The spherical aberration of the crystalline lens of the human eye

Postoperative optical aberrations in eyes implanted with AcrySof spherical and aspheric intraocular lenses

PURPOSE

To evaluate and compare optical and visual quality of eyes implanted with spherical and aspheric intraocular lenses (IOLs).

METHODS

Twenty eyes of 17 patients were implanted with the AcrySof Natural IQ aspheric IOL (SN60WF) and 20 eyes of 15 patients were implanted with the AcrySof Natural spherical IOL (SN60AT). Photopic monocular distance best spectacle-corrected visual acuity (BSCVA) was recorded at 6 months postoperatively. Corneal aberrations were measured with the CSO Eyetop topographer, and ocular aberrations were measured with a Hartmann-Shack aberrometer for a 6-mm pupil. Ocular spherical aberration was computed for different pupil diameters (3, 4, 5, and 6 mm).

RESULTS

No statistically significant differences were found between the BSCVA of the AcrySof IQ IOL (0.023 +/- 0.004 logMAR) and AcrySof Natural IOL (0.031 +/- 0.003 logMAR) (P = .15). The corneal higher order aberrations showed no statistically significant differences between groups (P > .1). However, spherical aberration and higher order ocular aberrations in the AcrySof IQ eyes were lower than eyes implanted with the AcrySof Natural IOL (P < .01). A statistically significant increase in the spherical aberration coefficient with pupil diameter was found only for the spherical IOL group (P = .0023). Statistically significant differences in the spherical aberration coefficient were found between groups at all pupil diameters (P < .001).

CONCLUSIONS

A significant reduction in ocular spherical aberration was noted after AcrySof IQ IOL implantation at all pupil diameters compared to the spherical IOL, although photopic BSCVA between groups remained similar.

On the compensation of horizontal coma aberrations in young human eyes

The nature of the compensation of horizontal coma (Z(3)(1)) between optical elements of the human eye has been studied and the compensative mechanism has been attributed to a passive process linked to angle kappa of the eye. We measured the horizontal coma in the anterior cornea, the whole eye and the internal optics for 221 young subjects. Thirty-three eyes with minimum angle lambda and 53 eyes with relatively large angle lambda were selected from these eyes to test the hypothesis that horizontal coma compensation is linked to angle kappa. Significant horizontal coma in the anterior cornea was observed for the group with minimum angle lambda in both the right (-0.12 +/- 0.07 microm) and left eyes (0.12 +/- 0.10 microm), and this was well compensated by the internal optics so that the level of horizontal coma in the whole eye over a 6-mm pupil size was very low (-0.05 +/- 0.07 microm for OD and 0.02 +/- 0.08 microm for OS). The horizontal coma in the anterior cornea was significantly correlated to the horizontal coma in the internal optics for both the right and the left eye. The results suggest that there is another source of horizontal coma, in addition to that linked to angle kappa, in the anterior cornea, and also a new compensative mechanism to balance the corneal coma, perhaps in the posterior cornea or the lens.

Exploring ocular aberrations with a schematic human eye model

PURPOSE

Advances in ophthalmic technologies now offer both the measurement and reduction of ocular aberrations by surgically or otherwise honing refraction in the anterior eye. Ocular aberrations, however, are known to change with a multitude of factors, including field position, accommodation level, and age. Thus, although static correction of aberrations provides some vision improvement, this may be less than expected.

METHODS

In this article, we use an aspheric, variable-focus, age-dependent, gradient index schematic eye to investigate where ocular aberrations arise in the eye and how these change with field position, accommodation, and age. Optical ray tracing was carried out using optical design software ZEMAX, and Seidel aberration analysis was performed with custom written software in MATLAB.

RESULTS AND CONCLUSIONS

Our modeling is consistent with clinical findings that certain corneal aberrations almost balance those arising from the lens. Our calculations also support the general notion that, by optical sculpting, corneal aberrations can be adjusted to completely balance out those of the lens. This can effectively eliminate the eye's total monochromatic aberrations, but for only one retinal image point at a time. Centered on this point of minimal aberration is a region (the isoplanatic patch) within which the aberrations produce a point spread smaller than some tolerable limit. Also, using available evidence in the literature concerning changes in critical ocular parameters with age and accommodation, our modeling results parallel established clinical findings, and additionally indicate that the major source of aberration change can be attributed to the gradient index distribution in the lens.

Posterior corneal aberrations and their compensation effects on anterior corneal aberrations in keratoconic eyes

PURPOSE

To characterize posterior corneal aberrations in keratoconic (KC) eyes and investigate compensatory effects between anterior and posterior corneal surfaces.

