This paper is about inverse-scattering from monostatic intensity-only measurements. We first formally rederive the geometrical optics approximation for a penetrable convex target. We then derive two direct imaging methods. The first one finds the point which best maps measurements over one circle onto a second one, due to amplitude decay of the scattered wave. The second one is a linearization of the problem, based on estimating the curvature of the object as a function of the measurements, due to the geometrical optics approximation. The first method aims at estimating the position of the target, whereas the second one aims at reconstructing the shape. The paper finishes with numerical tests showing the relevance and the limits of the proposed methods.
