On the Far Field in Obstacle Scattering
نویسندگان
چکیده
We will establish far eld identities for the scattering of time-harmonic acoustic waves from sound-soft and sound-hard obstacles and will illustrate two applications of these identities for the inverse obstacle scattering problem. Firstly, we will provide an alternate proof for the Fr echet diierentiability of the far eld pattern with respect to the boundary. Secondly, we will connect the identities with a new method for the approximate solution of the inverse obstacle scattering problem which was recently suggested by Potthast.
منابع مشابه
Uniqueness and numerical methods in inverse obstacle scattering
The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for i...
متن کاملOn the Scattering of Spherical Electromagnetic Waves by a Penetrable Chiral Obstacle
The problem of scattering of spherical electromagnetic waves by a bounded chiral obstacle is considered. General scattering theorems, relating the far–field patterns due to scattering of waves from a point source put in any two different locations (the reciprocity principle, the optical theorem, etc), and mixed scattering relations (relating the scattered fields due to a point source and a plan...
متن کاملStable determination of a scattered wave from its far-field pattern: the high frequency asymptotics
We deal with the stability issue for the determination of outgoing time-harmonic acoustic waves from their far-field patterns. We are especially interested in keeping as explicit as possible the dependence of our stability estimates on the wavenumber of the corresponding Helmholtz equation and in understanding the high wavenumber, that is frequency, asymptotics. Applications include stability r...
متن کاملElectromagnetic Scattering by a Homogeneous Chiral Obstacle: Scattering Relations and the Far-Field Operator
Time-harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle. The reciprocity principle, the basic scattering theorem and an optical theorem are proved. These results are used to prove that if the chirality measure of the obstacle is real, then the far-"eld operator is normal. Moreover, it is shown that the eigenvalues of the far-"eld operator are the same as the eigenvalu...
متن کاملStable Determination of the Surface Impedance of an Obstacle by Far Field Measurements
We deal with the inverse scattering problem of determining the surface impedance of a partially coated obstacle. We prove a stability estimate of logarithmic type for the impedance term by the far field measurements.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM Journal of Applied Mathematics
دوره 59 شماره
صفحات -
تاریخ انتشار 1999