To derive equation (16), I take the derivative of both sides of equation (15) with respect to s and map the result to Cartesian coordinates, which yields
The ray equation (6) gives Substituting these relations from equation (B.2) into equation (B.1) and multiplying both sizes by m(x,z) yields equation (16): When (x,z) tends to (x0,z0), s tends to s0 and tends to zero, which gives the initial condition.