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2019-01-23
On the Convergence of Numerical Computations for Both Exact and Approximate Solutions for Electromagnetic Scattering by Nonspherical Dielectric Particles (Invited Review)
By
Progress In Electromagnetics Research, Vol. 164, 27-61, 2019
Abstract
We summarize the size parameter range of the applicability of four lightscattering computational methods for nonspheric dielectric particles. These methods include two exact methods - the extended boundary condition method (EBCM) and the invariant imbedding T-matrix method (II-TM) and two approximate approaches - the physical-geometric optics method (PGOM) and the improved geometric optics method (IGOM). For spheroids, the single-scattering properties computed by EBCM and II-TM agree for size parameters up to 150, and the comparison gives us confidence in using IITM as a benchmark for size parameters up to 150 for other geometries (e.g., hexagonal columns) because the applicability of II-TM with respect to particle shape is generic, as demonstrated in our previous studies involving a complex aggregate. This study demonstrates the convergence of the exact II-TM and approximate PGOM solutions for the complete set of single-scattering properties of a nonspherical shape other than spheroids and circular cylinders with particle sizes of ~48λ, specifically a hexagonal column with a size parameter of length as kL=300, where k=2π/λ and L is the column length. IGOM is also quite accurate except near the exact 180º backscattering direction. This study demonstrates that a synergetic combination of the numerically-exact II-TM and the approximate PGOM can seamlessly cover the entire size parameter range of practical interest. To demonstrate the applicability of the approach, we compute the optical properties of dust particles with a downstream application to the retrieval of dust aerosol optical thickness and effective particle size from polarimetric observations.
Citation
Ping Yang Jiachen Ding Richard Lee Panetta Kuo-Nan Liou George Kattawar Michael I. Mishchenko , "On the Convergence of Numerical Computations for Both Exact and Approximate Solutions for Electromagnetic Scattering by Nonspherical Dielectric Particles (Invited Review)," Progress In Electromagnetics Research, Vol. 164, 27-61, 2019.
doi:10.2528/PIER18112810
http://www.jpier.org/PIER/pier.php?paper=18112810
References

1. Mishchenko, M. I., J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles, Academic Press, 2000.

2. Baran, A. J., "A review of the light scattering properties of cirrus," J. Quant. Spectrosc. Radiat. Transf., Vol. 110, No. 14–16, 1239-1260, Sep. 2009.
doi:10.1016/j.jqsrt.2009.02.026

3. Baran, A. J., "From the single-scattering properties of ice crystals to climate prediction: A way forward," Atmos. Res., Vol. 112, 45-69, Aug. 2012.
doi:10.1016/j.atmosres.2012.04.010

4. Baran, A. J., P. Yang, and S. Havemann, "Calculation of the single-scattering properties of randomly oriented hexagonal ice columns: A comparison of the T-matrix and the finite-difference time-domain methods," Appl. Opt., Vol. 40, No. 24, 4376, Aug. 2001.
doi:10.1364/AO.40.004376

5. Liou, K. N. and P. Yang, Light Scattering by Ice Crystals: Fundamentals and Applications, Cambridge University Press, 2016.
doi:10.1017/CBO9781139030052

6. Lu, J. Q., P. Yang, and X.-H. Hu, "Simulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method," J. Biomed. Opt., Vol. 10, No. 2, 024022, 2005.
doi:10.1117/1.1897397

7. Kolesnikova, I. V., S. V. Potapov, M. A. Yurkin, A. G. Hoekstra, V. P. Maltsev, and K. A. Semyanov, "Determination of volume, shape and refractive index of individual blood platelets," J. Quant. Spectrosc. Radiat. Transf., Vol. 102, No. 1, 37-45, Nov. 2006.
doi:10.1016/j.jqsrt.2006.02.050

8. Bi, L. and P. Yang, "Modeling of light scattering by biconcave and deformed red blood cells with the invariant imbedding T-matrix method," J. Biomed. Opt., Vol. 18, No. 5, 055001, May 2013.
doi:10.1117/1.JBO.18.5.055001

9. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag., Vol. 14, No. 3, 302-307, May 1966.
doi:10.1109/TAP.1966.1138693

10. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech House, Boston, MA, 2005.

