Abstract

Sprays and other industrially relevant turbid media can be quantitatively characterized by light scattering. However, current optical diagnostic techniques generate errors in the intermediate scattering regime where the average number of light scattering is too great for the single scattering to be assumed, but too few for the diffusion approximation to be applied. Within this transitional single-to-multiple scattering regime, we consider a novel crossed source–detector geometry that allows the intensity of single scattering to be measured separately from the higher scattering orders. We verify Monte Carlo calculations that include the imperfections of the experiment against analytical results. We show quantitatively the influence of the detector numerical aperture and the angle between the source and the detector on the relative intensity of the scattering orders in the intermediate single-to-multiple scattering regime. Monte Carlo and analytical calculations of double light-scattering intensity are made with small particles that exhibit isotropic scattering. The agreement between Monte Carlo and analytical techniques validates use of the Monte Carlo approach in the intermediate scattering regime. Monte Carlo calculations are then performed for typical parameters of sprays and aerosols with anisotropic (Mie) scattering in the intermediate single-to-multiple scattering regime.

© 2005 Optical Society of America

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  2. C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  3. A. Ishimaru, Wave Propagation and Scattering in Random Media (Oxford U. Press, Oxford, UK, 1997).
  4. B. A. van Tiggelen, S. E. Skipetrov, Wave Scattering in Complex Media: From Theory to Applications, Vol. 107 of NATO Science Series: II: Mathematics, Physics and Chemistry (Kluwer Academic, Dordrecht, The Netherlands, 2003).
    [Crossref]
  5. V. L. Kuz'min, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 39, 231–260 (1996).
    [Crossref]
  6. J. Q. Shen, U. Riebel, “Extinction by a large spherical particle located in a narrow Gaussian beam,” Part. Part. Syst. Charact. 18, 254–261 (2001).
    [Crossref]
  7. G. Gouesbet, B. Maheu, G. Grehan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [Crossref]
  8. Z. Ma, H. G. Merkus, H. G. van der Veen, M. Wong, B. Scarlett, “On-line measurement of particle size and shape using laser diffraction,” Part. Part. Syst. Charact. 18, 243–247 (2001).
    [Crossref]
  9. M. Kocifaj, M. Drzik, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol. Sci. 28, 797–804 (1997).
    [Crossref]
  10. M. Kerker, D. D. Cooke, “Remote sensing of particle size and refractive index by varying the wavelength,” Appl. Opt. 15, 2105–2111 (1976).
    [Crossref] [PubMed]
  11. A. R. Jones, “Scattering of electromagnetic radiation in particulate laden fluids,” Prog. Energy Combust. Sci. 5, 73–96 (1979).
    [Crossref]
  12. W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles (Wiley, New York, 1982).
  13. F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
    [Crossref]
  14. M. C. Jermy, D. A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710 (2000).
    [Crossref]
  15. I. M. Sobol', The Monte Carlo Method (University of Chicago, Chicago, Ill., 1974).
  16. G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Method in Atmospheric Optics (Springer, Berlin, 1980).
    [Crossref]
  17. V. P. Kandidov, “Monte Carlo methods in nonlinear statistical optics,” Usp. Fiz. Nauk 39, 1243–1272 (1996).
    [Crossref]
  18. S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller, D. H. Sliney, eds., Vol. IS5 of the SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.
  19. I. V. Meglinsky, S. J. Matcher, “Modeling the sampling volume for skin blood oxygenation measurements,” Med. Biol. Eng. Comput. 39, 44–50 (2001).
    [Crossref] [PubMed]
  20. 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]
  21. C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, C. Roze, “Comparison of iterative and Monte Carlo methods for calculation of the aureole about a point source in the Earth's atmosphere,” Appl. Opt. 38, 6237–6246 (1999).
    [Crossref]
  22. E. A. Bucher, “Computer simulation of light pulse propagation for communication through thick clouds,” Appl. Opt. 12, 2391–2400 (1973).
    [Crossref] [PubMed]
  23. A. I. Carswell, “Laser measurements in clouds,” in Clouds: Their Formation, Optical Properties and Effects, A. Deepak, P. V. Hobbs, eds. (Academic, New York, 1981), pp. 363–406.
  24. G. E. Thomas, K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, Cambridge, UK, 1999).
    [Crossref]
  25. M. C. Jermy, A. Allen, “Simulating the effects of multiple scattering on images of dense sprays and particle fields,” Appl. Opt. 41, 4188–4196 (2002).
    [Crossref] [PubMed]
  26. M. C. Jermy, A. Allen, A. K. Vuorenkoski, “Simulating the effect of multiple scattering on images of dense sprays,” in Optical and Laser Diagnostics: Proceedings of the First IOP Conference Series, C. Arcoumanis, K. T. V. Grattan, eds. (Institute of Physics, Bristol, UK, 2003), Vol. 177, pp. 89–94.
  27. E. Berrocal, A. Allen, M. Jermy, “Monte Carlo simulation of laser imaging diagnostics in polydisperse dense sprays,” http://optics.sgu.ru/SFM/2003/internet/berrocal/index_files/frame.htm .
  28. V. L. Kuzmin, I. V. Meglinski, “Coherent multiple scattering effects and Monte Carlo method,” JETP Lett. 79, 109–112 (2004).
    [Crossref]
  29. I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov, D. A. Greenhalgh, “Monte Carlo simulation of coherent effects in multiple scattering,” Proc. R. Soc. London Ser. A 461, 43–53 (2005).
    [Crossref]
  30. S. Bartel, A. H. Hielscher, “Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media,” Appl. Opt. 39, 1580–1588 (2000).
    [Crossref]
  31. X. Wang, L.-H. Wang, C.-W. Sun, C. C. Yang, “Polarized light propagation through the scattering media: time-resolved Monte Carlo and experiments,” J. Biomed. Opt. 8, 608–617 (2003).
    [Crossref] [PubMed]
  32. K. Muinonen, “Coherent backscattering of light by complex random media of spherical scatterers: numerical solution,” Waves Random Media 14, 365–388 (2004).
    [Crossref]
  33. S. V. Gangnus, S. J. Matcher, I. V. Meglinski, “Monte Carlo modeling of polarized light propagation in biological tissues,” Laser Phys. 14, 886–891 (2004).
  34. T. Iwai, H. Furukawa, T. Asakura, “Numerical analysis on enhanced backscatterings of light based on Rayleigh-Debye scattering theory,” Opt. Rev. 2, 413–419 (1995).
    [Crossref]
  35. A. S. Martinez, R. Maynard, “Polarization statistics in multiple scattering of light: a Monte Carlo approach,” in Photonic Band Gaps and Localization, C. M. Souloukis, ed. (Plenum, New York, 1993), pp. 99–114.
    [Crossref]
  36. V. L. Kuzmin, I. V. Meglinski, D. Y. Churmakov, “Coherent effects under multiple scattering of linearly polarized light,” Opt. Spectrosc. 98, 673–679 (2005).
  37. H. Ishimoto, K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
    [Crossref]
  38. M. J. Raković, G. W. Kattawar, M. Mehrübeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, G. L. Coté, “Light back-scattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38, 3399–3408 (1999).
    [Crossref]
  39. X. Wang, L. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
    [Crossref] [PubMed]
  40. S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarski, Principles of Statistical Radiophysics (Springer, Berlin, 1987).
    [Crossref]
  41. P. M. Chaikin, T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge U. Press, Cambridge, UK, 1995).
    [Crossref]
  42. V. L. Kuzmin, V. P. Romanov, L. A. Zubkov, “Propagation and scattering of light in fluctuating media,” Phys. Rep. 248, 71–368 (1994).
    [Crossref]
  43. G. Mie, “Considerations on the optic of turbid media, especially colloidal metal sols,” Ann. Phys. (Leipzig) 25, 377–442 (1908).
    [Crossref]
  44. L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [Crossref]
  45. J. R. Zijp, J. ten Bosch, “Use of tabulated cumulative density functions to generate pseudorandom numbers obeying specific distributions for Monte Carlo simulations,” Appl. Opt. 33, 533–534 (1994).
    [Crossref]
  46. D. Toublanc, “Henyey–Greenstein and Mie phase functions in Monte Carlo radiative transfer computations,” Appl. Opt. 35, 3270–3274 (1996).
    [Crossref] [PubMed]
  47. E. Tilnet, S. Avrillier, M. Tualle, “Fast semianalytical Monte Carlo simulation for time-resolved light propagation in turbid media,” J. Opt. Soc. Am. A 13, 1903–1915 (1996).
    [Crossref]
  48. L. V. Adzhemyan, L. Ts. Adzhemyan, L. A. Zubkov, V. P. Romanov, “Molecular light scattering of varying multiplicity,” Sov. Phys. JEPT 53, 278–281 (1981).
  49. K. K. Bizheva, A. M. Siegel, D. A. Boas, “Path-length resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
    [Crossref]

