Skip to main content
SpringerLink
Log in

Jones and Mueller matrices: structure, symmetry relations and information content

  • Chapter
Light Scattering Reviews 4

Part of the book series: Springer Praxis Books ((ENVIRONSCI))

Abstract

When light propagates through a linear medium, its polarization properties can be described either by the Stokes vector or, under definite conditions, by Jones vector formalisms. The effect of medium on the light is then to transform the Stokes or Jones vector, so that the medium can be represented by a transformation matrix. This transformation is usually known as the Mueller matrix (Bohren and Huffman, 1983; Brosseau; 1998) when it acts on the four-dimensional Stokes vector or as the Jones matrix (Azzam and Bashara, 1987; Collett, 1993; Shurcliff, 1962) when it acts on Jones vector. Information contained in the Mueller matrix has many useful applications in such diverse fields as interaction with various optical systems (Shurcliff, 1962; Azzam and Bashara, 1977; Collett, 1993; Brosseau, 1998), cloud diagnostics (van de Hulst, 1957; Bohren and Huffman, 1983; Mishchenko et al., 2000, 2002; Kokhanovsky, 2003b), remote sensing in the ocean, atmosphere and terrestrial (Boerner, 1992; Kokhanovsky, 2001, 2003a, 2003b; Muttiah, 2002), and tissue optics (Priezzhev et al., 1989; Tuchin, 2002, 2004).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Abhyankar, K.D., and A.L. Fymat, 1969: Relations between the elements of the phase matrix for scattering. J. Math. Phys., 10, 1935–1938.

    Article  Google Scholar 

  • Aiello, A., and J.P. Woerdman, 2005: Physical bounds to the entropy-depolarization relation in random light scattering. Phys. Rev. Lett., 94, 090406.

    Article  Google Scholar 

  • Anderson, D.G.M., and R. Barakat, 1994: Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix. J. Opt. Soc. Am. A, 11, 2305–2319.

    Article  Google Scholar 

  • Azzam, R.M., and N.M. Bashara, 1977: Ellipsometry and Polarized Light. New York: North-Holland.

    Google Scholar 

  • Barakat, R., 1987: Conditions for the physical realizability of polarization matrices characterizing passive systems. J. Mod. Optics, 34, 1535–1544.

    Article  Google Scholar 

  • Barakat, R., 1998: Jones matrix equivalence theorems for polarization theory. Eur. J. Phys., 19, 209–216.

    Article  Google Scholar 

  • Berry, M.V., and M.R. Dennis, 2003: The optical singularities of birefringent dichroic chiral crystals. Proc. R. Soc. London, Ser. A, 459, 1261–1292.

    Article  Google Scholar 

  • Berry, M.V., and M.R. Dennis, 2004: Black polarization sandwiches are square roots of zero. J. Opt. A, 6, S24–S25.

    Google Scholar 

  • Bicout, D., Ch. Brosseau, A.S. Martinez, and J.M. Schmitt, 1994: Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter. Phys. Rev. E, 49, 1767–1770.

    Article  Google Scholar 

  • Boerner, W.-M., 1992: Direct and Inverse Methods in Radar Polarimetry, Parts I and II. Dordrecht: Kluwer Academic.

    Google Scholar 

  • Bohren, C.F., and E.R. Huffman, 1983: Absorption and Scattering of Light of Light by Small Particles. New York: Wiley.

    Google Scholar 

  • Brosseau, Ch., 1990: Analysis of experimental data for Mueller polarization matrices. Optik (Stuttgart), 85, 83–86.

    Google Scholar 

  • Brosseau, Ch., 1995: Statistics of the normalized Stokes parameters for a Gaussian stochastic plane wave field. Appl. Optics, 34, 4788–4793.

    Article  Google Scholar 

  • Brosseau, Ch., 1998: Fundamentals of Polarized Light. A Statistical Optics Approach. New York: North-Holland.

    Google Scholar 

  • Brosseau, Ch., C.R. Givens, and A.B. Kostinski, 1993: Generalized trace condition on the Mueller-Jones polarization matrix. J. Opt. Soc. Am. A, 10, 2248–1151.

