Transport length: Difference between revisions

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The transport length in a strongly diffusing medium (noted l*) is the length over which the direction of propagation of the photon is randomized. It is related to the mean free path l by the relation:^[1]

$l^{*}={\frac {l}{1-g}}$

with g: the asymmetry coefficient. $g=\langle cos(\theta )\rangle$ or averaging of the scattering angle θ over a high number of scattering events.

g can be evaluated with the Mie theory.
If g=0, l=l*. A single scattering is already isotropic.
If g→1, l*→infinite. A single scattering doesn't deviate the photons. Then the scattering never gets isotropic.

This length is useful for renormalizing a non-isotropic scattering problem into an isotropic one in order to use classical diffusion laws (Fick law and Brownian motion). The transport length might be measured by transmission experiments and backscattering experiments.^[2]^[3]

Mean free path simple scheme

References

^ Ishimaru, A. (1978). Wave Propagation and Scattering in Random Media. New York: Academic Press.
^ Mengual, O.; Meunier, G.; Cayré, I.; Puech, K.; Snabre, P. (1999). "TURBISCAN MA 2000: Multiple light scattering measurement for concentrated emulsion and suspension instability analysis". Talanta. 50 (2): 445–456. doi:10.1016/S0039-9140(99)00129-0. PMID 18967735.
^ Snabre, Patrick; Arhaliass, Abdellah (1998). "Anisotropic scattering of light in random media: Incoherent backscattered spotlight". Applied Optics. 37 (18): 4017–26. Bibcode:1998ApOpt..37.4017S. doi:10.1364/AO.37.004017. PMID 18273374.

External links

Illustrated description (movies) of multiple light scattering and application to colloid stability^{[permanent dead link‍]}

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[1] Ishimaru, A. (1978). Wave Propagation and Scattering in Random Media. New York: Academic Press.

[2] Mengual, O.; Meunier, G.; Cayré, I.; Puech, K.; Snabre, P. (1999). "TURBISCAN MA 2000: Multiple light scattering measurement for concentrated emulsion and suspension instability analysis". Talanta. 50 (2): 445–456. doi:10.1016/S0039-9140(99)00129-0. PMID 18967735.

[3] Snabre, Patrick; Arhaliass, Abdellah (1998). "Anisotropic scattering of light in random media: Incoherent backscattered spotlight". Applied Optics. 37 (18): 4017–26. Bibcode:1998ApOpt..37.4017S. doi:10.1364/AO.37.004017. PMID 18273374.

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+{{Short description|Measurement of photon propagation}}
-The '''transport length''' in a strongly diffusing medium (noted l*) is the length over which the direction of propagation of the [[photon]] is randomized. It is related to the [[mean free path]] l by the relation:<ref>{{cite journal |first=A. |last=Ishimaru |year=1978 |title=Wave Propagation and Scattering in Random Media |publisher=Academic Press |location=New York}}</ref>
+The '''transport length''' in a strongly diffusing medium (noted l*) is the length over which the direction of propagation of the [[photon]] is randomized. It is related to the [[mean free path]] l by the relation:<ref>{{cite book |first=A. |last=Ishimaru |year=1978 |title=Wave Propagation and Scattering in Random Media |publisher=Academic Press |location=New York}}</ref>
 <math>l^*=\frac{l}{1-g}</math>
+with g: the asymmetry coefficient. <math>g=  \langle cos (\theta) \rangle </math> or averaging of the scattering angle θ over a high number of [[scattering event]]s.
-with:
-g: the asymmetry coefficient. <math>g=  \langle cos (\theta) \rangle </math> or averaging of the scattering angle θ over a high number of [[scattering event]]s.
 g can be evaluated with the [[Mie theory]].<br />