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In the plane, we study the transform $R_\gamma f$ of integrating a unknownfunction $f$ over circles centered at a given curve $\gamma$. This is asimplified model of SAR, when the radar is not directed but has otherapplications, like thermoacoustic tomography, for example. We study the problemof recovering the wave front set $\WF(f)$. If the visible singularities of $f$hit $\gamma$ once, we show that the "artifacts" cannot be resolved. If $\gamma$is a closed curve, we show that this is still true. On the other hand, if $f$is known a priori to have singularities in a compact set, then we show that onecan recover $\WF(f)$, and moreover, this can be done in a simple explicit way,using backpropagation for the wave equation.

Is a curved flight path in SAR better than a straight one?