Anterior corneal optical aberrations induced by photorefractive keratectomy for hyperopia.

PURPOSE: Photorefractive keratectomy (PRK) for hyperopia requires both a steepening of the central cornea and a flattening of the mid-periphery to achieve its effect and is likely to affect the optical aberrations of the eye. METHODS: Nine patients underwent PRK to correct between +2.00 and +4.00 D of hyperopia (first eye treated for each patient) using the Summit Technology Apex Plus excimer laser. Anterior corneal aberrations for pupil diameters of 3, 5.5 and 7 mm were estimated from corneal topography data (TMS-1), assuming a uni-index, single surface cornea. Refractive error was assessed using retinoscopy and standard subjective tests. RESULTS: Apart from the intended change in refraction (mean spherical equivalent manifest refraction, +4.60 +/- 1.60 D before surgery and +0.70 +/- 1.60 D at 1 year after surgery), the most significant change was in spherical aberration. Anterior corneal spherical aberration was positive (+1.60 +/- 0.60 D for a 5.5-mm pupil) before surgery and became negative after surgery (-1.80 +/- 1.20 D at 1 year). The change in spherical aberration was related to the achieved change in refractive error. CONCLUSIONS: The large change (approximately 3.00 D) in spherical aberration (from positive to negative aberration) has implications for the optical performance of the whole eye, where the effects of lenticular aberration must also be considered.

Corneal optical aberrations induced by photorefractive keratectomy.

BACKGROUND: Photorefractive keratectomy causes marked alteration to anterior corneal topography, and is likely to induce major changes to the optical aberrations of the eye. METHODS: Six diopters (D) of myopia correction was attempted on one eye of 50 patients, randomly allocated to one of three different treatments: 5-mm or 6-mm single ablation zone, or a double ablation (multizone; -5.00 D correction over 4.6 mm and -1.00 D over 6 mm). Topographic data was used to estimate corneal aberration coefficients. These were compared for effect of ablation zone, before and 1 year after photorefractive keratectomy. The coefficients were used to derive modulation transfer functions for the anterior corneal surface. RESULTS: Corneal spherical aberrations and coma-like aberrations both increased significantly following photorefractive keratectomy (p < 0.001). The mean spherical aberration coefficient increased from 0.36 +/- 0.11 before, to 0.91 +/- 0.37 after treatment, while the mean coma-like aberration coefficient changed from 0.28 +/- 0.16 before, to 0.60 +/- 0.31 after treatment. Ablation zone form had a significant effect on spherical aberration (p = 0.030), but not for coma (p = 0.96). The spherical aberration coefficient increased least for the 6-mm ablation (by 0.38 +/- 0.17), compared with the 5-mm ablation (0.69 +/- 0.45) and the multizone (0.62 +/- 0.38). Corneal modulation transfer functions were reduced significantly following the photorefractive procedure. The effect was greatest for large pupil diameters and for spatial frequencies between 2 and 15 cycles per degree. CONCLUSIONS: Corneal modulation transfer function calculations suggest that a significant loss of visual performance should be anticipated following photorefractive keratectomy, the effect being greatest for large pupil diameters. Results for three ablation zones show that induced aberrations are least for the largest (6 mm) ablation zone.

Effect of the menstrual cycle on corneal curvature.

The purpose of this research was to determine if a clinically significant variation in corneal curvature occurs with the menstrual cycle. The EyeSys Corneal Analysis System (CAS) was used to measure corneal curvature of a test group of three normally menstruating female subjects over three cycles and compared with a control group of three males, for three pseudocycles of 28 days. Measurements were taken on days 1, 4, 8, 15 and 22 of each of three menstrual cycles, with four CAS images taken on each day. Four points (along 45, 135, 225 and 315 degrees) were selected for each of rings 1, 3, 6 and 8, and the average curvature for each of these rings was calculated. The results showed that no detectable temporal effect occurred with the menstrual cycle, thus demonstrating that either cyclic variation in corneal topography was too small to be identified by this system or it did not take place.

Superposition of sphero-cylindrical lenses using contour graphs.

