Possible principles of optical 3D tensor stress field tomography

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 easily obtain experimentally the distribution of the difference of stress tensor components (σ₁-σ₂) and the shear component σ₆. In case of 3D stress distribution, our approach is based on searching equi-stressed surfaces (if such the surfaces are non-closed) with the imaging polarimetry methods and using the rotation of sample in the index-matching liquid. Reconstruction of these surfaces allows one to reconstruct the 3D stress distribution in the sample. When the equi-stressed 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) ¹3/ 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)¹3/ different directions.