Construction method of non-circular pupil Zernike orthogonal basis in wavefront reconstruction

To solve the problem of Zernike circle polynomials lost it's orthogonality and fitting coefficients cross coupling when reconstruct wavefront in non-circular domain. A non-circular orthogonal Zernike basis construction method is proposed. In the method, the circular Zernike is used as basis and the Gram-Schimdt orthogonal group construction method is adopted. The correctness of the method is verified by comparing Zernike annular polynomials with new basis which construct for different obscuration ratio. For a wavefront data in square aperture, the results fitted with Zernike circle polynomials and new basis are compared in terms of fitting accuracy, stability and anti-perturbation capacity. The experimental results show that, in the wavefront fitting of an interferogram with non-circular aperture, new basis demonstrate better fitting stability and anti-perturbation capacity. This method doesn't need to find out the analytical expression and only changes the orthogonal coefficient matrix in different non circular domains, provides a new way for the construction of the orthogonal basis of non-circular domains.