Abstract

Most optical measurements in turbid media (including sprays, fogs, particulate and colloidal suspensions) assume single scattering of the detected photons. Multiple scattering introduces error, which has been quantified in very few systems. To quantify this error, we have written a flexible Monte Carlo photon transport simulation code capable of handling any three-dimensional geometry. Simulations of planar laser spray imaging with large, nonabsorbing particles show that up to 50% of the photons reaching the camera are multiply scattered. Because forward scattering dominates, the image is affected little. For particles with more absorption or with size closer to the wavelength of the light than those we have simulated, the effects are expected to be more serious.

© 2002 Optical Society of America

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References

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  1. H. C. van de Hulst, Multiple Light Scattering, Volume II, (Academic Press, New York, 1980).
  2. A. A. Kokhanovsky, Optics of Light Scattering Media (Springer-Verlag, Berlin, 2001).
  3. D. G. Talley, J. F. Verdieck, S. W. Lee, V. G. McDonell, G. S. Samuelsen, Accounting for Laser Sheet Extinction in Applying PLIF to Sprays, (AIAA, 96-0469, 1996).
  4. D. G. Talley, J. F. Verdieck, “Accounting for laser sheet extinction and fluorescence signal attenuation in applying PLIF to sprays,” Proc. 9th Inst. Liquid Atomization and Sprays, iClass AA 33–38 (1996).
  5. T. M. Quagliaroli, G. Laufer, R. H. Krauss, J. C. McDaniel, AIAAJ. 31, 520–527 (1993).
    [CrossRef]
  6. H. M. Hertz, M. Alden, “Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames,” J. Appl. Phys. B 42, 97–102 (1987).
    [CrossRef]
  7. R. Abu-Gharbieh, J. L. Persson, M. Forsth, A. Rosen, A. Karlstrom, T. Gustavsson, “Compensation method for attenuated planar laser images of optically dense sprays,” Appl. Opt. 39, 1260–1267 (2000).
    [CrossRef]
  8. V. Sick, B. Stojkovic, “Attenuation effects on imaging diagnostics in hollow-cone sprays,” Appl. Opt. 40, 2435–2442 (2001).
    [CrossRef]
  9. 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]
  10. V. Tuchin, Tissue Optics (SPIE, Bellingham, Wa., 2000).
  11. V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics,” Physics-Uspe. 39, 1243–1272 (1996).
    [CrossRef]
  12. L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues” Comput. Methods Programs Biomed. 47, 131–146 (1995).
    [CrossRef] [PubMed]
  13. R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
    [CrossRef] [PubMed]
  14. H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
    [CrossRef] [PubMed]
  15. P. van der Zee, “Measurement and Modelling of the optical properties of human tissue in the near infrared” Ph. D. dissertation, University College London (1992).
  16. I. V. Meglinsky, S. J. Matcher, “Modelling the sampling volume for skin blood oxygenation measurements,” Med. Biol. Eng. Comput. 39, 44–50 (2001).
    [CrossRef] [PubMed]
  17. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Partially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
    [CrossRef] [PubMed]
  18. M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
    [CrossRef] [PubMed]
  19. A. N. Witt, “Multiple scattering in reflection nebulae I a Monte Carlo approach,” The Astrophysical J. Suppl Ser. 35, 1–6 (1977).
    [CrossRef]
  20. 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]
  21. 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]
  22. A. I. Carswell, “Laser Measurements in clouds,” pp 363–406 in Clouds: Their Formation, Optical Properties and Effects, A. Deepak, P. V. Hobbs, eds., (Academic Press, San Diego, Calif.1981), pp. 363–406.
    [CrossRef]
  23. K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1974).
    [CrossRef]
  24. E. A. Bucher, “Computer simulation of light pulse propagation for communication through thick clouds,” Appl. Opt. 12, 2391–2400 (1973).
    [CrossRef] [PubMed]
  25. 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]
  26. T. Girasole, C. Roze, B. Maheu, G. Grehan, J. Menard, “Visibility distances in a foggy atmosphere: comparisons between lighting installations by Monte Carlo simulation,” International Journal of Lighting Research and Technology. 30, 29–36 (1998).
    [CrossRef]
  27. R. Giddings, D. A. Holder, M. Philpott, D. A. Youngs, “Multiple scattering from particles in laser sheet gas mixing experiments,” Advances in Statistical Optics–IOP half day meeting, Imperial College, London (24th May 2000).
  28. L. G. Dodge, “Change of calibration of diffraction based particle sizes in dense sprays,” Opt. Eng. 23, 626–630 (1984).
    [CrossRef]
  29. P. G. Felton, A. A. Hamidi, A. K. Aigal, “Measurement of drop size distribution in dense sprays by laser diffraction,” Proc. 3rd Int. Conf. on Liquid Atomization and Sprays, London, IVA/4/1–11 (1985).
  30. A. A. Hamidi, J. Swithenbank, “Treatment of the multiple scattering of light in laser diffraction measurement techniques in dense sprays and particle fields,” J. Inst. Energy 59, 101–105 (1986).
  31. E. D. Hirleman, “General solution to the inverse near-forward-scattering particle-sizing problem in multiple-scattering environments: theory,” Appl. Opt. 30, 4832–4838 (1991).
    [CrossRef] [PubMed]
  32. A. A. Kokhanovsky, R. Weichert, “Multiple light scattering in laser particle sizing,” App. Opt. 40, 1507–1513 (2001).
    [CrossRef]
  33. K. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
    [CrossRef] [PubMed]
  34. E. D. Cashwell, C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems, (Pergamon Press, New York, 1959).
  35. M. H. Kalos, P. A. Whitlock, Monte Carlo Methods, I: Basics (John Wiley and Sons, Inc., New York, 1986).
    [CrossRef]
  36. A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37, 7392–7400 (1998).
    [CrossRef]
  37. V. Tuchin, Tissue Optics ISBN 0819434590, SPIE Press (2000).
  38. I. Lux, L. Koblinger, “Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press Boca Raton, Fla., 1991).
  39. D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
    [CrossRef]
  40. W. H. Press, S. A. Teutolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press Cambridge, UK, 1992).
  41. http://www.unternehmen.com/Bernhard-Michel/Java/mieApplet.html .

