Although spherical aberration cannot be eliminated for a single lens, it can be minimized by the appropriate bending of the lens into its best form. The degree of bending can be characterized by the Coddington shape factor:
R1 and R2 are the surface radii of the spherical lens surfaces.
The minimum spherical aberration also depends on the object and image distances, so another factor enters, called the Coddington position factor:
i and o are the image and object distances for the lens as in the lens equation.
The minimum spherical aberration occurs when
The higher the index of refraction n, the smaller the aberration for the optimum shape.