Luis Alberto Vieira de Carvalho

Different schematic eyes and their accuracy to the in vivo eye: a quantitative comparison study

Current ophthalmic technology allows the manipulation of eye components, such as anterior cornea and lens, of the human eye with a considerable precision and customization. This technology opens up the possibility of exploiting some characteristics of the eye in order to improve the methods of correcting optical aberrations. Moreover, product development and research for the eye-care professional has reached very high standards, since there is nowadays software available to design and simulate practically any mechanical or optical characteristic of the product, even before it is thrown into production line. Although quite similar in the general form, different human eye models simulate the image formation by considering different property combinations in the constitutive elements of the eye structure (such as refraction index and surface curvatures), producing retinal images that resemble very closely those of the biological eye. Using optical design software, we have implemented a simulation of 5 well-known schematic eyes available in the literature. These models were the Helmholtz-Laurance, Gullstrand, Emsley, Greivenkamp and Liou & Brennan. The optical performance of these different models was compared using different quantitative optical quality parameters. The model of Liou and Brennan, contains features of the biological eye that were not considered in previous models, as the distribution of a gradient refraction index and a decentered pupil. Furthermore, it has great reliability since it takes into account the mean value of empirical measurements of the in vivo eye in order to define size and parameters such as anterior and posterior curvature of cornea, lens, axial length, etc. Comparisons between the MTF (Modulation Transfer Function), spot diagrams and ray fan showed the difference in image quality between eye models, and the Strehl Ratio was also used as a parameter of comparison. A careful comparison between the different models showed that the first four schematic eyes have better optical quality than what is expected for the general and healthy emmetropic in vivo eye. Liou and Brennan schematic eye is the one that most closely resembles the in vivo biological eye. Therefore, in applications, such as research or product development for customized vision correction, which must consider optical properties intrinsic to the biological eye, we recommend this latter model; for applications that do not require refraction-limited performance, most of the other models should be a good approximation.

Keratoconus prediction using a finite element model of the cornea with local biomechanical properties

PURPOSE The ability to predict and understand which biomechanical properties of the cornea are responsible for the stability or progression of keratoconus may be an important clinical and surgical tool for the eye-care professional. We have developed a finite element model of the cornea, that tries to predict keratoconus-like behavior and its evolution based on material properties of the corneal tissue. METHODS Corneal material properties were modeled using bibliographic data and corneal topography was based on literature values from a schematic eye model. Commercial software was used to simulate mechanical and surface properties when the cornea was subject to different local parameters, such as elasticity. RESULTS The simulation has shown that, depending on the corneal initial surface shape, changes in local material properties and also different intraocular pressures values induce a localized protuberance and increase in curvature when compared to the remaining portion of the cornea. CONCLUSIONS This technique provides a quantitative and accurate approach to the problem of understanding the biomechanical nature of keratoconus. The implemented model has shown that changes in local material properties of the cornea and intraocular pressure are intrinsically related to keratoconus pathology and its shape/curvature.

A simple and effective algorithm for detection of arbitrary Hartmann-Shack patterns

The Hartmann-Shack sensor is well known for its capability of detecting optical aberrations from telescopic images, normally caused by the atmospheric turbulence. Since the mid-1990s, this sensor has been adapted to work with ophthalmic instrumentation to measure aberrations of the human eye. In astronomical applications, the image processing is implemented using robust closed-loop hardware systems, allowing for very high frequencies (usually in the range of 30-500 Hz). In ophthalmic instruments, this hardware solution is not proper, for two reasons: first, prices of ophthalmic instrumentation have to be at more accessible prices and, second, there is no need for ultra-high frequency closed-loop systems; in fact, as we will see along the text, recent studies of the dynamics of the eyes aberrations show that closed-loop systems of very much lower frequencies (from 10 to 40 Hz) may well eliminate the undesired micro-fluctuations in the eyes aberrations and allow for diffraction limited measurements. We have developed an effective algorithm for detection of HS patterns using an affordable commercial hardware configuration and easy to implement software. To our knowledge, this type of information has not been thoroughly disclosed elsewhere, probably due to proprietary reasons.

