SYNTHETIC MATRIX
To facilitate the use of the experimental data for multiple scattering calculations we construct the so-called Synthetic Scattering Matrix based on our measurements. The Synthetic Scattering Matrix is defined in the full range from 0 to 180 degrees. For the extension of the phase function, we have followed the procedure described by Liu et al. 2003, that is based on the assumption that the diffraction forward scattering peak for small randomly oriented particles with moderate aspect ratios mainly depends on the size of the particles and is largely independent of their shapes and refractive indices. For the relative scattering matrix elements Fij/F11 a polynomial extrapolation is used at both forward and backward scattering directions. Values at exact forward and backward scattering were determined so that they satisfy the conditions given by Hovenier et al., 2004, Section 2.7. In addition, we make use of the fact that for each element of the scattering matrix the right-hand derivative at 0 degrees scattering angle and the left-hand derivative at 180 degrees must both vanish as described by Hovenier and Guirado (2014). The resulting Synthetic Scattering Matrix satisfies the Cloude (coherency matrix) test at all scattering angles. For the Synthetic Scattering Matrix F11_au is normalized so that its average over all directions equals unity.
References:
- Van de Hulst, H.C., 1957. Light scattering by small particles, John Wiley, New York.
- Hovenier, J.W., van der Mee, C.V.M., Domke, H., 2004. Transfer of polarized light in planetary atmospheres: basic concepts and practical methods. Kluwer. Springer. Dordrecht. Berlin.
- Hovenier, J.W., Guirado, D. Zero slopes of the scattering function and scattering matrix for strict forward and backward scattering by mirror symmetric collections of randomly oriented particles. J. Quant. Spectrosc. Radiat. Trans. 133, 596-602, 2014.
- Liu, L. Mishchenko, M. I., Hovenier, J. W., Volten, H., Munoz, O. Scattering matrix of quartz aerosols: comparison and synthesis of laboratory and Lorenz-Mie results. J. Quant. Spectrosc. Radiat. Trans. 79-80, 911-920, 2003.