8 research outputs found
Numerical implementation of generalized Coddington equations for ophthalmic lens design
Postprint (author's final draft
Generalized ray tracing method for the calculation of the peripheral refraction induced by an ophthalmic lens
This thesis proposes a method to evaluate and quantify in a precise way the peripheral refraction induced by an ophthalmic lens. The motivation for this work stems from the progression of myopia and its possible causes; two of them are particularly key for this PhD: (a) Peripheral refraction of the eye may have an important role in the progression of myopia and (b) ophthalmic lenses are the compensating element more used in children and teenagers. These two elements fully justify the need for a reliable method to quantify the induced peripheral refraction by an ophthalmic lens. This method is based on two pillars: first, it must accurately assess the design of the ophthalmic lens and, second, it should consider what peripheral refractive pattern is acting, that is, without compensating element. The proposed method takes the advantages provided by the ray tracing strategies used in the classic design of ophthalmic lenses but applying them in parallel with amendments to evaluate the peripheral refraction. Thus, the simple scheme used in the classic design of ophthalmic lenses containing a remote sphere and a small aperture at the center of rotation of the eye becomes a scheme where the retina conjugate surface (RCS) and the nodal point of the eye play equivalent roles. In our case, the reference for ray tracing is the nodal point of the eye and the reference for measuring the induced peripheral refraction is the RCS. Ray tracing is based on a finite ray tracing (FRT) from the image space to the object space and on a generalized ray tracing (GRT) from object space to image space. Both have been implemented in a Matlab program and validated to provide a powerful tool for our purpose. GRT allows a quick and accurate assessment of the oblique astigmatism, ie the tangential and sagittal focal lens, in wide field of view considering accurately the lens design. This considers that each ray has a small wavefront associated traveling perpendicular to it. By GRT we are able to know how the wavefront shape changes when is propagated and refracted. Therefore, it is mandatory to have a locally description of the geometry of both the wavefront and the refractive surface at the point where the ray arrives to the refractive surface. This local description is determined by the normal and by the principal curvatures and directions of these surfaces at the point of interest; they can be obtained from a parametric description of the surface and then using Gaussian fundamental forms. This ray tracing procedure has been developed for the general case of any geometry to the surfaces of the ophthalmic lens and has been detailed for the case of an astigmatic lens. For calculating the induced peripheral refraction, a surface is modeled reflecting the peripheral refractive initial values before entering the lens; this is the aforementioned RCS. Two methods have been proposed to model this RCS. One is based on the trends observed in the different studies and uses three-dimensional surfaces power vectors associated with peripheral refraction. The second method uses experimental measurements obtained along four meridians of the retina to interpolate a surface. The expression of these surfaces by power vectors can easily be combined with the results obtained by tracing rays through the lens for the calculation of the induced peripheral refraction. We present in this manuscript some specific examples of how variations on the lens geometry modified the induced peripheral refraction. This opens up the possibility of custom designs ophthalmic lenses to prevent the progression of myopia.Esta Tesis tiene como objetivo la propuesta de un método para la evaluación cuantitativa de la refracción periférica inducida en el ojo de un paciente por una lente oftálmica. La motivación del trabajo radica en la importancia de este fenómeno en el progresión de la miopía y sus causas. La existencia de una refracción periférica hipermetrópica se ha relacionado directamente con la progresión de la miopía, y las lentes oftálmicas son el elemento compensador preferenteen niños y adolescentes, los sujetos más relevantes en cuanto al control de la progresión de l amiopía, en sí misma y como antesala d eotros problemas oculares más graves. Hasta la realización de esta Tesis no existía un método preciso, próximo a los métodos convencionales del diseño de lentes oftálmicas, que permitiera el cálculo de la refracción periférica inducida por la lente oftálmica y el análisi de los diseños de lente utilizados. Dicho diseño debe considerar tanto los efectos asociados a a óptica y la geometría del ojo, como al propio diseño de la lente compensadora. El método que se propone sigue una metodologia próxima a la del diseño convencional de lentes oftálmicas, sustituyendo el rol del centro de rotación del