Synthetic-aperture imaging from high-Doppler-resolution measurements

We develop the theory of radar imaging from data measured by a moving antenna emitting a single-frequency waveform. We show that, under a linearized (Born) scattering model, the signal at a given Doppler shift is due to a superposition of returns from stationary scatterers on a cone whose axis is the flight velocity vector. This cone reduces to a hyperbola when the scatterers are known to lie on a planar surface. In this case, reconstruction of the scatterer locations can be accomplished by a tomographic inversion in which the scattering density function is reconstructed from its integrals over hyperbolas. We give an approximate reconstruction formula and analyse the resolution of the resulting image. We provide a numerical shortcut and show results of numerical tests in a simple case.