Mechanism of compensation of aberrations in the human eye

We studied the mechanism of compensation of aberrations within the young human eye by using experimental data and advanced ray-tracing modeling. Corneal and ocular aberrations along with the alignment properties (angle kappa, lens tilt, and decentration) were measured in eyes with different refractive errors. Predictions from individualized ray-tracing optical models were compared with the actual measurements. Ocular spherical aberration was, in general, smaller than corneal spherical aberration without relation to refractive error. However, horizontal coma compensation was found to be significantly larger for hyperopic eyes where angle kappa tended to also be larger. We propose a simple analytical model of the relationship between the corneal coma compensation effect with the field angle and corneal and crystalline shape factors. The actual shape factors corresponded approximately to the optimum shapes that automatically provide this coma compensation. We showed that the eye behaves as an aplanatic optical system, an optimized design solution rendering stable retinal image quality for different ocular geometries.     

Comparison of real and computer-simulated outcomes of LASIK refractive surgery

Computer simulations of alternative LASIK ablation patterns were performed for corneal elevation maps of 13 real myopic corneas (range of myopia, -2.0 to -11.5 D). The computationally simulated ablation patterns were designed with biconic surfaces (standard Munnerlyn pattern, parabolic pattern, and biconic pattern) or with aberrometry measurements (customized pattern). Simulated results were compared with real postoperative outcomes. Standard LASIK refractive surgery for myopia increased corneal asphericity and spherical aberration. Computations with the theoretical Munnerlyn ablation pattern did not increase the corneal asphericity and spherical aberration. The theoretical parabolic pattern induced a slight increase of asphericity and spherical aberration, explaining only 40% of the clinically found increase. The theoretical biconic pattern controlled corneal spherical aberration. Computations showed that the theoretical customized pattern can correct high-order asymmetric aberrations. Simulations of changes in efficiency due to reflection and nonnormal incidence of the laser light showed a further increase in corneal asphericity. Consideration of these effects with a parabolic pattern accounts for 70% of the clinical increase in asphericity.     

Wave-front aberrations in the anterior corneal surface and the whole eye

In order to investigate the sources of wave-front aberrations in the human eye, we have measured the aberrations of the anterior cornea and the whole eye using a topographic system and a psychophysical wave-front sensor. We have also calculated the aberrations for the internal optics of both eyes of 45 young subjects (aged 9 to 29 years). The mean rms for the anterior cornea was similar to that for the internal optics and thewhole eye when astigmatism was included, but less than that for both the internal optics and the whole eye with astigmatism removed. For eyes with low whole-eye rms values, mean rms for the anterior cornea was greater than that for the whole eye, suggesting that the anterior corneal aberration is partially compensated by the internal optics of the eye to produce the low whole-eye rms. For eyes with larger whole-eye rms values, the rms values for both the anterior cornea and the internal optics were less than that for the whole eye. Thus the aberrations for the two elements tend to be primarily additive. This pattern exists whether or not astigmatism was included in the wave-front aberration rms. For individual Zernike terms, astigmatism and spherical aberration in the anterior cornea were partially compensated by internal optics, while some other Zernike terms showed addition between the anterior cornea and internal optics. Individual eyes show different combinations of compensation and addition across different Zernike terms. Our data suggest that the reported loss of internal compensation for anterior corneal aberrations in elderly eyes with large whole-eye aberrations [J. Opt. Soc. Am. A 19, 137 (2002)] may also occur in young eyes.     

Optical aberrations of the human cornea as a function of age

We investigated how the optical aberrations associated with the anterior surface of the human cornea change with age in a normal population. Aberrations were computed for a central part of the cornea (4, 5, and 6 mm in diameter) from the elevation data provided by a videokeratographic system. Measurements were obtained in 59 normal healthy, near-emmetropic [spherical equivalent lower than 2 diopters (D)] subjects of three age ranges: younger (20-30 years old), middle-aged (40-50 years old), and older (60-70 years old). The average corneal radius decreased with age and the cornea became more spherical. As a consequence, spherical aberration was significantly larger in the middle-aged and older corneas. Coma and other higher-order aberrations also were correlated with age. The root mean square of the wave aberration exhibited a linear positive correlation (P < 0.003) with age for the three ranges of pupil diameter. Despite a large intersubject variability, the average amount of aberration in the human cornea tends to increase moderately with age. However, this increase alone is not enough to explain the substantial reduction previously found in retinal image quality with age. The change in the aberrations of the lens with age and the possible loss of part of the balance between corneal and lenticular aberrations in youth may be the main factors responsible for the reduction of retinal image quality through the life span.     

