Reconstructing obstacles by the enclosure method using the far field measurements in one step

Abstract In this work, we are concerned with the reconstruction of the obstacles by the enclosure method using the far field measurements in one step. To justify this, first we state the indicator function of the enclosure method linking directly the far field pattern to the reflected solutions corresponding to the used complex geometrical optics solutions. Second, we use layer potential techniques to derive the needed estimates of the reflected solutions. No condition on the geometry of the obstacle or on the used frequency is needed.