Definition of an Aspheric Surface

A spherical surface is defined by only one parameter, the radius or curvature of the surface. If the surface is refractive, with different indices of refraction before and after the surface, then the power of the surface is defined by the surface radius and the indices of refraction of the two media. Radius and curvature are reciprocal to one another.

Figure 7.1a shows a plano convex lens element with a spherical radius, imaging an axial point from infinity. The spherical aberration is quite evident. The high angle of incidence of the upper limiting ray of approximately 45 to the surface normal causes this ray to refract very strongly and ultimately to cross the axis significantly closer to the lens than rays closer to the optical axis. A spherical surface has the property that the rate of change of the surface slope is exactly the same everywhere on the surface, and thus the aberration is inevitable. Let us consider reducing the slope of the surface toward the outer periphery of the surface in order to flatten the shape in the region surrounding the outer rays. If we make the surface shape gradually flatter as we proceed outward from the optical axis, we can differentially reduce the refracting ray angle so that the net effect is to bring all of the rays to a common focus position, as shown in Fig. 7.1b . Figure 7.1c compares the spherical surface, which is steeper at...