LEAST-SQUARES FITTING OF ORTHOGONAL POLYNOMIALS TO THE WAVE-ABERRATION FUNCTION

The wave-aberration function of systems with circular and square apertures can be expanded in terms of Zernike and Legendre polynomials. The polynomial terms form orthogonal sets; therefore each coefficient independently determined by an integral satisfies the principle of least squares. To evaluate the integral the pupil is divided into small areas where the wave-aberration function is approximated by the first three terms of a Taylor series expansion: the optical path difference and components of geometric aberration. In final form the coefficients are expressed by the sum of three bilinear terms by combining three matrices and six vectors. The former depend on the construction parameters and the latter on the ray pattern. %