Versatile Absorption Modeling for Transmissive Optical Elements Using Ray Tracing and Finite Element Analysis

The paper defines the absorption model and three point-to-node mapping schemes precisely, including q_front^surf = α_S Pray,inc, the Beer–Lambert segment recursion Prayi = Prayi−1 − qvoli−1, qvoli = Prayi(1 − e^{−αV lseg}), and the back-surface term q_back^surf = α_S (Pray_nseg − q_vol_nseg), as well as mapping formulas f_e = N^T(ξ_vol) q_vol (shape functions) and normalized inverse-distance weightings; it explicitly notes conservation for the global inverse-distance method and the formulas themselves ensure it for the other two . The candidate solution supplies the missing closed-form solution of the recursion, proves independence of Σ_i q_vol,i from n_seg, and writes down the full energy budget including the transmitted power P_out, which the paper does not explicitly derive but is fully consistent with its model. Hence both are correct; the model provides an explicit proof where the paper presents the algorithmic formulation.