2001 (3)

V. Sick, B. Stojkovic, “Attenuation effects on imaging diagnostics in hollow-cone sprays,” Appl. Opt. 40, 2435–2442 (2001).
[CrossRef]

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

A. A. Kokhanovsky, R. Weichert, “Multiple light scattering in laser particle sizing,” App. Opt. 40, 1507–1513 (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]

R. Abu-Gharbieh, J. L. Persson, M. Forsth, A. Rosen, A. Karlstrom, T. Gustavsson, “Compensation method for attenuated planar laser images of optically dense sprays,” Appl. Opt. 39, 1260–1267 (2000).
[CrossRef]

1999 (1)

1998 (2)

T. Girasole, C. Roze, B. Maheu, G. Grehan, J. Menard, “Visibility distances in a foggy atmosphere: comparisons between lighting installations by Monte Carlo simulation,” International Journal of Lighting Research and Technology. 30, 29–36 (1998).
[CrossRef]

A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37, 7392–7400 (1998).
[CrossRef]

1996 (2)

1995 (1)

L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

1993 (2)

T. M. Quagliaroli, G. Laufer, R. H. Krauss, J. C. McDaniel, AIAAJ. 31, 520–527 (1993).
[CrossRef]

M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef] [PubMed]

1991 (2)

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

E. D. Hirleman, “General solution to the inverse near-forward-scattering particle-sizing problem in multiple-scattering environments: theory,” Appl. Opt. 30, 4832–4838 (1991).
[CrossRef] [PubMed]

1990 (1)

K. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

1989 (1)

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
[CrossRef]

1987 (2)

H. M. Hertz, M. Alden, “Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames,” J. Appl. Phys. B 42, 97–102 (1987).
[CrossRef]

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
[CrossRef] [PubMed]

1986 (1)

A. A. Hamidi, J. Swithenbank, “Treatment of the multiple scattering of light in laser diffraction measurement techniques in dense sprays and particle fields,” J. Inst. Energy 59, 101–105 (1986).

1984 (1)

L. G. Dodge, “Change of calibration of diffraction based particle sizes in dense sprays,” Opt. Eng. 23, 626–630 (1984).
[CrossRef]

1978 (1)

1977 (1)

A. N. Witt, “Multiple scattering in reflection nebulae I a Monte Carlo approach,” The Astrophysical J. Suppl Ser. 35, 1–6 (1977).
[CrossRef]

1974 (1)

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1974).
[CrossRef]

1973 (1)

Abu-Gharbieh, R.

Aigal, A. K.

P. G. Felton, A. A. Hamidi, A. K. Aigal, “Measurement of drop size distribution in dense sprays by laser diffraction,” Proc. 3rd Int. Conf. on Liquid Atomization and Sprays, London, IVA/4/1–11 (1985).

