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. A 28, 747 (2011)]), which are necessary for automatic optical design [Appl. Opt. 2, 1209 (1963)].
© 2012 Optical Society of America
Original Manuscript: May 15, 2012
Manuscript Accepted: May 17, 2012
Published: June 21, 2012
Psang Dain Lin and Chung-Yu Tsai, "Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays: reply," J. Opt. Soc. Am. A 29, 1358-1358 (2012)