BACKGROUND: The superposition of thin sphero-cylindrical lenses with arbitrary angles between cylindrical axes is sometimes required in a clinical setting. For example, it may be useful in some instances to perform an overrefraction which, added to the spectacle or toric contact lens in place on the eye, yields a final correcting lens. METHODS: Computer calculations have been used to create contour graphs allowing a graphical solution to the problem of combining sphero-cylindrical lenses. Although conceptually strightforward, the method has not been presented before. RESULTS: The use of contour graphs to superpose sphero-cylindrical lenses is shown by examples to be accurate and much simpler than calculational methods. CONCLUSIONS: Lacking a pre-programmed computer, the method of contour graphs offers a practical method of combining sphero-cylindrical lenses.

Dependence on angle and wavelength of light scattered by the ocular lens.

Asymptotic expansions of formal expressions for scattered light make explicit their dependence on scattering angle and wavelength. Such expansions are given for two cases of scatter geometry. In one case the source of scatter are assumed randomly positioned and randomly oriented. In the other case lens fibers, incorporated into a model of the crystalline lens fiber architecture, are the assumed sources of scatter. Calculated results based on scatter by lens fibers are in much better agreement with recent measurements on excised lenses (van den Berg, T.J.T.P. and Ijspeert, J.K., Light scattering in donor lenses. Vision Res. 35, 169-177, 1995) than those based on randomly positioned and randomly oriented scatterers.

Optical consequences of asymmetries in normal corneas.

A survey of videokeratographs of normal corneas shows many with substantial peripheral asymmetries. For sufficiently large pupils (5.5 mm in this study) these asymmetries lead to coma-like axial aberrations large enough to produce measurable losses in vision in a number of cases. Starting from the output of a videokeratographic instrument, a method of estimating the optical effects of corneal asymmetries using Zernike circle polynomials is outlined. It is further shown that in a first approximation corneal asymmetries can be identified with the primary aberration coma and that this aberration is approximately due to a uniform gradient of refractive power across the cornea. Calculations for a representative case predict that a significant improvement in modulation transfer would follow from correction of this aberration.

Change with age of the refractive index gradient of the human ocular lens.

PURPOSE: To study age-related changes in the refractive index distribution of the human ocular lens. METHODS: Biometric data collected on 48 eyes in subjects ranging in age from 19 to 31 years and 48 eyes in subjects ranging in age from 49 to 61 years allowed estimation of a single parameter related to the refractive index distribution of the crystalline lens. The authors selected a gradient index model of the lens characterized by a fixed index at the lens center, a somewhat lower fixed index at the surface, and a continuum of index values between center and surface depending on a single parameter, beta. This parameter was evaluated for each of the two age groups. RESULTS: The distributions of the gradient index parameter beta for the two age groups were found to be statistically well separated. On average, the older group was found to have an index gradient that was flatter near the lens center and steeper near the surface, implying a lower refractive power of about 2 D for representative lens surface curvatures. CONCLUSIONS: It has been observed that surface curvatures and thicknesses of the ocular lens increase with age, whereas other ocular dimensions apparently do not change, implying a trend toward myopia. This trend has not been observed. The authors' results are consistent with and strongly in support of the hypothesis that subtle index changes in the aging lens compensate to a large extent for changes in surface curvatures.

Corneal optics from videokeratographs.

Recent developments in measuring corneal topography make possible an improved understanding of corneal optics. It is shown, using a wavefront analysis, that optical quantities of interest follow from knowledge of sagittal depths of a cornea, and that sagittal depths are provided by or readily found from the output of commercially available instruments. The errors for normal corneas are expected to be quite small based on measurements on calibration spheres and ellipsoids. As an example the optical consequences of a peripheral asymmetry are estimated for a particular normal cornea.

Method for estimating the spheric aberration of the human crystalline lens in vivo.

PURPOSE: The authors describe a method for estimating the spheric aberration (SA) of the human crystalline lens in vivo. METHODS: This method was based on a comparison of the measured change in contrast sensitivity (delta log (CSF)) of the eye and the calculated change in modulation transfer function of the cornea with undilated and dilated pupils. The method assumes that the total change in visual efficiency (delta log (CSF)) in these two states is caused entirely by the SA of the eye combined with the Stiles-Crawford effect. RESULTS: Data are reported for 20 subjects (age range, 20-56 yr). SA for the whole eye was found to be positive and in the range 0-0.83 D (0-0.80 D using Stiles-Crawford apodization). The SA of the crystalline lens was generally negative and in the range 0 to -0.81 D (0 to -0.78 D using apodization). CONCLUSIONS: The method gives results consistent with previous reports in the literature. Despite potential limitations, the technique offers a new method for estimating the SA of the human crystalline lens in vivo.

