Average paraxial power of a lens and visual acuity

Abstract

Abstract To provide a solution for average paraxial lens power (ApP) of a lens. Orthogonal and oblique sections through a lens of power $$F$$ F 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, ApP 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 ( $$\theta$$ θ ) and oblique meridians ( $$\gamma$$ γ ) as a function of the angle of incidence ( $$\alpha$$ α ) reduces for paraxial rays ( $$\alpha \sim 0$$ α ∼ 0 ) to $$F_{n,R} \left( {\alpha ,\theta ,\gamma } \right)\left. \right|_{\alpha \sim 0} = \frac{{n - n_{1} }}{R}\cos^{2} \theta \cos^{2} \gamma$$ F n , R α , θ , γ α ∼ 0 = n - n 1 R cos 2 θ cos 2 γ . The average of this function is $$F_{n,R} \left( {\alpha ,\theta ,\gamma } \right)\left. \right|_{\alpha \sim 0} = \frac{{n - n_{1} }}{4R} $$ F n , R α , θ , γ α ∼ 0 = n - n 1 4 R providing a solution of $$\frac{F}{4}$$ F 4 for ApP.For central (p = 0.04), but not peripheral (p = 0.17) viewing, correction with ApP was associated with better visual acuity than a MSE across all tested refractive errors (p = 0.04). These findings suggest that $$\frac{F}{4}$$ F 4 may be a more inclusive representation of the average paraxial power of a cylindrical lens than the MSE.