Modified forms of Tscherning ellipses.

Third-order equations are well known for determining sagittal and tangential powers of a thin lens, corresponding to an eye rotating behind a lens to view objects away from the optical axis of the lens. These equations are referenced to the back surface of the lens and do not take into account the peripheral thickness of the lens. They do not give the same results as finite raytracing at small angles in which powers are referenced to the vertex sphere, which is the same distance from the centre-of-rotation for all object angles. Modified forms of the third-order sagittal and tangential image vergence error equations are developed to overcome the discrepancies. These are used to determine Tscherning ellipses for zero oblique astigmatism and zero mean oblique power error. While solutions to oblique astigmatism are not affected by the modifications, there are considerable changes to mean oblique error solutions.