METHODS

The corneal topography of 113 eyes (37 advanced KC, 31 moderate KC, 14 mild KC, and 31 normal eyes) was used to compute the corneal aberrations. The central 6-mm diameter of both anterior and posterior corneal topographies was decomposed into Zernike polynomials. The magnitude and the orientation of each posterior corneal aberration were calculated by vector analysis. The compensation effects between anterior and posterior corneal aberrations were also assessed quantitatively with a linear regression model.

RESULTS

The average higher order RMS wavefront errors for the posterior corneas were 1.04, 0.54, 0.24, and 0.19 microm in the advanced, moderate, and mild KC and normal eyes, respectively. In the advanced KC eyes, posterior corneal coma was oriented in the superior-nasal direction with a mean orientation angle of 75 degrees +/- 19 degrees OD and 78 degrees +/- 20 degrees OS. On average, 22%, 24%, and 14% of the anterior corneal coma were compensated by the posterior cornea in the advanced, moderate, and mild KC eyes, respectively. However, no significant higher order aberration (HOA) compensation effects were found in normal corneas.

CONCLUSIONS

Significantly larger amounts of posterior corneal aberrations and stronger compensation effects were observed in KC eyes than in normal eyes. The uncorrected posterior corneal aberration in KC eyes was substantial and degraded retinal image quality. This may explain the relatively poor visual acuity obtained in eyes with rigid gas permeable (RGP) lenses, which correct only anterior corneal aberrations.

Biomechanical analysis of the accommodative apparatus in primates

BACKGROUND

The restoration of natural accommodation in the presbyopic and cataract affected eye is a subject of intense research effort. A new instrument has been developed to test the viability and efficacy of procedures and methods to restore accommodation ex vivo in animal or human eyes.

METHODS

A section of the globe containing the crystalline lens, zonules, ciliary muscle and sclera is bonded into eight curved shoes. After dissecting the sclera between the shoes, even radial load is applied to stretch the zonules and capsular bag to simulate the natural accommodative process. The associated change in optical power is measured using a modified Scheiner's disk method. Changes in the diameter of the lens and ciliary processes are recorded, as well as zonular load.

RESULTS

No effective change in power was observed for the three presbyopic human eyes under four millimetres diameter stretching; the diameter of the ciliary aperture increased by between 1.8 mm and 2.3 mm, while the maximum increase in lens diameter was 0.19 mm. For the three younger monkey eyes, the diameter of the ciliary aperture increased by 1.4 mm with a corresponding increase in the lens diameter of between 0.50 mm and 0.65 mm. Stretching forces were generally higher for the human than for the monkey eyes, reaching maxima of 35 mN and 52 mN, respectively. The monkey eyes changed power by between 9.1 and 10.1 dioptres. An almost identical, progressive increase for lens diameter, power and stretching force versus stretch distance was found for all three monkey eyes.

CONCLUSION

The better understanding of the mechanisms and forces involved in the primate accommodative apparatus will assist with the development of accommodating IOLs and other methods to restore accommodation.

Single dispersive gradient-index profile for the aging human lens

We provide a single gradient-index (GRIN) profile for the crystalline lens in an updated age-dependent emmetropic-eye model. The parameters defining the GRIN profile include their variation with age and the dispersion of the refractive index in order to account for the increase in the positive-wave spherical aberration, for the constant chromatic difference in the refraction of the human eye, as well as for the decrease in the retinal-image quality with aging. In accounting for these ocular properties, the results show that first, the value of the dispersion parameters are invariant with age. Second, those parameters defining the distribution of the lens index cause the lens-center-index value to decrease slightly, and its position along the lens axis changes with age. Furthermore, these findings are in agreement with the lens paradox.

Wide-field schematic eye models with gradient-index lens

We propose a wide-field schematic eye model, which provides a more realistic description of the optical system of the eye in relation to its anatomical structure. The wide-field model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarro's model for off-axis aberrations and Thibos's chromatic on-axis model (the Indiana eye). These two models are based on extensive experimental data, which makes the derived wide-field eye model also consistent with that data. A mathematical method to construct a GRIN lens with its iso-indicial contours following the optical surfaces of given asphericity is presented. The efficiency of the method is demonstrated with three variants related to different age groups. The role of the GRIN structure in relation to the lens paradox is analyzed. The wide-field model with a GRIN lens can be used as a starting design for the eye inverse problem, i.e., reconstructing the optical structure of the eye from off-axis wavefront measurements. Anatomically more accurate age-dependent optical models of the eye could ultimately help an optical designer to improve wide-field retinal imaging.

