Kato theorem

2014-01-06T12:39:47Z

92.229.15.243:

{{Orphan|date=January 2011}}

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>A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press, New York, 1978.</ref>

<math>l^*=\frac{l}{1-g}</math>

with:
g: the asymmetry coefficient. <math>g= <cos (\theta) > </math> or averaging of the scattering angle θ over a high number of scattering events.

g can be evaluated with the [[Mie theory]].<br />
If g=0, l=l*. A single scattering is already isotropic.<br />
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 of backscattering experiments.<ref>Talanta, Volume 50, Issue 2, 13 September 1999, Pages 445–456</ref><ref>P. Snabre, A. Arhaliass, Anisotropic scattering of light in random media. Incoherent backscattered spot light, Appl. Optics 37 (18) (1998) 211–225.</ref>

<gallery>
Image:figure_mean_free_path.png|Mean free path simple scheme
</gallery>

==References==
<references/>

==External links==
* [http://www.formulaction.com/MLS_video.html Illustrated description (movies) of multiple light scattering and application to colloid stability]

[[Category:Optics]]
[[Category:Colloids]]

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Kato theorem