Aperture dependence of the mixing efficiency, the signal-to-noise ratio, and the speckle number in coherent lidar receivers

With the aid of the van Cittert-Zernike theorem we develop an analytical expression for the ensemble-averaged heterodyne mixing efficiency in coherent lidar receivers that are looking at a diffuse target that is in the receiver's far field. Our extremely simple and straightforward analysis shows that the dependence of the mixing efficiency on the receive aperture size dR first follows a parabolic decrease and later approaches a (dR)(-2) function. As a consequence, the signal-to-noise ratio does not increase proportionally to the aperture area but saturates. For the system model chosen, the heterodyne mixing efficiency exhibits the same functional dependence on the lidar geometry as the reciprocal of the number of speckle cells within the receive aperture.