11. Yang, P. and K. N. Liou, "Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space," J. Opt. Soc. Am. A, Vol. 13, No. 10, 2072-2085, Oct. 1996.
doi:10.1364/JOSAA.13.002072

12. Yang, P., K. N. Liou, M. I. Mishchenko, and B.-C. Gao, "Efficient finite-difference time-domain scheme for light scattering by dielectric particles: Application to aerosols," Appl. Opt., Vol. 39, No. 21, 3727-3737, Jul. 2000.
doi:10.1364/AO.39.003727

13. Sun, W., N. G. Loeb, S. Tanev, and G. Videen, "Finite-difference time-domain solution of light scattering by an infinite dielectric column immersed in an absorbing medium," Appl. Opt., Vol. 44, No. 27, 1977-1983, Sep. 2005.
doi:10.1364/AO.44.001977

14. Ishimoto, H., "Radar backscattering computations for fractal-shaped snowflakes," J. Meteorol. Soc. Japan Ser. II, Vol. 86, No. 3, 459-469, 2008.
doi:10.2151/jmsj.86.459

15. Liu, Q. H., "The PSTD algorithm: A time-domain method requiring only two cells per wavelength," Microw. Opt. Technol. Lett., Vol. 15, No. 3, 158-165, Jun. 1997.
doi:10.1002/(SICI)1098-2760(19970620)15:3<158::AID-MOP11>3.0.CO;2-3

16. Liu, Q. H., "The pseudospectral time-domain (PSTD) algorithm for acoustic waves in absorptive media," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, Vol. 45, No. 4, 1044-1055, Jul. 1998.

17. Purcell, E. M. and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J., Vol. 186, 705-714, Dec. 1973.
doi:10.1086/152538

18. Draine, B. T. and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A, Vol. 11, No. 4, 1491-1499, Apr. 1994.
doi:10.1364/JOSAA.11.001491

19. Yurkin, M. A. and A. G. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spectrosc. Radiat. Transf., Vol. 106, No. 1–3, 558-589, Jul. 2007.

20. Yurkin, M. A., V. P. Maltsev, and A. G. Hoekstra, "The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength," J. Quant. Spectrosc. Radiat. Transf., Vol. 106, No. 1–3, 546-557, Jul. 2007.

21. Liu, C., R. Lee Panetta, and P. Yang, "Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200," J. Quant. Spectrosc. Radiat. Transf., Vol. 113, No. 13, 1728-1740, Sep. 2012.
doi:10.1016/j.jqsrt.2012.04.021

22. Waterman, P. C., "Matrix formulation of electromagnetic scattering," Proc. IEEE, Vol. 53, No. 8, 805-812, 1965.
doi:10.1109/PROC.1965.4058

23. Waterman, P. C., "Symmetry, unitarity, and geometry in electromagnetic scattering," Phys. Rev. D, Vol. 3, No. 4, 825-839, Feb. 1971.
doi:10.1103/PhysRevD.3.825

24. Mishchenko, M. I., "Light scattering by randomly oriented axially symmetric particles," J. Opt. Soc. Am. A, Vol. 8, No. 6, 871-882, Jun. 1991.
doi:10.1364/JOSAA.8.000871

25. Barber, P., "Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies," Appl. Opt., Vol. 14, No. 12, 2864-2872, Dec. 1975.
doi:10.1364/AO.14.002864

26. Mishchenko, M. I. and L. D. Travis, "Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation," Appl. Opt., Vol. 33, No. 30, 7206-7225, Oct. 1994.
doi:10.1364/AO.33.007206

