Electromagnetic Imaging and the Effect of Small Inhomogeneities I

Introductory Workshop on Inverse Problems and Applications August 23, 2010 - August 27, 2010

August 25, 2010 (02:00 PM PDT - 03:00 PM PDT)

Speaker(s): Michael Vogelius (National Science Foundation)

Primary Mathematics Subject Classification No Primary AMS MSC

Secondary Mathematics Subject Classification No Secondary AMS MSC

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v0164

Abstract

In this set of lectures I shall give a survey of work related to electromagnetic imaging that spans a 20 year period. A first part will be devoted to various representation formulas for the perturbations in the electromagnetic fields caused by volumetrically small sets of inhomogeneities. The imperfections studied range from sets of inhomogeneities consisting of a finite number of well separated objects of known (rescaled) shape and of fixed location, to sets of inhomogeneities of quite “random” geometry and location. The use of these representation formulas to design very effective numerical reconstruction algorithms will also be discussed. A second part of the lectures examines the relation between small inhomogeneities and approximate invisibility cloaks. In particular, I shall discuss the use of our representation formulas (or rather, estimates resulting from these formulas) to give quite precise estimates for the degree of approximate invisibility associated with one of these approximate cloaks. Time permitting, I shall touch upon recent approximate invisibility estimates that are also explicit (and sharp) in their dependence on frequency.

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