Average paraxial power of a lens and visual acuity

Stephen B. Kaye*, Jamila Surti, James S. Wolffsohn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


To provide a solution for average paraxial lens power (ApP) 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, 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 ([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 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 [Formula: see text] may be a more inclusive representation of the average paraxial power of a cylindrical lens than the MSE.

Original languageEnglish
Article number7118
Number of pages7
JournalScientific Reports
Issue number1
Early online date2 May 2023
Publication statusPublished - 2 May 2023

Bibliographical note

Copyright © The Author(s) 2023.
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  • Applied optics
  • Medical research
  • translational research


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