Strategy for the design of multifocal surfaces.

A method is proposed which may prove useful as an aid in the design of non-spherical surfaces with desired multifocal properties. More specifically, if an axially symmetrical surface is described by a polynomial then the coefficients of this polynomial can be found such that optical path lengths between given object and image points are nearly constant over desired portions of the surface. Three examples are given. One of the examples, a 'trifocal' surface, is compared to an aberration-free two-segment concentric bifocal contact lens.

Sources of intraocular light scatter from inversion of an empirical glare function.

Many questions remain concerning the sources of intraocular light scatter. One approach, inversion of the empirical disability glare function, implies that refractive-index fluctuations extend over distances of tens of micrometers. Randomly placed inhomogeneities of these sizes, such as protein aggregates, are ruled out. It is argued that refractive-index fluctuations associated with the lens fiber lattice are capable of contributing significantly to intraocular scatter and that they provide the necessary large spatial extent.

Is accommodative amplitude correlated with lens fluorescence?

We found a correlation between accommodative amplitude and lens fluorescence in a small population of subjects of nearly the same age. This supports the hypothesis that aging changes of the lens, including presbyopia, are related to lens growth.

Explanation for good visual acuity in uncorrected residual hyperopia and presbyopia after radial keratotomy.

It has been observed that, after radial keratotomy (RK), uncorrected residual hyperopes may have better visual acuity than expected and that some presbyopes, corrected only for distance, have adequate near-vision. We offer a possible explanation for these observations by showing that the increased spherical aberration after RK may produce a second focus 1.5 diopters or more in front of the principal focus of the eye.

Role of spherical aberration in contrast sensitivity loss with radial keratotomy.

A technique is described to determine the change in image contrast as a result of the spherical aberration induced by the radial keratotomy procedure. The hypothesis that the loss in contrast sensitivity of the RK eye is due to the change in spherical aberration postsurgically, is found to be acceptable for some patients. However, this is not a sufficient explanation in all cases. This conclusion may be due to assumptions inherent in the technique derived for calculating spherical aberration or to other factors of importance in the post-RK eye.

Ageing parameters of the ocular lens by scanning fluorophotometry.

A Beer-Lambert analysis of fluorophotometric scans of ocular lenses has been carried out. It is shown that an assumption of a single flourophor allows us to calculate the distribution of this fluorophor along the central lens axis. For the great majority of lenses in our study, covering a wide range of ages, our results are in essential agreement with published results on excised lenses. For a small subset of lenses in the study the assumption of a single fluorophor is found to be unsatisfactory. In these cases a reasonable symmetry assumption allows us to estimate the distribution of an additional agent which removes light from the entering or exiting beams without contributing to the fluorescence. The fact that this agent is restricted to the lens nucleus and that it occurs in lenses in which nuclear changes are clinically evident suggests that it is an expression of nuclear cataract.

Birefringence of a medium of tenuous parallel cylinders.

A general expression for the form birefringence of a medium of parallel cylinders of arbitrary sizes and separations has been developed. It is necessary to assume only that the refractive index fluctuations through the medium are sufficiently small. This expression has been evaluated for a model of retinal nerve fiber layers. The birefringence of these layers has considerable potential as a diagnostic tool since it is expected to be sensitive to structural changes associated with retinal pathologies. Although accurate measurements of this birefringence have not yet been carried out they appear to be feasible or may soon be so.

Small-angle intraocular light scatter: a hypothesis concerning its source.

The crystalline lens makes a major contribution to intraocular light scatter, yet the responsible structural features have not been identified. A hypothesis is presented that implicates the fiber architecture of the ocular lens in small-angle scatter, this being the only part contributing to the associated reduction in vision. The main evidence supporting this hypothesis is a calculation of light scatter by a model lattice of fibers simulating the fiber lattice of the ocular lens. The results agree well with the angular dependence of measured intraocular scatter and, for reasonable parametric values, agree also with the measured magnitude.