  We study the existence and suppression of artifacts for a Doppler-based
Synthetic Aperture Radar (DSAR) system. The idealized air- or space-borne
system transmits a continuous wave at a fixed frequency and a co-located
receiver measures the resulting scattered waves; a windowed Fourier transform
then converts the raw data into a function of two variables: slow time and
frequency. Under simplifying assumptions, we analyze the linearized forward
scattering map and the feasibility of inverting it via filtered backprojection,
using techniques of microlocal analysis which robustly describe how sharp
features in the target appear in the data. For DSAR with a straight flight
path, there is, as with conventional SAR, a left-right ambiguity artifact in
the DSAR image, which can be avoided via beam forming to the left or right. For
a circular flight path, the artifact has a more complicated structure, but
filtering out echoes coming from straight ahead or behind the transceiver, as
well as those outside a critical range, allows one to obtain an artifact-free
image. Initially derived under a start-stop approximation widely used in
range-based SAR, we show that some of these results are robust and hold under a
more realistic approximation.
