Spectral problem for the Jones matrix in remote scattering
Рубрика:
| 1Savenkov, SM, 1Kolomiets, IS, 1Oberemok, Ye.A, 1Kurylenko, RO 1Faculty of Radio Physics, Electronics and Computer Systems, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine |
| Space Sci. & Technol. 2025, 31 ;(1):27-34 |
| https://doi.org/10.15407/knit2025.01.027 |
| Язык публикации: English |
Аннотация: The paper addresses the study of anisotropy in remote scattering based on the spectral problem. The spectral problem is formulated as the determining of eigenpolarizations and eigenvalues for the Jones matrix, which describes the optical anisotropy of the medium. Jones matrices of media with complex anisotropy (media characterized by several types of anisotropy) are considered in terms of a homogeneous (differential) approach. The essence of this approach is that the anisotropy of the class of media under consideration does not depend on the thickness of this medium. An analysis of the Jones matrices for arbitrary homogeneous media (media characterized by all four main types of optical anisotropy: linear, circular, phase, and amplitude anisotropy) and media characterized by two types of anisotropy as a special case has been performed.
The main tool for such an analysis was the inhomogeneity parameter of the medium, which allows for characterizing the latter as a medium with orthogonal or non-orthogonal eigenpolarizations. The study reveals the peculiarities of complex anisotropy types (elliptical birefringence and Hermitian dichroism, improper dichroism, non-Hermitian dichroism, and degenerate anisotropy) based on the inhomogeneity parameter. A geometric interpretation of eigenpolarizations using the inhomogeneity parameter is demonstrated. The conditions for the anisotropy parameters under which the above-mentioned complex types of anisotropy are realized in the studied classes of medium were calculated. The research was motivated by the fundamental results of van de Hulst and Hovenier, which formed the basis for analyzing the inner structure of the Jones and Mueller matrices. The results obtained contribute to a deeper understanding of polarization phenomena in electromagnetic scattering and provide a basis for future research in polarization diagnostics and remote sensing.
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| Ключевые слова: amplitude linear and circular anisotropy, Jones matrix, Mueller matrix, phase linear and circular anisotropy, spectral problems |
References:
1. Azzam R. M. A., Bashara N. M. (1988). Ellipsometry and Polarized Light. North Holland: Elsevier, 558 p.
2. Bohren C. F., Huffman D. R. (1983). Absorption and Scattering of Light by Small Particles. New York: Wiley, 530 p.
https://doi.org/10.1002/9783527618156
3. Chowdhary J., Cairns B., Waquet F., Knobelspiesse K., Ottaviani M., Redemann J., Travis L., Mishchenko M. (2012). Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water‐leaving radiance: Analyses of RSP data acquired during the Milagro campaign. Remote Sens. Environ., 118, 284-308.
https://doi.org/10.1016/j.rse.2011.11.003
2. Bohren C. F., Huffman D. R. (1983). Absorption and Scattering of Light by Small Particles. New York: Wiley, 530 p.
https://doi.org/10.1002/9783527618156
3. Chowdhary J., Cairns B., Waquet F., Knobelspiesse K., Ottaviani M., Redemann J., Travis L., Mishchenko M. (2012). Sensitivity of multiangle, multispectral polarimetric remote sensing over open oceans to water‐leaving radiance: Analyses of RSP data acquired during the Milagro campaign. Remote Sens. Environ., 118, 284-308.
https://doi.org/10.1016/j.rse.2011.11.003
4. Cloude S. R., Pottier E. (1997). An entropy based classification scheme for land applications of polarimetric SAR. IEEE Trans. Geosci. Remote Sens., 35, No. 1, 68-78.
https://doi.org/10.1109/36.551935
https://doi.org/10.1109/36.551935
5. Dubovik O., Li Z., Mishchenko M. I., Tanre D., Karol Y., Bojkov B., et al. (2019). Polarimetric remote sensing of atmospheric aerosols: Instruments, methodologies, results, and perspectives. J. Quant. Spectrosc. and Radiat. Тransfer, 224, 474-511.