    Article  Google Scholar 

  • Bueno, J.M., 2001: Indices of linear polarization for an optical system. J. Opt. A: Pure Appl. Opt., 3, 470–476.

    Article  Google Scholar 

  • Chandrasekhar, S., 1950: Radiative Transfer. London: Oxford University Press.

    Google Scholar 

  • Chipman, R.A., 1995: Polarimetry, Handbook of Optics, Vol. II, New York: McGraw-Hill.

    Google Scholar 

  • Chipman, R.A., 1999: Depolarization. SPIE Proc., 3754, 14–20.

    Article  Google Scholar 

  • Chipman, R.A., 2005: Depolarization index and the average degree of polarization. Appl. Optics, 44, 2490–2495.

    Article  Google Scholar 

  • Cloude, S.R., 1986: Group theory and polarization algebra. Optik (Stuttgart), 7, 26–36.

    Google Scholar 

  • Cloude, S.R., and E. Pottier, 1995: Concept of polarization entropy in optical scattering. Opt. Eng., 34, 1599–1610.

    Article  Google Scholar 

  • Collett, E., 1993: Polarized Light: Fundamentals and Applications. New York: Marcel Dekker.

    Google Scholar 

  • Deibler, L.L., and M.H. Smith, 2001: Measurement of the complex refractive index of isotropic materials with Mueller matrix polarimetry. Appl. Optics, 40, 3659–3667.

    Article  Google Scholar 

  • de Lang, H., 1966: Polarization properties of optical resonators passive and active. Ph.D. dissertation, University of Utrecht.

    Google Scholar 

  • Espinosa-Luna, R., and E. Bernabeu, 2007: On the Q(M) depolarization metric, Opt. Commun., 277, 256–258.

    Article  Google Scholar 

  • Fry, E.S., and G.W. Kattawar, 1981: Relationships between elements of the Stokes matrix. Appl. Optics, 20, 2811–2814.

    Article  Google Scholar 

  • Gerrard, A., and J.M. Burch, 1975: Introduction to Matrix Methods in Optics. New York: Wiley.

    Google Scholar 

  • Gil, J.J., 2000: Characteristic properties of Mueller matrices. J. Opt. Soc. Am. A, 17, 328–334.

    Article  Google Scholar 

  • Gil, J.J., 2007: Polarimetric characterization of light and media. Eur. Phys. J. Appl. Phys., 40, 1–47.

    Article  Google Scholar 

  • Gil, J.J., and E. Bernabeu, 1985: A depolarization criterion in Mueller matrices. Opt. Acta, 32, 259–261.

    Google Scholar 

  • Gil, J.J., and E. Bernabeu, 1986: Depolarization and polarization indexes of an optical system, Opt. Acta, 33, 185–189.

    Google Scholar 

  • Gil, J.J., and E. Bernabeu, 1987: Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix. Optik (Stuttgart), 76, 67–71.

    Google Scholar 

  • Givens, C.R., and A.B. Kostinski, 1993: A simple necessary and sufficient condition on physically realizable Mueller matrices. J. Mod. Optics, 40, 471–481.

    Article  Google Scholar 

  • Gopala Rao, A.V., K.S. Mallesh, and Sudha, 1998a: On the algebraic characterization of a Mueller matrix in polarization optics I. Identifying a Mueller matrix from its N matrix. J. Mod. Optics, 45, 955–987.

    Google Scholar 

  • Gopala Rao, A.V., K.S. Mallesh, and Sudha, 1998b: On the algebraic characterization of a Mueller matrix in polarization optics II. Necessary and sufficient conditions for Jones-derived Mueller matrices. J. Mod. Optics, 45, 989–999.

    Google Scholar 

  • Hovenier, J.W., 1969: Symmetry relations for scattering of polarized light in a slab of randomly oriented particles. J. Atmos. Sci., 26, 488–499.

    Article  Google Scholar 

  • Hovenier, J.W., 1970: Principles of symmetry for polarization studies of planets. Astron. Astrophys., 7, 86–90.

    Google Scholar 

  • Hovenier, J.W., 1994: Structure of a general pure Mueller matrix. Appl. Opt., 33, 8318–8324.

