Abstract
In this paper, we are interested to define and analyze a general parametric form of nonsingular Mueller matrices. Starting from previous results about the nondepolarizing matrices, we generalize the method to any nonsingular Mueller matrices. We addressed this problem from the point of view of metrics and degrees of freedom in order to introduce a physical admissible solution to solve this question. Generators of this group are used to address the issue of the dimension of the full space in order to obtain an adequate number of degrees of freedom of the related Mueller subspace.
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Notes
- 1.
Lorentz group is the union of four disconnected pieces [15]. The restriction to those transformations which are continuously connected to the identity transformation is called the proper orthochronous Lorentz transformations and denoted SO(3, 1) e as the identity component of SO(3, 1), the associated special orthogonal group.
- 2.
Matrices with unit determinant and positive left upper corner element are the SO(N − 1, 1) e subgroup elements.
- 3.
It is possible to identify missing matrices as ones with equal depolarization factor along the three principal axis with a non-null polarizance or diattenuation vector.
References
Z. F. Xing, “On the deterministic and non-deterministic Mueller matrix”, J. Mod. Opt. 39, 461–484 (1992)
V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters”, J. Math. Phys. 34, 5072–5088 (1993)
J. W. Hovenier, “Structure of a general pure Mueller matrix”, App. Opt. 33, 8318–8324 (1994)
A. V. Gopala Rao, K. S. Mallesh, and J. Sudha, “On the algebraic characterization of a Mueller matrix in polarization optics. I. Identifying a Mueller matrix from its N matrix”, J. Mod. Opt. 45, 955–987 (1998)
M. S. Kumar and R. Simon, “Characterization of Mueller matrices in polarization optics”, Opt. Commun. 88, 464–470 (1992)
A. B. Kostinski, C. R. Given, and J. M. Kwiatkowski, “Constraints on Mueller matrices of polarization optics”, Appl. Opt. 32, 1646–1651 (1993)
C.R. Givens and B. Kostinski, “A simple necessary and sufficient condition on physically realizable Mueller matrices”, J. Mod. Opt. 40, 471–481 (1993)
R. Simon, “The connection between Mueller and Jones matrices of polarization optics”, Opt. Com. 42, 293–297 (1982)
D. G. M. Anderson and R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix”, J. Opt. Soc. Am. A 11, 2305–2319 (1994)
J. J. Gil, “Characteristic properties of Mueller matrices”, J. Opt. Soc. Am. A 17, 328–334 (2000)
E.S. Fry and G.W. Kattawar, “Relationships between elements of the Stokes matrix”, Appl. Opt. 20, 2811–2814 (1981)
S.R. Cloude, “Group theory and polarisation algebra”, Optik 75, 26–36 (1986)
K. Kim, L. Mandel, and E. Wolf, “Relationship between Jones and Mueller matrices for random media”, J. Opt. Soc. Am. A 4, 433–437 (1987)
Y. Takakura and M.-P. Stoll, “Passivity test of Mueller matrices in the presence of additive Gaussian noise”, Appl. Opt. 48, 1073–1083 (2009)
D. H. Sattiger and O. L. Weaver, Lie Group and Algebras with Applications to Physics, Geometry and Mechanics, (Springer Verlag, New York, 1991)
V. Devlaminck and P. Terrier, “Definition of a parametric form of nonsingular Mueller matrices”, J. Opt. Soc. Am. A 25, 2636–2643 (2008)
R. Sridhar and R. Simon, “Normal form for Mueller matrices in polarization optics”, J. Mod. Opt. 41, 1903–1915 (1994)
A. A. Sagle and R. E. Walde, Introduction to Lie groups and Lie algebras, (Academic Press, New York 1973)
S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition”, J. Opt. Soc. Am. A 13, 1106–1113 (1996)
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Devlaminck, V., Terrier, P. (2010). A Degree of Freedom and Metrics Approach for Nonsingular Mueller Matrices Characterizing Passive Systems. In: Javidi, B., Fournel, T. (eds) Information Optics and Photonics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7380-1_17
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