Best-fitting sphere of aspheric surface based on spherical aberration

Abstract

In order to understand the physical meaning of the best-fitting sphere of aspheric surface, based on the optical design idea of the aberration theory, the relationship between the curvature radius of the best-fitting sphere and the spherical aberration for the full aperture aspheric surface is set. The result is consistent with the traditional calculation method, which gets mainly from the geometric or algebraic. This formula explains the physical meaning of the best-fitting sphere of aspheric surface from the longitudinal spherical aberration: the curvature center of the best-fitting sphere moves compare with the vertex curvature center of the aspheric surface, and the amount of movement is one quarter of the longitudinal spherical aberration which the object is at the center of the vertex curvature of the aspheric mirror. Furthermore, the best-fitting sphere and asphericity for the annular aperture aspheric surface are also solved successfully. These formulas not only can help understand the best-fitting sphere from optics, but also calculation for off-axis aspheric surface is more convenient. The full aperture can be regarded as an annular aperture aspheric surface with zero inner diameter, the best-fitting spherical surface curvature radius and asphericity have unified calculation formulas for different aperture shapes of aspheric surfaces. All letters of the final expressions come from the parameters of aspheric surface itself, and each term is a clear physical quantity. Calculation is faster; concepts are easier to be understood. This is quite helpful for engineering.