Working[edit]
Light rays within the (x,y)-plane of the torus (as defined in the figure above) are refracted according to the greatest radius of curvature, R + r, i.e., the smallest refractive power, S = (n − 1) / (R + r).
Light rays within a plane through the axis of revolution (the z axis) of the torus are refracted according to the smallest radius of curvature, r, i.e., the greatest refractive power, s = (n − 1) / r. As a consequence, there are two different refractive powers at orientations perpendicular to each other. At intermediate orientations, the refractive power changes gradually from the greatest to the smallest value, or reverse. This will compensate for the astigmatic aberration of the eye.