Abstract

We present a Monte Carlo simulation for the scattering of light in the case of an isotropic light source. The scattering phase functions are studied particularly in detail to understand how they can affect the multiple light scattering in the atmosphere. We show that, although aerosols are usually in lower density than molecules in the atmosphere, they can have a non-negligible effect on the atmospheric point spread function. This effect is especially expected for ground-based detectors when large aerosols are present in the atmosphere.

© 2013 Optical Society of America

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References

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  1. N. S. Kopeika, I. Dror, and D. Sadot, “Causes of atmospheric blur: comment on atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am A 15, 3097–3106 (1998).
  2. J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface non-homogeneity,” Photogramm. Eng. Remote Sens. 46, 1173–1180 (1980).
  3. W. A. Pearce, “Monte Carlo study of the atmospheric spread function,” Appl. Opt. 25, 438–447 (1986).
    [CrossRef]
  4. D. Sadot and N. S. Kopeika, “Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol modulation transfer function,” J. Opt. Soc. Am. A 10, 172–179 (1993).
    [CrossRef]
  5. I. Dror and N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. P. N. Reinersman and K. L. Carder, “Monte Carlo simulation of the atmospheric point-spread function with an application to correction for the adjacency effect,” Appl. Opt. 34, 4453–4471 (1995).
    [CrossRef]
  9. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  10. H. C. Van De Hulst, Light Scattering by Small Particles (Dover, 1981).
  11. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
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    [CrossRef]
  13. B. Keilhauer and M. Will, for the Pierre Auger Collaboration, “Description of atmospheric conditions at the Pierre Auger Observatory using meteorological measurements and models,” Eur. Phys. J. Plus 127, 96 (2012).
  14. K. Louedec and R. Losno, for the Pierre Auger Collaboration, “Atmospheric aerosols at the Pierre Auger Observatory and environmental implications,” Eur. Phys. J. Plus 127, 97 (2012).
  15. G. Mie, “Beiträge zur Optik Trüber-Medien, speziell Kolloidaler Metallösungen,” Ann. Physik 25, 377–452 (1908).
  16. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [CrossRef]
  17. L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. K. Louedec and M. Urban, “Ramsauer approach for light scattering on non absorbing spherical particles and application to the Henyey-Greenstein phase function,” Appl. Opt 51, 7842–7852 (2012).
    [CrossRef]
  24. M. D. Roberts, “The role of atmospheric multiple scattering in the transmission of fluorescence light from extensive air showers,” J. Phys. G 31, 1291–1301 (2005).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  32. J. Baüml, for the Pierre Auger Collaboration, “Measurement of the optical properties of the Auger fluorescence telescopes,” in Proceedings of the 33rd ICRC, Rio de Janeiro, (2013), pp. 15–18. arxiv:astro-ph/1307.5059.
  33. P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

2012 (3)

K. Louedec and M. Urban, “Ramsauer approach for light scattering on non absorbing spherical particles and application to the Henyey-Greenstein phase function,” Appl. Opt 51, 7842–7852 (2012).
[CrossRef]

B. Keilhauer and M. Will, for the Pierre Auger Collaboration, “Description of atmospheric conditions at the Pierre Auger Observatory using meteorological measurements and models,” Eur. Phys. J. Plus 127, 96 (2012).

K. Louedec and R. Losno, for the Pierre Auger Collaboration, “Atmospheric aerosols at the Pierre Auger Observatory and environmental implications,” Eur. Phys. J. Plus 127, 97 (2012).

2011 (1)

P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

2010 (1)

J. Abraham, for the Pierre Auger Collaboration, “The fluorescence detector of the Pierre Auger Observatory,” Nucl. Instrum. Methods Phys. Res. A 620, 227–251 (2010).
[CrossRef]

2009 (1)

K. Louedec, S. Dagoret-Campagne, and M. Urban, “Ramsauer approach to Mie scattering of light on spherical particles,” Phys. Scr. 80, 035403 (2009).
[CrossRef]

2006 (1)

T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006).
[CrossRef]

2005 (1)

M. D. Roberts, “The role of atmospheric multiple scattering in the transmission of fluorescence light from extensive air showers,” J. Phys. G 31, 1291–1301 (2005).

1998 (2)

N. S. Kopeika, I. Dror, and D. Sadot, “Causes of atmospheric blur: comment on atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am A 15, 3097–3106 (1998).

O. Boucher, “On aerosol shortwave forcing and the Henyey-Greenstein phase function,” J. Atmos. Sci. 55, 128–134 (1998).
[CrossRef]

1997 (1)

1996 (1)

1995 (3)

1993 (1)

1992 (1)

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

1989 (1)

1987 (1)

D. Tanre, P. Y. Deschamps, P. Duhaut, and M. Herman, “Adjacency effect produced by the atmospheric scattering in thematic mapper data,” J. Geophys. Res. 92, 12000–12006 (1987).
[CrossRef]

1986 (1)

1984 (2)

1980 (2)

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef]

J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface non-homogeneity,” Photogramm. Eng. Remote Sens. 46, 1173–1180 (1980).