2005 (2)

I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov, D. A. Greenhalgh, “Monte Carlo simulation of coherent effects in multiple scattering,” Proc. R. Soc. London Ser. A 461, 43–53 (2005).
[Crossref]

V. L. Kuzmin, I. V. Meglinski, D. Y. Churmakov, “Coherent effects under multiple scattering of linearly polarized light,” Opt. Spectrosc. 98, 673–679 (2005).

2004 (3)

V. L. Kuzmin, I. V. Meglinski, “Coherent multiple scattering effects and Monte Carlo method,” JETP Lett. 79, 109–112 (2004).
[Crossref]

K. Muinonen, “Coherent backscattering of light by complex random media of spherical scatterers: numerical solution,” Waves Random Media 14, 365–388 (2004).
[Crossref]

S. V. Gangnus, S. J. Matcher, I. V. Meglinski, “Monte Carlo modeling of polarized light propagation in biological tissues,” Laser Phys. 14, 886–891 (2004).

2003 (1)

X. Wang, L.-H. Wang, C.-W. Sun, C. C. Yang, “Polarized light propagation through the scattering media: time-resolved Monte Carlo and experiments,” J. Biomed. Opt. 8, 608–617 (2003).
[Crossref] [PubMed]

2002 (3)

H. Ishimoto, K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
[Crossref]

X. Wang, L. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[Crossref] [PubMed]

M. C. Jermy, A. Allen, “Simulating the effects of multiple scattering on images of dense sprays and particle fields,” Appl. Opt. 41, 4188–4196 (2002).
[Crossref] [PubMed]

2001 (3)

I. V. Meglinsky, S. J. Matcher, “Modeling the sampling volume for skin blood oxygenation measurements,” Med. Biol. Eng. Comput. 39, 44–50 (2001).
[Crossref] [PubMed]

J. Q. Shen, U. Riebel, “Extinction by a large spherical particle located in a narrow Gaussian beam,” Part. Part. Syst. Charact. 18, 254–261 (2001).
[Crossref]

Z. Ma, H. G. Merkus, H. G. van der Veen, M. Wong, B. Scarlett, “On-line measurement of particle size and shape using laser diffraction,” Part. Part. Syst. Charact. 18, 243–247 (2001).
[Crossref]

2000 (2)

M. C. Jermy, D. A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710 (2000).
[Crossref]

S. Bartel, A. H. Hielscher, “Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media,” Appl. Opt. 39, 1580–1588 (2000).
[Crossref]

1999 (2)

C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, C. Roze, “Comparison of iterative and Monte Carlo methods for calculation of the aureole about a point source in the Earth's atmosphere,” Appl. Opt. 38, 6237–6246 (1999).
[Crossref]

M. J. Raković, G. W. Kattawar, M. Mehrübeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, G. L. Coté, “Light back-scattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38, 3399–3408 (1999).
[Crossref]

