No abstract

A method for general implementation in any software platform of the generalized Coddington equations is presented, developed, and validated within a Matlab environment. The ophthalmic lens design strategy is presented thoroughly, and the basic concepts of generalized ray tracing are introduced. The methodology for ray tracing is shown to include two inter-related processes. Firstly, finite ray tracing is used to provide the main direction of propagation of the considered ray at the incidence point of interest. Afterwards, generalized ray tracing provides the principal curvatures of the local wavefront at that point, and its orientation after being refracted by the lens. The curvature values of the local wavefront are interpreted as the sagital and tangential powers of the lens at the point of interest. The proposed approach is validated using a double-check of the calculated lens performance in the spherical lens case: while finite ray tracing is validated using a commercial ray tracing software, generalized ray tracing is validated using a software application for ophthalmic lens design based on the classical version of Coddington equations. Equations of the complete tracing process are developed in detail for the case of generic astigmatic ophthalmic lenses as an example. Three-dimensional representation of the sagital and tangential powers of the ophthalmic lens at all directions of gaze then becomes possible, and results are presented for lenses with different geometries.

Peripheral refraction, the refractive error present outside the main direction of gaze, has lately attracted interest due to its alleged relationship with the progression of myopia. The ray tracing procedures involved in its calculation need to follow an approach different from those used in conventional ophthalmic lens design, where refractive errors are compensated only in the main direction of gaze. We present a methodology for the evaluation of the peripheral refractive error in ophthalmic lenses, adapting the conventional generalized ray tracing approach to the requirements of the evaluation of peripheral refraction. The nodal point of the eye and a retinal conjugate surface will be used to evaluate the three-dimensional distribution of refractive error around the fovea. The proposed approach enables us to calculate the three-dimensional peripheral refraction induced by any ophthalmic lens at any direction of gaze and to personalize the lens design to the requirements of the user. The complete evaluation process for a given user prescribed with a-5.76D ophthalmic lens for foveal vision is detailed, and comparative results obtained when the geometry of the lens is modified and when the central refractive error is over-or undercorrected. The methodology is also applied for an emmetropic eye to show its application for refractive errors other than myopia.Postprint (published version