Average paraxial power of a lens and visual acuity

• Published in: Scientific reports 2023-05, Vol.13 (1), p.7118-7118, Article 7118
• Main Authors: Kaye, Stephen B., Surti, Jamila, Wolffsohn, James S.
• Format: Article
• Language: English
• Subjects: 639/624/1075; 692/308; 692/308/575; Acuity; Astigmatism; Humanities and Social Sciences; Humans; Lenses; multidisciplinary; Refraction, Ocular; Refractive Errors; Science; Science (multidisciplinary); Visual Acuity
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-023-34010-4

To provide a solution for average paraxial lens power (A p P) of a lens. Orthogonal and oblique sections through a lens of power 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, 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 ( θ ) and oblique meridians ( γ ) as a function of the angle of incidence ( α ) reduces for paraxial rays ( α ∼ 0 ) to 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 α , θ , γ α ∼ 0 = n - n 1 4 R providing a solution of F 4 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 F 4 may be a more inclusive representation of the average paraxial power of a cylindrical lens than the MSE.