Abstract

Modern optical diagnostics for quantitative characterization of polydisperse sprays and other aerosols which contain a wide range of droplet size encounter difficulties in the dense regions due to the multiple scattering of laser radiation with the surrounding droplets. The accuracy and efficiency of optical measurements can only be improved if the radiative transfer within such polydisperse turbid media is understood. A novel Monte Carlo code has been developed for modeling of optical radiation propagation in inhomogeneous polydisperse scattering media with typical drop size ranging from 2 μm to 200 μm in diameter. We show how strong variations of both particle size distribution and particle concentration within a 3D scattering medium can be taken into account via the Monte Carlo approach. A new approximation which reduces ~20 times the computational memory space required to determine the phase function is described. The approximation is verified by considering four log-normal drop size distributions. It is found valid for particle sizes in the range of 10–200 μm with increasing errors, due to additional photons scattered at large angles, as the number of particles below than 10 μm increases. The technique is applied to the simulation of typical planar Mie imaging of a hollow cone spray. Simulated and experimental images are compared and shown to agree well. The code has application in developing and testing new optical diagnostics for complex scattering media such as dense sprays.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. E. Berrocal, M. Jermy, F. Moukaideche and I. V. Meglinski, �??Dense Spray Analysis using Optical Measurements and Monte Carlo simulation,�?? presented at the 18th Annual Conference on Liquid Atomization and Spray System-America, Irvine, CA, USA, 22-25 May 2005.
  2. V. Sicks and B. Stojkovic, �??Attenuation effects on imaging diagnostics of hollow-cone sprays,�?? Appl. Opt. 40, 2435-2442, (2001).
    [CrossRef]
  3. I. V. Meglinski, V. .P. Romanov, D. Y. Churmakov, E. Berrocal , M. C. Jermy and D. A. Greenhalgh, �??Low and high orders light scattering in particulate media,�?? Laser Phys. Lett. 1, 387-390 (2004).
    [CrossRef]
  4. R. P. Meier and J. S. Lee, D. E. Anderson, �??Atmospheric scattering of middle UV radiation from an internal source,�?? Appl. Opt. 17, 3216-3225 (1978).
    [CrossRef] [PubMed]
  5. T. Girasole, C. Roze, B. Maheu, G. Grehan and J. Menard, �??Visibility distances in a foggy atmosphere: Comparisons between lighting installations by Monte Carlo simulation,�?? Int. Journal of Lighting Research and Technology 30, 29-36 (1998).
    [CrossRef]
  6. R. F. Bonner, R. Nossal, S. Havlin and G. H. Weiss, �??Model for photon migration in turbid biological media,�?? J. Opt. Soc. Am. A 4, 423-432 (1987).
    [CrossRef] [PubMed]
  7. I. R. Abubakirov and A. A. Gusev, �??Estimation of scattering properties of lithosphere of Kamchatka based on Monte-Carlo simulation of record envelope of a near earthquake,�?? Phys. Earth Planet. Inter. 64, 52-67 (1990).
    [CrossRef]
  8. M. C. Jermy and A. Allen, �??Simulating the effects of multiple scattering on images of dense sprays and particle fields,�?? Appl. Opt. 41, 4188-4196 (2002).
    [CrossRef] [PubMed]
  9. E. Berrocal, D. Y. Churmakov, V. P. Romanov, M. C. Jermy and I. V. Meglinski, �??Crossed source/detector geometry for novel spray diagnostic: Monte Carlo and analytical results,�?? Appl. Opt. 44, 2519-2529 (2005).
    [CrossRef] [PubMed]
  10. I. V. Meglinsky and S. J. Matcher, �??Modeling the sampling volume for the skin blood oxygenation measurements,�?? Med. Biol. Eng. Comput. 39, 44-50 (2001).
    [CrossRef] [PubMed]
  11. L. Wang, S. L. Jacques and L. Zheng, �??MCML �?? Monte Carlo modeling of light transport in multi-layered tissues,�?? Computer Methods and Programs in Biomedicine 47, 131-146 (1995).
    [CrossRef] [PubMed]
  12. I. V. Meglinski, D. Y. Churmakov, A. N. Bashkatov, E. A. Genina and V. V. Tuchin, �??The Enhancement of Confocal Images of Tissues at Bulk Optical Immersion,�?? Laser Phys. 13 , 65-69 (2003).
  13. I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov and D. A. Greenhalgh, �??Monte Carlo Simulation of Coherent Effects in Multiple Scattering,�?? Proc. Roy. Soc. A 461, 43-53 (2005).
    [CrossRef]
  14. B. T. Wong and M. P. Mengüç, �??Comparison of Monte Carlo Techniques to Predict the Propagation of a Collimated Beam in Participating Media,�?? Numerical Heat Transfer 42, 119-140 (2002).
    [CrossRef]
  15. H. C. van de Hulst, Light scattering by small particles (Dover, N.Y., 1981).
  16. C. Bohren, and D. Huffman, Absorption and scattering of light by small particles (Wiley, N.Y., 1983).
  17. L. G. Henyey and J. L. Greenstein, �??Diffuse radiation in the galaxy,�?? Astrophys. J. 93, 70-83 (1941).
    [CrossRef]

