NDTnet 1998 Aug, Vol.3 No.8

Abstract

Vector and tensor field tomography makes a number of new and interesting nondestructive methods possible [1]: diagnostics of magnetic field in plasma, of the Kerr-effect field, time of-flight tomography of fluid flow and Doppler tomography of atoms velocities in plasma. Interest in optical field tomography has been stimulated primarily by the possibility of applying integrated photoelasticity to the stress analysis of apparent models. Residual stress is one of the most important characteristics of glass articles the point of view of their strength and resistance. In the case of optical glass, birefringence due to the residual stresses characterizes the optical quality of the article. In integrated photoelasticity the threedimensional specimen is immersed in an immersion bath and a beam of polarized light is passed through the specimen.

Reconstruction of the spatial distribution of the stress tensor by interpretation of integrated optical effects of the rays that have passed through the medium may be considered a type of tensor field tomography. Distinguishing features of this tomography are considered. Since on the general case the measurements data is in a nonlinear way related to the stress field, optical phenomena are very complicated. However, if birefringence is weak, the optical theory of integrated photoelasticity can be simplified. Since glass is often weakly birefringent, this simplified theory can be used for the stress analysis in glass. Two particular cases are considered in detail: 1) weak birefringence, 2) constant principal stress distribution. In these cases it is possible to measure two linear integrals. One of them is connected with the transversal interactions of the two-dimensional vector field and the other with the transversal interactions of the two-dimensional tensor field.

Using the equilibrium equation enables one to reduce these integrals to the ordinary Radon transform of axial stress component. The other stress components can be determined using an additional measurements or additional information [2]. Theory of the fictitious temperature field allows us to analyze the problem using the mathematical apparatus of thermoelasticity. It is shown how the other components can be determined from the boundary-value problem of thermoelasticity [3]. Application of the techniques is illustrated by practical examples.

1. Aben, H., Puro, A. Inverse Problems. 1997, 13: 215-221.
2. Puro, A. Optics and Spectroscopy. 1996, 81, 1: 132-139.
3. Puro, A. J.Appl. Maths Mechs. 1993, 57, 1: 141-145.

Abstract Source:
Book of Abstracts, 7th European Conference on Non-Destructive Testing, 26-29 May 1998, ISBN: 87-986898-0-00

Full-Text Source:
Proceedings of the 7th European Conference on Non-Destructive Testing, 26-29 May 1998, ISBN:

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