Abstract
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.