Appl. Opt.

Astrophys. J.

L. G. Henyey and J. L. Greenstein, �??Diffuse radiation in the galaxy,�?? Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Computer Methods and Programs in Biomedi

L. Wang, S. L. Jacques and L. Zheng, �??MCML �?? Monte Carlo modeling of light transport in multi-layered tissues,�?? Computer Methods and Programs in Biomedicine 47, 131-146 (1995).
[CrossRef] [PubMed]

Int. Journal of Lighting Research and Te

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

J. Opt. Soc. Am. A

Laser Phys.

I. V. Meglinski, D. Y. Churmakov, A. N. Bashkatov, E. A. Genina and V. V. Tuchin, �??The Enhancement of Confocal Images of Tissues at Bulk Optical Immersion,�?? Laser Phys. 13 , 65-69 (2003).

Laser Phys. Lett.

I. V. Meglinski, V. .P. Romanov, D. Y. Churmakov, E. Berrocal , M. C. Jermy and D. A. Greenhalgh, �??Low and high orders light scattering in particulate media,�?? Laser Phys. Lett. 1, 387-390 (2004).
[CrossRef]

Med. Biol. Eng. Comput.

I. V. Meglinsky and S. J. Matcher, �??Modeling the sampling volume for the skin blood oxygenation measurements,�?? Med. Biol. Eng. Comput. 39, 44-50 (2001).
[CrossRef] [PubMed]

Numerical Heat Transfer

B. T. Wong and M. P. Mengüç, �??Comparison of Monte Carlo Techniques to Predict the Propagation of a Collimated Beam in Participating Media,�?? Numerical Heat Transfer 42, 119-140 (2002).
[CrossRef]

Phys. Earth Planet. Inter.

I. R. Abubakirov and A. A. Gusev, �??Estimation of scattering properties of lithosphere of Kamchatka based on Monte-Carlo simulation of record envelope of a near earthquake,�?? Phys. Earth Planet. Inter. 64, 52-67 (1990).
[CrossRef]

Proc. Roy. Soc. A

I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov and D. A. Greenhalgh, �??Monte Carlo Simulation of Coherent Effects in Multiple Scattering,�?? Proc. Roy. Soc. A 461, 43-53 (2005).
[CrossRef]

Other

H. C. van de Hulst, Light scattering by small particles (Dover, N.Y., 1981).

C. Bohren, and D. Huffman, Absorption and scattering of light by small particles (Wiley, N.Y., 1983).

E. Berrocal, M. Jermy, F. Moukaideche and I. V. Meglinski, �??Dense Spray Analysis using Optical Measurements and Monte Carlo simulation,�?? presented at the 18th Annual Conference on Liquid Atomization and Spray System-America, Irvine, CA, USA, 22-25 May 2005.