    Article  Google Scholar 

  • Hovenier, J.W., and D.W. Mackowski, 1998: Symmetry relations for forward and backward scattering by randomly oriented particles. J. Quant. Spectrosc. Radiat. Transfer, 60, 483–492.

    Article  Google Scholar 

  • Hovenier, J.W., and C.V.M. van der Mee, 1996: Testing scattering matrices: a compendium of recipes. J. Quant. Spectrosc. Radiat. Transfer, 55, 649–661.

    Article  Google Scholar 

  • Hovenier, J.W., and C.V.M. van der Mee, 2000: Relationships for matrices describing scattering by small particles. In Light scattering by nonspherical particles (M.I. Mischenko et al., Eds). San Diego: Academic Press, pp. 61–85.

    Chapter  Google Scholar 

  • Hovenier, J.W., H.C. van de Hulst, and C.V.M. van der Mee, 1986: Conditions for the elements of the scattering matrix. Astron. Astrophys., 157, 301–310.

    Google Scholar 

  • Hu, Ch.-R., G.W. Kattawar, M.E. Parkin, and P., Herb, 1987: Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer. Appl. Optics, 26, 4159–4173.

    Article  Google Scholar 

  • Huard, P., 1997: Polarization of Light. New York: Wiley.

    Google Scholar 

  • Hurwitz, H., and C.R. Jones, 1941: A new calculus for the treatment of optical systems II. Proof of three general equivalence theorems. J. Opt. Soc. Am., 31, 493–499.

    Article  Google Scholar 

  • Jellison, G.E., and F.A. Modine, 1997: Two-modulator generalized ellipsometry: theory. Appl. Optics, 36, 8190–8198.

    Article  Google Scholar 

  • Jones, R.C., 1941: A new calculus for the treatment of optical systems I. Description and discussion of the calculus. J. Opt. Soc. Am., 31, 488–493.

    Article  Google Scholar 

  • Jones, R.C., 1942: A new calculus for the treatment of optical systems IV. J. Opt. Soc. Am., 32, 486–493.

    Article  Google Scholar 

  • Jones, R.C., 1947: A new calculus for the treatment of optical systems V. A more general formulation and description of another calculus. J. Opt. Soc. Am., 37, 107–110.

    Article  Google Scholar 

  • Jones, R.C., 1948: A new calculus for the treatment of optical systems VII. Properties of the N-matrices. J. Opt. Soc. Am., 38, 671–685.

    Article  Google Scholar 

  • Jones, R.C., 1956: A new calculus for the treatment of optical systems VIII. Electromagnetic theory. J. Opt. Soc. Am., 46, 126–131.

    Article  Google Scholar 

  • Kaplan, B., and B. Drevillon, 2002: Mueller matrix measurements of small spherical particles deposited on a c-Si wafer. Appl. Optics, 41, 3911–3918.

    Article  Google Scholar 

  • Kaplan, B., G. Ledanois, and B. Drevillon, 2001: Mueller matrix of dense polystyrene latex sphere suspensions: measurements and Monte Carlo simulation. Appl. Optics, 40, 2769–2777.

    Article  Google Scholar 

  • Kim, K., L. Mandel, and E. Wolf, 1987: Relationship between Jones and Mueller matrices for random media. J. Opt. Soc. Am. A, 4, 433–437.

    Article  Google Scholar 

  • Kim, Y.L., P. Pradhan, M.H. Kim, and V. Backman, 2006: Circular polarization memory effect in low-coherence enhanced backscattering of light. Opt. Lett., 31, 2744–2746.

    Article  Google Scholar 

  • Kliger, D.S., J.W. Lewis, and C.E. Randall, 1990: Polarized Light in Optics and Spectroscopy. New York: Academic Press.

    Google Scholar 

  • Kokhanovsky, A.A., 2001: Light Scattering Media Optics: Problems and Solutions. Chichester: Praxis Publishing.

    Google Scholar 

  • Kokhanovsky, A.A., 2003a: Parameterization of the Mueller matrix of oceanic waters. J. Geophys. Res., 108, C6.

    Google Scholar 

  • Kokhanovsky, A.A., 2003b: Polarization Optics of Random Media. Chichester: Praxis Publishing.

