Luis M. González

Adaptive model of the gradient index of the human lens. I. Formulation and model of aging ex vivo lenses

A simple, parametric adaptive model of the refractive index distribution of the ex vivo crystalline lens is presented. It assumes conicoid (or nonrevolution quadric in 3D) iso-indical surfaces, concentric with the external surfaces of the lens. The model uses a minimum number of internal structural parameters, while the shape of the iso-indical surfaces adapts automatically to the external geometry. In this way, it is able to adapt and fit individual distributions as well as adapt to the changes of the lens shape and structure with age and accommodation. The model is fit to experimental data for individual eyes spanning ages 7 to 82 years, where for each eye the crystalline lens dimensions and iso-indical index data are known. The analysis demonstrates that only one age-dependent structural parameter is needed to replicate the internal iso-indical index structure, given age-dependent models for the external surfaces. An age-dependent-parameter global model is derived and is shown to predict age-dependent changes in the ex vivo lens power and longitudinal spherical aberration with age.

On the prediction of optical aberrations by personalized eye models.

Purpose. The purpose of this study is to develop and analyze a method to obtain optical schematic models of individual eyes. Each model should be able to reproduce the measured monochromatic wave aberration with high fidelity. Methods. First, we choose a generic eye model as the input guess and then apply a two-stage customization procedure. Stage 1 consists of replacing, in the initial generic model, those anatomic and optical parameters with experimental data measured on the eye under analysis. The set of experimental data was that provided by a standard clinical preoperative examination, namely lens topography, ultrasound biometry, and total wave aberration. Then, the second stage is to find the unknown lens structure that would reproduce the measured wave aberration through optical optimization. Two totally different initial eye models have been compared; one considers a simpler constant refractive index for the lens, whereas the second model has a gradient-index (GRIN) lens. Results. This automatic customization method has been applied to 19 eyes with different degrees of spherical ametropia (from +0.4 D to -8 D). Two models have been obtained for each eye (constant and gradient index lens). The results were highly satisfactory, with 100% convergence, and with average RMS prediction errors approximately &lgr;/100. This is one order of magnitude lower than typical measurement errors. The models with a constant refractive index lens tended to overestimate surface curvatures, whereas for the GRIN model, lens surfaces were too flat. Conclusions. The proposed method is highly efficient and robust giving a high-fidelity reproduction of the wavefront in all cases attempted so far. Limitations found in reproducing the geometry of the lens seem to be associated with the use of inaccurate models of its refractive index.

Adaptive model of the gradient index of the human lens. II. Optics of the accommodating aging lens

A simple, parametric model of the gradient refractive index distribution (GRIN) of the human lens with conicoid surfaces able to adapt to individual distributions as well as to the changes of the lens shape and structure with age and accommodation is presented. The first part of this work was published in a companion paper [J. Opt. Soc. Am. A24, 2175 (2007)]. It included the development of the mathematical formulation of the adaptive model; the validation of its customization capability by fitting, sample by sample, a set of in vitro refractive index distributions of lenses of different ages, ranging from 7 to 82 years, from the recent literature; and an average model of the (in vitro) aging crystalline lens. Here we extrapolate that in vitro GRIN model by assuming that the same structural parameters are valid for the living lens. Then, recent data of the changes of the shape of the aging lens with accommodation from the literature are used to build an aging and accommodating lens model. This is straightforward since the GRIN model adapts automatically to the chosen external lens geometry. A strong coupling was found between the adaptive GRIN distributions and the conic constants affecting the refractive power. To account for the lens paradox and the reported changes in lens spherical aberration with age and accommodation, age- and accommodation-dependent functions for the anterior and posterior internal conic constants were derived through optimization.

Accuracy and reproducibility of Zywave, Tracey, and experimental aberrometers.

PURPOSE To compare the accuracy and verify the reliability of different commercial and experimental prototypes of aberrometers using a small group of normal subjects with low myopia. METHODS Three different devices were used to measure the wavefront aberration of five normal myopic eyes: 1) Zywave--commercial aberrometer based on a Hartmann-Shack wavefront sensor; 2) Tracey--commercial system based on the laser ray tracing principle; and 3) an experimental laboratory laser ray tracing instrument working at two different wavelengths (532 and 786 nm). A series of five measurements were taken for each subject. Pupil diameter and alignment were controlled. All wave aberration maps were reduced to a common 6.5-mm pupil diameter, and then the mean and standard deviation were computed for the series, as well as the global average and standard deviation for each subject. RESULTS Despite several important differences among devices and sessions, the results obtained with the different devices were equivalent. The main difference found between aberrometers was due to the longitudinal chromatic aberration caused by the use of different wavelengths. The signal-to-noise ratio estimated from the raw data was moderate, 12, but could be improved by a factor of 2 by discarding those measurements with a higher deviation from the mean and averaging the remaining data, which was the approach implemented in the Zywave instrument. CONCLUSION The aberrometers tested were reliable in normal eyes with low myopia. Aberrometry is a robust but noisy technique. Accuracy is limited by noise and other sources of variability, including the size and alignment of the pupil. These conclusions might not apply to eyes with large aberrations.

