We introduce a dispersive point target model based on scattering by a
particle in the far-field. The synthetic aperture imaging problem is then
expanded to identify these targets and recover their locations and frequency
dependent reflectivities. We show that Kirchhoff migration (KM) is able to
identify dispersive point targets in an imaging region. However, KM predicts
target locations that are shifted in range from their true locations. We derive
an estimate for this range shift for a single target. We also show that because
of this range shift we cannot recover the complex-valued frequency dependent
reflectivity, but we can recover its absolute value and hence the radar
cross-section (RCS) of the target. Simulation results show that we can detect,
recover the approximate location, and recover the RCS for dispersive point
targets thereby opening opportunities to classifying important differences
between multiple targets such as their sizes or material compositions.