A kind of down-looking synthetic aperture imaging ladar (SAIL) is proposed, with a transmitter of two coaxial counter-deflected polarization-orthogonal beams of spatial parabolic phase difference and a receiver of self-heterodyne detection combined with phase complex-valued processing. In the orthogonal direction of travel, a linear phase modulation proportional to the lateral distance of target point and a quadratic phase history centered in the longitudinal position of target point in the travel direction are collected respectively. The image is focused by the Fourier transform and matched filtering in the two respective directions. Similar to the side-looking SAIL, the suggested down-looking SAIL achieves the fine-resolution, long-distance and two-dimensional imaging with modest aperture diameters, but it has inherent feature that the linear and quadratic phase terms and the size of optical footprint together with their associated imaging resolutions are controllable and variable in a large scale no matter in use or design. And, down-looking SAIL has overcome many difficulties in side-looking SAIL. The down-looking SAIL belongs to optics in the principle and means. This paper gives the general construction of down-looking SAIL, and details mathematically the principle including the data collection and the image processing.