Orthonormal polynomials for annular pupil including a cross-shaped obstruction

摘要

By nonrecursive matrix method using the Zernike circle polynomials as the basis functions, we derived a set of polynomials up to fourth order which is approximately orthonormal for optical systems with an annular pupil having a cross-shaped obstruction. The performance of the polynomials is compared with the strictly orthonormal polynomials with some numerical examples. (C) 2015 Optical Society of America