Effect of aberrations and scatter on image resolution assessed by adaptive optics retinal section imaging

The effect of increased high-order wavefront aberrations on image resolution was investigated, and the performance of adaptive optics (AO) for correcting wavefront error in the presence of increased light scatter was assessed in a model eye. An AO section imaging system provided an oblique view of a model retina and incorporated a wavefront sensor and deformable mirror for measurement and compensation of wavefront aberrations. Image resolution was quantified by the width of a Lorentzian curve fitted to a laser line image. Wavefront aberrations were significantly reduced with AO, resulting in improvement of image resolution. In the model eye, image resolution was degraded with increased high-order wavefront aberrations (horizontal coma and spherical) and improved with AO correction of wavefront error in the presence of increased light scatter. The findings of the current study suggest that AO imaging systems can potentially improve image resolution in aging eyes with increased aberrations and scatter.

Einfluss des Alters auf die optischen Aberrationen des menschlichen Auges

BACKGROUND

Currently the influence of age on corneal and ocular aberrations is still insufficiently known. The aim of this clinical study was to compare age-related aberrations of human eyes.

METHODS

In a prospective study 98 eyes of 49 healthy patients ranging from 17 to 65 years of age (38.6+/-10.0 years) were consecutively examined. The best corrected visual acuity ranged from 0.8 to 1.6; 48 eyes were emmetropic (SE+/-0.5 D), 42 eyes myopic (SE <-0.5 to -6.75 D), and 8 eyes hyperopic (SE >+0.5 to +3.88 D). The corneal aberrations were derived from corneal topography (Keratron Scout, Optikon). The measurement of ocular aberrations was performed with a Tscherning wavefront aberrometer (ORK, Schwind). The aberrations of the Zernike coefficients and RMS values (1st to 4th order) were determined.

RESULTS

The mean corneal and ocular Zernike coefficients of higher order were smaller than 0.2 microm. There was an evident decrease of wavefront aberrations with increasing order. Higher order corneal aberrations were larger than the corresponding ocular aberrations. With increasing age higher optical errors increased in complexity, and the correlation of corneal and ocular aberrations decreased with significant differences. Although the corneal ocular RMS value of the 3rd and 4th order correlated in the younger group (r=0.51, p=0.0001), there was no correlation in the older group (r=-0.48, p=0.832). The influence of age caused a significant increase of ocular aberrations of the 3rd and 4th order, in particular a tenfold extension of coma (C07) (p=0.002), a twofold extension of spherical aberration (C12) (p=0.0001), and an increase of the 3rd and 4th order RMS values (p=0.001).

CONCLUSIONS

Increased age induced an increase in optical aberrations of the eye, which demonstrates the influence of the lens on ocular aberrations. The combination of corneal and ocular diagnostic methods is recommendable for a better understanding of visual performance.

Intraindividual comparison of higher-order aberrations after implantation of aspherical and spherical intraocular lenses as a function of pupil diameter

PURPOSE

To compare intraindividual higher-order wavefront aberrations after implantation of aspherical and spherical intraocular lenses (IOLs) as function of pupil diameter.

SETTING

Department of Ophthalmology, Johann Wolfgang Goethe-University, Frankfurt am Main, Germany.

METHODS

In this prospective study, wavefront measurements of 21 patients after implantation of a spherical IOL (AMO AR40e) in 1 eye and an aspherical IOL (AMO Tecnis) in the contralateral eye were analyzed. Third-, 4th-, 5th-, total higher-order aberration (HOA) root-mean-square (RMS), and primary spherical aberration (Z(4)(0)) were compared at different virtual pupil diameters of 3 to 6 mm.

RESULTS

For both IOLs and each higher order analyzed, values increased with increasing pupil diameter. Fourth-order RMS and Z(4)(0) in the aspherical IOL group were significantly lower than with the spherical IOL at all analyzed pupil diameters. The total HOA RMS of the aspherical IOL was significantly lower than the spherical IOL only at 6 mm pupil diameter. For 3rd- and 5th-order RMS, no significant difference was found between the tested IOLs at any pupil diameter.

CONCLUSION

In comparison to a spherical IOL, the aspherical Tecnis IOL reduced Z(4)(0) and 4th-order RMS significantly for pupil diameters of 3 to 6 mm, whereas total HOA RMS was only significantly reduced for a pupil diameter of 6 mm.

Spherical aberration of the anterior and posterior surfaces of the human cornea

A ray-tracing procedure was applied to corrected Scheimpflug photography measurements to determine the spherical aberration of the anterior and posterior surfaces of the cornea. It was found that the total spherical aberration of the cornea increases slightly with age. The spherical aberration of the posterior corneal surface is negative at a young age and becomes positive at an older age. To make an accurate description of the spherical aberration for the whole eye, the posterior surface must also be measured.

