Integrated Photoelasticity

Aben, Hillar; Guillemet, Claude

doi:10.1007/978-3-642-50071-8_6

Cited by 77 publications

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“…(24), and we can therefore use the same line of arguments as before, if we put the matrix U † into the same form as (22),…”

Section: Characteristic Parameters Of Su (2) Matricesmentioning

confidence: 99%

“…Such a scenario arises naturally in the field of Photoelasticity [17,18,19,20,21,22,23,24]: Experience shows that certain materials, such as glasses and polymers, are optically isotropic and homogeneous when unloaded, but exhibit local anisotropy when strained by an external load. The relation between the resulting dielectric tensor ǫ ij and the stress tensor σ ij in the interior of the medium is called the stressoptical law; its basic form has been discovered long ago by Maxwell [25].…”

Section: Introductionmentioning

confidence: 99%

“…the matrix U , from measurements of the characteristic parameters. To this end, relations between the parameters of a normal form of unitary matrices and the characteristic parameters may be derived [22,23,26]. However, these relations only determine the squares of sines or cosines of angles and therefore the actual computation of these quantities is rather involved.…”

Section: Introductionmentioning

confidence: 99%

“…Although references to the equivalence theorem, or applications thereof, are made frequently in the literature [20,22,23,24,28,29], its precise content is apparently not widely published; a rigorous proof of the theorem, or some equivalent statement thereof, seems even less readily available. This observation constitutes the starting point of our paper: We rigorously prove a matrix decomposition theorem for unitary unimodular (2, 2) matrices [section 4], from which the Poincaré Equivalence Theorem follows as a corollary [section 5].…”

Section: Introductionmentioning

confidence: 99%

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Characteristic parameters in integrated photoelasticity: an application of Poincaré's equivalence theorem

Hammer

2004

Journal of Modern Optics

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The Poincaré Equivalence Theorem states that any optical element which contains no absorbing components can be replaced by an equivalent optical model which consists of one linear retarder and one rotator only, both of which are uniquely determined. This has many useful applications in the field of Optics of Polarized Light. In particular, it arises naturally in attempts to reconstruct spatially varying refractive tensors or dielectric tensors from measurements of the change of state of polarization of light beams passing through the medium, a field which is known as Tensor Tomography. A special case is Photoelasticity, where the internal stress of a transparent material may be reconstructed from knowledge of the local optical tensors by using the stress-optical laws. -We present a rigorous approach to the Poincaré Equivalence Theorem by explicitly proving a matrix decomposition theorem, from which the Poincaré Equivalence Theorem follows as a corollary. To make the paper self-contained we supplement a brief account of the Jones matrix formalism, at least as far as linear retarders and rotators are concerned. We point out the connection between the parameters of the Poincaré-equivalent model to previously introduced notions of the Characteristic Parameters of an optical model in the engineering literature. Finally, we briefly illustrate how characteristic parameters and Poincaré-equivalent models naturally arise in Photoelasticity.

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“…(24), and we can therefore use the same line of arguments as before, if we put the matrix U † into the same form as (22),…”

Section: Characteristic Parameters Of Su (2) Matricesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Characteristic parameters in integrated photoelasticity: an application of Poincaré's equivalence theorem

Hammer

2004

Journal of Modern Optics

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“…Numerous efforts have been made in the past to tackle the problem of Integrated Photoelasticity [3][4][5][6][7][8][9][10][11][12]. While the reconstruction of the optical tensors in the two-dimensional problem is well-established (for an overview see [5]), the three-dimensional (3D) case so far has been solved only for special cases involving a priori assumptions about the symmetry of the 3D stress distribution, the rotation of the principal axes of the stress tensor, or the strength of the anisotropy of the dielectric tensor.…”

Section: Introductionmentioning

confidence: 99%

Application of Sharafutdinov?s Ray Transform in Integrated Photoelasticity

Hammer¹,

Lionheart²

2004

J Elasticity

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Abstract. We explain the main concepts centered around Sharafutdinov's ray transform, its kernel, and the extent to which it can be inverted. It is shown how the ray transform emerges naturally in any attempt to reconstruct optical and stress tensors within a photoelastic medium from measurements on the state of polarization of light beams passing through the strained medium. The problem of reconstruction of stress tensors is crucially related to the fact that the ray transform has a nontrivial kernel; the latter is described by a theorem for which we provide a new proof which is simpler and shorter as in Sharafutdinov's original work, as we limit our scope to tensors which are relevant to Photoelasticity. We explain how the kernel of the ray transform is related to the decomposition of tensor fields into longitudinal and transverse components. The merits of the ray transform as a tool for tensor reconstruction are studied by walking through an explicit example of reconstructing the σ33-component of the stress tensor in a cylindrical photoelastic specimen. In order to make the paper self-contained we provide a derivation of the basic equations of Integrated Photoelasticity which describe how the presence of stress within a photoelastic medium influences the passage of polarized light through the material.

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Conduction and Breakdown in Dielectric Liquids

Zahn

1999

Wiley Encyclopedia of Electrical and Electronics Engineering

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The sections in this article are Overview of Liquid Dielectrics Liquid Insulation Systems Charge Injection and Conduction Streamers Space‐Charge Effects Zero Recombination Limit (α = 0) Langevin Recombination Limit Kerr Electrooptic Field Mapping Measurements Sensitive Kerr Electro‐Optic Measurements with Weakly Birefringent Materials Kerr Electro‐Optic Measurements with Electric Field Magnitude and Direction Varying Along the Light Path Acknowledgments

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Integrated Photoelasticity

Cited by 77 publications

References 0 publications

Characteristic parameters in integrated photoelasticity: an application of Poincaré's equivalence theorem

Characteristic parameters in integrated photoelasticity: an application of Poincaré's equivalence theorem

Application of Sharafutdinov?s Ray Transform in Integrated Photoelasticity

Conduction and Breakdown in Dielectric Liquids

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