Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays: reply

We reply to the comments on our paper previous paper. While the results obtained are the same as ours, we hold that, by using homogeneous coordinate notation, our method enables first-order and second-order derivatives of non-axially symmetrical systems to be computed numerically (such as [J. Opt. Soc. Am. A28, 747 (2011)]), which are necessary for automatic optical design [Appl. Opt.2, 1209 (1963)].