The DOI matches its Crossref record; 266 of the 268 references it cites were found in a registry or an index.
Polarimetric characterization of light and media: Physical quantities involved in polarimetric phenomena
Open accessAbstract
An objective analysis is carried out of the matricial models representing the polarimetric properties of light and material media leading to the identification and definition of their corresponding physical quantities, using the concept of the coherency matrix. For light, cases of homogeneous and inhomogeneous wavefront are analyzed, and a model for 3D polarimetric purity is constructed. For linear passive material media, a general model is developed on the basis that any physically realizable linear transformation of Stokes vectors is equivalent to an ensemble average of passive, deterministic nondepolarizing transformations. Through this framework, the relevant physical quantities, including indices of polarimetric purity, are identified and decoupled. Some decompositions of the whole system into a set of well-defined components are considered, as well as techniques for isolating the unknown components by means of new procedures for subtracting coherency matrices. These results and methods constitute a powerful tool for analyzing and exploiting experimental and industrial polarimetry. Some particular application examples are indicated.
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“Obviously, this situation is not general because the electric field of the electromagnetic wave evolves in the real three-dimensional (3D) space and therefore a general mathematical description of the states of polarization requires a 3D treatment [1,2].”
From Polarimetric purity and the concept of degree of polarization (2018) · cites this paper as [2]
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“It is worth noting that the mathematical definition of P 3D is, in fact, the 3D analog of the degree of polarimetric purity, P 4D, for the 4 × 4 Mueller matrices (depolarization index [20]) representing the transformation of polarization states by the action of a material medium [2].”
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“The fact that the inequality P 3D ⩾ 1 / 2 holds for 2D states [2,8,32] is nothing else than a natural consequence of the fact that they are characterized by Pd = 1.”
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“was introduced for the first time by Samson [13], and was also obtained later by Barakat [14] and by Gil [2] as the quadratic average of the relative differences between the eigenvalues of R”
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“among the different possible representations of R as compositions of mutually incoherent states, a privileged view of the structure of polarimetric purity of R is given by its characteristic (or trivial ) decomposition [2,10,18],”
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Cites
Horn, R. A., & Johnson, C. R. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810817 · Cited by 25,904
Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203
Absorption and Scattering of Light by Small Particles
Bohren, C. F., & Huffman, D. R. (1998) · doi:10.1002/9783527618156 · Cited by 18,474
Probability, Random Variables, and Stochastic Processes.
Abrahams, J., & Papoulis, A. (1984) · Journal of the American Statistical Association · doi:10.2307/2288754 · Cited by 16,301
Light Scattering by Small Particles
van de Hulst, H. C. (1981) · CERN Document Server (European Organization for Nuclear Research) · Cited by 7,938
Light Scattering by Small Particles
van de Hulst, H. C., & Twersky, V. (1957) · Physics Today · doi:10.1063/1.3060205 · Cited by 5,691
Ellipsometry and Polarized Light
Azzam, R. M. A., Bashara, N. M., & Ballard, S. S. (1978) · Physics Today · doi:10.1063/1.2994821 · Cited by 4,284
Mathematical Methods for Physicists
Arfken, G. B., & Mathews, J. (1972) · American Journal of Physics · doi:10.1119/1.1988084 · Cited by 4,069
Mathematical Methods for Physicists
Arfken, G. B., & Mullin, A. A. (1967) · American Journal of Physics · doi:10.1119/1.1973757 · Cited by 2,708
Absorption and Scattering of Light by Small Particles
Dobson, P. J. (1984) · Physics Bulletin · doi:10.1088/0031-9112/35/3/025 · Cited by 2,674
Flagged first, then by citations
2 of the 268 references couldn’t be matched to a known paper.