Higher-order wavefront aberrations in retinitis pigmentosa

PURPOSE

The purpose of this study was to characterize higher-order wavefront aberrations associated with posterior subcapsular (PSC) cataracts in patients with retinitis pigmentosa (RP).

METHODS

Wavefront aberrations were measured by Shack-Hartmann (SH) aberrometry in eight patients with RP who had PSC cataracts, 10 patients with RP who had minimal or no PSC cataracts, and 16 age-equivalent visually normal control subjects. Higher-order wavefront aberrations for 3-mm and 6-mm pupil diameters were defined as the root mean square (RMS) of the wavefront aberration functions.

RESULTS

For a 6-mm pupil diameter, the mean RMS for total higher-order wavefront aberrations was significantly larger for the patients with RP than for the control subjects, both for patients with PSC cataract (F = 17.30, p < 0.001) and for those with minimal or no PSC cataract (F = 4.80, p < 0.05). The mean RMS for third-order aberrations was not significantly different for patients with RP than for the control subjects. However, the mean RMS for fourth-order aberrations was significantly larger for the patients with RP than for the control subjects, both for patients with PSC cataract (F = 8.85, p < 0.01) and those with minimal or no PSC cataract (F = 5.07, p < 0.05). There were no significant differences in higher-order aberrations between the patients with RP and the control subjects for a 3-mm pupil diameter.

CONCLUSIONS

Increased higher-order wavefront aberrations were present in patients with RP with and without clinically observable PSC cataracts. The measurement of wavefront aberrations in patients with RP provides an objective and quantitative method for detecting and monitoring disease-related changes in the optics of the eye.

Effect of cataract surgery incision location and intraocular lens type on ocular aberrations

PURPOSE

To determine whether Hartmann-Shack wavefront sensing detects differences in optical performance in vivo between poly(methyl methacrylate) (PMMA) and foldable acrylic intraocular lenses (IOLs) and between clear corneal and scleral tunnel incisions and whether optical differences are manifested as differences in visual performance.

SETTING

Department of Optometry, University of Bradford, West Yorkshire, United Kingdom.

METHODS

This study comprised 74 subjects; 17 were phakic with no ocular pathology, 20 had implantation of a Pharmacia 722C PMMA IOL through a scleral tunnel, 21 had implantation of an Alcon AcrySof IOL through a scleral tunnel, and 16 had implantation of an AcrySof IOL through a corneal incision. Visual acuity and contrast sensitivity testing, ocular optical quality measurement using Hartmann-Shack wavefront sensing, and corneal surface measurement with a videokeratoscope were performed in all cases.

RESULTS

There were significant differences between groups in the total root-mean-square (RMS) wavefront aberration over a 6.0 mm pupil (F=3.91; degrees of freedom=3,70; P<.05) mediated at the 4th-order RMS, specifically spherical and tetrafoil aberrations. The PMMA-scleral group had the least aberrations and the AcrySof-corneal group the most. For a 3.5 mm diameter pupil, the total higher-order RMS wavefront aberration was not significantly different between the groups (P>.05). There were no differences between groups in corneal shape, visual acuity, or contrast sensitivity.

CONCLUSIONS

Implantation of the spherical PMMA IOL led to a slight reduction in total wavefront aberration compared to phakic eyes. AcrySof IOLs induced more aberrations, especially spherical aberration. Corneal-based incisions for IOL implantation compounded this increase. Studies of the optical performance of IOLs in vivo should use wavefront sensing as the main outcome measure rather than visual measures, which are readily confounded by multiple factors.

Optical Quality and Depth-of-field of Eyes Implanted With Spherical and Aspheric Intraocular Lenses

PURPOSE

To compare experimental optical performance in eyes implanted with spherical and aspheric intraocular lenses (IOLs).

METHODS

Corneal, total, and internal aberrations were measured in 19 eyes implanted with spherical (n=9) and aspheric (n=10) IOLs. Corneal aberrations were estimated by virtual ray tracing on corneal elevation maps, and total aberrations were measured using a second-generation laser ray tracing system. Corneal and total wave aberrations were fit to a Zernike polynomial expansion. Internal aberrations were measured by subtracting corneal from total wave aberrations. Optical performance was evaluated in terms of root-mean-square (RMS) wavefront error and Strehl ratio (estimated from the modulation transfer function). Depth-of-field was obtained from through-focus Strehl estimates from each individual eye.

