Le Grand Eye Research Articles

Design of optical system for binocular fundus camera

A non-mydriasis optical system for binocular fundus camera has been designed in this paper. It can capture two images of the same fundus retinal region from different angles at the same time, and can be used to achieve three-dimensional reconstruction of fundus. It is composed of imaging system and illumination system. In imaging system, Gullstrand Le Grand eye model is used to simulate normal human eye, and Schematic eye model is used to test the influence of ametropia in human eye on imaging quality. Annular aperture and black dot board are added into illumination system, so that the illumination system can eliminate stray light produced by corneal-reflected light and omentoscopic lens. Simulation results show that MTF of each visual field at the cut-off frequency of 90lp/mm is greater than 0.2, system distortion value is −2.7%, field curvature is less than 0.1 mm, radius of Airy disc is 3.25um. This system has a strong ability of chromatic aberration correction and focusing, and can image clearly for human fundus in which the range of diopters is from −10 D to +6 D(1 D = 1 m−1).

Minimizing the IOL Power Error Induced by Keratometric Power

To evaluate theoretically in normal eyes the influence on IOL power (PIOL) calculation of the use of a keratometric index (nk) and to analyze and validate preliminarily the use of an adjusted keratometric index (nkadj) in the IOL power calculation (PIOLadj). A model of variable keratometric index (nkadj) for corneal power calculation (Pc) was used for IOL power calculation (named PIOLadj). Theoretical differences (ΔPIOL) between the new proposed formula (PIOLadj) and which is obtained through Gaussian optics ((Equation is included in full-text article.)) were determined using Gullstrand and Le Grand eye models. The proposed new formula for IOL power calculation (PIOLadj) was prevalidated clinically in 81 eyes of 81 candidates for corneal refractive surgery and compared with Haigis, HofferQ, Holladay, and SRK/T formulas. A theoretical PIOL underestimation greater than 0.5 diopters was present in most of the cases when nk = 1.3375 was used. If nkadj was used for Pc calculation, a maximal calculated error in ΔPIOL of ±0.5 diopters at corneal vertex in most cases was observed independently from the eye model, r1c, and the desired postoperative refraction. The use of nkadj in IOL power calculation (PIOLadj) could be valid with effective lens position optimization nondependent of the corneal power. The use of a single value of nk for Pc calculation can lead to significant errors in PIOL calculation that may explain some IOL power overestimations with conventional formulas. These inaccuracies can be minimized by using the new PIOLadj based on the algorithm of nkadj.

Algorithm for Correcting the Keratometric Estimation Error in Normal Eyes

To obtain an accurate algorithm for calculating the keratometric index that minimizes the errors in the calculation of corneal power assuming only a single corneal surface in the range of corneal curvatures of the normal population. Corneal power was calculated by using the classical keratometric index and also by using the Gaussian equation. Differences between types of calculation of corneal power were determined and modeled by regression analysis. We proposed two options for the selection of the most appropriate keratometric index (n(k)) value for each specific case. First was the use of specific linear equations (depending on the ratio of the anterior to the posterior curvature, k ratio) according to the value of the central radius of curvature of the anterior corneal surface (r(1c)) in 0.1 mm steps and the theoretical eye model considered. The second was the use of a general simplified equation only requiring r(1c) (Gullstrand eye model, n(k) = -0.0064286r(1c) + 1.37688; Le Grand eye model, n(k) = -0.0063804r(1c) + 1.37806). The generalization of the keratometric index (n(k)) value is not an appropriate approximation for the estimation of the corneal power and it can lead to significant errors. We proposed a new algorithm depending on r(1c), with a maximal associated error in the calculation of the corneal power of 0.5 D and without requiring knowledge of the posterior corneal curvature.

Effects of measurement errors on refractive outcomes for pseudophakic eye based on eye model

With the Gullstrand–Le Grand eye model, the effects of various measurement errors on refractive outcomes for pseudophakic eye are studied. An equation to calculate the postoperative refractive error for pseudophakic eyes is derived. The accuracy to get a refractive error less than ca. 25 D is ±0.1 mm for the axial length, ±0.03 mm for the radius of the corneal anterior surface, ±0.12 D for the corneal power and ±0.16 mm for the postoperative anterior chamber depth (ACD). An error of 1 D in intraocular lens (IOL) power leads to a postoperative refractive error of −0.69 D. K-reading leads to a postoperative hyperopia from 0.18 to 0.74 D for eye with different refractive errors previously corrected. The constant velocity in ultrasound biometry assumption overestimates the axial length from 0.17 to 0.31 mm with actual axial length ranging from 21.31 to 32.31 mm. Errors in axial length, corneal power or radius of the corneal anterior surface and postoperative ACD play critical roles in determining the refractive outcomes. The constant-velocity assumption tends to overestimate the axial length. The change of the ratio of corneal anterior to the posterior surface is of minor importance for the overestimation of K-reading.