1979 (1)

1941 (1)

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

1908 (1)

G. Mie, “Beiträge zur Optik Trüber-Medien, speziell Kolloidaler Metallösungen,” Ann. Physik 25, 377–452 (1908).

Abraham, J.

J. Abraham, for the Pierre Auger Collaboration, “The fluorescence detector of the Pierre Auger Observatory,” Nucl. Instrum. Methods Phys. Res. A 620, 227–251 (2010).
[CrossRef]

Assis, P.

P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

Baüml, J.

J. Baüml, for the Pierre Auger Collaboration, “Measurement of the optical properties of the Auger fluorescence telescopes,” in Proceedings of the 33rd ICRC, Rio de Janeiro, (2013), pp. 15–18. arxiv:astro-ph/1307.5059.

Ben Dor, B.

Binzoni, T.

T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006).
[CrossRef]

Bissonnette, L. R.

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

Bohren, C. F.

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

Boucher, O.

O. Boucher, “On aerosol shortwave forcing and the Henyey-Greenstein phase function,” J. Atmos. Sci. 55, 128–134 (1998).
[CrossRef]

Bruscaglioni, P.

Bucholtz, A.

Carder, K. L.

Conceiçao, R.

P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

Dagoret-Campagne, S.

K. Louedec, S. Dagoret-Campagne, and M. Urban, “Ramsauer approach to Mie scattering of light on spherical particles,” Phys. Scr. 80, 035403 (2009).
[CrossRef]

Dave, J. V.

J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface non-homogeneity,” Photogramm. Eng. Remote Sens. 46, 1173–1180 (1980).

Delpy, D. T.

T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006).
[CrossRef]

Deschamps, P. Y.

D. Tanre, P. Y. Deschamps, P. Duhaut, and M. Herman, “Adjacency effect produced by the atmospheric scattering in thematic mapper data,” J. Geophys. Res. 92, 12000–12006 (1987).
[CrossRef]

Deschênes, F.

S. Metari and F. Deschênes, “A new convolution kernel for atmospheric point spread function applied to computer vision,” In Proceedings of the IEEE 11th International Conference on Computer Vision (ICCV) (IEEE, 2007), pp 1–8.

Devir, A. D.

Donelli, P.

Dror, I.

N. S. Kopeika, I. Dror, and D. Sadot, “Causes of atmospheric blur: comment on atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am A 15, 3097–3106 (1998).

I. Dror and N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995).
[CrossRef]

Duhaut, P.

D. Tanre, P. Y. Deschamps, P. Duhaut, and M. Herman, “Adjacency effect produced by the atmospheric scattering in thematic mapper data,” J. Geophys. Res. 92, 12000–12006 (1987).
[CrossRef]

Fraser, R. S.

Gandjbakhche, A. H.

T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006).
[CrossRef]

Gonçalves, P.

P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

Greenstein, J. L.

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Henyey, L. C.

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Herman, M.

D. Tanre, P. Y. Deschamps, P. Duhaut, and M. Herman, “Adjacency effect produced by the atmospheric scattering in thematic mapper data,” J. Geophys. Res. 92, 12000–12006 (1987).
[CrossRef]

Huffman, D. R.

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

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Ismaelli, A.

Keilhauer, B.

B. Keilhauer and M. Will, for the Pierre Auger Collaboration, “Description of atmospheric conditions at the Pierre Auger Observatory using meteorological measurements and models,” Eur. Phys. J. Plus 127, 96 (2012).

Kopeika, N. S.

Leung, T. S.

T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006).
[CrossRef]

Losno, R.

K. Louedec and R. Losno, for the Pierre Auger Collaboration, “Atmospheric aerosols at the Pierre Auger Observatory and environmental implications,” Eur. Phys. J. Plus 127, 97 (2012).

Louedec, K.

K. Louedec and R. Losno, for the Pierre Auger Collaboration, “Atmospheric aerosols at the Pierre Auger Observatory and environmental implications,” Eur. Phys. J. Plus 127, 97 (2012).

K. Louedec and M. Urban, “Ramsauer approach for light scattering on non absorbing spherical particles and application to the Henyey-Greenstein phase function,” Appl. Opt 51, 7842–7852 (2012).
[CrossRef]

K. Louedec, S. Dagoret-Campagne, and M. Urban, “Ramsauer approach to Mie scattering of light on spherical particles,” Phys. Scr. 80, 035403 (2009).
[CrossRef]

K. Louedec, for the Pierre Auger Collaboration, “Atmospheric monitoring at the Pierre Auger Observatory—Status and Update,” in Proceedings of the 32nd ICRC, Beijing, (2011), Vol. 2, pp. 63–66.

