Gram-Schmidt orthogonalization of the Zernike polynomials on apertures of arbitrary shape.

An orthonormal hexagonal Zernike basis set is generated from circular Zernike polynomials apodized by a hexagonal mask by use of the Gram–Schmidt orthogonalization technique. Results for the first 15 hexagonal Zernike polynomials are shown. The Gram–Schmidt orthogonalization technique presented can be extended to both apertures of arbitrary shape and other basis functions.