Shape and refractive powers in corneal topography.
To compare the relative advantages and disadvantages of four different representations of corneal power--identified as instantaneous, axial, position, and refractive--based on curvature, slope, coordinate position, and focal properties, respectively. The four types of corneal power were evaluated by examining their interrelationship for 12 hypothetical corneal shapes chosen to represent the general characteristics of regular, irregular, and surgically altered corneas. There is only a limited association between refractive power and the other three powers, which are based on shape properties. For corneal shapes represented by ellipsoids of low eccentricity (e), refractive power increased as a function of the distance from the reference axis, whereas axial and instantaneous powers were either constant (for e = 0) or decreased, with instantaneous power having the largest decrease. Refractive power decreased for elliptical corneal shapes with eccentricities greater than the reciprocal of the index of refraction, although always decreasing less than the axial or instantaneous power. For various corneal shapes formed by segments of circles (or a polynomial) with large differences in instantaneous power, the refractive power was more closely associated with axial than instantaneous or position powers. The Purkinje image measurements from videokeratograpy are most closely related to the slope-based axial power because it is slope that determines the direction of reflected rays forming the corneal image. Because of this direct connection, axial power is less sensitive to noise than is refractive, instantaneous, or position power. Present videokeratographs that report axial power provide an approximation of refractive power, but if an exact refractive power is needed it can be calculated easily. Instantaneous power provides the most sensitive measure of local curvature changes, such as those occurring in keratoconus or refractive surgery. There are unique practical applications for each of the four powers.