Metari, S.

S. Metari and F. Deschênes, “A new convolution kernel for atmospheric point spread function applied to computer vision,” In Proceedings of the IEEE 11th International Conference on Computer Vision (ICCV) (IEEE, 2007), pp 1–8.

Mie, G.

G. Mie, “Beiträge zur Optik Trüber-Medien, speziell Kolloidaler Metallösungen,” Ann. Physik 25, 377–452 (1908).

Oppenheim, U. P.

Otterman, J.

Pearce, W. A.

Pimenta, M.

P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

Reinersman, P. N.

Roberts, M. D.

M. D. Roberts, “The role of atmospheric multiple scattering in the transmission of fluorescence light from extensive air showers,” J. Phys. G 31, 1291–1301 (2005).

Rüfenacht, D.

T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006).
[CrossRef]

Sadot, D.

N. S. Kopeika, I. Dror, and D. Sadot, “Causes of atmospheric blur: comment on atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am A 15, 3097–3106 (1998).

D. Sadot and N. S. Kopeika, “Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol modulation transfer function,” J. Opt. Soc. Am. A 10, 172–179 (1993).
[CrossRef]

Shaviv, G.

Tanre, D.

D. Tanre, P. Y. Deschamps, P. Duhaut, and M. Herman, “Adjacency effect produced by the atmospheric scattering in thematic mapper data,” J. Geophys. Res. 92, 12000–12006 (1987).
[CrossRef]

Tomé, B.

P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

Toublanc, D.

Trakhovsky, E.

Urban, M.

K. Louedec and M. Urban, “Ramsauer approach for light scattering on non absorbing spherical particles and application to the Henyey-Greenstein phase function,” Appl. Opt 51, 7842–7852 (2012).
[CrossRef]

K. Louedec, S. Dagoret-Campagne, and M. Urban, “Ramsauer approach to Mie scattering of light on spherical particles,” Phys. Scr. 80, 035403 (2009).
[CrossRef]

Van De Hulst, H. C.

H. C. Van De Hulst, Light Scattering by Small Particles (Dover, 1981).

Will, M.

B. Keilhauer and M. Will, for the Pierre Auger Collaboration, “Description of atmospheric conditions at the Pierre Auger Observatory using meteorological measurements and models,” Eur. Phys. J. Plus 127, 96 (2012).

Wiscombe, W. J.

Zaccanti, G.

Ann. Physik (1)

G. Mie, “Beiträge zur Optik Trüber-Medien, speziell Kolloidaler Metallösungen,” Ann. Physik 25, 377–452 (1908).

Appl. Opt (1)

K. Louedec and M. Urban, “Ramsauer approach for light scattering on non absorbing spherical particles and application to the Henyey-Greenstein phase function,” Appl. Opt 51, 7842–7852 (2012).
[CrossRef]

Appl. Opt. (9)

Astrophys. J. (1)

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Astrophys. Space Sci. Trans. (1)

P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

Eur. Phys. J. Plus (2)

B. Keilhauer and M. Will, for the Pierre Auger Collaboration, “Description of atmospheric conditions at the Pierre Auger Observatory using meteorological measurements and models,” Eur. Phys. J. Plus 127, 96 (2012).

K. Louedec and R. Losno, for the Pierre Auger Collaboration, “Atmospheric aerosols at the Pierre Auger Observatory and environmental implications,” Eur. Phys. J. Plus 127, 97 (2012).

J. Atmos. Sci. (1)

O. Boucher, “On aerosol shortwave forcing and the Henyey-Greenstein phase function,” J. Atmos. Sci. 55, 128–134 (1998).
[CrossRef]

J. Geophys. Res. (1)

D. Tanre, P. Y. Deschamps, P. Duhaut, and M. Herman, “Adjacency effect produced by the atmospheric scattering in thematic mapper data,” J. Geophys. Res. 92, 12000–12006 (1987).
[CrossRef]

J. Opt. Soc. Am A (1)

N. S. Kopeika, I. Dror, and D. Sadot, “Causes of atmospheric blur: comment on atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am A 15, 3097–3106 (1998).

J. Opt. Soc. Am. A (3)

J. Phys. G (1)

M. D. Roberts, “The role of atmospheric multiple scattering in the transmission of fluorescence light from extensive air showers,” J. Phys. G 31, 1291–1301 (2005).

Nucl. Instrum. Methods Phys. Res. A (1)

J. Abraham, for the Pierre Auger Collaboration, “The fluorescence detector of the Pierre Auger Observatory,” Nucl. Instrum. Methods Phys. Res. A 620, 227–251 (2010).
[CrossRef]

Opt. Eng. (1)

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992).
[CrossRef]

Photogramm. Eng. Remote Sens. (1)

J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface non-homogeneity,” Photogramm. Eng. Remote Sens. 46, 1173–1180 (1980).

