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 its projection on the final receiving unit are revealed, based on paraxial approximation and geometric optics approach. The evaluation of the formulation is performed with ray tracing simulations, revealing an overall good performance with relative differences of the order of 5 % mainly attributed to aberrations that are not taken into account in paraxial approximation.