Estimation of the spatial distribution of a laser beam from the ratios of geometrical factors

Abstract

The spatial distribution of laser beam itself and the alignment of the receiving-transmitting system are very important parameters in quantitative analysis of Lidar signal. This is important because the beam shape and the inclination angle between axes of the transmitter and receiver change the physical quality of detecting elements, for example, the aerosol scattering coefficient and the concentration of pollutants, etc. In practical alignment of Lidar system, the inclination angle is allowed to fluctuate within the receiver field of view. At a long distance where geometric overlap is complete, this fluctuation has no influence on the final results, but at a short distance this effect is serious. If we know the distribution of laser beam and inclination angle, this effect can be corrected by using geometrical overlap function. In this study, we have calculated the geometrical overlap function for Gaussian and uniform distributions, respectively. It is found that the ratio-function, which is defined as the ratio of two geometrical functions obtained from different angles between the axes of the transmitter and receiver, behaves in different way for Gaussian and uniform laser beams. The completely different behavior of these two ratio-functions for different beam types can be used more conveniently in identifying the laser beam shape and inclination angle than geometrical functions only. This fact can be used for characterizing the spatial distribution of laser beam and for testing of alignment between receiver and transmitter.