Phys. Med. Biol. (1)

T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006).
[CrossRef]

Phys. Scr. (1)

K. Louedec, S. Dagoret-Campagne, and M. Urban, “Ramsauer approach to Mie scattering of light on spherical particles,” Phys. Scr. 80, 035403 (2009).
[CrossRef]

Other (6)

K. Louedec, for the Pierre Auger Collaboration, “Atmospheric monitoring at the Pierre Auger Observatory—Status and Update,” in Proceedings of the 32nd ICRC, Beijing, (2011), Vol. 2, pp. 63–66.

J. Baüml, for the Pierre Auger Collaboration, “Measurement of the optical properties of the Auger fluorescence telescopes,” in Proceedings of the 33rd ICRC, Rio de Janeiro, (2013), pp. 15–18. arxiv:astro-ph/1307.5059.

S. Metari and F. Deschênes, “A new convolution kernel for atmospheric point spread function applied to computer vision,” In Proceedings of the IEEE 11th International Conference on Computer Vision (ICCV) (IEEE, 2007), pp 1–8.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

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).

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Figures (7)

Fig. 1.
Fig. 1.

Scattering phase function per unit of polar angle ψ, and its dependence on atmospheric conditions. Scattering phase functions are in units of probability per solid angle Ω as opposed to probability per unit of ψ as necessary to get the probability density function of the polar angle ψ. Thus, the scattering phase functions Pmol(ψ) and Paer(ψ) have to be multiplied by 2πsinψ to remove the solid angle weighting. (Left) Paer(ψ) plotted for different values of g and fixed f=0.4 used in the DHG phase function and Pmol(ψ) for the molecular phase function. (Right) The joint probability phase function weighted by 2πsin(ψ), with different ratios of Λaer/Λmol (g is kept equal to 0.6).

Fig. 2.
Fig. 2.

Relative effect on the density distribution of indirect photons for aerosols and molecules in a real atmosphere, illustrated by simulations with aerosols and molecules independently and simultaneously present. (Left) An atmosphere consisting of molecules only. (Middle) An atmosphere consisting of only aerosols with parameters {g=0.6, Λaer0=10km, and Haer0=1.5km}. (Right) An atmosphere consisting simultaneously of both aerosols and molecules with the same atmospheric conditions.

Fig. 3.
Fig. 3.

Effect of changing the g value on the density distribution of photons propagating from an isotropic source. Simulations are for atmospheres of only aerosols with Λaer0=14.2km and Haer0=8km, i.e., an aerosol density distribution similar to molecules. Results are presented for three different values of g={0.3,0.6,0.9}, left, middle, and right, respectively.

Fig. 4.
Fig. 4.

Effect of the scattering phase function and the detection time. Simulations are run for sources of initial height hinit=10km and a detection time of tdet=100ns for the top panel and tdet=1000ns for the bottom panel, individually for atmospheres of (left) molecules only or aerosols only, (left) g=0.3 or (right) g=0.9. Aerosol density parameters are {Λaer0=25.0km,Haer0=1.5km}. Ray structures are related to a lack of statistics for simulation of scattered photons.

Fig. 5.
Fig. 5.

Diagram showing how the detector is simulated to have an extent of 2π in azimuthal angle to increase the amount of statistics retrieved for indirect photons.

Fig. 6.
Fig. 6.

Plots for an isotropic source placed at θinc=3°, D=1km for atmospheres where aerosols and molecules are simultaneously present. The aerosol concentration and the detection time are kept constant at Λaer0=25km and tdet=100ns, respectively. (Left) Percentage of signal due to indirect light for different integration angles ζ and different g values. The black line is an exclusive case where only molecules are present. (Right) Percentage of the detected indirect photons that were last scattered at different distances from the detector for the three same cases.

Fig. 7.
Fig. 7.

Plots to demonstrate the effect of increasing integration time tdet. The inclination angle is θinc=15° and the distance D=30km. Λaer0=25km and g=0.6. (Left) Percentage of signal due to indirect light for different integration angles ζ and different integration times tdet. (Right) Percentage of detected indirect photons that have undergone either one or two or more scatterings by aerosols or molecules.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

{Λmol(hagl)=Λmol0exp[(hagl+hdet)/Hmol0],Λaer(hagl)=Λaer0exp[hagl/Haer0],
Pmol(ψ)=316π(1+cos2ψ),
Paer(ψ|g,f)=1g24π[1(1+g22gcosψ)32+f(3cos2ψ12(1+g2)32)],
Pjpf(ψ)=Paer(ψ)1+(ΛaerΛmol)+Pmol(ψ)1+(ΛmolΛaer).
εtotal=dεdVrrel2sin(θrel)drreldθreldϕrel,

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