Alden, M.

H. M. Hertz, M. Alden, “Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames,” J. Appl. Phys. B 42, 97–102 (1987).
[CrossRef]

Alfano, R. R.

K. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Alianelli, L.

Anderson, D. E.

Arridge, S. R.

M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef] [PubMed]

Blumetti, C.

Bonner, R. F.

Bucher, E. A.

Carswell, A. I.

A. I. Carswell, “Laser Measurements in clouds,” pp 363–406 in Clouds: Their Formation, Optical Properties and Effects, A. Deepak, P. V. Hobbs, eds., (Academic Press, San Diego, Calif.1981), pp. 363–406.
[CrossRef]

Cashwell, E. D.

E. D. Cashwell, C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems, (Pergamon Press, New York, 1959).

Contini, D.

Cope, M.

M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef] [PubMed]

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]

Davies, E. R.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Delpy, D. T.

M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef] [PubMed]

Dodge, L. G.

L. G. Dodge, “Change of calibration of diffraction based particle sizes in dense sprays,” Opt. Eng. 23, 626–630 (1984).
[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]

Essenpreis, M.

M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef] [PubMed]

Everett, C. J.

E. D. Cashwell, C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems, (Pergamon Press, New York, 1959).

Felton, P. G.

P. G. Felton, A. A. Hamidi, A. K. Aigal, “Measurement of drop size distribution in dense sprays by laser diffraction,” Proc. 3rd Int. Conf. on Liquid Atomization and Sprays, London, IVA/4/1–11 (1985).

Fibrank, M.

M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teutolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press Cambridge, UK, 1992).

Forsth, M.

Giddings, R.

R. Giddings, D. A. Holder, M. Philpott, D. A. Youngs, “Multiple scattering from particles in laser sheet gas mixing experiments,” Advances in Statistical Optics–IOP half day meeting, Imperial College, London (24th May 2000).

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]

T. Girasole, C. Roze, B. Maheu, G. Grehan, J. Menard, “Visibility distances in a foggy atmosphere: comparisons between lighting installations by Monte Carlo simulation,” International Journal of Lighting Research and Technology. 30, 29–36 (1998).
[CrossRef]

Greenhalgh, D. A.

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]

Grehan, G.

T. Girasole, C. Roze, B. Maheu, G. Grehan, J. Menard, “Visibility distances in a foggy atmosphere: comparisons between lighting installations by Monte Carlo simulation,” International Journal of Lighting Research and Technology. 30, 29–36 (1998).
[CrossRef]

Gustavsson, T.

Hamidi, A. A.

A. A. Hamidi, J. Swithenbank, “Treatment of the multiple scattering of light in laser diffraction measurement techniques in dense sprays and particle fields,” J. Inst. Energy 59, 101–105 (1986).

P. G. Felton, A. A. Hamidi, A. K. Aigal, “Measurement of drop size distribution in dense sprays by laser diffraction,” Proc. 3rd Int. Conf. on Liquid Atomization and Sprays, London, IVA/4/1–11 (1985).

Havlin, S.

Hertz, H. M.

H. M. Hertz, M. Alden, “Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames,” J. Appl. Phys. B 42, 97–102 (1987).
[CrossRef]

Hibst, R.

Hiraoka, M.

M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef] [PubMed]

Hirleman, E. D.

Holder, D. A.

R. Giddings, D. A. Holder, M. Philpott, D. A. Youngs, “Multiple scattering from particles in laser sheet gas mixing experiments,” Advances in Statistical Optics–IOP half day meeting, Imperial College, London (24th May 2000).

Ismaelli, A.

Jackson, P. C.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Jacques, S. L.

L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Jermy, M. C.

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]

Kalos, M. H.

M. H. Kalos, P. A. Whitlock, Monte Carlo Methods, I: Basics (John Wiley and Sons, Inc., New York, 1986).
[CrossRef]

Kandidov, V. P.

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics,” Physics-Uspe. 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]

Karlstrom, A.

Key, H.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Kienle, A.

Koblinger, L.

I. Lux, L. Koblinger, “Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press Boca Raton, Fla., 1991).

Kokhanovsky, A. A.

A. A. Kokhanovsky, R. Weichert, “Multiple light scattering in laser particle sizing,” App. Opt. 40, 1507–1513 (2001).
[CrossRef]

A. A. Kokhanovsky, Optics of Light Scattering Media (Springer-Verlag, Berlin, 2001).

Krauss, R. H.