27. Mishchenko, M. I., L. D. Travis, and D. W. Mackowski, "T-matrix computations of light scattering by nonspherical particles: A review," J. Quant. Spectrosc. Radiat. Transf., Vol. 55, No. 5, 535-575, May 1996.
doi:10.1016/0022-4073(96)00002-7

28. Tsang, L., J. A. Kong, K.-H. Ding, and C. O. Ao, Scattring of Electromagnetic Waves: Theories and Applications, Wiley, New York, 2000.
doi:10.1002/0471224286

29. Mackowski, D. W. and M. I. Mishchenko, "Calculation of the T matrix and the scattering matrix for ensembles of spheres," J. Opt. Soc. Am. A, Vol. 13, No. 11, 2266-2278, Nov. 1996.
doi:10.1364/JOSAA.13.002266

30. Mackowski, D. W. and M. I. Mishchenko, "A multiple sphere T-matrix Fortran code for use on parallel computer clusters," J. Quant. Spectrosc. Radiat. Transf., Vol. 112, No. 13, 2182-2192, Sep. 2011.
doi:10.1016/j.jqsrt.2011.02.019

31. Mackowski, D. W., "A general superposition solution for electromagnetic scattering by multiple spherical domains of optically active media," J. Quant. Spectrosc. Radiat. Transf., Vol. 133, 264-270, Jan. 2014.
doi:10.1016/j.jqsrt.2013.08.012

32. Johnson, B. R., "Invariant imbedding T matrix approach to electromagnetic scattering," Appl. Opt., Vol. 27, No. 23, 4861-4873, Dec. 1988.
doi:10.1364/AO.27.004861

33. Bi, L., P. Yang, G. W. Kattawar, and M. I. Mishchenko, "Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles," J. Quant. Spectrosc. Radiat. Transf., Vol. 116, 169-183, Feb. 2013.
doi:10.1016/j.jqsrt.2012.11.014

34. Bi, L., P. Yang, G. W. Kattawar, and M. I. Mishchenko, "A numerical combination of extended boundary condition method and invariant imbedding method applied to light scattering by large spheroids and cylinders," J. Quant. Spectrosc. Radiat. Transf., Vol. 123, No. 4, 17-22, Jul. 2013.

35. Bi, L. and P. Yang, "Accurate simulation of the optical properties of atmospheric ice crystals with the invariant imbedding T-matrix method," J. Quant. Spectrosc. Radiat. Transf., Vol. 138, 17-35, May 2014.
doi:10.1016/j.jqsrt.2014.01.013

36. Doicu, A., T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles, Springer, Berlin, 2006.
doi:10.1007/978-3-540-33697-6

37. Mishchenko, M. I. and L. D. Travis, "Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers," J. Quant. Spectrosc. Radiat. Transf., Vol. 60, No. 3, 309-324, Sep. 1998.
doi:10.1016/S0022-4073(98)00008-9

38. Mishchenko, M. I. and A. Macke, "How big should hexagonal ice crystals be to produce halos?," Appl. Opt., Vol. 38, No. 9, 1626-1629, Mar. 1999.
doi:10.1364/AO.38.001626

39. Van de Hulst, H. C., Light Scattering by Small Particles, Wiley, New York, 1957.

40. Wendling, P., R. Wendling, and H. K. Weickmann, "Scattering of solar radiation by hexagonal ice crystals," Appl. Opt., Vol. 18, No. 15, 2663-2671, Aug. 1979.
doi:10.1364/AO.18.002663

41. Cai, Q. and K. N. Liou, "Polarized light scattering by hexagonal ice crystals: Theory," Appl. Opt., Vol. 21, No. 19, 3569-3580, Oct. 1982.
doi:10.1364/AO.21.003569

42. Takano, Y. and K.-N. N. Liou, "Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals," J. Atmos. Sci., Vol. 46, No. 1, 3-19, Jan. 1989.
doi:10.1175/1520-0469(1989)046<0003:SRTICC>2.0.CO;2

