Monochromatic aberrations of the human eye in a large population

Measurements of Ocular Aberrations and Light Scatter in Healthy Subjects

PURPOSE

To report and validate an optical imaging system that provides measurements of higher order ocular aberrations and light scatter in human eyes.

METHODS

An optical imaging system has been established that provides for combined measurements of ocular aberrations and light scatter. A laser beam was expanded and focused to a point on the retina by the optics of the eye. Wavefront sensing was performed with a Shack-Hartmann aberrometer to determine the wavefront aberration function and calculate the point spread function, giving information on ocular aberrations. A cylindrical lens was placed in the path of the incident laser beam path, and the line spread function was derived from the laser slit, giving information on combined ocular aberrations and light scatter. A relative index for ocular light scatter was determined by subtracting the area under the two line spread functions. Measurements were performed in one eye of 20 normal healthy subjects. The subjects' ages ranged between 21 and 78 years, and the average for all the eyes was 43 +/- 17 years (mean +/- SD).

RESULTS

Higher order ocular aberrations were correlated with subjects' ages (r = 0.6; p = 0.01; N = 20). Combined higher order ocular aberrations and light scatter were correlated with age (r = 0.7; p = 0.0002; N = 20). Light scatter was correlated with age (r = 0.6; p = 0.002; N = 20).

CONCLUSIONS

A method was established to measure age-related changes in ocular higher order aberrations and light scatter. Differentiating the contribution of ocular aberrations and light scatter to the retinal image quality has potential value for anticipating the outcome of procedures that attempt to compensate for ocular aberrations and for providing information on factors that degrade the optical performance of the eye in health and disease.

Gaussian weighting of ocular wave-front measurements

The measurement of ocular wave-front error gives insight into the optical performance of the eye and possibly a means for assessing visual performance. The visual system responds not only to the quality of the optical image formed on the retina but also to the processing that occurs in the retina and the brain. To develop a metric of visual performance based on wave-front error measurements, these latter processes must somehow be incorporated. In representing the wave-front error in terms of Zernike polynomials, it appears that terms with lower angular frequency have a greater deleterious effect on visual performance than higher-angular-frequency terms. A technique for weighting the pupil function of the eye with a Gaussian filter is demonstrated. It is further demonstrated that the variance of the Gaussian-weighted wave-front error is well correlated with visual performance.

Small foveal targets for studies of accommodation and the Stiles–Crawford effect

The properties of small monochromatic targets as accommodative stimuli are not well understood. We used a dynamic optometer to record accommodation responses to monochromatic disc targets (1.0-27.3 min arc) and to a Maltese cross. Accommodation responded adequately to points as small as 13.6 min arc. The response to these small targets is relevant to the question of whether the Stiles-Crawford (SC) effect could provide a stimulus to accommodation. Previous studies have used pupil apodizing filters to neutralise the natural SC function and so determine how visual performance or accommodation is influenced by the SC effect. However, these filters cannot correct for known inhomogeneities in the SC function across the retina for extended targets. Therefore, we calculated the SC function inhomogeneities across the retinal image of a smaller 13.6-min arc target. Unfortunately, even this small target is too large to permit a homogenous SC function across its extent. Alternatives to the apodizing filter approach are discussed.

Stroke amplifier for deformable mirrors

We demonstrate a simple optical configuration that amplifies the usable stroke of a deformable mirror. By arranging for the wavefront to traverse the deformable mirror more than once, we correct it more than once. The experimental implementation of the idea demonstrates a doubling of 2.0 and 2.04 by two different means.

Self-optimised vision correction with adaptive spectacle lenses in developing countries

It is estimated by the World Health Organization that about 1 billion people in the developing world would benefit immediately from distance vision and near vision correction if it were available to them. Here we address this problem and provide a solution by correcting vision in the field with adaptive liquid-filled variable focus lenses. We describe the details of the lens and present the results of a series of experiments performed in Ghana, Nepal, Malawi and South Africa that demonstrate that it is possible by simple means to self-determine and obtain correct refraction using such lenses.

A Method for Simulation of Foveal Vision During Wear of Corrective Lenses

PURPOSE

The aim was to simulate the visual appearance of images viewed through corrective lenses having known, arbitrary types and amounts of monochromatic aberration, so that the visual effect of changing the design parameters of the lens could be explored.

METHODS

We first calculate the optical response of the eye and any corrective lens using a numerical model eye. We then use this response as a filter, which we convolve with a selected original (unaberrated) image, to obtain an initial simulated retinal image. This image is then deconvolved by a second filter, which is calculated as the optical response of the eye of the observer who views the final image displayed on a video monitor. The originality of our approach to visual simulation is to take the aberrational characteristics of the observer's eye into account in the calculation. We validated our simulation by comparing images degraded by simulated dioptric blur with real defocused images seen through corresponding optical lenses.

