Abstract
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.
Highlights
Spectacle lenses can be designed considering several factors, such as visual performance, aesthetics, or manufacturing limitations
We would seek the conditions for which ET ( x ) = ES ( x ) = 0, that is, there are no oblique aberrations; the lens wearer perceives the same power for any oblique sight direction
There is previous work that used high-order aspherical terms to correct oblique aberrations in ophthalmic lenses [1,17], but the calculation has always been based on multiparametric optimization
Summary
Spectacle lenses can be designed considering several factors, such as visual performance, aesthetics (thickness or curvature of the front surface, known as base curve), or manufacturing limitations. When visual performance is considered, the usual strategies are primarily focused on the minimization of oblique aberrations, which are the residual defocus and astigmatism appearing at oblique gaze directions or when the lenses are tilted. Lens performance can be analyzed in terms of the number of oblique errors or the size of the geometrical blur patch on the retina [6,14]. The computation of geometrical wavefronts and the corresponding coefficients for higher-order aberrations or optical transfer functions have led many authors to conclude that ophthalmic lens performance is mainly determined by oblique errors [15]
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