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.