Target-plane intensity approximation for apertured Gaussian beams applied to heterodyne backscatter lidar systems

With an application in lidar systems in mind, we investigate the effects of transmit-aperture truncation of Gaussian beams by employing the extended Huygens-Fresnel principle. We derive an approximation to the top-hat aperture-transmission function by defining an abstract Gaussian aperture-transmission function. The two fitting parameters of the latter are found when the beam radius and the on-axis intensity for both aperture cases are equated in the observation plane. Bounds for the applicability of the approximation are established, and its accuracy and usefulness is demonstrated through application to the calculation of the return signal of a heterodyne lidar system.