Cloaking via change of variables in electric impedance tomography

被引:169
作者
Kohn, R. V. [1 ]
Shen, H. [1 ]
Vogelius, M. S. [2 ]
Weinstein, M. I. [3 ]
机构
[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA
[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08855 USA
[3] Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA
关键词
D O I
10.1088/0266-5611/24/1/015016
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
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页数:21
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