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February  2010, 4(1): 151-167. doi: 10.3934/ipi.2010.4.151

Gauge equivalence in stationary radiative transport through media with varying index of refraction

Stephen McDowall 1, , Plamen Stefanov 2, and  Alexandru Tamasan 3,

1. 

Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, United States
2. 

Department of Mathematics, Purdue University, 150 N University Street, West Lafayette, IN 47907
3. 

Department of Mathematics, University of Central Florida, Orlando, FL 32816, United States

Received  April 2009 Revised  December 2009 Published  February 2010

Three dimensional anisotropic attenuating and scattering media sharing the same albedo operator have been shown to be related via a gauge transformation. Such transformations define an equivalence relation. We show that the gauge equivalence is also valid in media with non-constant index of refraction, modeled by a Riemannian metric. The two dimensional model is also investigated.
Keywords: Inverse transport, gauge equivalence..
Mathematics Subject Classification: Primary: 35R30; Secondary: 78A4.
Citation: Stephen McDowall, Plamen Stefanov, Alexandru Tamasan. Gauge equivalence in stationary radiative transport through media with varying index of refraction. Inverse Problems and Imaging, 2010, 4 (1) : 151-167. doi: 10.3934/ipi.2010.4.151
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