Research works printed but not linked: 35
- R. Loudon, The quantum theory of light (Clarendon, Oxford, 1983)
- C. Brosseau, Fundamentals of polarized light. A statistical approach (Wiley, N.Y., 1998)
- Stokes, 1852, Trans. Cambridge Phil. Soc., 9, 399
- Mueller, 1948, J. Opt. Soc. Am., 38, 661
- N.G. Parke III, Matrix optics , Ph.D. thesis, M.I.T., 1948
- Gil, 1987, Optik, 76, 67
- Ichimoto, 2006, Publ. Natl. Astron. Obs. Jap., 9, 11
- Azzam, 1979, Optik, 52, 253
- Light scattering by Microstructures , edited by F. Moreno, F. González (Lecture Notes in Physics, Springer-Verlag, Berlin, 2000)
- Gil, 2004, Monogr. Sem. Mat. García de Galdeano, 31, 161
- McMaster, 1954, J. Opt. Soc. Am., 22, 351
- E.L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), Chap. 9
- Correas, 2003, Monogr. Sem. Mat. García de Galdeano, 27, 23
- Luis, 2005, Phys. Rev. A., 71, 1023810
- W.A. Holm, R.M. Barnes, in Proceedings of the 1988 IEEE USA radar conference , p. 249
- Cloude, 1996, IEEE Trans. GRS, 34, 498
- Réfrégier, 2004, J. Opt. Soc. Am. A, 21, 21124
- Indebetouw, 1990, Optik, 85, 78
- J.J. Gil, Ph.D. thesis, Facultad de Ciencias, Univ. Zaragoza, Spain, 1983; available from http://www.pepegil.es/PhD-Thesis-JJ-Gil.pdf
- Gil, 1982, Opt. Pure Appl., 15, 39
- Cloude, 1986, Optik, 75, 26
- Nagirner, 1993, Astron. Astrophys., 275, 318
- Kumar, 1994, Opt. Commun., 11, 2305
- Gopala, 1998, J. Mod. Opt., 45, 955
- Gopala, 1998, J. Mod. Opt., 45, 989
- Hovenier, 1986, Astron. Astrophys., 157, 301
- A. Aiello, G. Puentes, J.P. Woerdman, arXiv:quant-ph/0611179v1 (2006) · arXiv
- J.J. Gil, in Light scattering from microestructures (Springer, Lecture Notes in Physics, 2000)
- Brosseau, 1990, Optik, 85, 83
- Le Roy-Bréhonnet, 1996, Pure Appl. Opt., 6, 385, 10.1088/0963-9659/6/3/008 · DOI
- Ferreira, 2006, Monogr. Sem. Mat. García de Galdeano, 33, 115
- R.A. Chipman, in The Handbook of Optics (McGraw-Hill, N.Y., 1994), Chap. 22
- ESA Proceedings of POLinSAR2003: Workshop on Applications of SAR Polarimetry and Polarimetric Interferometry; available from http://earth.esa.int/workshops/polinsar2003/pr.html
- A.C. Levasseur-Regourd, in Photopolarimetry in Remote Sensing (NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 161, 2005)
- Chipman, 1989, Opt. Eng., 28, 90
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Metadata
- Authors
- Gil, J. J.
- Affiliations
- Universidad de Zaragoza (ES)
- Corresponding author
- Gil, J. J.
- ORCID
- Gil, J. J.
- Venue
- The European Physical Journal Applied Physics
- Publisher
- EDP Sciences
- Published
- 2007-10
- Volume
- 40
- Issue
- 1
- Pages
- 1-47
- ISSN
- 1286-0042 (ISSN-L)
- 1286-0050
- OpenAlex
- W2124319519
- Cited by
- 272
- References
- 268
- Citations by year
- 2026: 13 · 2025: 12 · 2024: 9 · 2023: 9 · 2022: 15 · 2021: 13 · 2020: 13 · 2019: 21 · 2018: 22 · 2017: 9 · 2016: 31 · 2015: 21 · 2014: 17 · 2013: 10 · 2012: 15
- FWCI
- 7.41
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The European Physical Journal Applied Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Springer Link (Chiba Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Optical Polarization and Ellipsometry
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Physical Sciences › Earth and Planetary Sciences › Geophysics › Synthetic Aperture Radar (SAR) Applications and Techniques
- Keywords
- polarimetry, coherency matrix, Stokes vector, passive media, matrix factorization
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