Is a Curved Flight Path in SAR Better than a Straight One?

In the plane, we study the transform R f of integrating a unknown function f over circles centered at a given curve . This is a simplified model of SAR, when the radar is not directed but has other applications, like thermoacoustic tomography, for example. We study the problem of recovering the wave front set WF.f /. If the visible singularities of f hit once, we show that WF.f / cannot be recovered in, i.e., the artifacts cannot be resolved. If D @ ̋ is the boundary of a strictly convex domain ̋, we show that this is still true. On the other hand, in the latter case, if f is known a priori to have singularities in a compact set, then we show that one can recover WF.f j ̋/, and moreover, this can be done in a simple explicit way, using backpropagation for the wave equation.