Carmen Vázquez

Complete algorithm for the calculation light patterns inside the ocular media

Realistic mathematical models are of great importance for studying the optical performance of the human eye. Light propagation algorithms provide robust methods to calculate field distributions inside a homogeneous medium, and thus they can be applied to the study of light patterns inside the anterior and posterior chambers of the eye. Dealing with real eyes implies using very short propagation distances together with highly refractive power surfaces. Thus, the general solutions of the field equation are used instead of paraxial Fresnel solutions. Conditions of application and sampling conditions of the method are clearly stated here. Numerical evaluation of the different refractive surfaces is also analysed. The main result is that a complete algorithm to obtain light patterns at any axial distance inside the eye is proposed. The method uses real corneal measures and axial distances together with crystalline models. Statistical results and individual predictions show the validity of the model. Application of the method is illustrated with the study of a bifocal intraocular lens.

The use of Newton's rings for characterising ophthalmic lenses

The interference technique of Newtons Rings is widely used for the quality control of optical surfaces because the precision obtained with this method proves to be very satisfactory. The dimensions of the rings permits calculation of the radii of curvature of the analysed surfaces and deformation of the interference pattern can be utilised to calculate other parameters, such as astigmatism. We describe the study of progressive surfaces by means of this technique, whereby the analysis of the various points of the progressive corridor is made, and also include information on the power function for these lenses, as well as the addition and corridor length.

Near-field light distributions propagated from human corneas: determination of relevant patterns

A procedure to determine the best image range of distances that can be obtained from an aphakic eye is presented. Corneal surfaces are calculated from videokeratographic data. Light distributions at different distances inside the eye are calculated with a near-field Fresnel diffraction algorithm. These patterns are evaluated using three different quality functions which quantify the appearance of the energy distributions in each plane. Local extremes in those functions will serve to locate relevant distributions as Sturm focal planes and even the best image plane which is affordable by the cornea. The study is applied to strongly aberrated corneas.

Real time modulable multifocality through annular optical elements

We present and analyze new multifocal optical elements based on an annular distribution of the transmittance. These elements provide selectable number of foci and can be designed to work between two fixed positions or even to provide extended focal depth. The energy of the foci can be modulated through a single parameter that controls the area of each ring. In our study we analyze the quality of the peaks and also the limit number of foci that can be obtained. The properties shown by these elements make them usable in instrumental optics or in ophthalmic optics, as new intraocular implants, where multifocal elements are required. The implementation has been done on a twisted nematic spatial light modulator, thus allowing real time reconfiguration of the element.

Determination of chromatic aberration in the human eye by means of Fresnel propagation theory

In this communication, the authors have determined the longitudinal chromatic aberrations in real eyes. The method that has been used combines real data of corneal morphology, central thickness of crystalline lens and biometric measures of axial length together with numerical calculation of the propagation process. The curvature of the crystalline lens has been adjusted to different curvature models and refractive index distributions. The wavelength dependence of all ocular media has been modelled through the Cauchy formula. Propagation through anterior and posterior chambers has been accomplished through numerical calculation of diffraction integral instead of classical ray-tracing approach. This imposes serous restrictions on the number of samples that are needed for a full propagation process. If we are only interested in amplitude calculations the method consists of evaluating propagation from cornea to crystalline lens with a spectrum propagation method. Propagation from the lens to the best image plane is accomplished by a direct calculation of Fresnel integral. With this model, we have obtained the refraction chromatic difference in diopters for several eyes. Results are compared with real measures of the chromatic aberration, showing a good agreement with numerical calculations. The capabilities of the technique have been demonstrated by applying the method to the study of the chromatic aberration of a keratoconus.

Objective quality criterions to determinate the best image plane in highly deformed human corneas

The cornea may be considered as the major contributor to the ocular aberrations. For normal corneas working with parallel beams, the best image plane correspond to the image distribution in the focal plane. Working with highly deformed corneas, the focal plane is not well defined and thus further analysis has to be done. Different light distribution propagated from the cornea will be analyzed here. In order to evaluate these patterns we propose three different simple parameters that will provide useful information at low computational cost. The method can be applied in optometry clinics. Since it would be convenient to optimize the image formation process by a correcting lens before performing any surgical process over the cornea.

Numerical calculation of the corneal transmittance

Obtention of the phase transmittance of the cornea under the paraxial assumption does not provide accurate estimation of the corneal aberrations for wide apertures of the pupil. On the other hand, exact ray tracing will require a huge amount of calculations and does not provide uniform sampling of the energy distribution at the output. We propose to use a simple approximation that takes into account non-paraxial effects. This approximation allow obtention of a well sampled output plane at no additional computational cost.

Influence of quadratic phase factors on optical imaging and Fourier transforming in anamorphic systems

Abstract Propagation of quadratic phase factors in coherent optical anamorphic processors is considered. They can be introduced in a first imaging two-lens system, in order to have an amplitude distribution affected by quadratic phase factors, which serves as the object for a second system. In imaging, the quadratic phase factors do not determine the position of the final image plane. On the contrary, in anamorphic Fourier transformers the quadratic phase factors influence the position of Fourier planes. Therefore, in the design of anamorphic processors their influence on Fourier transformer performance should be taken into account.