    Google Scholar 

  • Kokhanovsky, A.A., 2003c: Optical properties of irregularly shaped particles. J. Phys. D: Appl. Phys., 36, 915–923.

    Article  Google Scholar 

  • Kokhanovsky, A.A., 2003d: Parameterization of the Mueller matrix of oceanic waters. J. Geophys. Res., 108(C6), 3175–3178.

    Article  Google Scholar 

  • Kong, J.A. (Ed.), 1990: Polarimetric Remote Sensing (PIER 3 — Progress in Electromagnetic Reseach). New York: Elsevier.

    Google Scholar 

  • Kostinski, A.B., 1992: Depolarization criterion for incoherent scattering. Appl. Optics, 31, 3506–3508.

    Article  Google Scholar 

  • Kostinski, A.B., C.R. Givens, and J.M. Kwiatkowski, 1993: Constraints on Mueller matrices of polarization optics. Appl. Optics, 32, 1646–1651.

    Article  Google Scholar 

  • Lancaster, P., and M. Tismenetsky, 1985: The Theory of Matrices, 2nd edn, San Diego, CA: Academic Press.

    Google Scholar 

  • Landau, L.D., E.M. Lifshitz, and L.P. Pitaevskii, 1984: Electrodynamics of Continuous Media. Oxford: Pergamon Press.

    Google Scholar 

  • Lawless, R., Y. Xie, P. Yang, G.W. Kattawar, and I. Laszlo, 2006: Polarization and effective Mueller matrix for multiple scattering of light by nonspherical ice crystals. Opt. Express, 14, 6381–6393.

    Article  Google Scholar 

  • Le Roy-Brehonnet, F., and B. Le Jeune, 1997: Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties. Prog. Quant. Electr., 21, 109–151.

    Article  Google Scholar 

  • Lu, S.-Y., and R.A. Chipman, 1994: Homogeneous and inhomogeneous Jones matrices. J. Opt. Soc. Am. A, 11, 766–773.

    Article  Google Scholar 

  • Lu, S.-Y., and R.A. Chipman. 1996: Interpretation of Mueller matrices based on polar decomposition. J. Opt. Soc. Am. A, 13, 1106–1113.

    Article  Google Scholar 

  • MacKintosh, F.C., J.X. Zhu, D.J. Pine, and D.A. Weitz, 1989: Polarization memory of multiple scattered light. Phys. Rev. B, 40, 9342–9345.

    Article  Google Scholar 

  • Manickavasagam, S., and M.P. Menguc, 1998: Scattering-matrix elements of coated infinite-length cylinders. Appl. Optics, 37, 2473–2482.

    Article  Google Scholar 

  • Mar’enko, V.V., and S.N. Savenkov, 1994: Representation of arbitrary Mueller matrix in the basis of matrices of circular and linear anisotropy. Optics and Spectroscopy, 76, 94–96.

    Google Scholar 

  • Meira-Belo, L.C., and U.A. Leitao, 2000: Singular polarization eigenstates in anisotropic stratified structures. Appl. Optics, 39, 2695–2704.

    Article  Google Scholar 

  • Mishchenko, M.I., 1992: Enhanced backscattering of polarized light from discrete random media: calculations in exactly the backscattering direction. J. Opt. Soc. Am. A, 9, 978–982.

    Article  Google Scholar 

  • Mishchenko, M.I., and J.W. Hovenier, 1995: Depolarization of light backscattered by randomly oriented nonspherical particles. Opt. Letters, 20, 1356–1358.

    Article  Google Scholar 

  • Mishchenko, M.I., and L.D. Travis, 2000: Polarization and depolarization of Light. In Light Scattering from Microstructures (F. Moreno, and F. Gonzlez, Eds). Berlin: Springer-Verlag, 159–175.

    Chapter  Google Scholar 

  • Mishchenko, M.I., J.W. Hovenier, and L.D. Travis, 2000: Light Scattering by Nonspherical Particles. San Diego, CA: Academic Press.

    Google Scholar 

  • Mishchenko, M.I., L.D. Travis, and A.A. Lacis, 2002: Scattering, Absorption, and Emission of Light by Small Particles. Cambridge: Cambridge University Press.