ojo por el de su punto nodal, y el rol de la esfera del remoto por lo qque se ha denominado la superfície conjugada de la retina (RCS, de retinal conjugate surface, en el texto). Con este enfoque se han implementado algoritmos detallados de trazado de rayos finito y generalizado que permiten el trazado detallado de rayos en un conjunto de direcciones alrededor de la fóvea. Los algoritmos de trazado generalizado permiten el análisis de lentes oftálmicas de manera más eficiente que el trazado intensivo típico del software de diseño óptico, utilizando el concepto de trazado de frente d eonda, que analiza las deformaciones del frente de onda que acompaña a un rayo principal. Dichos algoritmos se han implementado y validado para un conjunto de lentes oftálmicas de diferentes geometrías en un software científico estándard (Matlab(R)) como parte de los trabajos desarrollados en esta Tesis. Mediante el uso de los algoritmos descritos es posible calcular la superficie refractada que induceuna lente oftálmica. A continuación se hen desarrollado modelos teóricos y experimentales para la RCS que permiten tener en cuanta la variabilidad de patrones de refracción periférica existente, y se ha propuesto el uso de vectores de potencia (M J0 y J45) para el cálculo de la refracción periférica inducida por la lente, mediante la combinación de la superficie refractada por la lente y la modelada para una determinada RCS. Se presentan casos para lentes esféricas, asféricas y astigmáticas, para ojos miopes y emétropes, y en condiciones de infra y sobre refracción, mostrando la potencialidad del método propuesto para diseñar lentes que compensen simultáneamente la refracción foveal y la periférica, que mediante el método propuesto podrán optimizarse simultáneamente
Numerical implementation of generalized Coddington equations for ophthalmic lens design
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.Postprint (published version
Aplicació d’eines TIC a la millora de les competències clíniques en l’àmbit de l’òptica i l’optometria: “OPTOstream”
Actualment, l’estudiantat de la Facultat d’Òptica i Optometria de les assignatures clíniques
(Grau i Màster) participen de forma activa en l’atenció de pacient reals, sota la supervisió
del professorat. Els casos atesos durant les sessions pràctiques es plantegen i discuteixen
en les sessions de seminari amb els docents i la resta del grup.
Malgrat el valor docent d’aquesta metodologia, l’estudiant no tenia la possibilitat de
comprovar la seva actuació durant l’atenció d’un cas real, a partir de les observacions del
docent. Aquesta situació dificulta un aprofitament òptim de l’experiència d’aprenentatge
per part de l’estudiant.
La incorporació de solucions tècniques contrastades en l’àmbit de la formació, com és el
cas de l’enregistrament i visionat posterior o en temps real de casos, permeten a
l’estudiant participar més activament en el seu procés d’aprenentatge i contribueixen a fer
més efectiva l’adquisició de determinats coneixements i competències bàsiques per al
desenvolupament de la seva carrera professional i investigadora.
El projecte “OPTOstream” ha permès desenvolupar una metodologia pròpia basada en
l’elaboració i anàlisi posterior de casos enregistrats en vídeo o bé la projecció en temps
real de les actuacions clíniques al nou auditori de la Facultat.Peer Reviewe
Numerical implementation of generalized Coddington equations for ophthalmic lens design
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
Generalized ray tracing method for the calculation of the peripheral refraction induced by an ophthalmic lens
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
Aplicació d’eines TIC a la millora de les competències clíniques en l’àmbit de l’òptica i l’optometria: “OPTOstream”
Actualment, l’estudiantat de la Facultat d’Òptica i Optometria de les assignatures clíniques
(Grau i Màster) participen de forma activa en l’atenció de pacient reals, sota la supervisió
del professorat. Els casos atesos durant les sessions pràctiques es plantegen i discuteixen
en les sessions de seminari amb els docents i la resta del grup.
Malgrat el valor docent d’aquesta metodologia, l’estudiant no tenia la possibilitat de
comprovar la seva actuació durant l’atenció d’un cas real, a partir de les observacions del
docent. Aquesta situació dificulta un aprofitament òptim de l’experiència d’aprenentatge
per part de l’estudiant.
La incorporació de solucions tècniques contrastades en l’àmbit de la formació, com és el
cas de l’enregistrament i visionat posterior o en temps real de casos, permeten a
l’estudiant participar més activament en el seu procés d’aprenentatge i contribueixen a fer
més efectiva l’adquisició de determinats coneixements i competències bàsiques per al
desenvolupament de la seva carrera professional i investigadora.
El projecte “OPTOstream” ha permès desenvolupar una metodologia pròpia basada en
l’elaboració i anàlisi posterior de casos enregistrats en vídeo o bé la projecció en temps
real de les actuacions clíniques al nou auditori de la Facultat.Peer Reviewe