In this paper,in order to measure the slant visibility at the airport runway using a lidar,a method based on the fixed-point principle is proposed to determine the boundary value of the atmospheric extinction coefficient.Using the method,the problem is reduced to the problem of searching for the fixed point of a function.A reference point in the bottom boundary layer was firstly selected and a boundary value of the extinction coefficient was assumed.The function between the mean extinction coefficient and its boundary value was constructed based on the Klett inversion algorithm.Secondly,the existence of the fixed point was judged according to the existence and uniqueness condition,and the extinction coefficient converged to the fixed point through iteration.Consequently,the mean extinction coefficient and its boundary value were obtained.After the availability of the method under non-uniform atmospheric conditions had been verified by numerical simulations,the method was applied to invert the extinction coefficient from the real lidar return signals.The vertical profiles of the atmospheric extinction coefficient were further obtained.The results show that under the lower atmospheric condition,the proposed method for determining the boundary value can be used to invert the atmospheric extinction coefficient more efficiently than the clean-layer method.