T. M. Quagliaroli, G. Laufer, R. H. Krauss, J. C. McDaniel, AIAAJ. 31, 520–527 (1993).
[CrossRef]

Kunkel, K. E.

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1974).
[CrossRef]

Langlois, S.

Laufer, G.

T. M. Quagliaroli, G. Laufer, R. H. Krauss, J. C. McDaniel, AIAAJ. 31, 520–527 (1993).
[CrossRef]

Lavigne, C.

Lee, J.-S.

Lee, S. W.

D. G. Talley, J. F. Verdieck, S. W. Lee, V. G. McDonell, G. S. Samuelsen, Accounting for Laser Sheet Extinction in Applying PLIF to Sprays, (AIAA, 96-0469, 1996).

Lilge, L.

Liu, F.

K. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Lux, I.

I. Lux, L. Koblinger, “Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press Boca Raton, Fla., 1991).

Maheu, B.

T. Girasole, C. Roze, B. Maheu, G. Grehan, J. Menard, “Visibility distances in a foggy atmosphere: comparisons between lighting installations by Monte Carlo simulation,” International Journal of Lighting Research and Technology. 30, 29–36 (1998).
[CrossRef]

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]

Martelli, F.

Matcher, S. J.

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

McDaniel, J. C.

T. M. Quagliaroli, G. Laufer, R. H. Krauss, J. C. McDaniel, AIAAJ. 31, 520–527 (1993).
[CrossRef]

McDonell, V. G.

D. G. Talley, J. F. Verdieck, S. W. Lee, V. G. McDonell, G. S. Samuelsen, Accounting for Laser Sheet Extinction in Applying PLIF to Sprays, (AIAA, 96-0469, 1996).

Meglinsky, I. V.

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

Meier, R. R.

Menard, J.

T. Girasole, C. Roze, B. Maheu, G. Grehan, J. Menard, “Visibility distances in a foggy atmosphere: comparisons between lighting installations by Monte Carlo simulation,” International Journal of Lighting Research and Technology. 30, 29–36 (1998).
[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]

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]

Nossal, R.

Outters, V.

Patterson, M. S.

Persson, J. L.

Philpott, M.

R. Giddings, D. A. Holder, M. Philpott, D. A. Youngs, “Multiple scattering from particles in laser sheet gas mixing experiments,” Advances in Statistical Optics–IOP half day meeting, Imperial College, London (24th May 2000).

Press, W. H.

W. H. Press, S. A. Teutolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press Cambridge, UK, 1992).

Quagliaroli, T. M.

T. M. Quagliaroli, G. Laufer, R. H. Krauss, J. C. McDaniel, AIAAJ. 31, 520–527 (1993).
[CrossRef]

Robin, A.

Rosen, A.

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]

T. Girasole, C. Roze, B. Maheu, G. Grehan, J. Menard, “Visibility distances in a foggy atmosphere: comparisons between lighting installations by Monte Carlo simulation,” International Journal of Lighting Research and Technology. 30, 29–36 (1998).
[CrossRef]

Samuelsen, G. S.

D. G. Talley, J. F. Verdieck, S. W. Lee, V. G. McDonell, G. S. Samuelsen, Accounting for Laser Sheet Extinction in Applying PLIF to Sprays, (AIAA, 96-0469, 1996).

Sassaroli, A.

Sick, V.

Steiner, R.

Stojkovic, B.

Swithenbank, J.

A. A. Hamidi, J. Swithenbank, “Treatment of the multiple scattering of light in laser diffraction measurement techniques in dense sprays and particle fields,” J. Inst. Energy 59, 101–105 (1986).

Talley, D. G.

D. G. Talley, J. F. Verdieck, “Accounting for laser sheet extinction and fluorescence signal attenuation in applying PLIF to sprays,” Proc. 9th Inst. Liquid Atomization and Sprays, iClass AA 33–38 (1996).

D. G. Talley, J. F. Verdieck, S. W. Lee, V. G. McDonell, G. S. Samuelsen, Accounting for Laser Sheet Extinction in Applying PLIF to Sprays, (AIAA, 96-0469, 1996).

Teutolsky, S. A.

W. H. Press, S. A. Teutolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press Cambridge, UK, 1992).

Tuchin, V.

