Cloaking via change of variables in electric impedance tomography

Robert Kohn, H. Shen, M. S. Vogelius, M. I. Weinstein

Research output: Contribution to journalArticle

Abstract

A recent paper by Pendry et al (2006 Science 312 1780-2) used the coordinate invariance of Maxwell's equations to show how a region of space can be 'cloaked' - in other words, made inaccessible to electromagnetic sensing - by surrounding it with a suitable (anisotropic and heterogenous) dielectric shield. Essentially the same observation was made several years earlier by Greenleaf et al (2003 Math. Res. Lett. 10 685-93, 2003 Physiol. Meas. 24 413-9) in the closely related setting of electric impedance tomography. These papers, though brilliant, have two shortcomings: (a) the cloaks they consider are rather singular; and (b) the analysis by Greenleaf, Lassas and Uhlmann does not apply in space dimension n = 2. The present paper provides a fresh treatment that remedies these shortcomings in the context of electric impedance tomography. In particular, we show how a regular near-cloak can be obtained using a nonsingular change of variables, and we prove that the change-of-variable-based scheme achieves perfect cloaking in any dimension n ≥ 2.

Original languageEnglish (US)
Article number015016
JournalInverse Problems
Volume24
Issue number1
DOIs
StatePublished - Feb 1 2008

Fingerprint

Electric impedance tomography
Change of Variables
Tomography
Impedance
tomography
impedance
Maxwell equations
Invariance
Maxwell's equations
Maxwell equation
invariance
Sensing
electromagnetism

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Cloaking via change of variables in electric impedance tomography. / Kohn, Robert; Shen, H.; Vogelius, M. S.; Weinstein, M. I.

In: Inverse Problems, Vol. 24, No. 1, 015016, 01.02.2008.

Research output: Contribution to journalArticle

Kohn, Robert ; Shen, H. ; Vogelius, M. S. ; Weinstein, M. I. / Cloaking via change of variables in electric impedance tomography. In: Inverse Problems. 2008 ; Vol. 24, No. 1.
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