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.

Keywords:

• reconstruction
• far field measurements
• Helmholtz equation
• complex geometrical optics solutions
• layer potentials

AMS Subject Classifications:

• 78A46
• 35J25
• 35Q35
• 35R30
• 76Q05

Notes

1. This is the point where we need the smoothness assumption of

2. Since is of class then Lemma 4.3 is valid also for see [5], and hence we can also take in (4.12(4.13) ).