RESULTS

When using a small (2.5 mm) pupil size and a "typical" observer wavefront aberration model, there was a close resemblance between optical and simulated blurs. Although it was not necessary to consider the measured aberrations of the subject when simulating vision with a small pupil size, this requirement could not be ignored when vision through a larger pupil was simulated. With a 5.7-mm pupil diameter, use of Shack-Hartmann measurements of the ocular aberrations of the individual observers rather than "typical" levels of aberrations for the entire population gave excellent agreement between the effects of simulated and real defocus blur in monochromatic and polychromatic light. A Bland-Altman analysis of the differences between matching simulated and real blurs for a 5.7-mm pupil in polychromatic light with the model including allowance for individual measured aberrations gave mean differences close to zero and 95% confidence limits of about +/-0.25 D over a defocus range of -2.00 to +2.00 D.

CONCLUSION

The simulation technique can be expected to be a useful tool to evaluate the potential performance of an eye that wears various designs of corrective lens.

Monochromatic ocular wavefront aberrations in the awake-behaving cat

Measurement of wavefront aberrations in human eyes has become a reliable, quantitative way of assessing the optical impact of experimental and corrective ocular manipulations. Wavefront measures have also been performed in several other species, but never in cats, an animal model of choice for many ocular studies. Our goal in this study was to measure wavefront aberrations reliably in live, awake-behaving cats in a manner that is directly comparable to that used in human subjects. Six adult cats (felis cattus) were trained to fixate small targets on a computer screen. A compact Shack-Hartmann wavefront sensor was aligned with each animal's pupil center and line of sight during fixation. Wavefront images were then collected from which the cats' ocular aberrations were measured up to tenth order Zernike polynomials over a 6 mm pupil. Results show that cat and human ocular wave aberrations were very similar. Second order Zernike modes accounted for more than 90% of the total wave aberration. In agreement with our observation that cat ocular optics were comparable with those of humans, the half height width of both the cat and human higher order point spread function was about 0.95 degrees. These results form a solid basis for future wavefront sensing studies aiming to quantify the effects of ocular manipulations in experimental animals.

Effect of positive and negative defocus on contrast sensitivity in myopes and non-myopes

This study investigated the effect of lens induced defocus on the contrast sensitivity function in myopes and non-myopes. Contrast sensitivity for up to 20 spatial frequencies ranging from 1 to 20 c/deg was measured with vertical sine wave gratings under cycloplegia at different levels of positive and negative defocus in myopes and non-myopes. In non-myopes the reduction in contrast sensitivity increased in a systematic fashion as the amount of defocus increased. This reduction was similar for positive and negative lenses of the same power (p = 0.474). Myopes showed a contrast sensitivity loss that was significantly greater with positive defocus compared to negative defocus (p = 0.001). The magnitude of the contrast sensitivity loss was also dependent on the spatial frequency tested for both positive and negative defocus. There was significantly greater contrast sensitivity loss in non-myopes than in myopes at low-medium spatial frequencies (1-8 c/deg) with negative defocus. Latent accommodation was ruled out as a contributor to this difference in myopes and non-myopes. In another experiment, ocular aberrations were measured under cycloplegia using a Shack-Hartmann aberrometer. Modulation transfer functions were calculated using the second order term for defocus as well as the fourth order Zernike term for spherical aberration. The theoretical maximal contrast sensitivity based on aberration data predicted the measured asymmetry in contrast sensitivity to positive and negative defocus that was observed in myopic subjects. The observed asymmetry in contrast sensitivity with positive and negative defocus in myopes may be linked to the altered accommodative response observed in this group.

Wavefront Aberrations Following Laser in situ Keratomileusis and Refractive Lens Exchange for Hypermetropia

PURPOSE

To compare the magnitude of aberrations in eyes after elective hypermetropic laser in situ keratomileusis (LASIK) and refractive lens exchange (clear lens replacement).

METHODS

Forty-nine patients (92 eyes) had hypermetropic LASIK and 28 (48 eyes) had refractive lens exchange; 23 hypermetropic subjects (41 eyes) were the control group. LASIK was performed with the Nidek EC-5000 excimer laser; ablation zones 5.5 to 6.0-mm in diameter with transition zones 7.5 to 8-mm in diameter. For refractive lens exchange, all but four IOLs were made of foldable acrylic. Aberrations and corneal topography were measured with the Nidek OPD-Scan model ARK-10000 more than 12 months after surgery. The higher-order root-mean-square (HORMS) wave aberrations for combined third to sixth Zernike aberration orders and the Zernike spherical aberration coefficient C(0)(4) at both 4.2-mm and 6.0-mm pupil sizes were calculated.

RESULTS

For the LASIK group, surgical refractive change correlated significantly with total, corneal, and internal HORMS and spherical aberrations (except with internal spherical aberration for a 4.2-mm diameter pupil). For the refractive lens exchange group, there were no significant correlations of surgical refractive change with any of these factors. Similarly, there were no significant correlations of refraction with any of these factors for the control group. For a 3-diopter change in refraction with 6-mm pupils, LASIK doubled the total HORMS aberrations. LASIK changed the sign of spherical aberration from positive to negative by increasing the negative asphericity of the anterior cornea. Taking age differences between groups into account, refractive lens exchange increased the total HORMS aberrations by 40% compared with that of the control group, but this was not statistically significant. However, refractive lens exchange significantly increased total spherical aberration.

