Antonio Guirao

Monochromatic aberrations of the human eye in a large population

From both a fundamental and a clinical point of view, it is necessary to know the distribution of the eyes aberrations in the normal population and to be able to describe them as efficiently as possible. We used a modified Hartmann-Shack wave-front sensor to measure the monochromatic wave aberration of both eyes for 109 normal human subjects across a 5.7-mm pupil. We analyzed the distribution of the eyes aberrations in the population and found that most Zernike modes are relatively uncorrelated with each other across the population. A principal components analysis was applied to our wave-aberration measurements with the resulting principal components providing only a slightly more compact description of the population data than Zernike modes. This indicates that Zernike modes are efficient basis functions for describing the eyes wave aberration. Even though there appears to be a random variation in the eyes aberrations from subject to subject, many aberrations in the left eye were found to be significantly correlated with their counterparts in the right eye.

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.

Compensation of corneal aberrations by the internal optics in the human eye.

The objective was to study the relative contribution of the optical aberrations of the cornea and the internal ocular optics (with the crystalline lens as the main component) to overall aberrations in the human eye. Three sets of wave-front aberration data were independently measured in the eyes of young subjects: for the anterior surface of the cornea, the complete eye, and internal ocular optics. The amount of aberration of both the cornea and internal optics was found to be larger than for the complete eye, indicating that the first surface of the cornea and internal optics partially compensate for each others aberrations and produce an improved retinal image. This result has a number of practical implications. For example, it shows the limitation of corneal topography as a guide for new refractive procedures and provides a strong endorsement of the value of ocular wave-front sensing for those applications.

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.

Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations

An ideal correcting method, such as a customized contact lens, laser refractive surgery, or adaptive optics, that corrects higher-order aberrations as well as defocus and astigmatism could improve vision. The benefit achieved with this ideal method will be limited by decentration. To estimate the significance of this potential limitation we studied the effect on image quality expected when an ideal correcting method translates or rotates with respect to the eyes pupil. Actual wave aberrations were obtained from ten human eyes for a 7.3-mm pupil with a Shack-Hartmann sensor. We computed the residual aberrations that appear as a result of translation or rotation of an otherwise ideal correction. The model is valid for adaptive optics, contact lenses, and phase plates, but it constitutes only a first approximation to the laser refractive surgery case where tissue removal occurs. Calculations suggest that the typical decentrations will reduce only slightly the optical benefits expected from an ideal correcting method. For typical decentrations the ideal correcting method offers a benefit in modulation 2-4 times higher (1.5-2 times in white light) than with a standard correction of defocus and astigmatism. We obtained analytical expressions that show the impact of translation and rotation on individual Zernike terms. These calculations also reveal which aberrations are most beneficial to correct. We provided practical rules to implement a selective correction depending on the amount of decentration. An experimental study was performed with an aberrated artificial eye corrected with an adaptive optics system, validating the theoretical predictions. The results in a keratoconic subject, also corrected with adaptive optics, showed that important benefits are obtained despite decentrations in highly aberrated eyes.

Contributions of the cornea and the lens to the aberrations of the human eye.

The relative contributions of optical aberrations of the cornea and the crystalline lens to the final image quality of the human eye were studied. The aberrations of the entire eye were obtained from pairs of double-pass retinal images, and the aberrations of the cornea were obtained from videokeratographic data. Third-order spherical aberration and coma were significantly larger for the cornea than for the complete eye, indicating a significant role of the lens in compensating for corneal aberrations. In a second experiment retinal images were recorded in an eye before and after we neutralized the aberrations of the cornea by having the subjects wear swimming goggles filled with saline water, providing a direct estimate of the optical performance of the crystalline lens.

