Optical turbulence correction in the elastic LiDAR equation

Abstract

The use of LIDARs to characterize atmospheric properties has become commonplace since near the invention of the laser. The accuracy of these measurements is generally limited by the signal-to-noise ratio of the optical channels making the measurementtypically constrained by several environmental and systematic parameters, such as solar background, power-aperture product, etc. These measurements are usually modeled according to various forms of the atmospheric LIDAR equation along with a solar background model. However, one of the limitations of current approaches is failing to account for the effects of optical turbulence on the LIDAR signal. While researchers have already established a correction factor for the hard target LIDAR equation, this factor has not yet been applied to atmospheric LIDAR systemssome of which aim to measure optical turbulence as a data product. This paper investigates the application of a correction factor to the elastic LIDAR equation to account for the effects of turbulence. Using mathematical modeling and simulation, it was observed that the number of photons detected by the system is overestimated and it decreases as turbulence increases as expected and in agreement with previously published results. Additionally, a preliminary investigation of the effects of turbulence on the relationships between the LIDAR system signal-to-noise ratio (SNR), the field of view (FOV), and transmitter divergence is addressed and opened up for future discussion. For example, increasing the beam divergence and FOV mitigates the effects of turbulence but increases the number of background photons detected, effectively reducing the SNR. It is expected that these results can be used by system designers to understand how turbulence will affect the performance of atmospheric LIDAR systems and provide quantitative tradeoffs in design decisions.