Aberration analysis for annular pupils by different Zernike polynomials

Due to the orthogonality of every Zernike annular polynomial in the annular field, the error in Seidel coefficients solved by wave front fitting with circular polynomial for annular pupils could be obtained. To accurately compare Seidel coefficients solved by circular polynomial with Zernike annular polynomial, an experiment model was built according to the theory of wave front aberration. The Seidel coefficients solved by wave front fitting for large obscuration pupils with Zernike annular polynomial and Zernike circular polynomial were compared. The result showed that the main relative errors remained in defocus, sphere and coma aberrations, when the Seidel coefficients were solved by Zernike circular polynomials. The Seidel coefficients solved by the 9 circular polynomial terms are more close to the results solved by the annular polynomial rather than the 36 circular polynomial terms. However, when the number of circular polynomial terms decreases to fewer than 9, the error in Seidel coefficients obtained by circular polynomial will increase.