Average paraxial power of a lens and visual acuity

To provide a solution for average paraxial lens power (A(p)P) of a lens. Orthogonal and oblique sections through a lens of power [Formula: see text] were reduced to a paraxial representation of lens power followed by integration. Visual acuity was measured using lenses of different powers (cylinders of − 1.0 and − 2.0D) and axes, mean spherical equivalent (MSE) of S + C/2, A(p)P and a toric correction, with the order of correction randomised. A digital screen at 6 m was used on which a Landolt C with crowding bars was displayed for 0.3 s before vanishing. The general equation for a symmetrical lens of refractive index (n), radius of curvature R, in medium of refractive index n1, through orthogonal ([Formula: see text] ) and oblique meridians ([Formula: see text] ) as a function of the angle of incidence ([Formula: see text] ) reduces for paraxial rays ([Formula: see text] ) to [Formula: see text] . The average of this function is [Formula: see text] providing a solution of [Formula: see text] for A(p)P.For central (p = 0.04), but not peripheral (p = 0.17) viewing, correction with A(p)P was associated with better visual acuity than a MSE across all tested refractive errors (p = 0.04). These findings suggest that [Formula: see text] may be a more inclusive representation of the average paraxial power of a cylindrical lens than the MSE.