Lidar s-Function: Definition, Meaning & Uses

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Lidar is defined by the equation S(r)=ln(P(r)r^2/(P(r0)r0^2)), where r represents distance and P indicates the intensity of detected light. The discussion revolves around understanding this equation's significance, particularly in relation to atmospheric propagation loss and the behavior of Gaussian beams. Participants suggest that the equation relates to atmospheric attenuation, though its specific derivation remains unclear. A recommended resource for further study is ERIM's Electro-Optic Handbook, volume 6, which covers Lidar extensively. The conversation highlights a gap in accessible explanations for this equation in academic literature.
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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.
 
ERIM's Electro-Optic handbook, volume 6, has an extensive section on Lidar. I suspect your equation has to do with propagation loss and spread of a Gaussian beam through the atmosphere, but I did not see that particular equation in the book. Whre did it come from?
 
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.
 
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