43. Macke, A., "Scattering of light by polyhedral ice crystals," Appl. Opt., Vol. 32, No. 15, 2780-2788, May 1993.
doi:10.1364/AO.32.002780

44. Macke, A., J. Mueller, and E. Raschke, "Single scattering properties of atmospheric ice crystals," J. Atmos. Sci., Vol. 53, No. 19, 2813-2825, Oct. 1996.
doi:10.1175/1520-0469(1996)053<2813:SSPOAI>2.0.CO;2

45. Lock, J. A., "Ray scattering by an arbitrarily oriented spheroid, I: Diffraction and specular reflection," Appl. Opt., Vol. 35, No. 3, 500-514, Jan. 1996.
doi:10.1364/AO.35.000500

46. Lock, J. A., "Ray scattering by an arbitrarily oriented spheroid, II: Transmission and crosspolarization effects," Appl. Opt., Vol. 35, No. 3, 515-531, Jan. 1996.
doi:10.1364/AO.35.000515

47. Yang, P. and K. N. Liou, "Geometric-optics — integral-equation method for light scattering by nonspherical ice crystals," Appl. Opt., Vol. 35, No. 33, 6568-6584, Nov. 1996.
doi:10.1364/AO.35.006568

48. Lorenz, L., "Lysbevaegelsen i og uden for en af plane Lysbolger belyst Kugle," Det Kongelige Danske Videnskabernes Selskabs Skrifter, Vol. 6, No. 6, 1-62, 1890.

49. Mie, G., "Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen," Ann. Phys., Vol. 330, No. 3, 377-445, 1908.
doi:10.1002/andp.19083300302

50. Yang, P. and K. N. Liou, "Light scattering by hexagonal ice crystals: Solutions by a ray-by-ray integration algorithm," J. Opt. Soc. Am. A, Vol. 14, No. 9, 2278-2289, Sep. 1997.
doi:10.1364/JOSAA.14.002278

51. Muinonen, K., "Scattering of light by crystals: A modified Kirchhoff approximation," Appl. Opt., Vol. 28, No. 15, 3044-3050, Aug. 1989.
doi:10.1364/AO.28.003044

52. Jackson, J. D., Classical Electrodynamics, 2nd Ed., Wiley, Inc., New York, 1975.

53. Bi, L., P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, "Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method," J. Quant. Spectrosc. Radiat. Transf., Vol. 112, No. 9, 1492-1508, Jun. 2011.

54. Sun, B., P. Yang, G. W. Kattawar, and X. Zhang, "Physical-geometric optics method for large size faceted particles," Opt. Express, Vol. 25, No. 20, 24044-24060, Oct. 2017.

55. Van Diedenhoven, B., et al., "Remote sensing of ice crystal asymmetry parameter using multidirectional polarization measurements — Part 1: Methodology and evaluation with simulated measurements," Atmos. Meas. Tech., Vol. 5, No. 10, 2361-2374, Oct. 2012.

56. Van Diedenhoven, B., B. Cairns, A. M. Fridlind, A. S. Ackerman, and T. J. Garrett, "Remote sensing of ice crystal asymmetry parameter using multi-directional polarization measurements — Part 2: Application to the research scanning polarimeter," Atmos. Chem. Phys., Vol. 13, No. 6, 3125-3203, Mar. 2013.

57. Van Diedenhoven, B., A. S. Ackerman, B. Cairns, and A. M. Fridlind, "A flexible parameterization for shortwave optical properties of ice crystals," J. Atmos. Sci., Vol. 71, No. 5, 1763-1782, May 2014.

58. Bohren, C. F. and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, New York, 1983.

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

60. Quirantes, A., "A T-matrix method and computer code for randomly oriented, axially symmetric coated scatterers," J. Quant. Spectrosc. Radiat. Transf., Vol. 92, No. 3, 373-381, May 2005.

