Improvement and application of linearized invariant imbedding T-matrix scattering method

Abstract

The Jacobians of particle scattering properties with respect to aspect ratio and effective radius (re) using the invariant imbedding T-matrix method (IITM) are significantly improved by circumventing the divergence of derivatives. The effective radius re is used in three definitions, which are rV, the equal-volume spherical radius, rS, the equal-surface-area spherical radius, and rVS, the ratio of three times the volume to surface area, respectively. The improved IITM and their Jacobians are applied to discuss the discrepancies between the three different definitions. The analytical Jacobians with respect to aspect ratios and effective radii associated with three effective radii are verified using the finite-difference method. Jacobians with respect to different effective radii are proportional since the ratios of different effective radii are only related to the aspect ratios. Jacobians with respect to aspect ratios are extremely sensitive to the definitions of effective radius.