### 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 language | English (US) |
---|---|

Article number | 015016 |

Journal | Inverse Problems |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2008 |

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### ASJC Scopus subject areas

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

### Cite this

*Inverse Problems*,

*24*(1), [015016]. https://doi.org/10.1088/0266-5611/24/1/015016

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

Research output: Contribution to journal › Article

*Inverse Problems*, vol. 24, no. 1, 015016. https://doi.org/10.1088/0266-5611/24/1/015016

}

TY - JOUR

T1 - Cloaking via change of variables in electric impedance tomography

AU - Kohn, Robert

AU - Shen, H.

AU - Vogelius, M. S.

AU - Weinstein, M. I.

PY - 2008/2/1

Y1 - 2008/2/1

N2 - 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.

AB - 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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U2 - 10.1088/0266-5611/24/1/015016

DO - 10.1088/0266-5611/24/1/015016

M3 - Article

VL - 24

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 1

M1 - 015016

ER -