Kato theorem: Difference between revisions

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{{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]]

Revision as of 13:39, 6 January 2014

Template:Orphan

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*=l1−g

with: g: the asymmetry coefficient. g=<cos(θ)> 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 of backscattering experiments.[2][3]

References

  1. ↑ A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press, New York, 1978.
  2. ↑ Talanta, Volume 50, Issue 2, 13 September 1999, Pages 445–456
  3. ↑ P. Snabre, A. Arhaliass, Anisotropic scattering of light in random media. Incoherent backscattered spot light, Appl. Optics 37 (18) (1998) 211–225.

External links

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