## 1 Introduction  
The Soil Moisture and Ocean Salinity (SMOS) space mission [1; 2] was launched in November 2009 by ESA and CNES and, for more than twelve years, this first-generation satellite has provided accurate and global radiometric brightness temperature maps in the L-band with a spatial resolution of \(\sim\)40 km. These maps have been used for retrieving surface soil moisture (SM) [3], even under dense vegetation canopies, as well as ocean salinity (OS) [4], even for cold waters. In addition, these brightness temperatures are operationally assimilated in numerical weather predictions at the European Centre for Medium-Range Weather Forecasts (ECMWF) [5]. SMOS has been the first attempt to apply, for remote sensing Earth's surface, the concept of imaging radiometry by aperture synthesis, initially developed for radio astronomy [6]. As a consequence of the long experience of radio astronomers in aperture synthesis, the interferometric array of SMOS has been clearly inspired by the Very Large Array (VLA) [7] as well as by the Cosmic Background Imager (CBI) [8]. At the time that agencies and industries are conducting preliminary studies for a SMOS follow-on mission, phase 0 and phase A studies have been conducted by the French space agency for a second generation devoted to a High Resolution (HR) imaging radiometer by aperture synthesis [9]. During these co-engineering investigations [10], trade-offs between driving parameters have sometimes given rise to tricky situations from the mathematical point of view as well as from the point of view of the physical interpretation. This is the case of the shortest spacing between the elementary antennas of the interferometric array, which is one of the key parameters impacting the ground swath and the revisit time. Within the frame of the preliminary results obtained with a candidate array for this SMOS-HR project [11], this contribution focuses on what happens when this shortest spacing is such that the field of view synthesized by the interferometric array seems to be wider than the field of view seen by each elementary antenna. More precisely, this study aims at addressing the impact of the shortest spacing on the stability of the inversion of the complex visibilities in presence of noise and in particular the existence of an unpleasant phantom in the retrieved brightness temperature maps when this distance between the closest elementary antennas becomes smaller than a geometrical limit. The observing equation of an imaging radiometer by aperture synthesis is detailed in Section 2, together with the regularized approach for inverting the complex visibilities in order to estimate the brightness temperature distribution of the scene seen by the interferometric array. The relation between the extent of the synthesized field of view and the shortest spacing between the elements of an antenna array is recalled in Section 3 with two different perspectives: the one from radio astronomy when observing the deep sky and the one from remote sensing when observing Earth's surface. It is illustrated in Section 4 why these two readings of the same relation could lead to situations where the field of view synthesized by an imaging radiometer by aperture synthesis seems to be wider than the field of view seen by each elementary antenna. The only way to study the consequences of this situation on the imaging capabilities and performances of an aperture synthesis radiometer is to conduct a parametric study with the aid of numerical simulations where the shortest spacing plays the central role. This study is detailed in Section 5. It is first shown that when the shortest spacing between the elementary antennas becomes smaller than a geometrical limit, the inversion of the complex visibilities becomes unstable in presence of noise and this instability is characterized by the undesirable presence of a phantom in the retrieved brightness temperature maps. Then, the origin of this phantom is explained and a solution to cure the interferometric array from that issue is proposed and assessed.