RESULTS

Corneal aberrations increased after IOL implantation, particularly astigmatism and trefoil terms. Third and higher order RMS (and the corresponding Strehl ratio) were significantly better in eyes with aspheric IOLs than with spherical IOLs; however, this tendency was reversed when astigmatism was included. Spherical aberration was not significantly different in eyes with aspheric IOLs, whereas it was significantly positive in eyes with spherical IOLs. Third order aberrations were not significantly different across groups. Depth-of-field was significantly larger in eyes with spherical IOLs. Spherical IOLs showed better absolute optical quality in the presence of negative defocus >1.00 D.

CONCLUSIONS

Our study shows a good degree of compensation of the corneal spherical aberration in eyes implanted with aspheric IOLs, as opposed to eyes implanted with spherical IOLs. Other sources of optical degradation, both with aspheric and spherical IOLs, are non-symmetric preoperative corneal aberrations, incision-induced aberrations, and third order internal aberrations. Although best corrected optical quality is significantly better with aspheric IOLs, tolerance to defocus tended to be lower.

Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)

Using a non-invasive MRI technique for measuring the refractive index distribution through the crystalline lens, refractive index maps were obtained through 20 intact isolated human lenses (7-82years). Focal length measurements, obtained by simulated light ray propagation through each index map were found to be in agreement with direct measurements performed on a scanning laser apparatus. With increasing age, the refractive index profiles became flatter in the central region, accompanied by steepening of the profile in the periphery. This appears to be an important mechanism underlying the observed changes in power and longitudinal aberration of the human lens.

Comparison of amplitude of apparent accommodation in pseudophakic eyes with that of normal accommodation in phakic eyes in various age groups

PURPOSE

To compare the amplitude of apparent accommodation in eyes with monofocal intraocular lenses with that of normal accommodation in the phakic fellow eyes in various age groups.

PATIENTS AND METHODS

In all, 130 eyes of 130 patients scheduled to undergo cataract surgery, and 130 fellow eyes that had little cataract and good visual acuity of 20/33 or better were studied. The following groups were studied: in their 40s and younger (n = 20) or in their 50s (n = 30), 60s (n = 30), 70s (n = 30), and 80s (n = 20). Using an accommodometer (Kowa HS-9E), the accommodative amplitude was measured at 1 month after surgery.

RESULTS

In the patients in their 40s and younger or in their 50s, the amplitude of apparent accommodation was significantly less than that of normal accommodation; no significant difference was observed in the patients in their 60s, 70s, or 80s. The incidence of patients in whom the amplitude of apparent accommodation was more than that of normal accommodation was greater in the patients in their 60s, 70s, and 80s than in the patients in their 40s and younger and in their 50s.

CONCLUSION

The amplitude of apparent accommodation is virtually equivalent to that of normal accommodation in patients older than 60 years of age.

Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study

PURPOSE

To evaluate best corrected visual acuity (BCVA) and photopic and mesopic contrast sensitivity in pseudophakic patients implanted either with the aspheric intraocular lens (IOL) designed to correct for corneal spherical aberration or with a conventional IOL.

SETTING

Three surgical centers participated this prospective randomized masked comparative study.

METHODS

Thirty eyes of 30 patients after aspheric lens implantation (Pfizer/Pharmacia Tecnis Z9000) were compared with 30 eyes of 30 age-matched patients after conventional lens implantation (Alcon AcrySof SA60AT). Two to three months after surgery, best spectacle corrected distance visual acuity was measured using the Early Treatment Diabetic Retinopathy Study chart. Contrast sensitivity was measured by sinusoidal grating charts for distance at photopic (85 cd/m(2)) and mesopic (6 cd/m(2)) luminance level with optical correction in place. Tested spatial frequencies were 1.5, 3, 6, 12, and 18 cycles per degree (cpd).

RESULTS

The mean BCVA was -0.053 +/- 0.044 logMAR in eyes with the aspheric Tecnis IOL and 0.006 +/- 0.059 logMAR in eyes with the conventional AcrySof IOL (P=.0001). Eyes with the aspheric IOL showed better contrast sensitivity at spatial frequencies of 3 cpd (P<.05) and 6, 12, and 18 cpd (P<.01) in photopic and in mesopic conditions. Peak improvement occurred at 18 cpd and was 36% (0.29 log units) in photopic and 54% (0.27 log units) in mesopic conditions.

CONCLUSIONS

The aspheric Tecnis IOL yielded better BCVA and better distance contrast sensitivity than the conventional IOL. The differences were clinically significant for higher spatial frequencies. The results give some suggestions for further studies.

Optical performance of 3 intraocular lens designs in the presence of decentration

PURPOSE

To study the theoretical optical performance of 3 intraocular lens (IOL) designs in the presence of IOL decentration.

