A 2D Fourier transform imaging algorithm for synthetic aperture imaging ladar (SAIL) is proposed. The collected data are first compensated with a conjugated quadratic phase and then imaged by 2D Fourier transform. Unified data collection equations for side-looking SAILs with chirped laser, down-looking SAILs with shifting of quadratic wavefronts and with deflection of plane wavefronts are formulated. Functions and relative imaging resolutions of the algorithm for these SAILs with rectangular and circular apertures are described and analyzed in terms of continuous variables and functions. Then, the expression of the 2D discrete Fourier transform is given. The feature of the algorithm is that the collected data in the time domain are transformed into the frequency domain both in the travel direction and in its orthogonal direction to be directly imaged. The mathematical formulation of the travel-direction imaging resolution varying along the orthogonal direction is deduced.