmetry axis (θ0 = 0°).

Fig. 12
Fig. 12

FOV transmittance calculated with the Monte Carlo method for four optical thicknesses τ for an axially symmetric source intensity (shaded source). The four detectors are located on the source symmetry axis (θ0 = 0°).

Tables (1)

Tables Icon

Table 1 Atmospheric Parameters Used in the Calculations

Equations (24)

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IScos θ=IS¯Scos θ,
0π Scos θsin θ dθ=2.
Φd=IScos θ0SDR2 e-τ,
dB1O, vˆ=IScosuˆ0·eˆzexp-kextRR2×βPμexp-kextr,
B1τ, uˆ0, vˆ=kext2aτ sin γexp-τ cos γ×γπdθ exp-τ sin γ tan θ/2×IScos θ0Pcos θ,
θ0=cos-1τ cos θ0-tsin γ cos ϕ sin θ0+cos γ cos θ0τ,
N1τ, uˆ0, vˆ=B1τ, uˆ0, vˆR2 sin γIS,
N1τ, uˆ0, vˆ=τa exp-τ cos γ×γπdθ exp-τ sin γ tan θ/2×Scos θ0Pcos θ.
Nnτ, uˆ0, vˆ=aτ2 sin γ 0+dt e-tτ20πdγ×02πdϕNn-1τ, uˆ0, vˆPcos θ.
Tτ, u0, Θ=exp-τ+1Scos θ0×02πdϕ 0Θ/2dγNτ, uˆ0, vˆ|cos γ|.
N¯τ, uˆ0, γ=12π02πdϕNτ, uˆ0, vˆ.
ϕ0=2πr1
2r2=0θ0 Scos θsin θdθ.
l=-Ln r3ksca.
φ=2πr4,
2r5=0θ Pcos θsin θdθ.
Tτ, uˆ0, Θ=i WiFγi; ΘNT/2θ0θ0+δθ0 Scos θsin θdθ,
Pμ=βRPRμ+βAPAμβR+βA,  ksca=βR+βA.
PRμ=316π1+μ2.
PAμ=1-g24π11+g2-2gμ3/2+f3μ2-121+g23/2.
Sθ0=21+αS21-αSLn1+1-αS1-1-αS×cos2 θ0+αS sin2 θ01/2,  αS<1,
Sθ0=1,  αS=1,
Sθ0=21+αSαS-1arcsinαS-1αS1/2×cos2 θ0+αS sin2 θ01/2,  αS>1.
θ0=cos-11-2r2.

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