1998 (1)

K. K. Bizheva, A. M. Siegel, D. A. Boas, “Path-length resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[Crossref]

1997 (2)

F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[Crossref]

M. Kocifaj, M. Drzik, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol. Sci. 28, 797–804 (1997).
[Crossref]

1996 (4)

V. P. Kandidov, “Monte Carlo methods in nonlinear statistical optics,” Usp. Fiz. Nauk 39, 1243–1272 (1996).
[Crossref]

V. L. Kuz'min, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 39, 231–260 (1996).
[Crossref]

D. Toublanc, “Henyey–Greenstein and Mie phase functions in Monte Carlo radiative transfer computations,” Appl. Opt. 35, 3270–3274 (1996).
[Crossref] [PubMed]

E. Tilnet, S. Avrillier, M. Tualle, “Fast semianalytical Monte Carlo simulation for time-resolved light propagation in turbid media,” J. Opt. Soc. Am. A 13, 1903–1915 (1996).
[Crossref]

1995 (1)

T. Iwai, H. Furukawa, T. Asakura, “Numerical analysis on enhanced backscatterings of light based on Rayleigh-Debye scattering theory,” Opt. Rev. 2, 413–419 (1995).
[Crossref]

1994 (2)

V. L. Kuzmin, V. P. Romanov, L. A. Zubkov, “Propagation and scattering of light in fluctuating media,” Phys. Rep. 248, 71–368 (1994).
[Crossref]

J. R. Zijp, J. ten Bosch, “Use of tabulated cumulative density functions to generate pseudorandom numbers obeying specific distributions for Monte Carlo simulations,” Appl. Opt. 33, 533–534 (1994).
[Crossref]

1988 (1)

1981 (1)

L. V. Adzhemyan, L. Ts. Adzhemyan, L. A. Zubkov, V. P. Romanov, “Molecular light scattering of varying multiplicity,” Sov. Phys. JEPT 53, 278–281 (1981).

1979 (1)

A. R. Jones, “Scattering of electromagnetic radiation in particulate laden fluids,” Prog. Energy Combust. Sci. 5, 73–96 (1979).
[Crossref]

1978 (1)

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]

1976 (1)

1973 (1)

1941 (1)

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

1908 (1)

G. Mie, “Considerations on the optic of turbid media, especially colloidal metal sols,” Ann. Phys. (Leipzig) 25, 377–442 (1908).
[Crossref]

Adzhemyan, L. Ts.

L. V. Adzhemyan, L. Ts. Adzhemyan, L. A. Zubkov, V. P. Romanov, “Molecular light scattering of varying multiplicity,” Sov. Phys. JEPT 53, 278–281 (1981).

Adzhemyan, L. V.

L. V. Adzhemyan, L. Ts. Adzhemyan, L. A. Zubkov, V. P. Romanov, “Molecular light scattering of varying multiplicity,” Sov. Phys. JEPT 53, 278–281 (1981).

Allen, A.

M. C. Jermy, A. Allen, “Simulating the effects of multiple scattering on images of dense sprays and particle fields,” Appl. Opt. 41, 4188–4196 (2002).
[Crossref] [PubMed]

M. C. Jermy, A. Allen, A. K. Vuorenkoski, “Simulating the effect of multiple scattering on images of dense sprays,” in Optical and Laser Diagnostics: Proceedings of the First IOP Conference Series, C. Arcoumanis, K. T. V. Grattan, eds. (Institute of Physics, Bristol, UK, 2003), Vol. 177, pp. 89–94.

E. Berrocal, A. Allen, M. Jermy, “Monte Carlo simulation of laser imaging diagnostics in polydisperse dense sprays,” http://optics.sgu.ru/SFM/2003/internet/berrocal/index_files/frame.htm .

Anderson, D. E.

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]

Asakura, T.

T. Iwai, H. Furukawa, T. Asakura, “Numerical analysis on enhanced backscatterings of light based on Rayleigh-Debye scattering theory,” Opt. Rev. 2, 413–419 (1995).
[Crossref]

Avrillier, S.

Bartel, S.

Berrocal, E.

E. Berrocal, A. Allen, M. Jermy, “Monte Carlo simulation of laser imaging diagnostics in polydisperse dense sprays,” http://optics.sgu.ru/SFM/2003/internet/berrocal/index_files/frame.htm .

Bizheva, K. K.

K. K. Bizheva, A. M. Siegel, D. A. Boas, “Path-length resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[Crossref]

Boas, D. A.

K. K. Bizheva, A. M. Siegel, D. A. Boas, “Path-length resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[Crossref]

Bohren, C.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bucher, E. A.

Cameron, B. D.

Carswell, A. I.

A. I. Carswell, “Laser measurements in clouds,” in Clouds: Their Formation, Optical Properties and Effects, A. Deepak, P. V. Hobbs, eds. (Academic, New York, 1981), pp. 363–406.

Chaikin, P. M.

P. M. Chaikin, T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge U. Press, Cambridge, UK, 1995).
[Crossref]

Churmakov, D. Y.

I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov, D. A. Greenhalgh, “Monte Carlo simulation of coherent effects in multiple scattering,” Proc. R. Soc. London Ser. A 461, 43–53 (2005).
[Crossref]

V. L. Kuzmin, I. V. Meglinski, D. Y. Churmakov, “Coherent effects under multiple scattering of linearly polarized light,” Opt. Spectrosc. 98, 673–679 (2005).

Cooke, D. D.

Coté, G. L.

Darbinjan, R. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Method in Atmospheric Optics (Springer, Berlin, 1980).
[Crossref]

Drzik, M.

M. Kocifaj, M. Drzik, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol. Sci. 28, 797–804 (1997).
[Crossref]

Elepov, B. S.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Method in Atmospheric Optics (Springer, Berlin, 1980).
[Crossref]

Furukawa, H.

