Differential method for freeform optics applied to two-mirror off-axis telescope design

In this Letter, we present a method to design the freeform surfaces of an off-axis unobscured two-mirror telescope by integration of a system of differential equations. The system is derived from the differentiation of Fermat’s path principle and is integrated as an ordinary differential equation problem. The method is used to design the freeform surfaces of a telescope whose performance is verified in off-the-shelf optical design software (Zemax).