Videokeratoscopes for dioptric power measurement during surgery

Purpose: To evaluate 2 versions of a computerized surgical videokeratoscope that measures a central region of the cornea of approximately 4.0 to 6.0 mm in diameter to provide information on dioptric power and astigmatism. Setting: Grupo de Optica Oftalmica Universidade de São Paulo, and Departamento de Oftalmologia da Escola Paulista de Medicina, São Paulo, Brazil. Methods: The first videokeratoscope system with 10 Placido rings is based on a 15 000 fiber‐optic illuminated disk attached to the objective lens of a surgical microscope. With this system, the light intensity can be adjusted during surgery for better contrast of the Placido image. The second system with 14 Placido rings is based on a neon light source behind the Placido disk. With both systems, a 480 × 640 pixel resolution charge‐coupled device camera and an IBM‐compatible personal computer frame grabber were used. Image processing was used for boundary detection of the rings. An axial curvature algorithm based on the spherical surfaces was used to calculate the dioptric power for each examination. Measurements of 4 real spherical surfaces and 4 simulated aspheric surfaces (ellipsotoric surfaces with different apical radii and different shape factors) were performed. Results: Twenty corneas of 10 healthy volunteers were measured on both videokeratoscope systems and an EyeSys System 2000 corneal topographer. The root‐ mean‐square error for the spherical and simulated aspheric surfaces was, respectively, less than 0.20 diopter (D) and 1.30 D for the 10‐disk videokeratoscope system and less than 0.16 D and 1.40 D for the 14‐disk system. The mean deviation in corneal measurements with both systems was 0.09 mm for the radius of curvature, 0.51 D for dioptric power, and 5 degrees for cylinder. Conclusion: The results indicate that the 2 surgical videokeratoscopes are sufficiently precise to aid the anterior segment surgeon in reducing residual astigmatism in cataract surgery and keratoplasty.

Spatial and frequency domain techniques for segmentation of Placido images and accuracy implications for videokeratography

OBJECTIVE Videokeratography (VK) has been a widespread technology for corneal surface analysis since the mid 1980s. Most manufactures use personal computers attached to a Placido disc apparatus in order to capture and process digital images. Although precision reported by most manufactures are within very good limits, none of them have disclosed, probably due to proprietary reasons, the nature of the algorithm used in their image-processing phase. This is a problem when researchers want to reproduce or test their own curvature or elevation algorithms on Placido images generated on different commercial videokeratographs or even compare their algorithms on data from different manufactures. Our main objective in this work was to develop certain basic techniques for Placido image edge detection and to compare the results of each algorithm in terms of precision at the image level and also the consequences for axial curvature computations. We also propose that manufactures come forward and at least explain which image-processing technique is used in their own algorithms so other researchers and laboratories can make better use of their data to improve VK algorithms. MATERIAL/METHODS Placido images from an Eyesys system 2000 were captured for four different spherical surfaces. Each image was saved in bitmap format at the hard disk of an IBM computer. Six different image-processing algorithms were developed using different techniques well documented in the literature. The six methods were as follows: (1) first order numerical derivative, (2) first and (3) second order Fourier derivative, (4) the Marr-Hildreth filter, (5) Cannys method and (6) Mathematical Morphology. Each algorithm was tested on each of the Placido images. RESULTS Edge radial distance from center of Placido image was compared for each algorithm and a computer simulation of the VK system. The simulated image was used as absolute reference. Another approach was to calculate Axial dioptric power using, again, well documented procedures, and compare the results for each image detection algorithm. Mean deviation in terms of pixels/millimeters/dioptric power for all spheres for methods (1-6) were, respectively, (1) 33.1695/0.7961/0.79, (2) 32.79/0.7870/0.7724, (3) 60.7150/1.4572/1.4192, (4)18.97/0.4553/0.4572, (5) 46.33/1.1119/1.0917 and (6) 20.55/0.4932/0.48. DISCUSSION All methods have great deviation propagation in terms of dioptric power calculations when the axial algorithm is used and the absolute reference simulated edges are used to generate the calibration curves. This indicates that researchers should be more careful when using resulting image processing files from different videokeratographs to compare their own curvature or elevation algorithms among different instruments or even to measure the absolute precision of their new algorithms.

