Reconstructing Obstacles by the Enclosure Method Using in One Step the Farfield Measurements

In this work, we are concerned with the reconstruction of the obstacles by the enclosure method using the farfield measurements in one step. To justify this, first we state the indicator function of the enclosure method linking directly the farfield 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.