Light Scattering by Feldspar Particles: Modeling Laboratory Measurements Evgenij Zubko1,2, Karri Muinonen1,3, Olga Muñoz4, Timo Nousiainen1, Yuriy Shkuratov2, Wenbo Sun5, and Gorden Videen6,7 1 Department of Physics, University of Helsinki, Finland 2 Institute of Astronomy, Kharkov National University, Ukraine 3 Finnish Geodetic Institute, Finland 4 Instituto de Astrofísica de Andalucía, CSIC, Spain 5 Science Systems and Applications, Inc., USA 6 US Army Research Laboratory, USA 7 Space Science Institute, USA

Laboratory measurements of single-scattering feldspar particles appear to be a huge challenge for modeling Data adapted from Volten et al. 2001: JGR 106, pp. 17375–17401 2

Results of fitting feldspar at 0.442 m Data adapted from Dubovik et al. 2006: JGR 111, D11208 3

Results of fitting feldspar at 0.633 m Data adapted from Dubovik et al. 2006: JGR 111, D11208 4

Little difficulties in modeling Unfortunately, the parameters were different for the different fits, and “Simultaneous inversions of scattering matrices measured at two wavelengths (0.442 m and 0.633 m) were not successful in that a reasonably good fit was not achieved. The root-mean-square (over all elements) fit for a single wavelength was about 7–10%, while for two wavelengths the root-mean-square fit did not drop below 20%.” from Dubovik et al. 2006: JGR 111, D11208 5

Little difficulties in modeling Besides, the best fits are obtained with a mixture of highly oblate and prolate spheroids. However, the feldspar particles look highly irregular with aspect ratio being somewhat about 1. from Dubovik et al. 2006: JGR 111, D11208 6

Modeling feldspar with agglomerated debris particles Method: Discrete Dipole Approximation (DDA) Concept: Modeling target with set of small sub-volumes Advantage: Arbitrary shape and internal structure 7

Modeling feldspar with agglomerated debris particles More details in, e.g., Zubko et al. 2009: JQSRT 110, pp. 1741–1749 8

Modeling feldspar with agglomerated debris particles Features of agglomerated debris particles: (1) Highly irregular (2) Equi-dimensional (3) Fluffy (packing density =0.236) 9

Laboratory measurements of single-scattering feldspar particles SEM image of feldspar Refractive index m is estimated to be in range m = 1.5–1.6 + 0.001–0.00001i Size distribution is retrieved with the laser diffraction method Data adapted from Volten et al., 2001 10

Modeling laboratory measurements of feldspar We consider the range of particle radii r from 0.21 m through 2.25 m at =0.442 m: x=3–32 at =0.633 m: x=2.1–22.3 SEM image of feldspar Size parameter: x = 2r/ Size distribution: r–2.9 Refractive index: m = 1.5 + 0i For each size parameter x, we consider a minimum of 500 samples of agglomerated debris particles in random orientations. This makes our analysis being statistically reliable! 11

Modeling laboratory measurements of feldspar at =0.442 m 12

Modeling laboratory measurements of feldspar at =0.633 m 13

Summary We model light-scattering response measured in feldspar particles at two wavelengths 0.442 and 0.633 m. We utilize model of agglomerated debris particles and compute light scattering with the discrete dipole approximation (DDA). Measurements can be satisfactorily reproduced under realistic assumptions on size distribution and refractive index of feldspar particles. Unlike spheroidal model, agglomerated debris particles can fit measurements at both wavelengths.