By analyzing the 1st order statistic specialty of the co coherence function of Gauss local field and Airy signal field, it gives the matching condition between the amplitudes, phases, and wave vectors of the signal beam and the local beam in CO 2 laser pulse heterodyne detection. In theory, the maximum of the heterodyne quantum efficiency is 0.82. In the condition of off focus, e.g. with spherical aberration, the phase difference between signal beam and local beam is mainly decided by the curvature of the Gauss local field which would lead to the reduction of the heterodyne quantum efficiency.