Effect of conicoid asphericity on the Tscherning ellipses of ophthalmic spectacle lenses

One of the criteria in ophthalmic spectacle lens design is the elimination of oblique astigmatism. For a range of equivalent powers, Seidel (primary or third-order) astigmatism can be eliminated, and the solutions of back- (or front-) surface power are commonly displayed graphically in the form of ellipses (Tscherning ellipses). The Tscherning ellipses apply only to lenses constructed from spherical surfaces. If one or both surfaces are made aspheric, the solutions for zero astigmatism are no longer in the form of ellipses. If one surface, usually the front surface, is made as a conicoid aspheric, the solutions for zero astigmatism can be presented graphically similarly to the Tscherning ellipses. For any given equivalent power, there are two or no solutions for spherical lenses. However, there is always one and up to three solutions for conicoid aspheric lenses.