The study of wavelength-dependent wavefront aberrations based on individual eye model

Theoretical calculations of the wavelength dependence of the ocular wavefront aberrations are performed with individual eye model. Individual eye model, based on the traditional Gullstrand–Le Grand eye model, has been established with measured individual cornea data, eyeball depth and wavefront aberrations. We analyze the wavelength-dependent wavefront aberrations at 12 different visible wavelengths (between 400 and 750 nm) for eight eyes. The change of defocus with wavelength (longitudinal chromatic aberration, LCA) is noticeable, and in good agreement with the results from references. In most cases, the primary spherical aberration changes significantly with wavelength. In comparison with the primary spherical aberration, the other higher-order wavefront aberrations have a smaller change with wavelength. These results have potential applications in those situations where defocus or higher-order wavefront aberrations information in arbitrary wavelength is required.

Ray tracing through a schematic eye containing second‐order (quadric) surfaces using 4 × 4 matrix notation

Ray tracing is used in ophthalmology for evaluation of the optical properties of the eye. We demonstrate an algebraic method for tracing a bundle of rays through the optical system of an eye containing aspheric surfaces. Restricting to second-order surfaces (quadric surfaces) such as ellipsoids, paraboloids or hyperboloids, a surface is described by a 4 x 4 matrix. In this case, the normal vector can be derived analytically and the ray-surface intersection is calculated by solving a quadratic equation. We applied this straightforward matrix-based strategy to the spherical 4-surface Le Grand schematic eye, and the Le Grand eye modified by Kooijman containing four aspheric surfaces. We calculated the spot diagram for the focal plane as well as a pre- and post-focal plane for both model eyes, and found that the optical quality of the aspheric model characterized by the ray scatter in the spot diagram at the focal plane is much better than that of the spherical model. This calculation strategy may be helpful for evaluating the image distortion of decentred or tilted spherical or aspheric artificial intra-ocular lenses.

Determination of pseudophakic accommodation with translation lenses using Purkinje image analysis

To determine pseudophakic accommodation of an accommodating posterior chamber intraocular lens (translation lens) using Purkinje image analysis and linear matrix methods in the paraxial space. A 2 x 2 system matrix was defined for each Purkinje image I to IV using refraction, translation and mirror matrices. Image size (m) and axial image position (z) was determined as an example for an off-axis object (a 0.2 m off-axis object located 0.5 m in front of the cornea.). First, our method was applied to the phakic relaxed (emmetropic) and accommodated (6.96 D) Le Grand eye. Secondly, for demonstration of the applicability of the calculation scheme to the pseudophakic eye, we provide a clinical example where we determine the accommodation amplitude of the translation lens (1 CU, HumanOptics, Erlangen, Germany) from photographed Purkinje images in the relaxed and accommodated state. From the biometric data: axial length 23.7 mm, corneal power 43.5, corneal thickness 550 microns, implanted intraocular lens (IOL) with a refractive power of 20.5 D (shape equi-biconvex, refractive index 1.46), and refractive indices of the cornea, aqueous and vitreous from the Le Grand model eye, we calculated the refractive state and the sizes of Purkinje images I and III initiated from two off-axis light sources. For the Le Grand model eye, Purkinje image II (z/m = 3.5850 mm/0.0064) is slightly smaller than and directly in front of image I (z/m = 3.8698 mm/0.0077). Purkinje image III (z/m = 10.6097 mm/0.0151) is nearly double the size of image I and during accommodation it moves from the vitreous into the crystalline lens. Purkinje IV (z/m = 4.3244 mm/-0.0059) is inverted, three quarters the size of image I, lies in the crystalline lens and moves slightly towards the retina. For the pseudophakic eye, pseudophakic accommodation of 1.10 D was calculated from the proportion of distances between both Purkinje images I and III in the relaxed (3.04) and accommodated (2.75) state, which is in contrast to the total subjective accommodation of 2.875 D evaluated with an accommodometer. We present a straightforward mathematical strategy for calculation of the Purkinje images I-IV. Results of our model calculation resemble the values provided by Le Grand. In addition, this approach yields a simple en bloc scheme for determination of pseudophakic accommodation in pseudophakic eyes with accommodative lenses (translation lenses) using Purkinje image photography.

