Return signal strength - CL61

In general form, the instantaneous return signal power can be derived from the lidar equation:

$\mathrm{Pr}\left(z\right)=E_0\times \frac{c}{2}\times \frac{A}{z^2}\times \beta \left(z\right)\times e^{-2\underset{0}{\overset{z}{\int }}\sigma (z\prime )dz\prime }$

Table 1. Signal power formula

Variable	Description
Pr(z)	Instantaneous power received from distance z
EO	Effective pulse energy (taking all optics attenuation into account) [Ws]
c	Speed of light [m/s]
A	Receiver aperture [m2]
z	Distance [m]
ß(z)	Volume backscatter coefficient at distance z [m-1srad-1, srad = steradian]
$e^{-2\underset{0}{\overset{z}{\int }}\sigma (z\prime )dz\prime }$	Two-way atmospheric transmittance, accounts for the attenuation of transmitted and backscattered power. The transmittance equals 1 in clear atmosphere, that is, with no attenuation.