title: Orthonormal polynomials for annular pupil including a cross-shaped obstruction.
abstract: 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.
authors.forename: Fengzhao
authors.initials: F
authors.lastname: Dai
authors.forename: Xiangzhao
authors.initials: X
authors.lastname: Wang
authors.forename: Osami
authors.initials: O
authors.lastname: Sasaki