Photoelastic tomography for three-dimensional flow birefringence studies

Abstract

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.

Full Tomographic Reconstruction of 2D Vector Fields using Discrete Integral Data

“…Several applications of vector field tomography have been considered in the literature. These include: blood flow imaging [4,5]; fluid mesoscale velocity imaging in ocean acoustic tomography [6][7][8]; fluid-flow imaging [9][10][11][12][13][14][15][16]; electric field imaging in Kerr materials [17][18][19]; imaging of the component of the gradient of the refractive index field, which is transversal to the beam, in Schlieren tomography [14]; velocity field imaging of heavy particles in plasma physics [20]; density imaging in supersonic expansions and flames in beam deflection optical tomography [21]; non-destructive stress distribution imaging of transparent specimens in photoelasticity [22,23]; determination of temperature distributions and velocity vector fields in furnaces [24]; and magnetic field imaging in Tokamak in polarimetric tomography [25].…”

Experiment and modelling of birefringent flows using commercial CFD code

“…In order to understand what is happening within the flow and overcome this integrating effect, either additional experimental or computational techniques must be used augment the information available. Aben and Puro (1997) have investigated the use of optical tomography for 3-D flow, but this method is intensive both in terms of storage and processing requirements.…”

Reconstruction of spatially inhomogeneous dielectric tensors through optical tomography

“…It should be mentioned that the determination of anisotropic dielectric tensors as presented here has a closely related variant in the problem of reconstruction of a stress tensor field inside a loaded transparent material; the phenomenon that an initially isotropic medium becomes optically anisotropic when under strain is called Photoelasticity [8][9][10][11][12] and may be used to obtain information about the internal stress in a strained medium from polarization transformation data obtained by tomographical methods. The photoelastic effect as a means to retrieve information about internal stresses has been studied extensively: A method termed "Integrated Photoelasticity" [13][14][15][16][17] is well-known, and it was pointed out [18][19][20][21] that information about the difference of principal stress components could be retrieved from appropriate Radon transformations of polarization transformation data. 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.…”