    Google Scholar 

  • Mishchenko, M.I., L.D. Travis, and A.A. Lacis, 2006: Multiple Scattering of Light by Particles. Radiative Transfer and Coherent Backscattering. Cambridge: Cambridge University Press.

    Google Scholar 

  • Morio, J., and F. Goudail, 2004: Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices. Optics Letters, 29, 2234–2236.

    Article  Google Scholar 

  • Mosino, J.F., O. Barbosa-Garcia, M.A. Meneses-Nava, L.A. Diaz-Torres, E. De la Rosa-Cruz, and J.T. Vega-Duran, 2002: Anisotropic media with orthogonal eigenpolarizations. J. Opt. A: Pure Appl. Optics, 4, 419–423.

    Article  Google Scholar 

  • Moxon, J.R.L., and A.R. Renshow, 1990: The simultaneous measurement of optical activity and circular dichroism in birefringent linearly dichroic crystal section: 1. Introduction and description of the method. J. Phys. Condens. Matter, 2, 6807–6836.

    Article  Google Scholar 

  • Mueller, H., 1948: The foundation of optics. J. Opt. Soc. Am., 38, 661.

    Google Scholar 

  • Muttiah, R.S., 2002: From Laboratory Spectroscopy to Remotely Sensed Spectra of Terrestrial Ecosystems. Dordrecht: Kluwer Academic.

    Google Scholar 

  • Nagirner, D.I., 1993: Constrains on matrices transforming Stokes vectors. Astron. Astrophys., 275, 318–324.

    Google Scholar 

  • Ossikovski, R., 2008: Interpretation of nondepolarizing Mueller matrices based on singularvalue decomposition. J. Opt. Soc. Am. A, 25, 473–482.

    Article  Google Scholar 

  • Ossikovski, R., A. De Martino, and Guyot, S., 2007: Forward and reverse product decompositions of depolarizing Mueller matrices. Opt. Letters, 32, 689–691.

    Article  Google Scholar 

  • Pancharatnam, S., 1955a: The propagation of light in absorbing biaxial crystals — I. Theoretical. Proc. Indian Acad. Sci. Sect. A, 42, 89–109.

    Google Scholar 

  • Pancharatnam, S., 1955b: The propagation of light in absorbing biaxial crystals — II. Experimental. Proc. Indian Acad. Sci. Sect. A, 42, 235–248.

    Google Scholar 

  • Parke III, N.G., 1948: Matrix optics. Ph.D. thesis, M.I.T.

    Google Scholar 

  • Parke III, N.G., 1949: Optical algebra. J. Math. Phys., 28, 131–139.

    Google Scholar 

  • Perrin, F., 1942: Polarization of light scattering by isotropic opalescent media. J. Chem. Phys., 10, 415–427

    Article  Google Scholar 

  • Potton, R.J., 2004: Reciprocity in optics. Rep. Progr. Phys., 67, 717–754.

    Article  Google Scholar 

  • Priezzhev, A.V., V.V. Tuchin, and L.P. Shubochkin, 1989: Laser Diagnostics in Biology and Medicine. Moscow: Nauka (in Russian).

    Google Scholar 

  • Quinby-Hunt, M.S., P.G. Hull, and A.J. Hunt, 2000: Polarized light scattering in the marine environment. In Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (M.I. Mishchenko et al., Eds). San Diego: Academic Press, pp. 525–554.

    Chapter  Google Scholar 

  • Rojas-Ochoa, L.F., D. Lacoste, R. Lenke, P. Schurtenberger and F. Scheffold, 2004: Depolarization of backscattered linearly polarized light. J. Opt. Soc. Am. A, 21, 1799–1804.

    Article  Google Scholar 

  • Rozenberg, G.V., 1973: Coherence, observability, and the photometric aspect of beam optics. Appl. Optics, 12, 2855–2863.

    Article  Google Scholar 

  • Rozenberg, G.V., 1977: Beam of light, Sov. Physics-Uspekhi, 121, 97–138.