Supplementary Material (6)

» Media 1: AVI (1380 KB)     
» Media 2: AVI (983 KB)     
» Media 3: AVI (1364 KB)     
» Media 4: AVI (859 KB)     
» Media 5: AVI (1136 KB)     
» Media 6: AVI (610 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

Illustration of Monte Carlo modeling in inhomogeneous polydisperse scattering medium

Fig. 2.
Fig. 2.

Normalized Log-Normal distributions of particle size for different d¯ and σ.

Fig. 3.
Fig. 3.

Representation of 25 Cumulative Probability Density Functions (CPDF) calculated from Mie theory. Each CPDF represents a class of drop size. Scattering particle diameters range from 2 to 200 μm.

Fig. 4.
Fig. 4.

The scattering medium is a single homogeneous cube of L = 50 mm. The source S is a cylindrical laser beam.

Fig. 5.
Fig. 5.

Intensity distribution for forward (front face) and backward (back face) light scattering at different scattering coefficient. μsca =0.12 mm -1 for (a) (c) (e) (g) and μsca =0.24 mm -1 for (b) (d) (f) (h). The detection acceptance angle θa = 90°. 100 million photons are sent. The intensity scale represents the number of photons detected per pixel. Pixels are 25 μm sides. [Media 1] [Media 2] [Media 3] [Media 4]

Fig. 6.
Fig. 6.

Intensity distribution for forward light scattering (front face). μsca =0.12 mm -1 for (a) (c) and μsca =0.24 mm -1 for (b) (d). The detection acceptance angle θa = 5°. 100 millions of photons are sent. The intensity scale represents the number of photon detected per pixel. Each pixel is square with 25 μm sides. [Media 5] [Media 6]

Fig. 7.
Fig. 7.

Intensity ratio, along a beam profile, between the 2 MC methods. Forward scattering is in (a) and (b) and backscattering in (c) and (d). Both single and multiple scattering are detected together. Detector acceptance angle θa = 90°.

Fig. 8.
Fig. 8.

Intensity profile ratio between the 2 MC methods for forward light scattering. Single and multiple scattering are detected with an acceptance angle θa = 5°. μsca =0.12 mm -1 for (a) (c) and μsca =0.24 mm -1 for (b) (d).

Fig. 9.
Fig. 9.

Intensity profile ratio between the 2 MC methods for forward light scattering with μsca =0.12 mm -1. Single scattering only is detected with an acceptance angle θa = 90°(a) and θa = 5°(b). No singly scattered photons are detected with either method at X>40mm in (b).

Fig. 10.
Fig. 10.

Intensity profile ratio between the 2 MC methods for μsca =0.12 mm -1. Single and multiple light scattering are detected on the front face with an acceptance angle θa = 90°. The log-normal distributions of particle size are characterized by: (a): d¯ = 40 μm with à = 4 μm (10%), (b): d¯ = 5 μm with σ = 4 μm (80%), (c): d¯ = 5 μm with σ = 0.5 μm (10%).

Fig. 11.
Fig. 11.

Extinction coefficient (a) and droplet diameter (b) through the central plane of a hollow cone spray. By rotating the data around the central vertical axis MC input data are generated in 3D.

Fig. 12.
Fig. 12.

Comparison between the experimental (a) and MC (b,c) images for a planar Mie imaging of a hollow cone spray. (c) is generated from the singly scattered detected photons only.

Tables (1)

Tables Icon

Table 1. Scattering turbid media types and required optical properties

Equations (5)

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

P ( d ) = 1 T 2 πd e ( ln d M ) 2 ( 2 T ) 2
d ¯ = e M + T 2 2
σ = e T 2 + 2 M · ( e T 2 1 )
f ¯ ( θ s ) = d = 0 n ( d ) σ ext ( d ) f ( d , θ s ) dd d = 0 n ( d ) σ ext ( d ) dd with 4 π f ¯ ( θ s ) d Ω ( θ s ) = 1
P ( d 1 ) = n ( d 1 ) * σ ext ( d 1 ) d = 0 n ( d ) * σ ext ( d )

Metrics