## 6 Conclusions  
A comprehensive comparative study between near-field and far-field imaging radiometry in synthetic aperture interferometry has been conducted. At the modeling level, the integral relation between the brightness temperature distribution of an observed scene and the corresponding complex visibilities has been established for near-field imaging conditions when considering spherical waves as well as for far-field ones with plane waves. Three differences between the two regions have been clearly identified and their potential impacts on the synthesis imaging have been reported. The first dissemblance is at the level of the difference between the distances from any pixel in the field of view to any pair of elementary antennas that is estimated in the far-field approximation by the scalar product between the corresponding baseline and the viewing direction. The second difference is the significant presence of a multiplicative fraction that tends towards 1 as soon as the far-field conditions are met. The third dissemblance is at the level of the antennas' voltage pattern where local viewing directions vary from one antenna to another in near-field imaging, whereas they are assumed to be equal in the far-field approximation. All these differences have been taken into account throughout this study, and their impact has been quantified. From an algebraic point of view, the properties of the corresponding linear operators have been compared with an emphasis on their singular values. As expected, the modeling matrices are both rank-deficient with the same effective rank. However, they exhibit significantly different distributions of their singular values: those kept in the inversion are very similar, whereas those discarded prior to the inversion are not. As a consequence, the propagation of random noise does not vary from far-field to near-field conditions, as it is governed by the former singular values. This is not the case for the reconstruction floor error, which depends on the latter ones. At the imaging synthesis level, numerical simulations have been conducted for the antenna array of SMOS in order to compare near-field and far-field imaging performances when observing a point source or when looking at an extended source. In the first situation, no significant difference has been observed provided the visibilities are inverted with the appropriate resolving matrix. Nevertheless, when inverting near-field visibilities with the far-field operator,strong errors have been observed in the reconstructed point-spread functions, as expected. In the second case, when the extended source is limited to the field of view synthesized by the antenna array, no difference has been found between near-field and far-field imaging: the reconstruction floor error is close to zero in both imaging conditions. On the contrary, when the brightness temperature distribution of an observed scene extends beyond the synthesized field of view, field aliasing is observed and the reconstruction floor error is at a higher level for near-field imaging than it is for the far-field one. Finally, with regard to the propagation of random noise, no difference has been found between near-field and far-field inversions, as expected. Although it is admitted that there is no clear boundary between the Fresnel and the Fraunhofer regions, the well-known distance \(2D^{2}/\lambda\) is often used as a criterion for separating the near-field region from the far-field one. This criterion has been historically established for elementary antennas with diameter \(D\) and operating at a wavelength \(\lambda\) outside any imaging context. It was not therefore unreasonable to take advantage of this comparative study to check how this distance is consistent with a collection of elementary antennas working all together for synthesis imaging from interferometric data and when \(D\) is now the longest baseline of the antenna array.