Multizone model for postsurgical corneas: analysis of standard and custom LASIK outcomes

A multizone model for postsurgical corneal topography is presented and applied to a comparative analysis of the outcome of standard and customized myopic LASIK. The different zones are segmented automatically by a clustering algorithm. The algorithm uses a set of three local descriptors, which correspond to normalized physical magnitudes computed for each point of the corneal topography map: Gauss curvature, root-mean-square (RMS) fit error to an ellipsoid surface model, and distance to the center of the topographic map. Both presurgical and post-LASIK corneal topographies of 31 eyes were analyzed using monozone and multizone models. The patients were classified into three groups according to the different LASIK treatments applied: Allegretto, Zyoptix, and PlanoScan. For post-LASIK corneas, the multizone model provided a lower fit error, an average of 1.2+/-0.4 microm versus 2.4+/-0.7 microm (monozone). The comparative analysis of the three different LASIK treatments showed no improvement of custom over standard treatments. The outcomes of Zyoptix and PlanoScan were basically equivalent and consistent with previous findings: The higher-order aberration (HOA) increased by a factor of two. The increase in HOA was higher, by a factor of three, after the Allegretto treatment. The multizone model shows a higher-fidelity representation and permits a deeper understanding of the postsurgical cornea.

MIRI Telescope Simulator

The MTS, MIRI Telescope Simulator, is developed by INTA as the Spanish contribution of MIRI (Mid InfraRed Instrument) on board JWST (James Web Space Telescope). The MTS is considered as optical equipment which is part of Optical Ground Support Equipment for the AIV/Calibration phase of the instrument at Rutherford Appleton Laboratory, UK. It is an optical simulator of the JWST Telescope, which will provide a diffractionlimited test beam, including the obscuration and mask pattern, in all the MIRI FOV and in all defocusing range. The MTS will have to stand an environment similar to the flight conditions (35K) but using a smaller set-up, typically at lab scales. The MTS will be used to verify MIRI instrument-level tests, based on checking the implementation/realisation of the interfaces and performances, as well as the instrument properties not subject to interface control such as overall transmission of various modes of operation. This paper includes a functional description and a summary of the development status.

Detailed design of the imaging magnetograph experiment (IMaX): a visible imager magnetograph for the Sunrise mission

In this work, it is described the Imaging Magnetograph eXperiment, IMaX, one of the three postfocal instruments of the Sunrise mission. The Sunrise project consists on a stratospheric balloon with a 1 m aperture telescope, which will fly from the Antarctica within the NASA Long Duration Balloon Program. IMaX will provide vector magnetograms of the solar surface with a spatial resolution of 70 m. This data is relevant for understanding how the magnetic fields emerge in the solar surface, how they couple the photospheric base with the million degrees of temperature of the solar corona and which are the processes that are responsible of the generation of such an immense temperatures. To meet this goal IMaX should work as a high sensitivity polarimeter, high resolution spectrometer and a near diffraction limited imager. Liquid Crystal Variable Retarders will be used as polarization modulators taking advantage of the optical retardation induced by application of low electric fields and avoiding mechanical mechanisms. Therefore, the interest of these devices for aerospace applications is envisaged. The spectral resolution required will be achieved by using a LiNbO3 Fabry-Perot etalon in double pass configuration as spectral filter before the two CCDs detectors. As well phase-diversity techniques will be implemented in order to improve the image quality. Nowadays, IMaX project is in the detailed design phase before fabrication, integration, assembly and verification. This paper briefly describes the current status of the instrument and the technical solutions developed to fulfil the scientific requirements.

The MIRI cold telescope simulator

The MIRI Telescope Simulator (MTS) is part of the Optical Ground Support System (OGSE) for the verification and calibration phase of the James Webb Space Telescope (JWST) Mid-Infrared Instrument (MIRI). The MTS will simulate the optical characteristics of the JWST output beam in an environment similar to the flight conditions. The different functionalities of the MTS are briefly described and its current design, including the illumination and imaging subsystems, is presented.

Ray tracing in the human eye: measurement and modeling of optical aberrations

The rapid development of cataract and refractive surgery requires new methods to assess the optical quality of the eye. The optimized optical design of custom treatments to improve the optical performance of individual eyes requires, at least, to have the technology to (1) measure the geometry (anatomy) of the optics of the eye; (2) measure the optical performance (refractive state, aberrations, etc); (3) Build a custom optical and anatomical model of the individual eye to treat; (4) Optimal design of custom treatments. In this communication we will present the work carried out by our group to develop methods for measuring and modeling the optical performance of the eye. In particular, we will focus, first, on the Laser Ray Tracing method that we have developed to measure the optical aberrations of the eye, as a physical in vivo implementation of the classical numerical ray tracing used by optical designers; and second, on the development of custom optical models of the eye to perform that numerical ray tracing which predicts with a high fidelity experimental measurements. The methods developed have been applied to design both custom surgery and optical aids to improve optical performance.

Efficient numerical modeling of the cornea, and applications

Corneal topography has shown to be an essential tool in the ophthalmology clinic both in diagnosis and custom treatments (refractive surgery, keratoplastia), having also a strong potential in optometry. The post processing and analysis of corneal elevation, or local curvature data, is a necessary step to refine the data and also to extract relevant information for the clinician. In this context a parametric cornea model is proposed consisting of a surface described mathematically by two terms: one general ellipsoid corresponding to a regular base surface, expressed by a general quadric term located at an arbitrary position and free orientation in 3D space and a second term, described by a Zernike polynomial expansion, which accounts for irregularities and departures from the basic geometry. The model has been validated obtaining better adjustment of experimental data than other previous models. Among other potential applications, here we present the determination of the optical axis of the cornea by transforming the general quadric to its canonical form. This has permitted us to perform 3D registration of corneal topographical maps to improve the signal-to-noise ratio. Other basic and clinical applications are also explored.