Lidar equations for turbid media with pulse stretching

Lidar equations for a system with multiple-scattering beam spreading and pulse stretching are developed from an analytical model for the beam spread function. The resulting lidar equations are transparent to the physics and with some simple approximations for system transfer functions become mathematically simple engineering models for system studies. Application to and comparison with a variety of lidar applications in ocean environments (turbidity and bathymetry) and clouds (aerosol scattering) are presented. These examples provide model validation. The lidar model developed represents a significant extension beyond historical lidar models that exclude pulse stretching. Their mathematical simplicity should foster use in a broader class of problems involving light propagation in turbid media.