V. Tuchin, Tissue Optics ISBN 0819434590, SPIE Press (2000).

V. Tuchin, Tissue Optics (SPIE, Bellingham, Wa., 2000).

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering, Volume II, (Academic Press, New York, 1980).

van der Zee, P.

M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef] [PubMed]

P. van der Zee, “Measurement and Modelling of the optical properties of human tissue in the near infrared” Ph. D. dissertation, University College London (1992).

Verdieck, J. F.

D. G. Talley, J. F. Verdieck, S. W. Lee, V. G. McDonell, G. S. Samuelsen, Accounting for Laser Sheet Extinction in Applying PLIF to Sprays, (AIAA, 96-0469, 1996).

D. G. Talley, J. F. Verdieck, “Accounting for laser sheet extinction and fluorescence signal attenuation in applying PLIF to sprays,” Proc. 9th Inst. Liquid Atomization and Sprays, iClass AA 33–38 (1996).

Vettering, W. T.

W. H. Press, S. A. Teutolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press Cambridge, UK, 1992).

Wang, L.

L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Weichert, R.

A. A. Kokhanovsky, R. Weichert, “Multiple light scattering in laser particle sizing,” App. Opt. 40, 1507–1513 (2001).
[CrossRef]

Weinman, J. A.

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1974).
[CrossRef]

Weiss, G. H.

Wells, P. N. T.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Whitlock, P. A.

M. H. Kalos, P. A. Whitlock, Monte Carlo Methods, I: Basics (John Wiley and Sons, Inc., New York, 1986).
[CrossRef]

Wilson, B. C.

Witt, A. N.

A. N. Witt, “Multiple scattering in reflection nebulae I a Monte Carlo approach,” The Astrophysical J. Suppl Ser. 35, 1–6 (1977).
[CrossRef]

Wyman, D. R.

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
[CrossRef]

Yoo, K.

K. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Youngs, D. A.

R. Giddings, D. A. Holder, M. Philpott, D. A. Youngs, “Multiple scattering from particles in laser sheet gas mixing experiments,” Advances in Statistical Optics–IOP half day meeting, Imperial College, London (24th May 2000).

Zaccanti, G.

Zheng, L.

L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

AIAAJ. (1)

T. M. Quagliaroli, G. Laufer, R. H. Krauss, J. C. McDaniel, AIAAJ. 31, 520–527 (1993).
[CrossRef]

App. Opt. (1)

A. A. Kokhanovsky, R. Weichert, “Multiple light scattering in laser particle sizing,” App. Opt. 40, 1507–1513 (2001).
[CrossRef]

Appl. Opt. (8)

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Partially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
[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]

E. A. Bucher, “Computer simulation of light pulse propagation for communication through thick clouds,” Appl. Opt. 12, 2391–2400 (1973).
[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]

R. Abu-Gharbieh, J. L. Persson, M. Forsth, A. Rosen, A. Karlstrom, T. Gustavsson, “Compensation method for attenuated planar laser images of optically dense sprays,” Appl. Opt. 39, 1260–1267 (2000).
[CrossRef]

V. Sick, B. Stojkovic, “Attenuation effects on imaging diagnostics in hollow-cone sprays,” Appl. Opt. 40, 2435–2442 (2001).
[CrossRef]

A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37, 7392–7400 (1998).
[CrossRef]

E. D. Hirleman, “General solution to the inverse near-forward-scattering particle-sizing problem in multiple-scattering environments: theory,” Appl. Opt. 30, 4832–4838 (1991).
[CrossRef] [PubMed]

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]

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

International Journal of Lighting Research and Technology. (1)

T. Girasole, C. Roze, B. Maheu, G. Grehan, J. Menard, “Visibility distances in a foggy atmosphere: comparisons between lighting installations by Monte Carlo simulation,” International Journal of Lighting Research and Technology. 30, 29–36 (1998).
[CrossRef]

J. Appl. Phys. B (1)

H. M. Hertz, M. Alden, “Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames,” J. Appl. Phys. B 42, 97–102 (1987).
[CrossRef]

J. Atmos. Sci. (1)

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1974).
[CrossRef]

J. Comput. Phys. (1)

D. R. Wyman, M. S. Patterson, B. C. Wilson, “Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles,” J. Comput. Phys. 81, 137–150 (1989).
[CrossRef]

J. Inst. Energy (1)

A. A. Hamidi, J. Swithenbank, “Treatment of the multiple scattering of light in laser diffraction measurement techniques in dense sprays and particle fields,” J. Inst. Energy 59, 101–105 (1986).

