A Comprehensive Comparison of Far-Field and Near-Field Imaging Radiometry in Synthetic Aperture Interferometry

Synthetic aperture interferometry (SAI) is a signal processing technique that mixes the signals collected by pairs of elementary antennas to obtain high-resolution images with the aid of a computer. This note aims at studying the effects of the distance between the synthetic aperture interferometer and an observed scene with respect to the size of the antenna array onto the imaging capabilities of the instrument. Far-field conditions and near-field ones are compared from an algebraic perspective with the aid of simulations conducted at microwave frequencies with the Microwave Imaging Radiometer by Aperture Synthesis (MIRAS) onboard the Soil Moisture and Ocean Salinity (SMOS) mission. Although in both cases the signals kept by pairs of elementary antennas are cross-correlated to obtain complex visibilities, there are several differences that deserve attention at the modeling level, as well as at the imaging one. These particularities are clearly identified, and they are all taken into account in this study: near-field imaging is investigated with spherical waves, without neglecting any terms, whereas far-field imaging approximation is considered with plane waves according to the Van–Citter Zernike theorem. From an algebraic point of view, although the corresponding modeling matrices are both rank-deficient, we explain why the singular value distributions of these matrices are different. It is also shown how the angular synthesized point-spread function of the antenna array, whose shape varies with the distance to the instrument, can be helpful for estimating the boundary between the Fresnel region and the Fraunhofer one. Finally, whatever the region concerned by the aperture synthesis operation, it is shown that the imaging capabilities and the performances in the near-field and far-field regions are almost the same, provided the appropriate modeling matrix is taken into account.