## Crossed source-detector geometry for a novel spray diagnostic: Monte Carlo simulation and analytical results

Applied Optics, Vol. 44, Issue 13, pp. 2519-2529 (2005)

http://dx.doi.org/10.1364/AO.44.002519

Acrobat PDF (215 KB)

### 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

**OCIS Codes**

(010.1110) Atmospheric and oceanic optics : Aerosols

(080.2710) Geometric optics : Inhomogeneous optical media

(120.1740) Instrumentation, measurement, and metrology : Combustion diagnostics

(290.4210) Scattering : Multiple scattering

(290.7050) Scattering : Turbid media

**Citation**

Edouard Berrocal, Dmitry Y. Churmakov, Vadim P. Romanov, Mark C. Jermy, and Igor V. Meglinski, "Crossed source-detector geometry for a novel spray diagnostic: Monte Carlo simulation and analytical results," Appl. Opt. **44**, 2519-2529 (2005)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-44-13-2519

Sort: Year | Journal | Reset

### References

- H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
- C. Bohren and 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 and 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).
- V. L. Kuz'min and V. P. Romanov, "Coherent phenomena in light scattering from disordered systems," Usp. Fiz. Nauk 39, 231-260 (1996).
- J. Q. Shen and U. Riebel, "Extinction by a large spherical particle located in a narrow Gaussian beam," Part. Part. Syst. Charact. 18, 254-261 (2001).
- G. Gouesbet, B. Maheu, and 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).
- Z. Ma, H. G. Merkus, H. G. van der Veen, M. Wong, and B. Scarlett, "On-line measurement of particle size and shape using laser diffraction," Part. Part. Syst. Charact. 18, 243-247 (2001).
- M. Kocifaj and 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).
- M. Kerker and D. D. Cooke, "Remote sensing of particle size and refractive index by varying the wavelength," Appl. Opt. 15, 2105-2111 (1976).
- A. R. Jones, "Scattering of electromagnetic radiation in particulate laden fluids," Prog. Energy Combust. Sci. 5, 73-96 (1979).
- W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles (Wiley, New York, 1982).
- F. Zhao, Z. Gong, H. Hu, M. Tanaka, and 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).
- M. C. Jermy and 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).
- 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, and B. S. Elepov, The Monte Carlo Method in Atmospheric Optics (Springer, Berlin, 1980).
- V. P. Kandidov, "Monte Carlo methods in nonlinear statistical optics," Usp. Fiz. Nauk 39, 1243-1272 (1996).
- S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, "A Monte Carlo model of light propagation in tissue," in Dosimetry of Laser Radiation in Medicine and Biology, G. J. Müller and D. H. Sliney, eds., Vol. IS5 of the SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102-111.
- I. V. Meglinsky and S. J. Matcher, "Modeling the sampling volume for skin blood oxygenation measurements," Med. Biol. Eng. Comput. 39, 44-50 (2001).
- R. R. Meier, J.-S. Lee, and D. E. Anderson, "Atmospheric scattering of middle UV radiation from an internal source," Appl. Opt. 17, 3216-3225 (1978).
- C. Lavigne, A. Robin, V. Outters, S. Langlois, T. Girasole, and 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).
- E. A. Bucher, "Computer simulation of light pulse propagation for communication through thick clouds," Appl. Opt. 12, 2391-2400 (1973).
- A. I. Carswell, "Laser measurements in clouds," in Clouds: Their Formation, Optical Properties and Effects, A. Deepak and P. V. Hobbs, eds. (Academic, New York, 1981), pp. 363-406.
- G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, Cambridge, UK, 1999).
- 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).
- M. C. Jermy, A. Allen, and 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 and K. T. V. Grattan, eds. (Institute of Physics, Bristol, UK, 2003), Vol. 177, pp. 89-94.
- E. Berrocal, A. Allen, and 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.
- V. L. Kuzmin and I. V. Meglinski, "Coherent multiple scattering effects and Monte Carlo method," JETP Lett. 79, 109-112 (2004).
- I. V. Meglinski, V. L. Kuzmin, D. Y. Churmakov, and D. A. Greenhalgh, "Monte Carlo simulation of coherent effects in multiple scattering," Proc. R. Soc. London Ser. A 461, 43-53 (2005).
- S. Bartel and A. H. Hielscher, "Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media," Appl. Opt. 39, 1580-1588 (2000).
- X. Wang, L.-H. Wang, C.-W. Sun, and C. C. Yang, "Polarized light propagation through the scattering media: time-resolved Monte Carlo and experiments," J. Biomed. Opt. 8, 608-617 (2003).
- K. Muinonen, "Coherent backscattering of light by complex random media of spherical scatterers: numerical solution," Waves Random Media 14, 365-388 (2004).
- S. V. Gangnus, S. J. Matcher, and I. V. Meglinski, "Monte Carlo modeling of polarized light propagation in biological tissues," Laser Phys. 14, 886-891 (2004).
- T. Iwai, H. Furukawa, and T. Asakura, "Numerical analysis on enhanced backscatterings of light based on Rayleigh-Debye scattering theory," Opt. Rev. 2, 413-419 (1995).
- A. S. Martinez and 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.
- V. L. Kuzmin, I. V. Meglinski, and D. Y. Churmakov, "Coherent effects under multiple scattering of linearly polarized light," Opt. Spectrosc. 98, 673-679 (2005).
- H. Ishimoto and 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).
- M. J. Rakovic, G. W. Kattawar, M. Mehrübeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, "Light backscattering polarization patterns from turbid media: theory and experiment," Appl. Opt. 38, 3399-3408 (1999).
- X. Wang and L. V. Wang, "Propagation of polarized light in birefringent turbid media: a Monte Carlo study," J. Biomed. Opt. 7, 279-290 (2002).
- S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarski, Principles of Statistical Radiophysics (Springer, Berlin, 1987).
- P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge U. Press, Cambridge, UK, 1995).
- V. L. Kuzmin, V. P. Romanov, and L. A. Zubkov, "Propagation and scattering of light in fluctuating media," Phys. Rep. 248, 71-368 (1994).
- G. Mie, "Considerations on the optic of turbid media, especially colloidal metal sols," Ann. Phys. (Leipzig) 25, 377-442 (1908).
- L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 93, 70-83 (1941).
- J. R. Zijp and 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).
- D. Toublanc, "Henyey-Greenstein and Mie phase functions in Monte Carlo radiative transfer computations," Appl. Opt. 35, 3270-3274 (1996).
- E. Tilnet, S. Avrillier, and M. Tualle, "Fast semianalytical Monte Carlo simulation for time-resolved light propagation in turbid media," J. Opt. Soc. Am. A 13, 1903-1915 (1996).
- L. V. Adzhemyan, L. Ts. Adzhemyan, L. A. Zubkov, and V. P. Romanov, "Molecular light scattering of varying multiplicity," Sov. Phys. JEPT 53, 278-281 (1981).
- K. K. Bizheva, A. M. Siegel, and 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).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.