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In order to achieve 3-D imaging with an airborne down-looking linear-array synthetic aperture radar (LASAR), a uniform virtual antenna array may be obtained by aperture synthesis of the cross-track sparse multiple-input–multiple-output array. However, the actual 3-D imaging quality is unavoidably degraded by errors in the virtual element position. In this letter, we investigate the effects of these errors on the forms and the degrees of image quality degradation by decomposing the error-related stochastic processes via an orthogonal transform based on discrete Legendre polynomials. It should be noted that these analyses are helpful for designing a LASAR system and providing a reference for specifying the requisite precision of measurement devices and calibration methods. Finally, we briefly consider the use of calibration methods to eliminate the effects of errors.

In this letter, a novel 3-D imaging algorithm for down-looking linear-array synthetic aperture radar is presented. The usual algorithms involve either time-consuming interpolations or huge oversampling operations, which adds huge burden to the image formation processor. The proposed algorithm, in contrast, is not only accurate because little approximation has been made but also quite efficient because of two major endeavors that we have made: First, a novel 3-D pseudopolar domain is introduced for the focused data to avoid any oversampling and to make it possible to formulate the image formation process as an interpolation-free image series expansion, and second, convergence acceleration theory in computational mathematics is introduced to accelerate the convergence of the image series expansion. The 3-D imaging capability is evaluated, and the validation of the proposed algorithm is done by exploiting simulated data.