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Possible Principles of Optical 3D Tensor Stress Field
Tomography
^{1}Vlokh R., ^{1}Krupych
O., ^{2}Maksymuk O.
^{1}Institute of Physical Optics, Dragomanov Str.23,
79005, Lviv, Ukraine
^{2}Institute of Applied Problems of Mechanics
and Mathematics, 3,b Naukova Str., Lviv, 79000, Ukraine
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In the present paper the approach for solving the problem of 3D stress
tensor field tomography is suggested. It is shown that the stress tensor
field tomography can be based on the imaging polarimetry. The problem can
be divided into three separate stages. In case of 2D stress distribution,
one can easy obtain experimentally the distribution of the difference of
stress tensor components (s_{1}s_{2})
and the shear component s_{6}. In case
of 3D stress distribution, our approach is based on searching equistressed
surfaces (if such the surfaces are nonclosed) with the imaging polarimetry
methods and using the rotation of sample in the indexmatching liquid.
Reconstruction of these surfaces allows one to reconstruct the 3D stress
distribution in the sample. When the equistressed surfaces are closed,
we suggest the cell model of the stressed medium and the approach based
on the Jones matrices. We show that solving the system of 6N nonlinear
equations of (N)^{1/3} power with 6N variables (N being the number
of cells, into which the stressed sample is divided) requires sample probing
by a broad beam in 2(N)^{1/3} different directions.
Key words: optical tomography, imaging polarimetry, stress tensor
PACS: 42.30.Wb
doi 10.3116/16091833/4/1/41/2003 

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