Using paraxial approximation to describe the optical setup of a typical EARLINET lidar system

The mathematical formulation for the optical setup of a typical EARLINET lidar system is given here. The equations describing a lidar system from the emitted laser beam to the projection of the telescope aperture on the final receiving unit (i.e., photomultiplier or photodiode) are presented, based on paraxial approximation and geometric optics approach. The receiving optical setup includes a telescope, a collimating lens, an interference filter and the ensemble objective eyepiece. The set of the derived equations interconnects major parameters of the optical components (e.g., focal lengths, diameters, angles of incidence), revealing their association with the distance of full overlap of the system. These equations may used complementarily with an optical design software, for the preliminary design of a system or can be used as a quick check up tool of an existing lidar system. The evaluation of the formulation on a real system is performed with ray-tracing simulations, revealing an overall good performance with relative differences of the order of 5 % mainly attributed to the limitations of the thin lens approximation.