Practical numerical solutions of Wassermann–Wolf equations

In this paper, we present a complete method for determining the two surfaces of an aspheric singlet by numerical integration based on the classical Wassermann–Wolf equations (hereinafter WW). Although aplanatic optics is mainly treated in WW, we also show some other examples that can be determined by the WW. This indicates that surface shape determination by optimization software such as Zemax or CodeV is not necessary for some aspherical singlet designs, including the aplanatic case. A link to an executable Mathematica code for this purpose is also provided.