T. Iwai, H. Furukawa, T. Asakura, “Numerical analysis on enhanced backscatterings of light based on Rayleigh-Debye scattering theory,” Opt. Rev. 2, 413–419 (1995).
[Crossref]

Gangnus, S. V.

S. V. Gangnus, S. J. Matcher, I. V. Meglinski, “Monte Carlo modeling of polarized light propagation in biological tissues,” Laser Phys. 14, 886–891 (2004).

Girasole, T.

C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, C. Roze, “Comparison of iterative and Monte Carlo methods for calculation of the aureole about a point source in the Earth's atmosphere,” Appl. Opt. 38, 6237–6246 (1999).
[Crossref]

Gong, Z.

F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[Crossref]

Gouesbet, G.

Greenhalgh, D. A.

I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov, D. A. Greenhalgh, “Monte Carlo simulation of coherent effects in multiple scattering,” Proc. R. Soc. London Ser. A 461, 43–53 (2005).
[Crossref]

M. C. Jermy, D. A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710 (2000).
[Crossref]

Greenstein, J. L.

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

Grehan, G.

Hayasaka, T.

F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[Crossref]

Henyey, L. G.

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

Hielscher, A. H.

Hinds, W. C.

W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles (Wiley, New York, 1982).

Hu, H.

F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[Crossref]

Huffman, D.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Oxford U. Press, Oxford, UK, 1997).

Ishimoto, H.

H. Ishimoto, K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
[Crossref]

Iwai, T.

T. Iwai, H. Furukawa, T. Asakura, “Numerical analysis on enhanced backscatterings of light based on Rayleigh-Debye scattering theory,” Opt. Rev. 2, 413–419 (1995).
[Crossref]

Jacques, S. L.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller, D. H. Sliney, eds., Vol. IS5 of the SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Jermy, M.

E. Berrocal, A. Allen, M. Jermy, “Monte Carlo simulation of laser imaging diagnostics in polydisperse dense sprays,” http://optics.sgu.ru/SFM/2003/internet/berrocal/index_files/frame.htm .

Jermy, M. C.

M. C. Jermy, A. Allen, “Simulating the effects of multiple scattering on images of dense sprays and particle fields,” Appl. Opt. 41, 4188–4196 (2002).
[Crossref] [PubMed]

M. C. Jermy, D. A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710 (2000).
[Crossref]

M. C. Jermy, A. Allen, A. K. Vuorenkoski, “Simulating the effect of multiple scattering on images of dense sprays,” in Optical and Laser Diagnostics: Proceedings of the First IOP Conference Series, C. Arcoumanis, K. T. V. Grattan, eds. (Institute of Physics, Bristol, UK, 2003), Vol. 177, pp. 89–94.

Jones, A. R.

A. R. Jones, “Scattering of electromagnetic radiation in particulate laden fluids,” Prog. Energy Combust. Sci. 5, 73–96 (1979).
[Crossref]

Kandidov, V. P.

V. P. Kandidov, “Monte Carlo methods in nonlinear statistical optics,” Usp. Fiz. Nauk 39, 1243–1272 (1996).
[Crossref]

Kargin, B. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Method in Atmospheric Optics (Springer, Berlin, 1980).
[Crossref]

Kattawar, G. W.

Keijzer, M.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller, D. H. Sliney, eds., Vol. IS5 of the SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Kerker, M.

Kocifaj, M.

M. Kocifaj, M. Drzik, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol. Sci. 28, 797–804 (1997).
[Crossref]

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarski, Principles of Statistical Radiophysics (Springer, Berlin, 1987).
[Crossref]

Kuzmin, V. L.

V. L. Kuzmin, I. V. Meglinski, D. Y. Churmakov, “Coherent effects under multiple scattering of linearly polarized light,” Opt. Spectrosc. 98, 673–679 (2005).

I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov, D. A. Greenhalgh, “Monte Carlo simulation of coherent effects in multiple scattering,” Proc. R. Soc. London Ser. A 461, 43–53 (2005).
[Crossref]

V. L. Kuzmin, I. V. Meglinski, “Coherent multiple scattering effects and Monte Carlo method,” JETP Lett. 79, 109–112 (2004).
[Crossref]

V. L. Kuzmin, V. P. Romanov, L. A. Zubkov, “Propagation and scattering of light in fluctuating media,” Phys. Rep. 248, 71–368 (1994).
[Crossref]

Kuz'min, V. L.

V. L. Kuz'min, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 39, 231–260 (1996).
[Crossref]

Langlois, S.

C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, C. Roze, “Comparison of iterative and Monte Carlo methods for calculation of the aureole about a point source in the Earth's atmosphere,” Appl. Opt. 38, 6237–6246 (1999).
[Crossref]

Lavigne, C.

C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, C. Roze, “Comparison of iterative and Monte Carlo methods for calculation of the aureole about a point source in the Earth's atmosphere,” Appl. Opt. 38, 6237–6246 (1999).
[Crossref]

Lee, J.-S.

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]

Lubensky, T. C.

P. M. Chaikin, T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge U. Press, Cambridge, UK, 1995).
[Crossref]

Ma, Z.

Z. Ma, H. G. Merkus, H. G. van der Veen, M. Wong, B. Scarlett, “On-line measurement of particle size and shape using laser diffraction,” Part. Part. Syst. Charact. 18, 243–247 (2001).
[Crossref]

Maheu, B.

Marchuk, G. I.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Method in Atmospheric Optics (Springer, Berlin, 1980).
[Crossref]

Martinez, A. S.

A. S. Martinez, R. Maynard, “Polarization statistics in multiple scattering of light: a Monte Carlo approach,” in Photonic Band Gaps and Localization, C. M. Souloukis, ed. (Plenum, New York, 1993), pp. 99–114.
[Crossref]

Masuda, K.

H. Ishimoto, K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
[Crossref]

Matcher, S. J.

