Microwave radiometer, as one of the most useful tools in remote sensing of earth resources and environment, has been developed rapidly. The recent research in this area is to concentrate how to improve spatial resolution. But the methods, which depend on increasing antenna aperture or decreasing carrier wavelength to obtain high spatial resolution, are inapplicable to aerospace engineering. The synthetic aperture technique needs the coherence effect of active microwave transmitted signal, so it cannot be used by passive radiometer. In this paper, a new approach is introduced. Firstly, the radiation of far-field target is received by 2D linear antenna array. The incident signals received by all array elements have an amount of delay among them. These coherent signals of same wave front are amplified individually and applied to piezoelectric transducers of a multi-channel Bragg cell. The electronic signals are converted into traveling acoustic waves in acousto-optic cell. The refractive index of crystal is changed proportionally to the input voltages. When collimated laser is incident upon the crystal, Bragg diffraction occurs. Fourier transform lens produces optically a 2D Fourier transform of the signals in a charge- coupled device plane. The direction and radiation intensity of arrival signal can be obtained simultaneously. Since the radiation signal of some far field target in the antenna coverage can be detected individually, that means the spatial resolution of radiometer can be improved. Theoretical derivation will be given in detail in this paper.