61. Havemann, S. and A. J. Baran, "Extension of T-matrix to scattering of electromagnetic plane waves by non-axisymmetric dielectric particles: Application to hexagonal ice cylinders," J. Quant. Spectrosc. Radiat. Transf., Vol. 70, No. 2, 139-158, Jul. 2001.

62. Kahnert, M., "The T-matrix code Tsym for homogeneous dielectric particles with finite symmetries," J. Quant. Spectrosc. Radiat. Transf., Vol. 123, 62-78, Jul. 2013.

63. Kahnert, M., "T-matrix computations for particles with high-order finite symmetries," J. Quant. Spectrosc. Radiat. Transf., Vol. 123, 79-91, Jul. 2013.

64. Tai, C. T., Dyadic Green Functions in Electromagnetic Theory, 2nd Ed., IEEE Press, New York, 1994.

65. Hovenier, J. W., C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres, Springer, Dordrecht, 2004.

66. Mishchenko, M. I. and M. A. Yurkin, "On the concept of random orientation in far-field electromagnetic scattering by nonspherical particles," Opt. Lett., Vol. 42, No. 3, 494-497, Feb. 2017.

67. Hu, C. R., G. W. Kattawar, M. E. Parkin, and P. Herb, "Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer," Appl. Opt., Vol. 26, No. 19, 4159-4173, Oct. 1987.

68. Tsang, L., J. A. Kong, and R. T. Shin, "Theory of Microwave Remote Sensing," Wiley-Interscience, 1985.

69. Ren, K. F., F. Onofri, C. Roze, and T. Girasole, "Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle," Opt. Lett., Vol. 36, No. 3, 370-372, Feb. 2011.

70. Sun, B., G. W. Kattawar, P. Yang, and K. F. Ren, "Rigorous 3-D vectorial complex ray model applied to light scattering by an arbitrary spheroid," J. Quant. Spectrosc. Radiat. Transf., Vol. 179, 1-10, Aug. 2016.

71. Morse, P. and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York, 1953.

72. Foley, J. D., A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics: Principles and Practice, Addison-Wesley, Boston, MA, 1997.

73. Cauchy, A., "Memoire sur la rectification des courbes et la quadrature des surfaces courbes," Mem. Acad. Sci. Paris, 22, 3ff, 1950.

74. Vouk, V., "Projected area of convex bodies," Nature, Vol. 162, No. 4113, 330-331, Aug. 1948.

75. Xie, Y., P. Yang, G. W. Kattawar, B. A. Baum, and Y. Hu, "Simulation of the optical properties of plate aggregates for application to the remote sensing of cirrus clouds," Appl. Opt., Vol. 50, No. 8, 1065-1081, Mar. 2011.

76. Chang, P. C. Y., J. G. Walker, and K. I. Hopcraft, "Ray tracing in absorbing media," J. Quant. Spectrosc. Radiat. Transf., Vol. 96, No. 3–4, 327-341, Dec. 2005.

77. Brillouin, L., "The scattering cross section of spheres for electromagnetic waves," J. Appl. Phys., Vol. 20, No. 11, 1110-1125, Nov. 1949.

78. Sun, B., P. Yang, G. W. Kattawar, and M. I. Mishchenko, "On Babinet's principle and diffraction associated with an arbitrary particle," Opt. Lett., Vol. 42, No. 23, 5026-5029, Dec. 2017.

79. Ishimoto, H., K. Masuda, Y. Mano, N. Orikasa, and A. Uchiyama, "Irregularly shaped ice aggregates in optical modeling of convectively generated ice clouds," J. Quant. Spectrosc. Radiat. Transf., Vol. 113, No. 8, 632-643, May 2012.

80. Yang, P., et al., "Spectrally consistent scattering, absorption, and polarization properties of atmospheric ice crystals at wavelengths from 0.2 to 100 μm," J. Atmos. Sci., Vol. 70, No. 1, 330-347, Jan. 2013.

81. Bi, L., P. Yang, G. W. Kattawar, and R. Kahn, "Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra," Appl. Opt., Vol. 49, No. 3, 334-342, Jan. 2010.

