We develop a linearized imaging theory that combines the spatial, temporal, and spectral aspects of scattered waves. We consider the case of fixed sensors 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 narrowband waveforms in the case when the targets are moving slowly relative to the speed of light. From this model, we develop 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 phase-space point-spread function (PSF). We show plots of the phase-space point-spread function for various geometries. We also show that in special cases, the theory reduces to: 1) range-Doppler imaging, 2) inverse synthetic aperture radar (ISAR), 3) synthetic aperture radar (SAR), 4) Doppler SAR, and 5) tomography of moving targets.

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