2D example for calculating the Λ_Ω, ν-matrix elements at a grid point (i − α, j − β) (upper panel) and (i, j − β) (lower panel). The matrix elements correspond to the intensity at the considered grid points calculated for a source function S_ij = 1 and zero everywhere else. For such a configuration, the downwind source function is interpolated from grid points indicated with the green dots, while the upwind source function and upwind intensity are obtained from the red dots (for simplicity we here assume linear interpolations for determining upwind and downwind quantities). We emphasize that the upwind intensity vanishes only when considering the grid point (i − α, j − β).