S. V. Gangnus, S. J. Matcher, I. V. Meglinski, “Monte Carlo modeling of polarized light propagation in biological tissues,” Laser Phys. 14, 886–891 (2004).

I. V. Meglinsky, S. J. Matcher, “Modeling the sampling volume for skin blood oxygenation measurements,” Med. Biol. Eng. Comput. 39, 44–50 (2001).
[Crossref] [PubMed]

Maynard, R.

A. S. Martinez, R. Maynard, “Polarization statistics in multiple scattering of light: a Monte Carlo approach,” in Photonic Band Gaps and Localization, C. M. Souloukis, ed. (Plenum, New York, 1993), pp. 99–114.
[Crossref]

Meglinski, I. V.

V. L. Kuzmin, I. V. Meglinski, D. Y. Churmakov, “Coherent effects under multiple scattering of linearly polarized light,” Opt. Spectrosc. 98, 673–679 (2005).

I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov, D. A. Greenhalgh, “Monte Carlo simulation of coherent effects in multiple scattering,” Proc. R. Soc. London Ser. A 461, 43–53 (2005).
[Crossref]

V. L. Kuzmin, I. V. Meglinski, “Coherent multiple scattering effects and Monte Carlo method,” JETP Lett. 79, 109–112 (2004).
[Crossref]

S. V. Gangnus, S. J. Matcher, I. V. Meglinski, “Monte Carlo modeling of polarized light propagation in biological tissues,” Laser Phys. 14, 886–891 (2004).

Meglinsky, I. V.

I. V. Meglinsky, S. J. Matcher, “Modeling the sampling volume for skin blood oxygenation measurements,” Med. Biol. Eng. Comput. 39, 44–50 (2001).
[Crossref] [PubMed]

Mehrübeoglu, M.

Meier, R. R.

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]

Merkus, H. G.

Z. Ma, H. G. Merkus, H. G. van der Veen, M. Wong, B. Scarlett, “On-line measurement of particle size and shape using laser diffraction,” Part. Part. Syst. Charact. 18, 243–247 (2001).
[Crossref]

Mie, G.

G. Mie, “Considerations on the optic of turbid media, especially colloidal metal sols,” Ann. Phys. (Leipzig) 25, 377–442 (1908).
[Crossref]

Mikhailov, G. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Method in Atmospheric Optics (Springer, Berlin, 1980).
[Crossref]

Muinonen, K.

K. Muinonen, “Coherent backscattering of light by complex random media of spherical scatterers: numerical solution,” Waves Random Media 14, 365–388 (2004).
[Crossref]

Nazaraliev, M. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Method in Atmospheric Optics (Springer, Berlin, 1980).
[Crossref]

Outters, V.

C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, C. Roze, “Comparison of iterative and Monte Carlo methods for calculation of the aureole about a point source in the Earth's atmosphere,” Appl. Opt. 38, 6237–6246 (1999).
[Crossref]

Prahl, S. A.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller, D. H. Sliney, eds., Vol. IS5 of the SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Rakovic, M. J.

Rastegar, S.

Riebel, U.

J. Q. Shen, U. Riebel, “Extinction by a large spherical particle located in a narrow Gaussian beam,” Part. Part. Syst. Charact. 18, 254–261 (2001).
[Crossref]

Robin, A.

C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, C. Roze, “Comparison of iterative and Monte Carlo methods for calculation of the aureole about a point source in the Earth's atmosphere,” Appl. Opt. 38, 6237–6246 (1999).
[Crossref]

Romanov, V. P.

V. L. Kuz'min, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 39, 231–260 (1996).
[Crossref]

V. L. Kuzmin, V. P. Romanov, L. A. Zubkov, “Propagation and scattering of light in fluctuating media,” Phys. Rep. 248, 71–368 (1994).
[Crossref]

L. V. Adzhemyan, L. Ts. Adzhemyan, L. A. Zubkov, V. P. Romanov, “Molecular light scattering of varying multiplicity,” Sov. Phys. JEPT 53, 278–281 (1981).

Roze, C.

C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, C. Roze, “Comparison of iterative and Monte Carlo methods for calculation of the aureole about a point source in the Earth's atmosphere,” Appl. Opt. 38, 6237–6246 (1999).
[Crossref]

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarski, Principles of Statistical Radiophysics (Springer, Berlin, 1987).
[Crossref]

Scarlett, B.

Z. Ma, H. G. Merkus, H. G. van der Veen, M. Wong, B. Scarlett, “On-line measurement of particle size and shape using laser diffraction,” Part. Part. Syst. Charact. 18, 243–247 (2001).
[Crossref]

Shen, J. Q.

J. Q. Shen, U. Riebel, “Extinction by a large spherical particle located in a narrow Gaussian beam,” Part. Part. Syst. Charact. 18, 254–261 (2001).
[Crossref]

Siegel, A. M.

K. K. Bizheva, A. M. Siegel, D. A. Boas, “Path-length resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[Crossref]

Skipetrov, S. E.

B. A. van Tiggelen, S. E. Skipetrov, Wave Scattering in Complex Media: From Theory to Applications, Vol. 107 of NATO Science Series: II: Mathematics, Physics and Chemistry (Kluwer Academic, Dordrecht, The Netherlands, 2003).
[Crossref]

Sobol', I. M.

I. M. Sobol', The Monte Carlo Method (University of Chicago, Chicago, Ill., 1974).

Stamnes, K.

G. E. Thomas, K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, Cambridge, UK, 1999).
[Crossref]

Sun, C.-W.

X. Wang, L.-H. Wang, C.-W. Sun, C. C. Yang, “Polarized light propagation through the scattering media: time-resolved Monte Carlo and experiments,” J. Biomed. Opt. 8, 608–617 (2003).
[Crossref] [PubMed]

Tanaka, M.

F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[Crossref]

Tatarski, V. I.

