dorsal/arxiv
View SchemaCharacteristic Parameters in Integrated Photoelasticity: An Application of Poincare's Equivalence Theorem
| Authors | Hanno Hammer |
|---|---|
| Categories | |
| ArXiv ID | physics/0305034 |
| URL | https://arxiv.org/abs/physics/0305034 |
| DOI | 10.1080/09500340310001631671 |
| Journal | Journal of Modern Optics, Vol. 51, No. 4, 2004, pp. 597-618 |
Abstract
The Poincare 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 Poincare Equivalence Theorem by explicitly proving a matrix decomposition theorem, from which the Poincare 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 Poincare-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 Poincare-equivalent models naturally arise in Photoelasticity.
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"abstract": "The Poincare Equivalence Theorem states that any optical element which\ncontains no absorbing components can be replaced by an equivalent optical model\nwhich consists of one linear retarder and one rotator only, both of which are\nuniquely determined. This has many useful applications in the field of Optics\nof Polarized Light. In particular, it arises naturally in attempts to\nreconstruct spatially varying refractive tensors or dielectric tensors from\nmeasurements of the change of state of polarization of light beams passing\nthrough the medium, a field which is known as Tensor Tomography. A special case\nis Photoelasticity, where the internal stress of a transparent material may be\nreconstructed from knowledge of the local optical tensors by using the\nstress-optical laws. - We present a rigorous approach to the Poincare\nEquivalence Theorem by explicitly proving a matrix decomposition theorem, from\nwhich the Poincare Equivalence Theorem follows as a corollary. To make the\npaper self-contained we supplement a brief account of the Jones matrix\nformalism, at least as far as linear retarders and rotators are concerned. We\npoint out the connection between the parameters of the Poincare-equivalent\nmodel to previously introduced notions of the Characteristic Parameters of an\noptical model in the engineering literature. Finally, we briefly illustrate how\ncharacteristic parameters and Poincare-equivalent models naturally arise in\nPhotoelasticity.",
"arxiv_id": "physics/0305034",
"authors": [
"Hanno Hammer"
],
"categories": [
"physics.optics",
"physics.gen-ph",
"quant-ph"
],
"doi": "10.1080/09500340310001631671",
"journal_ref": "Journal of Modern Optics, Vol. 51, No. 4, 2004, pp. 597-618",
"title": "Characteristic Parameters in Integrated Photoelasticity: An Application of Poincare\u0027s Equivalence Theorem",
"url": "https://arxiv.org/abs/physics/0305034"
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