Axial and instantaneous power conversion in corneal topography.

PURPOSE To determine if a direct relationship exists between the two common measures of corneal topography--axial and instantaneous powers--that are based on corneal slope or curvature, respectively. METHOD The theoretical relationship between axial and instantaneous powers was derived for unrestricted shapes using equations of basic calculus. RESULTS It was found that axial power at any point y on the cornea is exactly equal to the average of the instantaneous powers from the axis to point y. CONCLUSIONS A simple relationship exists between axial and instantaneous powers that is valid for the intersection of any surface by a meridional plane. This provides a practical means for converting between axial and instantaneous powers for clinical applications of corneal topography.