Influences of reference plane and direction of measurement on eye aberration measurement

We explored effects of measurement conditions on wave aberration estimates for uncorrected, axially myopic model eyes. Wave aberrations were initially referenced to either the anterior corneal pole or the natural entrance pupil of symmetrical eye models, with rays traced into the eye from infinity (into the eye) to simulate normal vision, into the eye from infinity and then back out of the eye from the retinal intercepts (into/out of the eye), or out of the eye from the retinal fovea (out of the eye). The into-the-eye and out-of-the-eye ray traces gave increases in spherical aberration as myopia increased, but the into/out-of-the-eye ray trace showed little variation in spherical aberration. Reference plane choice also affected spherical aberration. Corresponding residual aberrations were calculated after the models had been optically corrected, either by placing the object or image plane at the paraxial far point or by modifying corneas to simulate laser ablation corrections. Correcting aberrations by ablation was more complete if the original aberrations were referenced to the cornea rather than to the entrance pupil. For eyes corrected by spectacle lenses, failure to allow for effects of pupil magnification on apparent entrance pupil diameter produced larger changes in measured aberrations. The general findings regarding choice of reference plane and direction of measurement were found to be equally applicable to eyes that lacked rotational symmetry.     

Design, calibration, and testing of a laser flare meter

A laser flare meter, insensitive to corneal, lens, and eye background scattering and calibrated by measurements and theoretical modeling, is reported. Calibration measurements and theoretical calculations of light scattering from albumin solutions were found to agree within the limits of error. The results from in vivo measurements of normal eyes of different ages agreed well with normal protein content of aqueous humor. A special aperture design was used to reduce the unwanted background scattering resulting in signal-to-background ratios between 1:1 and 1:3 for normal eyes. Moderately cataractous eyes, with increased scattering from the lens, could be measured with sufficient accuracy. The reproducibility was measured to be ~ 12%. We studied how the flare is affected by sex, right/left eye, eye color, time of day, pupillary dilation, and an intraocular pressure measurement. No differences of practical importance were found.     

非球面人工晶体设计及其光学性能研究

提出了非球面人工晶体的设计思路及方法,即根据个体人眼的角膜地形图,将其转换为波前图,获得Zemike系数Z40(球差)项,在该球差值基础上设计并得到非球面人工晶体结构参数.对植入9.5D和20.5D人工晶体的两实际患眼成像质量的模拟分析表明:以本丈方法设计的非球面人工晶体在对人眼系统的MTF,对比敏感度及离焦MTF的改善上都明显优于传统的球面人工晶体,光学性能良好.本文为非球面人工晶体的设计提供了切实可行的方法,并为其在临床上应用提供了一定的理论基础.     

Interferometric measurement of near-cylindrical surfaces with high amplitude resolution

Subaperture interferometric measurements of highly curved surfaces with a shape close to a cylinder have been performed in a normal-incident setup that consists of a Fizeau interferometer in combination with a plano-concave cylindrical lens. Since the field of view in the circumferential direction is limited by spherical aberration, the optical components were designed to minimize spherical aberration. For reference measurements a second plano-convex cylindrical lens was used. The subaperture setup leads to three-dimensional surface maps of the objects under test. To eliminate the influence of residual geometric aberrations, rectangular polynomials have been fitted and subtracted from the raw data. For deformations with spatial wavelengths below 30 mm, a rms amplitude resolution of 1 nm and a rms amplitude accuracy of 3 nm were achieved. Measurements on Wolter-type-I mirror shells are discussed in detail.     

Interocular high-order corneal wavefront aberration symmetry

The interocular symmetry of the high-order corneal wavefront aberration (WA) in a population of myopic eyes was analyzed before and after photorefractive keratectomy (PRK). The preoperative and one-year postoperative corneal aberration data (from third to seventh Zernike orders) for 4- and 7-mm pupils from right and left eyes were averaged after correcting for the effects of enantiomorphism to test for mirror symmetry. Also, the mean corneal point-spread function (PSF) for right and left eyes was calculated. Preoperatively, a moderate and high degree of correlation in the high-order corneal WA between eyes was found for 4- and 7-mm pupils, respectively. Myopic PRK did not significantly change the interocular symmetry of corneal high-order aberrations. No discernible differences in the orientation PSF between eyes were observed one year after surgery in comparison with the preoperative state over the two analyzed pupils.     

