Average paraxial power of a lens and visual acuity

Stephen B. Kaye; Jamila Surti; James S. Wolffsohn

doi:10.1038/s41598-023-34010-4

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 journal › Article › peer-review

Abstract

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 language	English
Article number	7118
Number of pages	7
Journal	Scientific Reports
Volume	13
Issue number	1
Early online date	2 May 2023
DOIs	https://doi.org/10.1038/s41598-023-34010-4
Publication status	Published - 2 May 2023

Bibliographical note

Copyright © The Author(s) 2023.
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Keywords

Applied optics
Medical research
translational research

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title = "Average paraxial power of a lens and visual acuity",

abstract = "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.",

keywords = "Applied optics, Medical research, translational research",

author = "Kaye, {Stephen B.} and Jamila Surti and Wolffsohn, {James S.}",

note = "Copyright {\textcopyright} The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.",

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doi = "10.1038/s41598-023-34010-4",

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N2 - 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.

AB - 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.

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SN - 2045-2322

VL - 13

JO - Scientific Reports

JF - Scientific Reports

IS - 1

M1 - 7118

ER -

Average paraxial power of a lens and visual acuity

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