For characteristic of a lithographic lens, wide field, a series of coefficients of Zernike polynomial cannot express the characteristic of aberration of the whole system.In this paper, we relate coefficient of Zernike polynomial to field coordinates by introducing double Zernike polynomial to represent field dependent aberrations of lithographic lens. The new aberration function is a sum of some four dimensions polynomial, which consist of fringe Zernike of pupil coordinates and field coordinates. We emulate the manufacturing error of lithographic lens by code V, a software of optical design, and fit a set of double Zernike polynomial coefficients by using single Zernike coefficients of a lot of field points to represent the global aberration of lithographic lens.
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