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

Med. Biol. Eng. Comput. (1)

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

Opt. Eng. (1)

L. G. Dodge, “Change of calibration of diffraction based particle sizes in dense sprays,” Opt. Eng. 23, 626–630 (1984).
[CrossRef]

Phys. Med. Biol. (2)

M. Hiraoka, M. Fibrank, M. Essenpreis, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in homogeneous tissue and it’s application to near infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
[CrossRef] [PubMed]

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

K. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Physics-Uspe. (1)

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics,” Physics-Uspe. 39, 1243–1272 (1996).
[CrossRef]

The Astrophysical J. Suppl Ser. (1)

A. N. Witt, “Multiple scattering in reflection nebulae I a Monte Carlo approach,” The Astrophysical J. Suppl Ser. 35, 1–6 (1977).
[CrossRef]

Other (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]

A. I. Carswell, “Laser Measurements in clouds,” pp 363–406 in Clouds: Their Formation, Optical Properties and Effects, A. Deepak, P. V. Hobbs, eds., (Academic Press, San Diego, Calif.1981), pp. 363–406.
[CrossRef]

R. Giddings, D. A. Holder, M. Philpott, D. A. Youngs, “Multiple scattering from particles in laser sheet gas mixing experiments,” Advances in Statistical Optics–IOP half day meeting, Imperial College, London (24th May 2000).

E. D. Cashwell, C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems, (Pergamon Press, New York, 1959).

M. H. Kalos, P. A. Whitlock, Monte Carlo Methods, I: Basics (John Wiley and Sons, Inc., New York, 1986).
[CrossRef]

P. G. Felton, A. A. Hamidi, A. K. Aigal, “Measurement of drop size distribution in dense sprays by laser diffraction,” Proc. 3rd Int. Conf. on Liquid Atomization and Sprays, London, IVA/4/1–11 (1985).

P. van der Zee, “Measurement and Modelling of the optical properties of human tissue in the near infrared” Ph. D. dissertation, University College London (1992).

V. Tuchin, Tissue Optics (SPIE, Bellingham, Wa., 2000).

H. C. van de Hulst, Multiple Light Scattering, Volume II, (Academic Press, New York, 1980).

A. A. Kokhanovsky, Optics of Light Scattering Media (Springer-Verlag, Berlin, 2001).

D. G. Talley, J. F. Verdieck, S. W. Lee, V. G. McDonell, G. S. Samuelsen, Accounting for Laser Sheet Extinction in Applying PLIF to Sprays, (AIAA, 96-0469, 1996).

D. G. Talley, J. F. Verdieck, “Accounting for laser sheet extinction and fluorescence signal attenuation in applying PLIF to sprays,” Proc. 9th Inst. Liquid Atomization and Sprays, iClass AA 33–38 (1996).

W. H. Press, S. A. Teutolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press Cambridge, UK, 1992).

http://www.unternehmen.com/Bernhard-Michel/Java/mieApplet.html .

V. Tuchin, Tissue Optics ISBN 0819434590, SPIE Press (2000).

I. Lux, L. Koblinger, “Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press Boca Raton, Fla., 1991).

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Figures (6)

Fig. 1
Fig. 1

Typical light sheet imaging geometry and the three geometries used in simulation 2. Dimensions in millimeters.

Fig. 2
Fig. 2

Geometry of simulation 1. Dimensions in arbitrary units.

Fig. 3
Fig. 3

Scattering angle probability tables used in the simulations. The third curve is the table used in simulation 2 multiplied by 500 to show the fine structure.

Fig. 4
Fig. 4

Images from simulation 1 for different scattering orders. The highest gray level is reached at 100 counts in each image.

Fig. 5
Fig. 5

Images from simulation 2 for different scattering orders. The highest gray level is reached at 130 counts.

Fig. 6
Fig. 6

Plots of attenuation-corrected photon count from the 11th row from the bottom of the images in Fig. 5, (a) all orders, (b) first order, (c) second order. The spray density is also plotted, in arbitrary units, at two different scale factors to allow easy comparison with different parts of the photon count plots.

Tables (1)

Tables Icon

Table 1 Intensity Ratios from Simulation 1

Equations (7)

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

ΦE, P¯=v SE, r¯T E, P¯-r¯d3r¯,
Pscatter, j=njσlj.
Δθ=i Δα,
RN1- j=0i PjΔα<Δα2π,
Δϕ=k Δα,
RN2-m=0k PmΔα<Δα2π,
n=100r2z2r  z0r > z.

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