Analytical design of freeform surface parameters of optical system based on double Zernike polynomials

This paper presents what we believe to be a novel approach for determining the parameters of freeform surfaces using double Zernike polynomials. We derive the analytical expressions for the double Zernike aberration contributions of freeform surfaces in detail. Additionally, we address the influence of incident ray angles on the aberration contributions and propose a solution to the issue of inaccurate freeform surface aberration calculations caused by large field angles. The derived double Zernike aberration coefficients enable a direct computation of the full-field RMS, which is essential for optical system performance evaluation. Experimental results demonstrate that the optical systems designed using our method achieve reduced freeform surface parameter magnitudes while maintaining high imaging quality.