inverse scattering theory

Inverse scattering theory

A theory whose objective is to determine the scattering object, or an interaction potential energy, from the knowledge of a scattered field. This is the opposite problem from direct scattering theory, where the scattering amplitude is determined from the equations of motion, including the potential. The equations of motion are usually linear (operator-valued) equations. See Scattering experiments (atoms and molecules), Scattering experiments (nuclei)

Inverse scattering theories can be divided into two types: (1) pure inverse problems, when the data consist of complete, noise-free information of the scattering amplitude; and (2) applied inverse problems, when incomplete data which are corrupted by noise are given. Many different applied inverse problems can be obtained from any pure inverse problem by using different band-limiting procedures and different noise spectra.

The difficulty of determining the exact object which produced a scattering amplitude is evident. It is often a priori information about the scatterer that makes the inversion possible.

Much of the basic knowledge of systems of atoms, molecules, and nuclear particles is obtained from inverse scattering studies using beams of different particles as probes. For the Schrödinger equation with spherical symmetry or in one dimension, there is an exact solution of the inverse problem.

A number of high-technology areas (nondestructive evaluation, medical diagnostics including acoustic and ultrasonic imaging, x-ray absorption and nuclear magnetic resonance tomography, radar scattering and geophysical exploration) use inverse scattering theory. Several classical waves including acoustic, electromagnetic, ultrasonic, x-rays, and others are used.

All of the inverse scattering technologies require the solution to ill-posed or improperly posed problems. A model equation is well posed if it has a unique solution which depends continuously on the initial data. It is ill posed otherwise. The ill-posed problems which are amenable to analysis, called regularizable ill-posed problems, are those which depend discontinuously upon the data. This destroys uniqueness, although solutions (in fact, many solutions) exist.

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

inverse scattering theory

[′in‚vərs ′skad·ə·riŋ ‚thē·ə·rē]
The discipline that determines the nature of the scattering object, or an interaction potential energy, in a scattering process or collision, from knowledge of the amplitudes of the scattered fields.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Moreover, one might even think about using this simple model potential to examine different solution schemes of the inverse scattering theory, and this is the main idea developed in this paper.
The implementation of the methods of the inverse scattering theory is not at all a trivial task.
Kirsch, "The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media," Inverse Problems, vol.
[6.] Kirsch, A., "The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media," Inverse Problems, Vol.
of Delaware-Newark) describe the oldest and most developed of the qualitative methods in inverse scattering theory that have been developed to replace the weak scattering approximations used with radar, which are not accurate enough for many current applications.