Efficient numerical orientation averaging of light scattering properties with a quasi-Monte-Carlo method

We studied numerical orientation averaging with three methods for selection of orientations: lattice-grid division, crude Monte-Carlo (CMC) method, and quasi-Monte-Carlo (QMC) method. Numerical orientation averaging with these methods are carried out with a fixed orientation version of the T-matrix method for clusters of spheres. The errors of numerical orientation averaging as a function of number of orientations are investigated by comparison with results from analytical orientation averaging of the T-matrix method.We studied four types of aggregates: a bisphere, ballistic cluster-cluster aggregates of 4 and 128 monomers (BCCA4 and BCCA128), and a ballistic particle-cluster aggregate of 128 monomers (BPCA128).We studied convergence of the scattering efficiency Qsca, absorption efficiency Qabs, asymmetry parameter g, intensity 4S11/xv2, and degree of linear polarization P=-S12/S11. For the polarization, scattering angles of maximum (Θmax) and minimum (Θmin) polarization in results of analytical orientation averaging are considered. For the intensity, in addition to Θmax and Θmin, forward scattering angle (Θ=10∘) is also considered.Qsca, Qabs and g of bisphere, BCCA4, and BPCA128 can be obtained accurately with smallest number of orientations by using QMC among three methods. Errors in Qsca, Qabs and g of BCCA128 were already small for smaller number of orientations (e.g., 100) with all the three methods.P(Θmin) generally shows slow convergence requiring several thousands of orientations to have errors less than 1%. There are also cases where convergence of P(Θmin) within 1% error is not attained even for largest number of orientations studied in this paper (i.e., BCCA4 with lattice-grid, BCCA128 with lattice-grid, BCCA128 with CMC).Intensity of Θ=10∘, Θmax and Θmin, and polarization of Θmax generally show convergence within 1% error for several hundreds to 1000 orientations with three methods for selection of orientation angles. Among three methods, QMC requires smallest number of orientations for intensity and polarization.We also investigated convergence of Θmax and Θmin. Convergence of Θmax and Θmin is generally attained for 100-1000 orientations.We also described the application of the method to the discrete dipole approximation. In these calculations, we considered three shape models with different number of dipoles and different dipole representations to describe BCCA4. The results show that scattering and absorption efficiencies, and asymmetry parameter can generally be obtained within 1% errors for all the three shape models. On the other hand, errors are larger for intensity (up to 10%) and polarization (up to 50-70%).