Common Mathematical Framework for Real and Synthetic Aperture by Interferometry Radiometers

This work focuses on the relationship between real and synthetic aperture radiometers giving a general and common mathematical framework for both of them. It will be demonstrated that a real aperture radiometer array can be understood as a synthetic aperture one, with a high level of redundancy. Therefore, all the recent results from synthetic aperture radiometry can be translated to real aperture radiometer arrays. This fact can be used to create beamforming arrays in a new way. To do this, the beamforming array equation will be written in terms of cross-correlations between all pair of antenna signals (visibility samples). By properly combining the visibility samples, a new type of digital beamforming radiometer can be implemented, which will benefit from the high calibration accuracy achieved in synthetic aperture radiometers (e.g., The Y-shaped MIRAS radiometer used in the Soil Moisture and Ocean Salinity mission of the European Space Agency) and the flexibility to electronically steer the beam.