Components of Lens Power That Regulate Surface Principal Powers and Relative Meridians Independently

Paraxial light rays incident in air on alternate refracting surfaces of a thick lens can yield complementary powers. This paper aims to test when these powers are invariant as surface refractive powers interchange in the expression. We solve for relevant surface powers. Potential anticommutators yield the nature of surface principal refractions along obliquely crossing perpendicular meridians; commutators yield meridians that align with those on the next surface. An invariant power component orients relative meridians or the nature of the matrix power on each noncylindrical surface demands that the other component varies. Another component of lens power aligns relative meridian positions for distinct principal powers. Interchanging surface power matrices affects this component. A symmetric lens power results if perpendicular principal meridians are associated with meridians on an opposite rotationally symmetric surface. For thin lenses, meridian alignment may be waived. An astigmatic contact lens can be specified by symmetric power despite having separated surfaces.