The mixing efficiency of a heterodyne laser radar system is a critical performance factor. This paper deals with a special system configuration whereby a laser radar beam is directed by a remote agile mirror. In order to track the target, the mirror surface normal must point halfway between the vector direction to the target and the laser radar's telescope aperture plane normal. Ideally, the mirror's surface must be perfectly flat to avoid any distortion of the return target signal. The effect of mirror surface aberrations upon the heterodyne laser radar's mixing efficiency, and therefore upon the system signal-to-noise ratio, is the the subject of this paper. A computer model is used is used to introduce the spatial wavefront distortions upon the return plane wave signal (representing a point target) and to represent the field pattern on the detector plane using a 2-D discrete Fourier transform. The relative mixing efficiency is calculated for several classical types of mirror surface aberrations using Zernike polynomial representations. Effects such as thermal gradients across the face of the mirror, thermal gradients between the front and the back of the mirror and gravity loading of the mirror are modeled. The mirror surface height aberrations are expressed in wavelengths in order to increase the general applicability of the results. The imperfect mirror surface acts like a phase grating which changes the spatial phase of the reflected plane wave return signal. Mixing efficiency is computed relative to the mixing efficiency that would be obtained with a perfect undistorted plane wave return signal. It is assumed that the local oscillator produces a uniform intensity and constant spatial phase plane wave signal at the telescope aperture plane. The mirror diameter is assumed to be 2.4 times larger than the telescope aperture diameter. This keeps the telescope aperture fully illuminated for a target angles of up to 65 degrees with respect to the mirror surface normal. Results are presented for both a finite extent and infinite extent detector aperture. Example diffraction patterns are plotted in a 3-D surface plot form to provide a visual appreciation of the effects of the mirror surface aberrations.
A. L. Kachelmyer,
"Mirror Surface Aberrations And Mixing Efficiency", Proc. SPIE 1045, Modeling and Simulation of Laser Systems, (31 May 1989); doi: 10.1117/12.951315; https://doi.org/10.1117/12.951315