SETTING

Optics Center, Bausch & Lomb, Rochester, New York, USA.

METHODS

A ray-tracing program was used to evaluate the effect of IOL decentration on the optical performance of 3 silicone IOLs (LI61U, Bausch & Lomb; Tecnis Z9000, Advanced Medical Optics; and a new aberration-free IOL [SofPort AO, Bausch & Lomb]) in an experimental model eye. The study was done using pupil diameters of 3.0 mm, 4.0 mm, and 5.0 mm and IOL decentrations of 0 mm, 0.25 mm, 0.50 mm, 0.75 mm, and 1.00 mm. The modulation transfer functions were computed and plotted. A Monte Carlo simulation analysis with 1000 trials with IOL decentration randomly varying for each pupil size was performed.

RESULTS

Decentration of LI61U and Tecnis Z9000 IOLs led to asymmetrical higher-order aberrations that adversely affected the optical performance of the model eye; performance was not affected with the aberration-free IOL because it lacks inherent spherical aberration. Optical performance with the aberration-free IOL was better than with the LI61U IOL as the former has less spherical aberration and did not introduce other aberrations when decentered. Performance with the aberration-free IOL was better than with the Tecnis Z9000 IOL for 3.0 mm, 4.0 mm, and 5.0 mm pupils when decentration exceeded 0.15 mm, 0.30 mm, and 0.38 mm, respectively. Performance with the LI61U IOL was better than with the Tecnis Z9000 IOL for 3.0 mm, 4.0 mm, and 5.0 mm pupils when decentration exceeded 0.3 mm, 0.5 mm, and 0.5 mm, respectively. Monte Carlo simulations showed the expected postoperative results of the LI61U IOL and aberration-free IOL would be repeatable and predictable, whereas the outcomes with the Tecnis Z9000 IOL would vary widely.

CONCLUSIONS

The optical performance of the model eye was not affected by decentration of an aspheric IOL designed to have no inherent spherical aberration. With decentration, the performance with the new IOL was better than with a conventional spherical IOL and an aspheric IOL designed to offset the spherical aberration of an average cornea.

Change in shape of the aging human crystalline lens with accommodation

The objective was to measure the change in shape of the aging human crystalline eye lens in vivo during accommodation. Scheimpflug images were made of 65 subjects between 16 and 51 years of age, who were able to accommodate at least 1D. The Scheimpflug images were corrected for distortion due to the geometry of the camera and the refraction of the cornea and anterior lens surface, which is necessary to determine the real shape of the lens. To ensure accurate correction for the refraction of the anterior lens surface, the refractive index of the crystalline lens must be determined. Therefore, axial length was also measured, which made it possible to calculate the equivalent refractive index of the lens and possible changes in this index during accommodation. The results show that during accommodation there is a decrease in both the anterior and the posterior radius of the lens, although the change in mm per diopter of the latter is much smaller. The increase in lens thickness with accommodation is higher than the decrease in the anterior chamber depth, indicating that the posterior lens surface moves backwards with accommodation. During accommodation the anterior lens surface becomes more hyperbolic. Furthermore, an increase in the equivalent refractive index during accommodation was determined.

Aberrationen h�herer Ordnung nach Implantation von asph�rischen und sph�rischen Intraokularlinsen in Abh�ngigkeit von der Pupillenweite

BACKGROUND

The implantation of aspherical IOLs with negative spherical aberration should equalize the positive spherical aberration of the cornea. The aim of our study was the intraindividual comparison of higher order aberrations (HOA) after implantation of an aspherical and spherical IOL.

PATIENTS AND METHODS

In ten patients we randomly implanted an aspherical IOL in one eye and a spherical IOL in the other. After 3 months, we used a Hartmann-Shack sensor to measure total HOA, 3rd to 5th order as well as spherical aberration Z4.0, in mydriasis. We compared all aberrations intraindividually for pupil diameters of 3.5-6 mm.

RESULTS

For both IOLs, all aberrations rose with increasing pupil diameter. However, after implantation of the aspherical IOL total HOA, 4th order and spherical aberration Z4.0 were lower, for 4th order aberration and Z4.0 even significantly. For 3rd and 5th order aberrations, there was no difference between both IOLs.

CONCLUSIONS

With implantation of aspherical IOLs, total HOA, 4th order and spherical aberration Z4.0 could be reduced compared to spherical IOLs.

Wavefront-customized intraocular lenses

PURPOSE OF REVIEW

Recent advances in ocular wavefront measurement and in intraocular lens materials and manufacturing methods have brought cataract surgery to the brink of a period in which customized correction of higher-order aberrations with intraocular lenses may become standard practice.