6. Gastellu‐Etchegorry J.-P., Lauret N., Yin T., Landier L., Kallel A., Malenovsky Z. (2017). Dart: Recent advances in remote sensing data modeling with atmosphere, polarization, and chlorophyll fluorescence. IEEE J. Selected Topics Appl. Earth Observ. and Remote Sens., 10, No. 6, 2640-2649.
https://doi.org/10.1109/JSTARS.2017.2685528
https://doi.org/10.1109/JSTARS.2017.2685528
7. Gil J. J., Ossikovski R. (2022). Polarized Light and the Mueller Matrix Approach. New York: CRC Press, 516 p.
https://doi.org/10.1201/9780367815578
https://doi.org/10.1201/9780367815578
8. Hovenier J.W. (1994) Structure of a general pure Mueller matrix. Appl. Opt.., 33, No. 36, 8318-8324.
https://doi.org/10.1364/AO.33.008318
https://doi.org/10.1364/AO.33.008318
9. Hovenier J. W., Mackowski D. W. (1998). Symmetry relations for forward and backward scattering by randomly oriented particles. J. Quant. Spectrosc. Radiat. Тransfer, 60, No. 3, 483-492.
https://doi.org/10.1016/S0022-4073(98)00022-3
https://doi.org/10.1016/S0022-4073(98)00022-3
10. Hovenier J. W., Mee C., Domke H. (2004). Transfer of Polarized Light in Planetary Atmospheres. Dordrecht, Netherlands: Kluwer Academic Publsihers, 258 p.
https://doi.org/10.1007/978-1-4020-2856-4
11. Hu Ch.-R., Kattawar G. W., Parkin M. E., Herb P. (1987). Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer. Appl. Opt., 26, No. 19, 4159-4173.
https://doi.org/10.1364/AO.26.004159
12. Hulst H. C. (1981). Light Scattering by Small Particles. New York: Dover Publications, 470 p.
13. Hurwitz H., Jones R.C. (1941). A new calculus for the treatment of optical systems. II. Proof of three general equivalence theorems. J. Opt. Soc. Amer., 31, 493-499.
https://doi.org/10.1364/JOSA.31.000493
https://doi.org/10.1007/978-1-4020-2856-4
11. Hu Ch.-R., Kattawar G. W., Parkin M. E., Herb P. (1987). Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer. Appl. Opt., 26, No. 19, 4159-4173.
https://doi.org/10.1364/AO.26.004159
12. Hulst H. C. (1981). Light Scattering by Small Particles. New York: Dover Publications, 470 p.
13. Hurwitz H., Jones R.C. (1941). A new calculus for the treatment of optical systems. II. Proof of three general equivalence theorems. J. Opt. Soc. Amer., 31, 493-499.
https://doi.org/10.1364/JOSA.31.000493
14. Jones R.C. (1948). A new calculus for the treatment of optical systems. VII. Properties of the N-matrices. J. Opt. Soc. Amer., 38, 671-685.
https://doi.org/10.1364/JOSA.38.000671
https://doi.org/10.1364/JOSA.38.000671
15. Lu S.-Y., Chipman R.A. (1994). Homogeneous and inhomogeneous Jones matrices. J. Opt. Soc. Amer. A, 11, No. 2, 766-773.
https://doi.org/10.1364/JOSAA.11.000766
https://doi.org/10.1364/JOSAA.11.000766
16. Maghsoudi Y., Collins M., Leckie D. G. (2012). Polarimetric classification of Boreal forest using nonparametric feature selection and multiple classifiers. Int. J. Appl. Earth Observ. Geoinf., 19, 139-150.
https://doi.org/10.1016/j.jag.2012.04.015
17. Munoz A.G. (2018). On mapping exoplanet atmospheres with high dispersion spectro-polarimetry: Some model predictions. Astrophys. J., 854, No. 2, 108.
https://doi.org/10.3847/1538-4357/aaaa1f
18. Ottaviani M., Chowdhary J., Cairns B. (2019). Remote sensing of the ocean surface refractive index via short wave infrared polarimetry. Remote Sensing Environ., 221, 14-23.
https://doi.org/10.1016/j.rse.2018.10.016
https://doi.org/10.1016/j.jag.2012.04.015
17. Munoz A.G. (2018). On mapping exoplanet atmospheres with high dispersion spectro-polarimetry: Some model predictions. Astrophys. J., 854, No. 2, 108.
https://doi.org/10.3847/1538-4357/aaaa1f
18. Ottaviani M., Chowdhary J., Cairns B. (2019). Remote sensing of the ocean surface refractive index via short wave infrared polarimetry. Remote Sensing Environ., 221, 14-23.
