Modifications to the lidar equation due to nonlinear propagation in air

We study how the well-known lidar equation is affected by the use of ultra- short, high-power laser pulses. Because of the self-focusing and self-guidi ng, the overlap function xi, representing the reduction fraction of the sig nal resulting from geometrical effects inside the experimental system, need s to be reconsidered. The losses due to multiphoton ionisation in the filam ent entail a heavy weakening of the return signal. We also investigate the contribution of the white-light components generated by self-phase modulati on.