Optimal selection of aspheric surfaces in optical design

Optical systems frequently use aspheric surfaces to improve performance. Typically the designer uses a combination of experience and trail and error to decide which surfaces to make aspheric, then the shape of the aspheric surface is optimized as part of the optical system. In this paper, a method of optimally choosing which surfaces are to be made aspheric is developed. This is implemented by allowing the surface number of the asphere to become a variable in the optimization. Imaginary surfaces are used as an intermediary to make the problem continuous for the optimization. The method of implementation and design examples are given.