Unique determination of the shape of a scattering screen from a passive measurement

TL;DR

This paper proves that the shape of a flat sound-soft screen in a 3D space can be uniquely determined from a single far-field measurement of scattered waves caused by any non-antisymmetric incident wave, even for complex smooth shapes.

Contribution

It establishes the unique determination of arbitrary smooth, simply connected screens from a single measurement with arbitrary incident waves, extending previous results limited to plane waves or polygonal shapes.

Findings

Unique shape determination from a single measurement

Applicable to arbitrary smooth, simply connected screens

Works with any non-antisymmetric incident wave

Abstract

We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely the obstacle is restricted to a two-dimensional plane and interacting with a arbitrary incident wave, it scatters acoustic waves to three-dimensional space. The model is particularly relevant in the study and design of reflecting sonars and antennas, cases where one cannot assume that the incident wave is a plane wave. Our main result is that given the plane where the screen is located, the far-field pattern produced by any single arbitrary incident wave determines the exact shape of the screen, as long as it is not antisymmetric with respect to the plane. This holds even for screens whose shape is an arbitrary simply connected smooth domain. This is in contrast to earlier work where the incident wave had to be a plane wave, or more recent work where only polygonal scatterers are determined.