The possibility of applying photoelastic tomography (integrated photoelasticity) for investigating a three-dimensional birefringent flow is studied. Tomographic equations of the strain rates are reduced to a vector analogue of the Radon equation by dividing the flow-velocity field into an axial component, a transversal rotational, and a transversal potential component. It is shown how the axial and potential parts can be determined by tomographic photoelastic measurements.

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A method of using a magnetopolariscope for reconstructing stress fields by means of the tomography technique is proposed. Stresses are determined within the framework of the Maxwell piezo-optic law (linear dependence of the permittivity tensor on stresses) and weak optical anisotropy. The path difference and isocline parameter values measured by the tomography technique in the presence and absence of a magnetic field are used as initial information. Up to now, the magnetopolariscope has been employed only to determine bending and membrane stresses in plane models. Their novel application allows us to determine the residual stress completely.

A variety of inversions of the exponential Radon transform have been derived based on the circular harmonic transform in Fourier space by several research groups. In this paper, we derive a Cormack-type inversion of the exponential Radon transform by employing the circular harmonic transform directly in the projection space and in the image space instead of the Fourier space. This solution of the generalized Cormack equation is applicable to the exponential Radon transform with a complex parameter and can be used for reconstruction not only in single-photon emission tomography but also in polarized tomography of stress tensor fields.

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