    Google Scholar 

  • Savenkov, S.N., 2002a: Mueller-matrix description of depolarization in elastic light scattering. SPIE Proc., 4481, 180–187.

    Article  Google Scholar 

  • Savenkov, S.N., 2002b: Optimization and structuring of the instrument matrix for polarimetric measurements, Opt. Eng., 41, 965–972.

    Article  Google Scholar 

  • Savenkov, S.N., and K.E. Yushtin, 2000: New classes of objects in polarimetry including the isotropic depolarization. Radiotechnika, 116, 3–11 (in Russian).

    Google Scholar 

  • Savenkov, S.N., and K.E Yushtin, 2005: Peculiarities of depolarization of linearly polarized radiation by a layer of the anisotropic inhomogeneous medium. Ukr. J. Phys., 5, 235–239.

    Google Scholar 

  • Savenkov, S.N., O.I. Sydoruk, and R.S. Muttiah, 2005: The conditions for polarization elements to be dichroic and birefringent. J. Opt. Soc. Am. A, 22, 1447–1452

    Article  Google Scholar 

  • Savenkov, S.N., V.V. Marienko, E.A. Oberemok, and O.I. Sydoruk, 2006: Generalized matrix equivalence theorem for polarization theory. Phys. Rev. E, 74, 056607.

    Article  Google Scholar 

  • Savenkov, S.N., R.S. Muttiah, K.E. Yushtin, and S.A. Volchkov, 2007a: Mueller-matrix model of an inhomogeneous, linear, birefringent medium: single scattering case. J. Quant. Spectrosc. Radiat. Transfer, 106, 475–486.

    Article  Google Scholar 

  • Savenkov, S.N., O.I. Sydoruk, and R.S. Muttiah, 2007b: Eigenanalysis of dichroic, birefringent, and degenerate polarization elements: a Jones-calculus study. Appl. Optics, 46, 6700–6709.

    Article  Google Scholar 

  • Saxon, D.S., 1955: Tensor scattering matrix for electromagnetic fields. Phys. Rev., 100, 1771–1775.

    Article  Google Scholar 

  • Schonhoffer, A., and H.-G. Kuball, 1987: Symmetry properties of the Mueller matrix. Chem. Phys., 115, 159–167.

    Article  Google Scholar 

  • Sekera, Z., 1966: Scattering matrices and reciprocity relationships for various representations of the state of polarization. J. Opt. Soc. Am., 56, 1732–1740.

    Article  Google Scholar 

  • Shindo, Y., 1995: Applications of polarized modulator technique in polymer science. Opt. Eng., 34, 3369–3384.

    Article  Google Scholar 

  • Shurcliff, W.A., 1962: Polarized Light-Production and Use. Harvard: Harvard University Press.

    Google Scholar 

  • Soleillet, P., 1929: Sur les parametres caracterisant la polarisation partielle de la lumiere dans les phenomenes de fluorescence. Ann. Physique, 12, 23.

    Google Scholar 

  • Simon, R., 1982: The connection between Mueller and Jones matrices of polarization optics. Opt. Commun., 42, 293–297

    Article  Google Scholar 

  • Simon, R., 1987: Mueller matrices and depolarization criteria. J. Mod. Opt., 34, 569–575.

    Article  Google Scholar 

  • Sridhar, R., and R. Simon, 1994: Normal form for Mueller matrices in polarization optics. J. Mod. Optics, 41, 1903–1915.

    Article  Google Scholar 

  • Stokes, G.G., 1852: On the composition and resolution of streams of polarized light from different sources. Trans. Cambridge Philos. Soc., 9, 399–416.

    Google Scholar 

  • Sudha and A.V. Gopala Rao, 2001: Polarization elements: a group-theoretical study. J. Opt. Soc. Am. A, 18, 3130–3134.

    Article  Google Scholar 

  • Tang, S.T., and H.S. Kwok, 2001: 3×3 matrix for unitary optical systems. J. Opt. Soc. Am. A, 18, 2138–2145.

    Article  Google Scholar 

  • Tuchin, V.V. (Eds) 2002: Handbook of Optical Biomedical diagnostics. Bellingham: SPIE Press.

