Spatial, Temporal, and Spectral Aspects of Far-Field Radar Data

We develop a linearized imaging theory that combines the spatial, temporal, and spectral aspects of scattered waves. We consider the case of fixed, distributed transmitters and receivers, and a general distribution of objects, each undergoing linear motion; thus the theory deals with imaging distributions in phase space. We derive a model for the data that is appropriate for any waveform, and show how it specializes to familiar results when the targets are far from the antennas and narrowband waveforms are used. We use a phase-space imaging formula that can be interpreted in terms of filtered backprojection or matched filtering. For this imaging approach, we derive the corresponding point-spread function. We plot examples of this point-spread function for three different geometrical placements of the transmitters and receivers. Special cases of the theory reduce to: a) Range-Doppler imaging, b) Inverse Synthetic Aperture Radar (ISAR) and Spotlight Synthetic Aperture Radar (SAR), c) Diffraction Tomography or Ultra-Narrowband Tomography, and d) Tomography of Moving Targets.