The truncated Gaussian lidar antenna problem revisited

Two papers1,2 have presented inter alia numerical values for the return signal from a coherent lidar having the following properties: Gaussian beam profiles, beam truncation in the antenna plane by circular apertures of equal area, monostatic geometry (common transmitter/receiver axis), incoherent backscatter target of infinite extent lateral to the lidar axis, infinite photodetector area, no refractive turbulence, hard target with no depth, both transmitter and receiver focused on the target, fixed transmitter laser power, and fixed local oscillator (LO) power on a uniform photodetector. The optimal truncation, defined as that giving maximum receiver output subject to these constraints, was computed. The results of the two calculations differ and the reasons for the discrepancy have not previously been resolved. Although the discrepancy is only about 10% in the estimated signal powers, the questions involved are rather fundamental to coherent lidar, and are relevant to future computations for more complex geometries.