https://doi.org/10.1016/j.rse.2018.10.016
19. Savenkov S. (2010). Eigenview on Jones matrix models of homogeneous anisotropic media. EPJ Web of Conf., 5, 04007.
https://doi.org/10.1051/epjconf/20100504007
https://doi.org/10.1051/epjconf/20100504007
20. Savenkov S. N., Marienko V. V., Oberemok E. A., Sydoruk O. (2006). Generalized matrix equivalence theorem for polarization theory. Phys. Rev. E, 74, No. 5, 056607.
https://doi.org/10.1103/PhysRevE.74.056607
https://doi.org/10.1103/PhysRevE.74.056607
21. Savenkov S. N., Sydoruk O. I., Muttiah R. S. (2005). Conditions for polarization elements to be dichroic and birefringent. J. Opt. Soc. Amer. A, 22, No. 7, 1447-1452.
https://doi.org/10.1364/JOSAA.22.001447
https://doi.org/10.1364/JOSAA.22.001447
22. Savenkov S. N., Sydoruk O. I., Muttiah R. S. (2007). Eigenanalysis of dichroic, birefringent, and degenerate polarization elements: a Jones-calculus study. Appl. Opt., 46, No. 27, 6700-6709.
https://doi.org/10.1364/AO.46.006700
https://doi.org/10.1364/AO.46.006700
23. Shurcliff W. A. (1962). Polarized light-production and use. Harvard: Harvard University Press, 218 p.
https://doi.org/10.4159/harvard.9780674424135
24. Sun Z., Wu D., Lv Y. (2022). Optical properties of snow surfaces: Multiangular photometric and polarimetric hyperspectral measurements. IEEE Trans. Geosci. and Remote Sens., 60, 1-16.
https://doi.org/10.1109/TGRS.2022.3231215
doi:%2010.1109/TGRS.2021.3078170
25. Sun Z., Zhao Y. (2011). The effects of grain size on Bidirectional polarized reflectance factor measurements of snow. J. Quant. Spectrosc. Radiat. Тransfer, 112, No. 14, 2372-2383.
https://doi.org/10.1016/j.jqsrt.2011.05.011
26. Wang H., Wang M., Zhao M., Yang L. (2021). Shadow Has Little Effect on the Spectral Response of Urban Surface Polarized Reflectance. IEEE Geosci. and Remote Sens. Lett., 18, No. 9, 1535-1539.
https://doi.org/10.1109/LGRS.2020.3005805
27. Xie D., Cheng T., Wu Y., Fu H., Zhong R., Yu J. (2017). Polarized reflectances of urban areas: Analysis and models. Remote Sens. Environ., 193, 29-37.
https://doi.org/10.1016/j.rse.2017.02.026
28. Yang B., Zhao H., Chen W. (2019). Modeling polarized reflectance of snow and ice surface using polder measurements. J.Quant. Spectrosc. Radiat. Тransfer, 236, 106578, 248.
https://doi.org/10.1016/j.jqsrt.2019.106578
https://doi.org/10.4159/harvard.9780674424135
24. Sun Z., Wu D., Lv Y. (2022). Optical properties of snow surfaces: Multiangular photometric and polarimetric hyperspectral measurements. IEEE Trans. Geosci. and Remote Sens., 60, 1-16.
https://doi.org/10.1109/TGRS.2022.3231215
doi:%2010.1109/TGRS.2021.3078170
25. Sun Z., Zhao Y. (2011). The effects of grain size on Bidirectional polarized reflectance factor measurements of snow. J. Quant. Spectrosc. Radiat. Тransfer, 112, No. 14, 2372-2383.
https://doi.org/10.1016/j.jqsrt.2011.05.011
26. Wang H., Wang M., Zhao M., Yang L. (2021). Shadow Has Little Effect on the Spectral Response of Urban Surface Polarized Reflectance. IEEE Geosci. and Remote Sens. Lett., 18, No. 9, 1535-1539.
https://doi.org/10.1109/LGRS.2020.3005805
27. Xie D., Cheng T., Wu Y., Fu H., Zhong R., Yu J. (2017). Polarized reflectances of urban areas: Analysis and models. Remote Sens. Environ., 193, 29-37.
https://doi.org/10.1016/j.rse.2017.02.026
28. Yang B., Zhao H., Chen W. (2019). Modeling polarized reflectance of snow and ice surface using polder measurements. J.Quant. Spectrosc. Radiat. Тransfer, 236, 106578, 248.
https://doi.org/10.1016/j.jqsrt.2019.106578