RECENT FINDINGS

Retinal image quality in pseudophakic eyes is limited by the wavefront aberrations of the cornea and the intraocular lens. The Tecnis Z9000 is the first commercially available intraocular lens designed to account for the wavefront aberrations of the cornea, specifically spherical aberration. Clinical findings with the Tecnis Z9000 intraocular lens show improved contrast sensitivity at low and mid spatial frequencies. However, if the lens decenters or tilts modestly, higher-order aberrations are created, and the lens may underperform relative to standard intraocular lenses. At present, one firm is developing an intraocular lens that may be modified in vivo with near ultraviolet energy. Such a technology offers tremendous potential for a fully customized intraocular lens.

SUMMARY

Wavefront-customized intraocular lenses offer the promise of near perfect retinal image quality, such that only diffraction, chromatic aberration, retinal sampling and neural factors will limit vision in pseudophakic eyes.

A population study on changes in wave aberrations with accommodation

Wave aberrations were measured with a Shack-Hartmann wavefront sensor (SHWS) in the right eye of a large young adult population when accommodative demands of 0, 3, and 6 D were presented to the tested eye through a Badal system. Three SHWS images were recorded at each accommodative demand and wave aberrations were computed over a 5-mm pupil (through 6th order Zernike polynomials). The accommodative response was calculated from the Zernike defocus over the central 3-mm diameter zone. Among all individual Zernike terms, spherical aberration showed the greatest change with accommodation. The change of spherical aberration was always negative, and was proportional to the change in accommodative response. Coma and astigmatism also changed with accommodation, but the direction of the change was variable. Despite the large inter-subject variability, the population average of the root mean square for all aberrations (excluding defocus) remained constant for accommodative levels up to 3.0 D. Even though aberrations change with accommodation, the magnitude of the aberration change remains less than the magnitude of the uncorrected aberrations, even at high accommodative levels. Therefore, a typical eye will benefit over the entire accommodative range (0-6 D) if aberrations are corrected for distance viewing.

Optical aberrations of intraocular lenses measured in vivo and in vitro

Corneal and ocular aberrations were measured in a group of eyes before and after cataract surgery with spherical intraocular lens (IOL) implantation by use of well-tested techniques developed in our laboratory. By subtraction of corneal from total aberration maps, we also estimated the optical quality of the intraocular lens in vivo. We found that aberrations in pseudophakic eyes are not significantly different from aberrations in eyes before cataract surgery or from previously reported aberrations in healthy eyes of the same age. However, aberrations in pseudophakic eyes are significantly higher than in young eyes. We found a slight increase of corneal aberrations after surgery. The aberrations of the IOL and the lack of balance of the corneal spherical aberrations by the spherical aberrations of the intraocular lens also degraded the optical quality in pseudophakic eyes. We also measured the aberrations of the IOL in vitro, using an eye cell model, and simulated the aberrations of the IOL on the basis of the IOL's physical parameters. We found a good agreement among in vivo, in vitro, and simulated measures of spherical aberration: Unlike the spherical aberration of the young crystalline lens, which tends to be negative, the spherical aberration of the IOL is positive and increases with lens power. Computer simulations and in vitro measurements show that tilts and decentrations might be contributors to the increased third-order aberrations in vivo in comparison with in vitro measurements.

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.

Correlation Between Corneal and Total Wavefront Aberrations in Myopic Eyes

PURPOSE

Corneal topography data expressed as corneal aberrations are frequently used to report corneal laser surgery results. However, the optical image quality depends on all optical elements of the eye, including the human lens. We investigated correlations between corneal and total wavefront aberrations and the relevance of corneal aberrations for representing the optical quality of the total eye.

METHODS

Thirty-three eyes of 22 myopic patients were measured using a corneal topography system and a Tscherning-type wavefront analyzer. Pupils were dilated to at least 6 mm in diameter. All measurements were centered with respect to the line of sight. Corneal and total wavefront aberrations were calculated up to the 6th Zernike order in the same reference plane.

RESULTS

Statistically significant correlations (P<.05) between corneal and total wavefront aberrations were found for astigmatism (C3,C5) and all 3rd Zernike order coefficients such as coma (C7,C8). No statistically significant correlations were found for 4th, 5th, or 6th order Zernike coefficients. On average, all Zernike coefficients for corneal aberrations were larger than the Zernike coefficients for total wavefront aberrations.

CONCLUSIONS

Due to the lack of correlation between corneal and total wavefront aberrations in most of the higher order aberrations, measurement of corneal aberrations are of limited use for representation of the optical quality of the human eye, especially after corneal laser surgery. Corneal aberrations and optical elements within the eye are optically balanced. As a consequence, ideal customized ablations must take both corneal and total wavefront aberrations into consideration.

