On problem of polarization tomography, I

Details On problem of polarization tomography, I On problem of polarization tomography, I

2007-02-23

arxiv.org/abs/math-ph/0702080v1

Inverse Problems 23 (2007) 1229-1257

Physics

Mathematical Physics

Scientific paper

10.1088/0266-5611/23/3/023

The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation $D\eta/dt=\pi_{\dot\gamma}f\eta$ known for every geodesic $\gamma$ of a given Riemannian metric. Here $\pi_{\dot\gamma}$ is the orthogonal projection onto the hyperplan $\dot\gamma^{\perp}$. The problem arises in optical tomography of slightly anisotropic media. The local uniqueness theorem is proved: a $C^1$- small function f can be recovered from the data uniquely up to a natural obstruction. A partial global result is obtained in the case of the Euclidean metric on $R^3$.

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