    Google Scholar 

  • Tuchin, V.V. (Eds) 2004: Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental and Material Science, Vols I and II. Boston: Kluwer Academic.

    Google Scholar 

  • Tudor, T., 2003: Generalized observables in polarization optics. J. Phys. A, 36, 9577–9590.

    Article  Google Scholar 

  • Tudor, T., 2006: Non-Hermitian polarizers: a biorthogonal analysis. J. Opt. Soc. Am. A, 23, 1513–1522.

    Article  Google Scholar 

  • Tudor, T., and A. Gheondea, 2007: Pauli algebraic forms of normal and nonnormal operators. J. Opt. Soc. Am. A, 24, 204–210.

    Article  Google Scholar 

  • Tyo, J.S., 2002: Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic errors, Appl. Opt., 41, 619–630.

    Article  Google Scholar 

  • Tyo, J.S., D.L. Goldstein, D.B. Chenault, and J.A. Shaw, 2006: Review of passive imaging polarimetry for remote sensing applications, Appl. Opt., 45, 5453–5469.

    Article  Google Scholar 

  • van Albada, M.P., M.B. van der Mark, and A. Lagendijk, 1988: Polarization effects in weak localization of light. J. Phys. D, 21, 28–31.

    Article  Google Scholar 

  • van de Hulst, H.C., 1957: Light Scattering by Small Particles. New York: Wiley.

    Google Scholar 

  • van der Mee, C.V.M., 1993: An eigenvalue criterion for matrices transforming Stokes parameters. J. Math. Phys., 34, 5072–5088.

    Article  Google Scholar 

  • van der Mee, C.V.M., and J.W. Hovenier, 1992: Structure of matrices transforming Stokes parameters. J. Math. Phys., 33, 3574–3584.

    Article  Google Scholar 

  • Vansteenkiste, N., P. Nignolo, and A. Aspect, 1993: Optical reversibility theorems for polarization: application to remote control of polarization. J. Opt. Soc. Am. A, 10, 2240–2245.

    Article  Google Scholar 

  • Volten, H., J.-P. Jalava, K. Lumme, J.F. de Haan, W. Vassen, and J.W. Hovenier, 1999: Laboratory measurements and T-matrix calculations of the scattering matrix of rutile particles in water. Appl. Optics, 38, 5232–5240.

    Article  Google Scholar 

  • Voss, K. J., and E. S. Fry, 1984: Measurement of the Mueller matrix for ocean water. Appl. Optics, 23, 4427–4436.

    Article  Google Scholar 

  • Whitney, C., 1971: Pauli-algebraic operators in polarization optics. J. Opt. Soc. Am., 61, 1207–1213.

    Article  Google Scholar 

  • Williams, M., 1986: Depolarization and cross polarization in ellipsometry of rough surfaces. Appl. Optics, 25, 3616–3622.

    Article  Google Scholar 

  • Xing, Z.-F., 1992: On the deterministic and nondeterministic Mueller matrix. J. Mod. Opt., 39, 461–484.

    Article  Google Scholar 

  • Xu, L., Ding J., and A.Y.S. Cheng, 2002: Scattering matrix of infrared radiation by ice finite circular cylinders. Appl. Optics, 41, 2333–2348.

    Article  Google Scholar 

  • Zubko, E., Y.G. Shkuratov, and G. Videen, 2004: Coherent backscattering effect for nonzero elements of Mueller matrix of discrete media at different illumination-observation geometries. J. Quant. Spectrosc. Radiat. Transfer, 89, 443–452

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Radiophysics, Kiev Taras Shevchenko University, Vladimirskaya Street 64, Kiev, 01033, Ukraine

    Sergey N. Savenkov

Authors
  1. Sergey N. Savenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Environmental Physics, University of Bremen, Bremen, Germany

    Alexander A. Kokhanovsky

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Praxis Publishing Ltd, Chichester, UK

About this chapter

Cite this chapter

Savenkov, S.N. (2009). Jones and Mueller matrices: structure, symmetry relations and information content. In: Kokhanovsky, A.A. (eds) Light Scattering Reviews 4. Springer Praxis Books. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74276-0_3

Download citation

Publish with us

Policies and ethics

Search

Navigation