S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarski, Principles of Statistical Radiophysics (Springer, Berlin, 1987).
[Crossref]

ten Bosch, J.

J. R. Zijp, J. ten Bosch, “Use of tabulated cumulative density functions to generate pseudorandom numbers obeying specific distributions for Monte Carlo simulations,” Appl. Opt. 33, 533–534 (1994).
[Crossref]

Thomas, G. E.

G. E. Thomas, K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, Cambridge, UK, 1999).
[Crossref]

Tilnet, E.

Toublanc, D.

Tualle, M.

van de Hulst, H. C.

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

van der Veen, H. G.

Z. Ma, H. G. Merkus, H. G. van der Veen, M. Wong, B. Scarlett, “On-line measurement of particle size and shape using laser diffraction,” Part. Part. Syst. Charact. 18, 243–247 (2001).
[Crossref]

van Tiggelen, B. A.

B. A. van Tiggelen, S. E. Skipetrov, Wave Scattering in Complex Media: From Theory to Applications, Vol. 107 of NATO Science Series: II: Mathematics, Physics and Chemistry (Kluwer Academic, Dordrecht, The Netherlands, 2003).
[Crossref]

Vuorenkoski, A. K.

M. C. Jermy, A. Allen, A. K. Vuorenkoski, “Simulating the effect of multiple scattering on images of dense sprays,” in Optical and Laser Diagnostics: Proceedings of the First IOP Conference Series, C. Arcoumanis, K. T. V. Grattan, eds. (Institute of Physics, Bristol, UK, 2003), Vol. 177, pp. 89–94.

Wang, L. V.

Wang, L.-H.

X. Wang, L.-H. Wang, C.-W. Sun, C. C. Yang, “Polarized light propagation through the scattering media: time-resolved Monte Carlo and experiments,” J. Biomed. Opt. 8, 608–617 (2003).
[Crossref] [PubMed]

Wang, X.

X. Wang, L.-H. Wang, C.-W. Sun, C. C. Yang, “Polarized light propagation through the scattering media: time-resolved Monte Carlo and experiments,” J. Biomed. Opt. 8, 608–617 (2003).
[Crossref] [PubMed]

X. Wang, L. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[Crossref] [PubMed]

Welch, A. J.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller, D. H. Sliney, eds., Vol. IS5 of the SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Wong, M.

Z. Ma, H. G. Merkus, H. G. van der Veen, M. Wong, B. Scarlett, “On-line measurement of particle size and shape using laser diffraction,” Part. Part. Syst. Charact. 18, 243–247 (2001).
[Crossref]

Yang, C. C.

X. Wang, L.-H. Wang, C.-W. Sun, C. C. Yang, “Polarized light propagation through the scattering media: time-resolved Monte Carlo and experiments,” J. Biomed. Opt. 8, 608–617 (2003).
[Crossref] [PubMed]

Zhao, F.

F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[Crossref]

Zijp, J. R.

J. R. Zijp, J. ten Bosch, “Use of tabulated cumulative density functions to generate pseudorandom numbers obeying specific distributions for Monte Carlo simulations,” Appl. Opt. 33, 533–534 (1994).
[Crossref]

Zubkov, L. A.

V. L. Kuzmin, V. P. Romanov, L. A. Zubkov, “Propagation and scattering of light in fluctuating media,” Phys. Rep. 248, 71–368 (1994).
[Crossref]

L. V. Adzhemyan, L. Ts. Adzhemyan, L. A. Zubkov, V. P. Romanov, “Molecular light scattering of varying multiplicity,” Sov. Phys. JEPT 53, 278–281 (1981).

Ann. Phys. (Leipzig) (1)

G. Mie, “Considerations on the optic of turbid media, especially colloidal metal sols,” Ann. Phys. (Leipzig) 25, 377–442 (1908).
[Crossref]

Appl. Opt. (4)

J. R. Zijp, J. ten Bosch, “Use of tabulated cumulative density functions to generate pseudorandom numbers obeying specific distributions for Monte Carlo simulations,” Appl. Opt. 33, 533–534 (1994).
[Crossref]

F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[Crossref]

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]

C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, C. Roze, “Comparison of iterative and Monte Carlo methods for calculation of the aureole about a point source in the Earth's atmosphere,” Appl. Opt. 38, 6237–6246 (1999).
[Crossref]

Appl. Opt. (6)

Appl. Phys. B (1)

M. C. Jermy, D. A. Greenhalgh, “Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase Doppler measurement,” Appl. Phys. B 71, 703–710 (2000).
[Crossref]

Astrophys. J. (1)

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

J. Aerosol. Sci. (1)

M. Kocifaj, M. Drzik, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol. Sci. 28, 797–804 (1997).
[Crossref]

J. Biomed. Opt. (2)

X. Wang, L.-H. Wang, C.-W. Sun, C. C. Yang, “Polarized light propagation through the scattering media: time-resolved Monte Carlo and experiments,” J. Biomed. Opt. 8, 608–617 (2003).
[Crossref] [PubMed]

X. Wang, L. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (1)

H. Ishimoto, K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transfer 72, 467–483 (2002).
[Crossref]

JETP Lett. (1)

V. L. Kuzmin, I. V. Meglinski, “Coherent multiple scattering effects and Monte Carlo method,” JETP Lett. 79, 109–112 (2004).
[Crossref]

Laser Phys. (1)

S. V. Gangnus, S. J. Matcher, I. V. Meglinski, “Monte Carlo modeling of polarized light propagation in biological tissues,” Laser Phys. 14, 886–891 (2004).

