Optical tensor field tomography: the Kerr effect and axisymmetric integrated photoelasticity

Appearance of optical singularities at the light propagation through glasses with residual stresses

“…A lot of theoretical approaches for solving the problems of integrated photoelasticity have been offered for the difficult case of asymmetrical objects. The principle idea of these approaches consists in consideration of the problem from the viewpoint of optical tensor field tomography [3][4][5]. However, these considerations too often represent no more than theoretical suggestions in need of further experimental verifications.…”

Reconstruction of spatially inhomogeneous dielectric tensors through optical tomography

“…However, these methods do not succeed in reconstructing the stress components separately and therefore the full stress tensor, and the linearly related dielectric tensor, can be obtained in this way only for systems exhibiting a certain degree of symmetry, such as an axial symmetry. Other methods of reconstruction have been suggested, for example, a three-beam measurement scheme [22], where for axisymmetric systems an onion-peeling reconstruction algorithm was proposed [23,24]. Another method, which in principle is capable of determining a general three-dimensional permittivity tensor, is the "load incremental approach" [25].…”

3D reconstruction of tensors and vectors

“…Originally, the most active area of application of tensor tomography was photoelasticity [36,37,38,39,40,41,42,43] and that continues to be so [44,45,46,47,48,49,50]. An early book on the subject of photoelasticity was written by Aben [36].…”

“…In addition, there are other areas of physics where the results of this report may prove to be stimulating. These include nonlinear optics (reconstruction of the susceptibility tensor); anisotropic electromagnetic [67,68] and elastic media (the latter being of significant current interest); stress tensor polarization tomography in photo-and magnetoelastic materials which are already being pursued vigorously [41,42,45,46,47,48,49,50]; second and fourth-order tensor tomography from seismic traveltime tomographic data [69]; neutron spin tensor tomography [70]; and general relativity tensor tomography using gravitational delay time tomographic data [71]. Tomography also can be applied to finding inverse solutions of integral transforms of differential forms [72] or finding a symmetric tensor field from its integrals over all geodesics of a Riemannian metric [51].…”