 By K.I. Hopcraft, P.R. Smith

This remedy could be of use to somebody embarking on a theoretical or useful research of inverse electromagnetic scattering.

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Additional resources for An Introduction to Electromagnetic Inverse Scattering

Example text

This series, when truncated at the n'th power of J1 is called the n'th Born approximation and in common with most other workers we shall refer to the first term of this series as being the 'Born approximation', although the Rayleigh-Gans approximation would be historically more correct. Refmements to the Born approximation are considered in chapter 4. For this expansion to make sense and to be of value, the series should be convergent and the error in truncating the series after a finite number of terms should be acceptably small.

Exp(st)F(s)ds a-IOO where, to effect the inversion, the contour of integration in the complex plane must be chosen such that all the singularities of F(s) lie to the left of the line Re s =a . The Laplace transform is an integral transform like the Fourier transform but with notable differences. We can illustrate these differences by comparison of the forward Laplace and Fourier transforms. Firstly note that although both transform kernels are exponentials, in the Fourier transform the argument of the exponential is purely imaginary leading to the real frequency domain CD, whilst for the Laplace transform it has real and imaginary parts leading to the complex domain s.

E. IElnC - Escat I « IElnC I. When applied to an electromagnetic wave equation this assumption does lead to a reduced or approximate equation because the scattering interaction is then linear. This is different from acoustical problems for example, where linearization of the fields is performed at the outset. Indeed the process leads to an ordering of the equation in which specific terms may be neglected in contrast to others. However we are concerned with the electromagnetic wave equations so how can we apply the linearization process for this case?