The theoretical analysis of aperture synthesis in the along-track direction of a synthetic aperture radiometer is presented under the theory of convolution.The baseline design is accomplished according to a spatial frequency domain analysis.The brightness temperature of the earth in the along-track direction is reconstructed by two numerical approaches

i.e.the method of moment and the linear algorithm based on the Backus-Gilbert theory.Numerical simulated test cases show that the reconstruction of the brightness temperature agrees well with the original on the base that the antenna array is effectively thinned in the along-track direction.