Med. Biol. Eng. Comput. (1)

I. V. Meglinsky, S. J. Matcher, “Modeling the sampling volume for skin blood oxygenation measurements,” Med. Biol. Eng. Comput. 39, 44–50 (2001).
[Crossref] [PubMed]

Opt. Rev. (1)

T. Iwai, H. Furukawa, T. Asakura, “Numerical analysis on enhanced backscatterings of light based on Rayleigh-Debye scattering theory,” Opt. Rev. 2, 413–419 (1995).
[Crossref]

Opt. Spectrosc. (1)

V. L. Kuzmin, I. V. Meglinski, D. Y. Churmakov, “Coherent effects under multiple scattering of linearly polarized light,” Opt. Spectrosc. 98, 673–679 (2005).

Part. Part. Syst. Charact. (1)

Z. Ma, H. G. Merkus, H. G. van der Veen, M. Wong, B. Scarlett, “On-line measurement of particle size and shape using laser diffraction,” Part. Part. Syst. Charact. 18, 243–247 (2001).
[Crossref]

Part. Part. Syst. Charact. (1)

J. Q. Shen, U. Riebel, “Extinction by a large spherical particle located in a narrow Gaussian beam,” Part. Part. Syst. Charact. 18, 254–261 (2001).
[Crossref]

Phys. Rep. (1)

V. L. Kuzmin, V. P. Romanov, L. A. Zubkov, “Propagation and scattering of light in fluctuating media,” Phys. Rep. 248, 71–368 (1994).
[Crossref]

Phys. Rev. E (1)

K. K. Bizheva, A. M. Siegel, D. A. Boas, “Path-length resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy,” Phys. Rev. E 58, 7664–7667 (1998).
[Crossref]

Proc. R. Soc. London Ser. A (1)

I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov, D. A. Greenhalgh, “Monte Carlo simulation of coherent effects in multiple scattering,” Proc. R. Soc. London Ser. A 461, 43–53 (2005).
[Crossref]

Prog. Energy Combust. Sci. (1)

A. R. Jones, “Scattering of electromagnetic radiation in particulate laden fluids,” Prog. Energy Combust. Sci. 5, 73–96 (1979).
[Crossref]

Sov. Phys. JEPT (1)

L. V. Adzhemyan, L. Ts. Adzhemyan, L. A. Zubkov, V. P. Romanov, “Molecular light scattering of varying multiplicity,” Sov. Phys. JEPT 53, 278–281 (1981).

Usp. Fiz. Nauk (1)

V. L. Kuz'min, V. P. Romanov, “Coherent phenomena in light scattering from disordered systems,” Usp. Fiz. Nauk 39, 231–260 (1996).
[Crossref]

Usp. Fiz. Nauk (1)

V. P. Kandidov, “Monte Carlo methods in nonlinear statistical optics,” Usp. Fiz. Nauk 39, 1243–1272 (1996).
[Crossref]

Waves Random Media (1)

K. Muinonen, “Coherent backscattering of light by complex random media of spherical scatterers: numerical solution,” Waves Random Media 14, 365–388 (2004).
[Crossref]

Other (15)

A. S. Martinez, R. Maynard, “Polarization statistics in multiple scattering of light: a Monte Carlo approach,” in Photonic Band Gaps and Localization, C. M. Souloukis, ed. (Plenum, New York, 1993), pp. 99–114.
[Crossref]

M. C. Jermy, A. Allen, A. K. Vuorenkoski, “Simulating the effect of multiple scattering on images of dense sprays,” in Optical and Laser Diagnostics: Proceedings of the First IOP Conference Series, C. Arcoumanis, K. T. V. Grattan, eds. (Institute of Physics, Bristol, UK, 2003), Vol. 177, pp. 89–94.

E. Berrocal, A. Allen, M. Jermy, “Monte Carlo simulation of laser imaging diagnostics in polydisperse dense sprays,” http://optics.sgu.ru/SFM/2003/internet/berrocal/index_files/frame.htm .

A. I. Carswell, “Laser measurements in clouds,” in Clouds: Their Formation, Optical Properties and Effects, A. Deepak, P. V. Hobbs, eds. (Academic, New York, 1981), pp. 363–406.

G. E. Thomas, K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, Cambridge, UK, 1999).
[Crossref]

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller, D. H. Sliney, eds., Vol. IS5 of the SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles (Wiley, New York, 1982).

I. M. Sobol', The Monte Carlo Method (University of Chicago, Chicago, Ill., 1974).

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, B. S. Elepov, The Monte Carlo Method in Atmospheric Optics (Springer, Berlin, 1980).
[Crossref]

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

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Oxford U. Press, Oxford, UK, 1997).

B. A. van Tiggelen, S. E. Skipetrov, Wave Scattering in Complex Media: From Theory to Applications, Vol. 107 of NATO Science Series: II: Mathematics, Physics and Chemistry (Kluwer Academic, Dordrecht, The Netherlands, 2003).
[Crossref]

S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarski, Principles of Statistical Radiophysics (Springer, Berlin, 1987).
[Crossref]

P. M. Chaikin, T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge U. Press, Cambridge, UK, 1995).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1

Schematic presentation of the scattering intensity as a series of ladder diagrams.5,4042

Fig. 2
Fig. 2

Computational/proposed experimental geometry. The laser source S and detector D sample two cylindrical volumes V1 and V2, within which single scattering occurs at points r1 and r2. If the volumes are separated by distance h, the detector collects only double and higher orders of scattering. ki, k′, and ks are the wave vectors of the incident, intermediate, and detected double-scattered light, respectively. The scattering volume is a cube of L = 50 mm defined in a three-dimensional coordinate system. One of the corners of the cube corresponds to the origin of the (X, Y, Z) frame.

Fig. 3
Fig. 3

Intensity of the double light scattering I(2) with respect to the distance h between V1 and V2: (a) µs = 0.04 mm−1, (b) µs = 0.16 mm−1. The solid curve represents the results of calculation by the exact Eq. (7), the dotted curve by the approximate Eq. (13), and (○) are the results of the MC simulation.

