Theory of passive synthetic aperture imaging

Abstract

We present a unified theory for passive synthetic aperture imaging based on inverse scattering, estimation-detection theory, and microlocal analysis. Passive synthetic aperture imaging uses sources of opportunity for illumination and moving receivers to measure scattered field. We consider passive airborne receivers that fly along arbitrary, but known, flight trajectories and static or mobile sources of opportunity transmitting two types of waveforms: Single-frequency or ultra-narrowband continuous-wave (CW) waveforms and wideband pulsed waveforms. Our theory results in two new and novel synthetic aperture imaging modalities: Doppler synthetic aperture hitchhiker (DSAH) that uses single-frequency or ultra-narrowband CW waveforms, and synthetic aperture hitchhiker (SAH) that uses wideband pulsed waveforms. We use inverse scattering and estimation-detection theory to develop measurement models in the form of Fourier integral operators (FIOs) for DSAH and SAH. These models are based on windowed, scaled, and translated correlations of the measurements from two different receiver locations. This processing removes the transmitter-related terms from the phase of the resulting FIOs that map the radiance of the scene to correlated measurements. We use microlocal analysis to develop approximate inversion formulas for these FIOs. The inversion formulas involve backprojection of the correlated measurements onto certain manifolds where the passive range and passive Doppler are constant for SAH and DSAH imaging, respectively. We present resolution analysis and numerical simulations to demonstrate our theoretical results. While we focus primarily on the passive synthetic aperture radar, the theory we present is also applicable to other wave-based passive synthetic aperture imaging problems such as those in acoustics and geophysics.