Double scattering background in a CW lidar

The equation for lidar probing of a homogeneous medium is written for the case of two-fold scattering in terms of the radiated power, speed of light, the back-scatter coefficient, path attenuation, the one-time scattered signal from the given range, the normalized scattering indicator in the back direction, the scattering coefficient and the angular field of view of the receiver. The solution of this equation is an estimate of the contribution of information contained in a doubly scattered signal from a CW lidar, modulated by a sine wave. An analytical expression is derived for the phase of the received signal and the change in the modulation level with double scattering. The equations are used to plot the phase and modulation level for modulating frequencies of 100 KHz, 1 MHz and 10 MHz as a function of the path attenuation. An expression is also adduced for the ratio of the power of the ac component of a double scattered transmission to the analogous component of a one-time scattered signal. The behavior of this function shows that the doubly scattered signal is greatly dependent on the type of scattering aerosol and thus permits the possibility of identifying an atmospheric aerosol by studying such signals.