The Recovery of Posterior Cornea and Anterior Lens Radii by a Novel Ray-Tracing Method

Methods for estimating ocular surface radii are typically based on paraxial vergence calculations, need to account for finite source positions, and require refocusing of the camera. This article describes (1) a telecentric ray-finding method; and (2) its application to the problem of determining posterior cornea (R2) and anterior lens (R3) radii by a regression procedure that addresses these issues. The ray-finding algorithm simulates Purkinje image heights Pj(h) (for j = 2, 3; for the Le Grand eye) for the expected range of Rj. A two-step cubic regression procedure fits this image data globally and then over a refined interval to estimate Rj locally. The goodness of fit is measured by the R statistic. A standard method is compared with the new method in simulation. Mean absolute errors and SD's are recorded for 10 randomly chosen R2 and R3. The effect of errors caused by (1) axial shift of the posterior cornea and anterior lens (axially up to +/-0.1 mm); and (2) camera digitization (pixel sizes of 20 microm) are simulated. The method can make use of general surface height information; therefore, it is tested on an eye with nonspherical cornea shape (a toroidal surface). The time to generate Rj is no more than 45 s (R3), with R > 0.9999. The errors for the unmodified eye are (1.3 +/- 2.1) x 10 mm (R2) and (2.4 +/- 1.6) x 10 mm (R3) (new) vs. (5.6 +/- 0.9) x 10 mm (R2) and (1.1 +/- 1.0) x 10 mm (R3) (standard). Digitization increases errors to 0.32 +/- 0.16 mm (R2) and 0.10 +/- 0.10 (R3) (new) vs. 0.45 +/- 0.33 mm (R2) and 0.48 +/- 0.13 mm (R3) (standard). Axial shift error for R2 is similar between methods, with a tendency toward lower error for the new method given digitization error. This trend is found for R3, although the new method now does consistently better with digitization error. Shift contributes the smaller proportion of total error (approximately 10 mm) compared with digitization (approximately 10 mm). The errors for the toroidal surface are (5.7 +/- 7.6) x 10 mm (R2) and (1.1 +/- 0.7) x 10 mm (R3) (new) compared with errors of 0.18 +/- 0.01 mm (R2) and 0.44 +/- 0.07 mm (R3) (standard). The new method produces better results in this case. A telecentric image-computing algorithm produces accurate image positions. A two-step cubic regression produces accurate estimates of R2 and R3 (errors approximately 10 mm). This error increases with axial shift (approximately 10 mm) and digitization (approximately 10 mm). The new method does better than a standard method ignoring all the errors and tends to handle digitization error better. The new method works well on a toroidal anterior cornea. Testing on model/real eyes is required. Efforts are continuing to refine methods for videophakometry.

Geometric ray tracing for design of customized ablation in laser in situ keratomileusis.

By means of an individualized optical model of the visual system, a customized surgical correction is proposed to achieve emmetropia and best visual acuity. The study included 64 eyes with myopia or myopic astigmatism that underwent LASIK with the Nidek EC-5000 excimer laser. The mean age was 33 years (19 to 54 yr). Mean myopia was -3.70 D (0 to -7.50 D) and mean astigmatism was -0.90 D (0 to -4.00 D). The model included a personalized Le Grand eye model, a geometric ray tracing process, and a statistical study of postoperative corneal flattening. As a final result, the model provided an interval of corneal radius to be sculpted in the stroma to maximize visual acuity attainable without correction. The mean radius of the interval was used to obtain the sphere-cylinder correction. In 100% of eyes with 0 to +0.50 D of residual spherical equivalent refraction (n = 39), the sculpted radius was inside the surgical interval and in the 30% of the "non-satisfactory" surgeries (7/25 eyes) the sculpted radius was outside the interval. An objective optical method has been developed to obtain a customized ablation for LASIK.

Le Grand eye for the study of ocular chromatic aberration

In this technical note we study the prediction of ocular chromatic aberration which provides Le Grand's complete theoretical eye model. Theoretical computations of the longitudinal chromatic aberration are lower than experimental results. However, we show that experimental results of the chromatic difference of position (CDP) agree with theoretical predictions. The fit of the CDP for this model is practically the same as the one obtained for the Thibos reduced eye.

Le Grand eye for the study of ocular chromatic aberration

In this technical note we study the prediction of ocular chromatic aberration which provides Le Grand's complete theoretical eye model. Theoretical computations of the longitudinal chromatic aberration are lower than experimental results. However, we show that experimental results of the chromatic difference of position (CDP) agree with theoretical predictions. The fit of the CDP for this model is practically the same as the one obtained for the Thibos reduced eye.