Phakometry and lens tilt and decentration using a custom-developed Purkinje imaging apparatus: validation and measurements

We present a Purkinje imaging system for phakometry and measurement of tilt and decentration of crystalline and intraocular lenses (IOLs). Crystalline lens radii of curvature were estimated by using both a merit function and the equivalent mirror approaches. Tilts and decentrations were estimated by using Phillips's linear analysis. We present a complete validation of the technique through exhaustive computer simulations and control experiments, and measurements in 17 normal eyes (mean age 26.67 +/- 2.31) and nine postcataract surgery eyes (mean age 74 +/- 2.3). Crystalline lens radii ranged from 12.7 to 8.81 mm and from -5.64 to -7.09 mm for anterior and posterior surfaces, respectively. Crystalline lens tilt ranged from 2.8 to -2.87 deg horizontally and from 2.58 to -1 deg vertically. Crystalline lens decentration ranged from 0.09 to 0.45 mm horizontally and from 0.09 to -0.22 mm vertically. IOL tilt ranged from 3.6 to -1.51 deg horizontally and from 5.97 to -1.85 deg vertically. IOL decentration ranged from 0.53 to -0.31 mm horizontally and from 0.13 to -0.96 mm vertically.     

Long-term optical quality of the photoablated cornea

High-order coreal wavefront analysis was performed in a population of 60 myopic eyes that underwent photorefractive keratectomy. Corneal aberration data over 3, 5, and 7 mm pupils were collected for up to three years after surgery. The optical performance of the anterior cornea was characterized by estimation of the modulation transfer function (MTF) and the point-spread function. The high-order corneal wavefront aberrations were shown to stabilize one year after surgery. Over photopic pupils, after an early slight increase, corneal RMS-high-order aberrations (HOA) tended to decrease toward preoperative values. On the other hand, over mid- and large-pupil sizes, corneal HOA significantly increased compared with the preoperative state, while the optical performance of the cornea was diminished. The MTF ratio showed a distinct decline in the optical quality of postoperative corneas at low and middle spatial frequencies over larger pupils in the range between 6 and 19 c/deg, especially for deeper ablations.     

Anterior corneal and internal contributions to peripheral aberrations of human eyes

Anterior corneal and internal component contributions to overall peripheral aberrations of five human eyes were determined, based on corneal topography and overall aberration measurements. Anterior corneal position and orientation (tilt) were referenced to the line of sight. Ray tracing was performed through the anterior cornea for 6-mm-diameter pupils at angles out to 40 degrees in both the temporal and the nasal visual fields. In general, both component and overall Zernike aberrations were greater for the nasal than for the temporal visual field. In general, the anterior corneal aberration components were considerably higher than the overall aberrations across the visual field and were balanced to a considerable degree by the internal ocular aberration components. The component and overall levels of Zernike third-order aberrations showed linear trends away from the fixation axis, and the component levels of Zernike fourth-order aberrations showed quadratic trends away from the fixation axis. The second-order, but not higher-order, aberration components were susceptible to the choice of image radius of curvature, while disregarding corneal position and orientation affected second- and higher-order aberration components.     

Statistical variation of aberration structure and image quality in a normal population of healthy eyes

A Shack-Hartmann aberrometer was used to measure the monochromatic aberration structure along the primary line of sight of 200 cyclopleged, normal, healthy eyes from 100 individuals. Sphero-cylindrical refractive errors were corrected with ophthalmic spectacle lenses based on the results of a subjective refraction performed immediately prior to experimentation. Zernike expansions of the experimental wave-front aberration functions were used to determine aberration coefficients for a series of pupil diameters. The residual Zernike coefficients for defocus were not zero but varied systematically with pupil diameter and with the Zernike coefficient for spherical aberration in a way that maximizes visual acuity. We infer from these results that subjective best focus occurs when the area of the central, aberration-free region of the pupil is maximized. We found that the population averages of Zernike coefficients were nearly zero for all of the higher-order modes except spherical aberration. This result indicates that a hypothetical average eye representing the central tendency of the population is nearly free of aberrations, suggesting the possible influence of an emmetropization process or evolutionary pressure. However, for any individual eye the aberration coefficients were rarely zero for any Zernike mode. To first approximation, wave-front error fell exponentially with Zernike order and increased linearly with pupil area. On average, the total wave-front variance produced by higher-order aberrations was less than the wave-front variance of residual defocus and astigmatism. For example, the average amount of higher-order aberrations present for a 7.5-mm pupil was equivalent to the wave-front error produced by less than 1/4 diopter (D) of defocus. The largest pupil for which an eye may be considered diffraction-limited was 1.22 mm on average. Correlation of aberrations from the left and right eyes indicated the presence of significant bilateral symmetry. No evidence was found of a universal anatomical feature responsible for third-order optical aberrations. Using the Marechal criterion, we conclude that correction of the 12 largest principal components, or 14 largest Zernike modes, would be required to achieve diffraction-limited performance on average for a 6-mm pupil. Different methods of computing population averages provided upper and lower limits to the mean optical transfer function and mean point-spread function for our population of eyes.     

