Frequency domain analysis for orthogonal polynomials based on annulus sector area

The power spectrum density (PSD) distribution of Zernike polynomials and the polynomials orthogonalized in an annulus sector area (POAS) were obtained by Fourier transformation. The peak radial spatial frequency and the halfpeak radial spatial frequency range corresponding to each item of the orthogonal polynomials were calculated. In comparison with Zernike polynomials, the orthogonal polynomials have similar PSD distribution, but higher spatial frequencies. Computer simulation indicates that each item of POAS represents only a specific frequency range. According to the spatial frequency distribution of the surface figure of a mirror with annulus sector shape, the calculation time is reduced and the fitting accuracy is guaranteed if the proper items of orthogonal polynomials are selected.