Lidar s-Function: Definition, Meaning & Uses

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Fr34k
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What is it, what does it mean/do and why is it used for? Its defined as:
S(r)=ln(P(r)r^2/(P(r0)r0^2)), where r is distance in atmosphere and P is intensity of detected light.
 
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Really no one can explain this to me?

Anyone know of a good book on the subject (lidar, atmosphere research ...) where this might be explained.
 
Well I am doing some research for school, and many of the papers I've been reading have the same equation and associated graphs with it and it's never explained why exactly in this form. From what I managed to come up with is some sort of attenuation of atmosphere.