Videokeratograph (VKS) for monitoring corneal curvature during surgery

Objetivo: Os autores desenvolveram um videoceratografo para uso durante a cirurgia. Uma regiao central da cornea de aproximadamente 7,00 mm de diâmetro pode ser analisada, fornecendo informacao ao cirurgiao sobre poder dioptrico e astigmatismo. Metodos: O sistema e baseado em discos de Placido em forma conica, iluminados por uma fonte de luz construida com fibras opticas. O cone e acoplado a lente objetiva de um microscopio padrao Zeiss. Uma placa de captura e instalada num microcomputador IBM compativel e imagens de Placido sao digitalizadas numa resolucao de 640x480 pontos. Processamento digital das imagens e utilizado para deteccao dos discos de Placido. Resultados: Curvas de calibracao baseadas em 4 esferas foram geradas e aproximadamente 3600 valores de poder dioptrico sao computados para cada exame. Exames preliminares em 10 corneas sadias foram comparados com exames nos mesmos olhos feitos num Videoceratografo Eyesys System 2000. O desvio medio padrao foi de 0,05 mm para o raio de curvatura, 0,24 dioptrias para o poder e 5 graus para o cilindro. Conclusoes: Este videoceratoscopio cirurgico podera ser utilizado para reduzir o astigmatismo residual em procedimentos convencionais de catarata e ceratoplastia. Podera tambem ser utilizado para colher dados imediatamente anteriores as em cirurgias refrativas (PRK e LASIK).

The placido wavefront sensor and preliminary measurement on a mechanical eye.

Purpose. The hardware and software of a novel wavefront sensor was developed (The sensor presented here is patent pending.). It has the same principal of the Hartmann-Shack (HS) and other sensors that are based on slope information for recovery of wavefront surface, but a different symmetry, and does not use individual microlenses. This polar symmetry might offer differences during practical measurements that may add value to current and well-established “gold standard” techniques. Methods. The sensor consists of a set of concentric “half-donut” surfaces (longitudinally sectioned toroids) molded on an acrylic surface with a CCD located at the focal plane. When illuminated with a plane wavefront, it focuses a symmetric pattern of concentric discs on the CCD plane; for a distorted wavefront, a nonsymmetric disc pattern is formed (similar to images of a placido-based videokeratographer). From detection of shift in the radial direction, radial slopes are computed for a maximum of 2880 points, and the traditional least-squares procedure is used to fit these partial derivatives to a set of 15 conventional OSA-VSIA Zernike polynomials. Theoretical computations for several synthetic surfaces containing low-order aberration (LOA) and high-order aberration (HOA) were implemented for both the HS and the new sensor. Results. Root mean square error (RMSE) in microns when theoretical data was taken as control, for HS sensor and new sensor, was 0.02 and 0.00003 for LOA (defocus, astigmatism) and 0.07 and 0.06 for HOA (coma, spherical, and higher terms), respectively. After this, practical preliminary measurements on a mechanical eye with a 5-mm pupil and 10 different defocus aberrations ranging from –5 D to 5 D, in steps of 1 D, were compared between sensors. RMSE for difference in measurements for HS and new sensor for sphere, cylinder, and axis, was 0.13 D, 0.07 D, and 110. Measurements were taken only on defocus aberrations. Qualitative images for astigmatism are shown. Discussion. Although practical in vivo tests were not conducted in this first study, we also discuss certain possible alignment differences that may arise as a result of the different symmetry of the new sensor. To take any conclusive assumption regarding the accuracy and/or precision of this new sensor, when compared with other well–established sensors, statistically significant in vivo measurements will need to be conducted.

Quantitative comparison of different-shaped wavefront sensors and preliminary results for defocus aberrations on a mechanical eye