Effective spherical aberration compensation by use of a nematic liquid-crystal device

The next generation of optical data storage system beyond DVDs will use blue laser light and an objective lens with a high numerical aperture of 0.85 to increase storage capacity. Such high numerical aperture systems have an inherent higher sensitivity to aberrations. In particular, the spherical aberration caused by cover layer thickness tolerances and--more obvious--by dual-layer disks with a typical separation of approximately 20 microm between the two layers must be compensated. We propose a novel transmissive nematic liquid-crystal device, which is capable of compensating spherical aberration that occurs during the operation of optical pickup systems.     

The Aberrations of Cat's Eyes in Fourier Spectrometers

If two cat's eyes with spherical mirrors are used in interferometers for Fourier spectroscopy, their aberrations do not match when one is displaced to change the optical path. The most important aberrations, fourth-order coma and sixth-order spherical aberration, then limit the angular aperture that can be used. An approximate theory has been developed and checked against computations. The results confirm the practical experience that spherical mirrors can be used at reasonable apertures.     

The design of a triplet with a shape-dependent third-order aberration optimization technique

Abstract

We have derived a series of shape-dependent third-order aberration equations involving lens thickness. These equations are used in a simple and direct method to correct real aberrations and to find the minimum aberration for triple design that has been proposed. These calculated third-order aberrations can exactly meet the target values for each stage by means of the damped least-squares method. The shape of the three elements permits the control of three third-order aberrations: spherical aberration, coma and astigmatism. The spherical aberration is targeted first. The minimal value of the real on-axis aberration is obtained. Similarly, the coma and astigmatism target values are adjusted so as to force the full field angle real off-axis aberrations down to a minimum. Finally, the manual adjustment of the lens thickness and air spacing is used to attain the minimum aberration at the 0.7 field angle. To verify the method, two triplet design examples are presented.     

Validation of a combined corneal topographer and aberrometer based on Shack-Hartmann wave-front sensing

A corneal aberrometer based on Shack-Hartmann wave-front sensing was developed and validated by using calibrated aspheric surfaces. The aberrometer was found to accurately measure corneal reflective aberrations, from which corneal topography and corneal refractive aberrations were derived. Measurements of reflective aberrations correlated well with theory (R2 = 0.964 to 0.994). The sag error root mean square (RMS) was small, ranging from 0.1 to 0.17 microm for four of the five calibrated surfaces with the fifth at 0.36 microm as a result of residual defocus. Measured refractive aberrations matched with theory and whole-eye aberrometry to within a small fraction of a wavelength. Measurements on three human corneas revealed very large refractive astigmatism (0.65-1.2 microm) and appreciable levels of trefoil (0.08-0.47 microm), coma (0.14-0.19 microm), and spherical aberration (0.18-0.25 microm). The mean values of these aberrations were significantly larger than the RMS in repeated measurements.     

Contribution of the cornea and internal surfaces to the change of ocular aberrations with age.

We studied the age dependence of the relative contributions of the aberrations of the cornea and the internal ocular surfaces to the total aberrations of the eye. We measured the wave-front aberration of the eye with a Hartmann-Shack sensor and the aberrations of the anterior corneal surface from the elevation data provided by a corneal topography system. The aberrations of the internal surfaces were obtained by direct subtraction of the ocular and corneal wave-front data. Measurements were obtained for normal healthy subjects with ages ranging from 20 to 70 years. The magnitude of the RMS wave-front aberration (excluding defocus and astigmatism) of the eye increases more than threefold within the age range considered. However, the aberrations of the anterior corneal surface increase only slightly with age. In most of the younger subjects, total ocular aberrations are lower than corneal aberrations, while in the older subjects the reverse condition occurs. Astigmatism, coma, and spherical aberration of the cornea are larger than in the complete eye in younger subjects, whereas the contrary is true for the older subjects. The internal ocular surfaces compensate, at least in part, for the aberrations associated with the cornea in most younger subjects, but this compensation is not present in the older subjects. These results suggest that the degradation of the ocular optics with age can be explained largely by the loss of the balance between the aberrations of the corneal and the internal surfaces.