A New Intraocular Lens Design to Reduce Spherical Aberration of Pseudophakic Eyes

PURPOSE

The aim of this study was to design and evaluate in the laboratory a new intraocular lens (IOL) intended to provide superior ocular optical quality by reducing spherical aberration.

METHODS

Corneal topography measurements were performed on 71 cataract patients using an Orbscan I. The measured corneal surface shapes were used to determine the wavefront aberration of each cornea. A model cornea was then designed to reproduce the measured average spherical aberration. This model cornea was used to design IOLs having a fixed amount of negative spherical aberration that partially compensates for the average positive spherical aberration of the cornea. Theoretical and physical eye models were used to assess the expected improvement in optical quality of an eye implanted with this lens.

RESULTS

Measurements of optical quality provided evidence that if this modified prolate IOL was centered within 0.4 mm and tilted less than 7 degrees, it would exceed the optical performance of a conventional spherical IOL. This improvement occurred without an apparent loss in depth of focus.

CONCLUSION

A new IOL with a prolate anterior surface, designed to partially compensate for the average spherical aberration of the cornea, is intended to improve the ocular optical quality of pseudophakic patients.

Corneal and total optical aberrations in a unilateral aphakic patient

PURPOSE

To measure corneal and total optical aberrations in the normal and treated eye of a unilateral aphakic patient to (1) cross-validate techniques in an eye in which corneal and total aberrations should be almost identical (aphakic eye) and (2) compare the interactions of corneal and internal aberrations in the normal eye with those in the aphakic eye.

SETTING

Instituto de Optica, Consejo Superior de Investigaciones Científicas, Madrid, Spain.

METHODS

Aberrations in both eyes of a unilateral aphakic patient were measured using laser ray tracing. Corneal aberrations were obtained from corneal elevation data measured with a corneal videokeratoscope (Humphrey Instruments) using custom software that performs virtual ray tracing on the measured front corneal surface.

RESULTS

There was a 98.4% correspondence between the total and corneal aberration pattern in the aphakic eye (6.5 mm pupil). In the normal eye, the total spherical aberration was much lower than the corneal spherical aberration; this did not occur in the aphakic eye.

CONCLUSIONS

The posterior corneal surface contributed slightly to the aberrations in the normal cornea (2% at most). The crystalline lens appears to play a compensatory role in the total spherical aberration in normal eyes.

Refractive error and monochromatic aberrations in Singaporean children

Higher order optical aberrations were measured in 273 cyclopleged Singaporean school children using a Bausch and Lomb Zywave aberrometer, with 268 of these subjects also undergoing corneal topography measurements (Tomey TMS 2 system). Subjects with low myopia (> -3.00 to -0.50 D) showed slightly, but significantly, less positive levels of spherical aberration than other refractive error groups. Chinese subjects also showed significantly higher amounts of aberrations than Malay subjects, particularly for vertical coma, but also for horizontal coma and spherical aberration. Anterior corneal spherical aberration (calculated from topography) was significantly correlated with whole eye spherical aberration, but did not vary significantly with refractive error or racial background. Residual spherical aberration (i.e. of posterior cornea and crystalline lens) did vary significantly with refractive error and race. Our results do not provide any evidence for aberration-driven form-deprivation as a major mechanism of myopia development.

Validation of the Estimation of Corneal Aberrations From Videokeratography in Keratoconus

PURPOSE

To validate the estimation of corneal aberrations from videokeratography against a laser ray tracing technique that measured total eye aberrations, in eyes without keratoconus (ie, cornea-dominated wave aberrations).

METHODS

We measured total and corneal wave aberrations of three eyes diagnosed with keratoconus by slit-lamp microscopy and corneal topography: two eyes from one patient with early keratoconus and one eye with more advanced keratoconus. Total aberrations were measured with laser ray tracing. Corneal aberrations were obtained from corneal elevation data measured with a corneal videokeratoscope using custom software that performs virtual ray tracing on the measured front corneal surface.

RESULTS

The keratoconus eyes showed a dramatic increase in aberrations (both corneal and total) particularly coma-like terms, which were 3.74 times higher on average than normal. Anterior corneal surface aberrations and total aberrations Were similar in keratoconus. This similarity was greater for the early keratoconus patient, suggesting a possible implication of the posterior corneal surface in advanced keratoconus.

CONCLUSIONS

The similarity found between corneal and total aberration patterns in keratoconus provided a cross-validation of both types of measurements (corneal topography and aberrometry). Both techniques were useful in diagnosing and quantifying optical degradation imposed by keratoconus.