Corneal wave aberration from videokeratography: accuracy and limitations of the procedure

A procedure to calculate the wave aberration of the human cornea from its surface shape measured by videokeratography is presented. The wave aberration was calculated as the difference in optical path between the marginal rays and the chief ray refracted at the surface, for both on- and off-axis objects. The corneal shape elevation map was obtained from videokeratography and fitted to a Zernike polynomial expansion through a Gram-Schmidt orthogonalization. The wave aberration was obtained also as a Zernike polynomial representation. The accuracy of the procedure was analyzed. For calibrated reference surface elevations, a root-mean-square error (RMSE) of 1 to 2 microm for an aperture 4-6 mm in diameter was obtained, and the RMSE associated with the experimental errors and with the fitting method was 0.2 microm. The procedure permits estimation of the corneal wave aberration from videokeratoscopic data with an accuracy of 0.05-0.2 microm for a pupil 4-6 mm in diameter, rendering the method adequate for many applications.

Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes

We calculated the impact of higher-order aberrations on retinal image quality and the magnitude of the visual benefit expected from their correction in a large population of human eyes. Wave aberrations for both eyes of 109 normal subjects and 4 keratoconic patients were measured for 3-, 4-, and 5.7-mm pupils with a Shack-Hartmann sensor. Retinal image quality was estimated by means of the modulation transfer function (MTF) in white light. The visual benefit was calculated as the ratio of the MTF when the monochromatic higher-order aberrations are corrected to the MTF corresponding to the best correction of defocus and astigmatism. On average, the impact of the higher-order aberrations for a 5.7-mm pupil in normal eyes is similar to an equivalent defocus of approximately 0.3 D. The average visual benefit for normal eyes at 16 c/deg is approximately 2.5 for a 5.7-mm pupil and is negligible for small pupils (1.25 for a 3-mm pupil). The benefit varies greatly among eyes, with some normal eyes showing almost no benefit and others a benefit higher than 4 at 16 c/deg across a 5.7-mm pupil. The benefit for keratoconic eyes is much larger. The benefit at 16 c/deg is 12 and 3 for 5.7- and 3-mm pupils, respectively, averaged across four keratoconics. These theoretical benefits could be realized in normal viewing conditions but only under specific conditions.

Visual Benefit of Correcting Higher Order Aberrations of the Eye

There is currently considerable debate concerning the visual impact of correcting the higher order aberrations of the eye. We describe new measurements of a large population of human eyes and compute the visual benefit of correcting higher order aberrations. We also describe the increase in contrast sensitivity when higher order aberrations are corrected with an adaptive optics system. All these results suggest that many, though not all, observers with normal vision would receive worthwhile improvements in spatial vision from customized vision correction, at least over a range of viewing distances and particularly when the pupils are large. Keratoconic patients or patients suffering from spherical aberration as a result of laser refractive surgery as it is presently performed would especially benefit. These results encourage the development of methods to correct higher order aberrations.

A Method to Predict Refractive Errors from Wave Aberration Data

We explored the impact of the eye’s higher-order aberrations on subjective refraction comparing two classes of methods for estimating refractive state, one based directly on the wave aberration defined in the pupil plane and another based on the retinal image plane. The method defined in the pupil plane chose the sphere and cylinder that either minimized the wave aberration root mean square or minimized the sum of all the spherical and cylindrical components in the wave aberration. The method defined in the image plane chose the sphere and cylinder that optimized an image-quality metric such as the Strehl intensity ratio, the entropy and the intensity variance of the point-spread function, the volume under the modulation transfer function, or the volume under the contrast-sensitivity function. All these methods were compared in a population of six eyes for which we measured both the wave aberration with a Shack-Hartmann wavefront sensor and the subjective refraction under identical conditions. Pupil plane methods predicted subjective refraction poorly. The mean absolute error of the prediction, in spherical equivalent, was about 0.5 D (range, 0.1 to 0.8 D) and increased with increases in higher-order aberrations. However, for all the retinal image plane methods, the mean error between predicted and subjective refraction was about 0.1 D (range, 0 to 0.25 D). The reliability of the method based on the image-quality optimization was further confirmed in a large population of 146 eyes. In conclusion, higher-order aberrations influence the amount of sphere and cylinder required to correct vision. The results indicate that subjective refraction can be predicted from the eye’s optics alone by optimizing computed retinal image quality.