Cloaking via change of variables in electric impedance tomography

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.

Locations

• Inverse Problems - View
• CiteSeer X (The Pennsylvania State University) - View - PDF