Fig. 4
Fig. 4

Intensity of different scattering orders I(n) as a function of h: ●, double scattering I(2); □, triple scattering I(3), ▴, fourth-order scattering I(4); ▿, fifth-order scattering I(5), and x, tenth-order scattering I(10). The intensity of each scattering order is normalized to the intensity of single scattering I(1) at h = 0.

Fig. 5
Fig. 5

Normalized intensity of different scattering orders versus h: (a) single light scattering, (b) double scattering, (c) triple scattering, (d) fifth-order scattering. The symbols represent different values of the detector numerical aperture: ▿, 2°; ▾, 10°; ○, 20°; ●, 40°; □, 60°; ■, 90°.

Fig. 6
Fig. 6

Normalized intensities of nth scattering orders and single-scattering intensity at h = 0, I(n)(0)/I(1)(0) as a function of scattering coefficient µs: □, triple scattering I(3); ▴, fourth-order scattering I(4); ▿, fifth-order scattering I(5); x, tenth-order scattering I(10).

Fig. 7
Fig. 7

Normalized intensity of the double light scattering I(2) with respect to the distance h between V1 and V2: ○, isotropic scattering with µs = 0.04 mm−1; ●, isotropic scattering with µs = 0.16 mm−1; ▿, anisotropic scattering with µs = 0.04 mm−1 for particle diameter a = 15 µm.

Fig. 8
Fig. 8

Results of MC calculation of the different scattering order intensities I(n)/I(tot) at h = 0 versus the acceptance angle θa: (a) isotropic scattering with µs = 0.04 mm−1, (b) anisotropic scattering with µs = 0.04 mm−1 for particle diameter a = 15 µm. The symbols represent different scattering orders: ◊, single scattering I(1); ●, double scattering I(2); □ triple scattering I(3), ▴, fourth-order scattering I(4).

Fig. 9
Fig. 9

Effect of the source–detector angle β on the single-scattering detection at h = 0 with an acceptance angle of 2°: ○, isotropic scattering with µs = 0.04 mm−1; ▿, anisotropic scattering with µs = 0.04 mm−1 for particle diameter a = 15 µm; ▾, anisotropic scattering with µs = 0.04 mm−1 for particle diameter a = 1 µm. (a) Amount of single scattering I(1)/I(tot) detected versus β. (b) Total intensity detected versus β.

Fig. 10
Fig. 10

Results of I(1)/I(tot) versus acceptance angle θa for anisotropic scattering with β = 10° and with different scattering coefficients: ◊, µs = 0.04 mm−1 for particle diameter a = 15 µm; □, µs = 0.16 mm−1 for particle diameter a = 15 µm; (□), µs = 0.04 mm−1 forparticle diameter a = 1 µm; ■, µs = 0.16 mm−1 for particle diameter a = 1 µm.

Equations (14)

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

I ( 1 ) = I 0 V r 2 k 0 4 ( 4 π ) 2 ( δ α β k s α k s β k 2 ) 2 G ( q ) exp [ µ t ( l 1 + l 2 ) ] .
G ( q ) ( 2 π Δ ɛ 3 ) 2 a 6 N .
I ( 2 ) = I 0 k 0 8 r 2 ( 4 π ) 4 V 1 d r 1 V 2 d r 2 F α β ( k s , k i , k ) 1 | r 2 r 1 | 2 × G ( k k i ) G ( k s k ) exp [ µ t ( l 1 + l 2 + | r 2 r 1 | ) ] ,
F α β ( k s , k i , k ) = ( δ α η k i α k i η k 2 ) ( δ α ν k i α k i ν k 2 ) × ( δ β η k s β k s η k 2 ) ( δ β ν k s β k s ν k 2 )
I ( 1 ) = I 0 V r 2 k 0 4 ( Δ ɛ 6 ) 2 a 6 N exp [ µ t ( l 1 + l 2 ) ] ,
I ( 2 ) = I 0 k 0 8 r 2 ( Δ ɛ 6 ) 4 V 1 d r 1 V 2 d r 2 1 | r 2 r 1 | 2 k y 2 k 2 × [ 1 k y 2 k 2 ( k s k ) 2 k 4 ] a 12 N 2 × exp [ µ t ( l 1 + l 2 + | r 2 r 1 | ) ] ,
I ( 2 ) = A L 1 / 2 L 1 / 2 d l 1 L 2 / 2 L 2 / 2 d l 2 0 R 1 r 1 d r 1 0 R 2 r 2 d r 2 × 0 2 π d ϕ 1 0 2 π d ϕ 2 1 | r 2 r 1 | 2 × exp [ µ t ( l 1 + l 2 + | r 2 r 1 | ) ] ,
l i = ln ( ξ ) µ s ,
[ u s x u s y u s z ] = [ 1 ( 1 u i z 2 ) 1 / 2 u i x u i z 1 ( 1 u i z 2 ) 1 / 2 u i y u i x 1 ( 1 u i z 2 ) 1 / 2 u i y u i z 1 ( 1 u i z 2 ) 1 / 2 u i x u i y ( 1 u i z 2 ) 1 / 2 0 u i z ] × [ sin θ s cos ϕ sin θ s sin ϕ cos θ s ] .
p ( k i , k s ) = σ ( k i , k s ) 4 π σ ( k i , k s ) d Ω s .
W = p ( k d k ) d Ω d exp ( µ t , d ) .
r 1 = ( r 1 cos ϕ 1 , r 1 sin ϕ , l 1 ) , r 2 = ( l 2 , h + r 2 cos ϕ 2 , r 2 , sin ϕ 2 ) .
I 2 ( h ) = A π 2 R 1 2 R 2 2 L 1 / 2 L 1 / 2 d x L 2 / 2 L 2 / 2 d z 1 x 2 + z 2 + h 2 × exp { µ t [ L + z x + ( x 2 + z 2 + h 2 ) ] 1 / 2 } .
I ( tot ) ( h ) = I ( 1 ) ( r 0 ) + I ( 2 ) ( h ) + I ( p ) ( h ) ,

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