In most methods of automatic optical design it is necessary to compute the derivatives of the traced rays with respect to construction parameters of the optical system. Exact differentiation of the algebraic formulae is the most accurate way to compute these derivatives. In a previous paper I gave such equations, but they contained an approximation for skew rays. In this paper, the approximation is removed and the method extended to conics and general surfaces of revolution.
DONALD P. FEDER, "Differentiation of Ray-Tracing Equations with Respect to Construction Parameters of Rotationally Symmetric Optics," J. Opt. Soc. Am. 58, 1494-1495 (1968)