Laser system range calculations and the Lambert W function

The knowledge of range performance versus atmospheric transmission, often given by the visibility, is critical for the design, use, and prediction of laser and passive electro-optic systems. I present a solution of the ladar-lidar equation based on Lambert's W function. This solution will reveal the dependence of the maximum range on the system and target parameters for different atmospheric attenuations and will also allow us to take the signal statistics into account by studying the influence on the threshold signal-to-noise ratio. The method is also applicable to many range calculations for passive systems where the atmospheric loss can be approximated by an exponential term. (C) 2008 Optical Society of America