Simulation of Wavefront Reconstruction Based on Polynomials Orthogonalized in an Annulus Sector Domain

A series of polynomials orthogonalized in an annulus sector domain is derived from Zernike polynomials by using Gram-Schmidt orthogonalizing method. The same terms of the two polynomials are found to have similar distributions and physical meanings in their respective orthogonal domains. An aberrated wavefront on an annulus sector domain is expanded with Zernike polynomials, annular Zernike polynomials, circumcircle Zernike polynomials and annulus sector Zernike polynomials respectively. The 4 sets of coefficients are compared in cases where the aberrated wavefront is without and with additional perturbations. It is found that the coefficients of the annulus sector domain orthogonalized polynomials are the most stable ones and have the best anti-perturbation capability.