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Photoelasticity: theoretical aspects
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We use an experimental technique to retrieve grain-scale stresses. The technique is based on birefringence properties of disks. In a birefringent material, the speed of light, and consequently the index of refraction depends on wave polarization. In other cases, such as glass and polymeric materials, birefringence arises only when the material is subject to anisotropic stress. In other words, the refractive indexes depend on the eigenvalues of local stress tensor. This phenomenon is called photoelasticity and has been utilized in granular experiments for several decade (Howell
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et al., 1999).
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Using photo-elasticity, we can measure the internal stress. This measurement is
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best performed using circularly polarized light, which provides isotropic polarization.
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Circularly polarized light is a composition of two orthogonal linearly polarized waves
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with a quarter-wave phase shift. As shown in Fig. 3.3, this polarization can be
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obtained by passing unpolarized light through a linear polarizer and a quarter-wave
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plate. The quarter-wave plate creates a π{2 phase shift between two orthogonal com-
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ponents of the light polarization. Passing unpolarized light through the combination
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of linear polarizer and quarter-wave, as shown in the figure, results in circularly po-
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larized light. On the other side, covering the camera, sits another circular polarizer
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with opposite polarity, which blocks the unperturbed light. If there exists a photo-
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elastic material in between under anisotropic stress, the wave components, polarized
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in the principles directions of local stress tensor, travel with different speeds. This
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speed difference results in phase shifts in the components of the wave and changes
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circularly polarized light to elliptical. Consequently, a part of the wave subject to
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this change is not completely blocked by the second circular polarizer and is passed
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through it, recorded by the camera.
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Photo-elasticity can be used to quantitatively measure local stress. Assuming
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that the relation between stress and refractive index is linear:
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$´n_1-n_2=C(\sigma_1-\sigma_2)´$
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Right now there is not so much here so we prefer to send you to the excellent [wikipedia page about photoelasticity](https://en.wikipedia.org/wiki/Photoelasticity) or to [this lecture by W. Wang](http://depts.washington.edu/mictech/optics/me557/photoelasticity.pdf).
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[<go back to home](https://git-xen.lmgc.univ-montp2.fr/PhotoElasticity/Main/wikis/home) |
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