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 any waveform, and show how it specializes to familiar results in the cases when: (a) the targets are moving slowly, (b) the targets are far from the antennas and (c) narrowband waveforms are used. From these models, 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 point-spread function. We show that special cases of the theory reduce to: (a) range-Doppler imaging, (b) inverse synthetic aperture radar (ISAR), (c) synthetic aperture radar (SAR), (d) Doppler SAR, (e) diffraction tomography and (f) tomography of moving targets. We also show that the theory gives a new SAR imaging algorithm for waveforms with arbitrary ridge-like ambiguity functions.

84.40.Xb Telemetry: remote control, remote sensing; radar

41.20.Jb Electromagnetic wave propagation; radiowave propagation

84.40.Ua Telecommunications: signal transmission and processing; communication satellites

35L05 Wave equation

78A45 Diffraction, scattering (See also 34E20 for WKB methods)

94A08 Image processing (compression, reconstruction, etc.) (See also 68U10)

Accelerators, beams and electromagnetism

Electronics and devices

Issue 3 ( 1 June 2008)

Received 15 August 2007 , in final form 25 January 2008

Published 8 April 2008