82. Yang, P. and K. N. Liou, "Single-scattering properties of complex ice crystals in terrestrial atmosphere," Contr. Atmos. Phys., Vol. 71, No. 2, 223-248, 1998.

83. Volten, H., O. Munoz, J. W. Hovenier, and L. B. F. M. Waters, "An update of the Amsterdam light scattering database," J. Quant. Spectrosc. Radiat. Transf., Vol. 100, No. 1–3, 437-443, Jul. 2006.

84. Nakajima, T., M. Tanaka, M. Yamano, M. Shiobara, K. Arao, and Y. Nakanishi, "Aerosol optical characteristics in the yellow sand events observed in May 1982 in Nagasaki: Part 2, models," J. Meteorol. Soc. Japan Ser. II, Vol. 67, No. 2, 279-291, 1989.

85. Okada, K., A. Kobayashi, Y. Iwasaka, H. Naruse, T. Tanaka, and O. Nemoto, "Features of individual Asian dust-storm particles collected at Nagoya, Japan," J. Meteorol. Soc. Japan, Vol. 65, No. 3, 515-521, 1987.

86. Reid, E. A., "Characterization of African dust transported to Puerto Rico by individual particle and size segregated bulk analysis," J. Geophys. Res., Vol. 108, No. D19, 8591, Oct. 2003.

87. Hill, S. C., A. C. Hill, and P. W. Barber, "Light scattering by size/shape distributions of soil particles and spheroids," Appl. Opt., Vol. 23, No. 7, 1025-1031, Apr. 1984.

88. Mishchenko, M. I., A. A. Lacis, B. E. Carlson, and L. D. Travis, "Nonsphericity of dust like tropospheric aerosols: Implications for aerosol remote sensing and climate modeling," Geophys. Res. Lett., Vol. 22, No. 9, 1077-1080, May 1995.

89. Mishchenko, M. I., L. D. Travis, R. A. Kahn, and R. A. West, "Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids," J. Geophys. Res. Atmos., Vol. 102, No. D14, 16831-16847, Jul. 1997.

90. Dubovik, O., et al., "Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust," J. Geophys. Res. Atmos., Vol. 111, No. D11, D11208, Jun. 2006.

91. Deschamps, P. Y., et al., "The POLDER mission: Instrument characteristics and scientific objectives," IEEE Trans. Geosci. Remote Sens., Vol. 32, No. 3, 598-615, May 1994.

92. Labonnote, L. C., G. Brogniez, J. C. Buriez, M. Doutriaux-Boucher, J. F. Gayet, and A. Macke, "Polarized light scattering by inhomogeneous hexagonal monocrystals: Validation with ADEOSPOLDER measurements," J. Geophys. Res., Vol. 106, No. D11, 12139-12153, Jun. 2001.

93. Huang, X., P. Yang, G. Kattawar, and K. N. Liou, "Effect of mineral dust aerosol aspect ratio on polarized reflectance," J. Quant. Spectrosc. Radiat. Transf., Vol. 151, 97-109, Jan. 2015.

94. Cox, C. and W. Munk, "Measurement of the roughness of the sea surface from photographs of the sun's glitter," J. Opt. Soc. Am., Vol. 44, No. 11, 838-850, Nov. 1954.

95. Stegmann, P. G. and P. Yang, "A regional, size-dependent, and causal effective medium model for Asian and Saharan mineral dust refractive index spectra," J. Aerosol. Sci., Vol. 114, 327-341, Dec. 2017.

96. Jarvis, R. A., "On the identification of the convex hull of a finite set of points in the plane," Inf. Process. Lett., Vol. 2, No. 1, 18-21, Mar. 1973.

97. ElGindy, H., H. Everett, and G. Toussaint, "Slicing an ear using prune-and-search," Pattern Recognit. Lett., Vol. 14, No. 9, 719-722, Sep. 1993.