在光学设计中，为了给光学系统的设计与优化提供更多的设计自由度，常常使用旋转对称非球面。旋转对称非球面的标准表达式通常为基准二次曲面与附加多项式的组合，附加多项式可以为偶次幂级数多项式、Zernike多项式和Q型多项式等。鉴于此，推导基准二次曲面和基于不同附加多项式的非球面的表达式，对各类旋转对称非球面的非球面系数和非球面表面斜率进行比较，利用设计实例来对比基于不同附加多项式的非球面在光学设计中的应用并指出各自的特点。结果表明，相比于其他非球面，基于Q型多项式的非球面能够更好地控制非球面的面型，优化效率更高。

In optical design, to provide more design freedom for optical system design and optimization, a rotationally symmetric aspheric surface is often used. The standard expression for a rotationally symmetric aspheric surface is usually a combination of a base quadric surface and an additional polynomial, which can be an even-power-series polynomial, Zernike polynomial, or Q-type polynomial, among others. Hence, the expressions for the base quadric surface and aspheric surface based on different additional polynomials are derived, the aspheric coefficient and the slope of the aspheric surface of various rotationally symmetric aspheric surfaces are compared, and the application of an aspheric surface based on different additional polynomials in optical design is compared with design examples, and the characteristics of each aspheric surface are identified. The results show that, compared with other aspheric surfaces, the aspheric surface based on a Q-type polynomial can better control the surface shape of the aspheric surface, and the optimization efficiency is higher.