Improved Analytical Theory of Ophthalmic Lens Design



Downloads per month over past year

Pascual, Eduardo and Gómez Pedrero, José Antonio and Alonso Fernández, José (2021) Improved Analytical Theory of Ophthalmic Lens Design. Applied Sciences, 11 (5696). ISSN 2076-3417

[thumbnail of applsci-11-05696-v2.pdf]
Creative Commons Attribution.


Official URL:


A revisited form of the classic third-order ophthalmic lens design theory that provides a more precise and meaningful use of aspheric surfaces and a generalization of the standard oblique errors is presented. The classical third-order theory follows from the application of the Coddington equations to a ray trace through the lens and the expansion of the incidence angles and the surface sagittas appearing on them up to order two of the radial coordinate. In this work we show that the approximations for surface sagittas and angles can be decoupled, and the lens oblique powers predicted by the proposed theory provides a better fit to the numerical results obtained by exact raytracing and multi-parametric optimization than the classical third-order theory does. Modern ophthalmic lens design uses numerical optimization and exact ray tracing, but the methods presented in this paper provide a deeper understanding of the problem and its limitations. This knowledge and the more general merit functions that are also presented may help guide the numerical approaches.

Item Type:Article
Additional Information:

Received: 31 May 2021 / Revised: 16 June 2021 / Accepted: 17 June 2021 / Published: 19 June 2021.

Uncontrolled Keywords:Ophthalmic lenses; Coddington equations; Optimization; Exact ray tracing
Subjects:Medical sciences > Optics > Visual perception
ID Code:67754
Deposited On:14 Dec 2021 13:46
Last Modified:14 Dec 2021 13:46

Origin of downloads

Repository Staff Only: item control page