Ray diagram showing the calculation of path length traveled by a ray in an exoplanetary atmosphere at an arbitrary impact parameter b. Here, rⁱ_up is the upper boundary radius of a layer, ﹩d{l}_{\,\rm{agg}\,}^{i}﹩ is the total path length traveled by the ray in the half geometry until the i − 1 layer, and dlⁱ is the path length of the ray in the ith layer.