PURPOSE There is a general acceptance among the scientific community of Cartesian symmetry wavefront sensors (such as the Hartmann-Shack (HS) sensor) as a standard in the field of optics and vision science. In this study it is shown that sensors of different symmetries and/or configurations should also be tested and analyzed in order to quantify and compare their effectiveness when applied to visual optics. Three types of wave-aberration sensors were developed and tested here. Each sensor has a very different configuration and/or symmetry (dodecagonal (DOD), cylindrical (CYL) and conventional Hartmann-Shack (HS)). METHODS All sensors were designed and developed in the Physics Department of the Universidade de São Paulo--São Carlos. Each sensor was mounted on a laboratory optical bench used in a previous study. A commercial mechanical eye was used as control. This mechanical eye has a rotating mechanism that allows the retinal plane to be positioned at different axial distances. Ten different defocus aberrations were generated: 5 cases of myopia from -1D to -5D and 5 cases of hyperopia, from +1D to +5D, in steps of 1D following the scale printed on the mechanical eye. For each wavefront sensor a specific image-processing and fitting algorithm was implemented. For all three cases, the wavefront information was fit using the first 36 VSIA standard Zernike polynomials. Results for the mechanical eye were also compared to the absolute Zernike surface generated from coefficients associated with the theoretical sphere-cylinder aberration value. RESULTS Precision was analyzed using two different methods: first, a theoretical approach was used by generating synthetic Zernike coefficients from the known sphere-cylinder aberrations, simply by applying sphere-cylinder equations in the backward direction. Then comparisons were made of these coefficients with the ones obtained in practice. Results for DOD, HS and CYL sensors were, respectively, as follows: mean of root mean square (RMSE) for all aberrations, when theoretical Zernike coefficients were used as control, was 0.22, 0.66 and 0.26 microns; RMSE of sphere-cylinder values when compared to autorefractor measurements was 0.18D, 0.22D and 0.35D for sphere, 0.14D, 0.24D and 0.17D for cylinder, 34.36 degrees, 35.16 degrees and 26.36 degrees for axis; RMSE of sphere-cylinder values when theoretical values were used as control was 0.11D, 0.29D and 0.46D for sphere, 0.15D, 0.28D and 0.17D for cylinder, 19.71 degrees, 25.56 degrees and 18.56 degrees for axis. CONCLUSION The main conclusion is that the symmetry of an optical sensor is not an important consideration when measuring typical eye aberrations such as defocus (myopic and hyperopic), but there are differences. In this sense, the polar symmetry sensors render results that are equivalent to the traditional Cartesian Hartmann-Shack sensor, but furnish an easier method for determining the optical center.

Preliminary Results of an Instrument for Measuring the Optical Aberrations of the Human Eye

Laborat´orio de Optica Oft´´ almica - Grupo deOptica, IFSC-USP´S˜ao Carlos, SP, CEP 13560-900, BrazilReceived on 31 August, 2002The human eye, as our biological vision instrument, contains intrinsic optical defects, referred to as opticalaberrations or ametropia. The immediate consequence of such aberrations is poor quality of images formed atthe retina. With the advent of more precise pulsed lasers for eye surgery, the development of instrumentationto determine precisely the higher order aberrations of the eye became a crucial chalange. Current instrumentsavailable commercially (refractometers) measure only the lower optical aberrations of the eye, i. e., myopia,hyperopia and astigmatism. In the present work we have developed a high resolution refractometer based on theHartmann-Shack(HS) wave-front sensor. The HS sensor was originally developed for aberration measurementsin general optical systems, and is of wide-spread usage in adaptive optics applications such as astronomicaltelescopes. Preliminary results for a mechanical eye are presented here and the RMSE in dioptric power (D)and cylinder axis (in degrees) were as follows: 0.04D for sphere and cylinder and

A new wavefront sensor with polar symmetry: Quantitative comparisons with a Shack-Hartmann wavefront sensor

PURPOSE A novel wavefront sensor has been developed. It follows the same principle of the Shack-Hartmann wavefront sensor in that it is based on slope information. However, it has a different symmetry, which may offer benefits in terms of application. METHODS The new wavefront sensor consists of a set of donut-shaped acrylic lenses with a charge coupled device located at the focal plane. From detection of shift in the radial direction, radial slopes are computed for 2880 points. Theoretical computations for higher order aberrations and lower order aberrations were implemented for the Shack-Hartmann wavefront sensor and the new wavefront sensor, and practical measurements were conducted on several sphere-cylinder trial lenses. RESULTS The overall mean value of root mean square error (RMSE) (in microns) for theoretical computations was 0.03 for the Shack-Hartmann wavefront sensor and 0.02 for the new wavefront sensor. The mean value of RMSE for lower order aberrations (1-5) was 0.01 and 0.00003, and for higher order aberrations was 0.02 and 0.02, for the Shack-Hartmann and new wavefront sensors, respectively. For practical measurements (sphere, cylinder, axis), the standard deviation was 0.04 diopters (D), 0.04 D, and 4 degrees for the new wavefront sensor and 0.02 D, 0.02 D, and 5 degrees for the Shack-Hartmann wavefront sensor. CONCLUSIONS Precision of the new wavefront sensor when measuring astigmatic and spherical surfaces is compatible with the Shack-Hartmann wavefront sensor. Centration with this new sensor is an absolute process using the center of the entrance pupil, which is where the line of site passes. This wavefront sensor, similar to the Shack-Hartmann sensor, does not eliminate the possibility of tilt. For more conclusive and statistically valid data, in vivo measurements are needed.