Analytical and numerical approaches to study echo laser pulse profile affected by target and atmospheric turbulence

The integrated model of echo laser pulse profile (ELPP) of a target with arbitrary shape is studied under the condition of the ELPP affected by target and atmospheric turbulence simultaneously. The ELPPs of four typical targets (a plane, a cone, a sphere and an aspherical surface) are employed to test the validity of the model by analytical and numerical approaches. Based on simulations of the ELPP under different targets and atmospheric turbulence intensity, the results show a good agreement between two methods, and the ELPP of a target with discontinuous surface is more easily affected by atmospheric turbulence than that with a continuous surface. Besides that, we study the relationship between the number of grids and the relative error of analytical and numerical approaches, which are of interest to obtain the optimal number of grids used in the simulations.