Atmospheric turbulence can be the source of some systematic and random range error, and of the decrease of maximum range measured. Formulas are collected for energy density decrease and for some of the errors, including systematic photon trajectory lenghts increase, not mentioned before according to authors knowledge.
Formulaes were developed for the range error due to descreet generation and gain of photoelectrons in multiphotoelectron case for some signal processing methods, as constant threshold and constant fraction of photomultiplier current or charge and some others. In many methods, including near optimum estimation, the error decreases when filter response width increases. Simple estimation methods can give nearly as good results as optimum methods, when using proper filtration and fraction values. Simulation and experimental results are in fair agreement with the theory. The results can be used to improve many existing laser stations.