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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.