Robust, efficient computational methods for axially symmetric optical aspheres

Whether in design or the various stages of fabrication and testing, an effective representation of an asphere's shape is critical. Some algorithms are given for implementing tailored polynomials that are ideally suited to these needs. With minimal coding, these results allow a recently introduced orthogonal polynomial basis to be employed to arbitrary orders. Interestingly, these robust and efficient methods are enabled by the introduction of an auxiliary polynomial basis.