title: Orthonormal polynomials for hexagonal pupils.
abstract: The problem of determining the orthonormal polynomials for hexagonal pupils by the Gram-Schmidt orthogonalization of Zernike circle polynomials is revisited, and closed-form expressions for the hexagonal polynomials are given. We show how the orthonormal coefficients are related to the corresponding Zernike coefficients for a hexagonal pupil and emphasize that it is the former that should be used for any quantitative wavefront analysis for such a pupil.
authors.affiliation: The Aerospace Corporation, 2350 East El Sugundo Boulevard, El Sugundo, CA 90245, USA. virendra.n.mahajan@aero.org
authors.forename: Virendra N
authors.initials: VN
authors.lastname: Mahajan
authors.forename: Guang-ming
authors.initials: GM
authors.lastname: Dai