Generalization of the Van Cittert-Zernike theorem to observers moving with respect to sources

A new concept based on a passive spatio-temporal interferometry has been proposed as the newest generation of the well-known SMOS mission successfully operating since November 2, 2009 [1]. While existing missions fail to address the more and more demanding users' requirements in terms of spatial and radiometric resolutions, the aim of the proposed concept is an enhancement of the currently achieved geometric resolution to meet the stringent users' needs in specific local-scale hydrological applications where sub-kilometric resolutions are needed [2]. The new interferometric concept proposal is based on the idea of integrating the observer's motion, and hence the time variable, in the calculation of the visibility function. This yields the creation of virtual baselines, between the positions of different antennas at different instants, in addition to the physical ones formed between the instantaneous antennas' spatial positions. The visibility function as formulated using the standard form of the Van Cittert-Zernike theorem in existing satellite-based Earth observation with passive radiometers does not take into account the relative motion of the observer (the satellite antenna) with respect to sources of the electro-magnetic fields at the surface of the Earth. The inclusion of the observer/sources relative motion in the visibility function yields a pixel-dependence of the generated Doppler shift which is neglected in existing satellite-based passive radiometers. One may hope that these created virtual baselines engender additional information which, when combined with a classical spatial aperture synthesis, can be employed for a spatio-temporal aperture synthesis. A recent detailed study of the proposed concept yielded a generalization of the classical formulation of the Van Cittert-Zernike theorem to the case of moving observers with respect to the sources at the surface of the Earth [3]. This study leads to the remarkable conclusion that the additional information due to the observer motion is exactly cancelled by the linear Doppler effect. It allows on the one hand the generalization of the theorem to the case of moving observers with respect to sources and on the other hand the justification of the neglect of the Doppler effect in existing imaging systems based on the standard form of the theorem.