CONCLUSION

Refractive lens exchange was a better refractive procedure than LASIK for minimizing total higher order optical aberrations that accompany hypermetropic refractive surgery.

Monte Carlo Simulation of Irradiance Distribution on the Retina After Refractive Surgery

PURPOSE

Generation of random wavefronts for ocular wave aberration statistics across the population has been used for various analyses. We propose a more accurate simulation procedure. This simulation technique is not intended to be a perfect representation of an eye, but instead is a tool for those applications where a correct distribution of aberrations across a population is necessary.

METHODS

Our technique consists of the generation of coefficients of the wavefront expansion into Zernike modes. The simulation makes use of the variance of every mode measured on a large population by using compact and reliable wavefront sensors.

RESULTS

The simulation procedure was verified by reproducing two statistical functions that characterize eye behavior. This tool can be used to predict the performance of sensing techniques and to evaluate the consequences of customized ophthalmic elements and refractive surgery. It may also be useful for deriving both first and second order photon statistics of the point-spread function on the human retina (a key parameter in certain visual perception models).

CONCLUSIONS

A new tool for analysis of customized refractive surgery is presented and the evolution of the light intensity probability density function on the retina with compensation attained after customized correction of the eye's aberrations is analyzed.

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.

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.

Wavefront-optimized ablation profiles

PURPOSE

To describe a method for calculating wavefront-optimized ablation profiles to precompensate for the spherical aberration and higher-order astigmatism induced by myopic, hyperopic, and astigmatic corneal laser corrections.

SETTING

IROC-Institut für Refraktive und Ophthalmo-Chirurgie, and Institute for Biomedical Engineering, Swiss Federal Institute of Technology, Zürich, Switzerland.

METHODS

The basic ablation profile for myopic, hyperopic, and astigmatic correction is derived from the 2nd-order Zernike representation of wavefront aberrations. Including 4th-order spherical aberration and higher-order astigmatism in the theoretical calculation of the ablation profile allows precompensation for the expected amount of higher-order aberrations (HOAs). The shapes of wavefront-optimized ablation profiles are compared with the shapes of "classic" ablation profiles for myopic and astigmatic corrections.

RESULTS

The introduction of precompensating spherical aberration and higher-order astigmatism leads to a more aspheric ablation profile with a significant increase in ablation depth (up to 35%) in the midperiphery of the optical zone. The central ablation depth remains unchanged in the myopic correction but increases by 3% in cylinder correction.

CONCLUSIONS

Wavefront-optimized ablation profiles provide a simple method to precompensate for the expected 4th-order spherical aberration and higher-order astigmatism in the average eye. Further clinical studies must be performed to prove the theoretical results; demonstrate the reduction in HOAs; and predict safety, predictability, and stability of wavefront-optimized ablation profiles.

Correcting ocular spherical aberration with soft contact lenses

Following aberroscopy, aspheric front surface soft contact lenses (SCLs) were custom-made to correct spherical refractive error and ocular spherical aberration (SA) of 18 myopic and five hypermetropic subjects (age, 20.5 +/- 5 yr). On-eye residual aberrations, logMAR visual acuity, and contrast sensitivity were compared with the best-correcting spectacle lens, an equally powered standard SCL, and an SCL designed to be aberration free in air. Custom-made and spherical SCLs reduced SA (p < 0.001; p < 0.05) but did not change total root-mean-square (rms) wave-front aberration (WFA). Aberration-free SCLs increased SA (p < 0.05), coma (p < 0.05), and total rms WFA. Visual acuity remained unchanged with any of the SCL types compared with the spectacle lens correction. Contrast sensitivity at 6 cycles/degree improved with the custom-made SCLs (p < 0.05). Increased coma with aspheric lens designs and uncorrected astigmatism limit the small possible visual benefit from correcting ocular SA with SCLs.

LADARWave Wavefront Measurement in Normal Eyes

PURPOSE

We evaluated the correlation of Alcon LADARWave wavefront measurements with clinical refraction and corneal topography.

METHODS

In a retrospective, non-comparative case series, 60 eyes (30 patients) of healthy individuals evaluated by preoperative examination for refractive surgery were enrolled (manifest sphere, -11.00 to +4.50 D; manifest cylinder, 0 to -4.75 D; 45 eyes were myopic, 12 eyes were hyperopic, and 3 had mixed astigmatism). Correlation of manifest refraction, cycloplegic refraction, and topographic data with wavefront refraction and higher order aberration was assessed. Match percentage given by the wavefront was analyzed. This number represents how much of the wavefront refraction is due to sphere and cylinder (high percentage match) or is influenced by higher order aberration (low percentage match), in which case aberrometer refraction will not be close to phoropter refraction. Pearson's correlation coefficient was assessed for two continuous variables, adjusting for repeated measurements.

RESULTS

The median match percentage was 91%. Mean values for all higher order aberration components in a 7.0-mm pupil were: coma = 0.35 +/- 0.29 microm, spherical aberrations = 0.36 +/- 0.31 microm, and other terms of higher order aberrations = 0.31 +/- 0.14 microm. Wavefront sphere, cylinder, and axis terms were highly correlated to manifest and cycloplegic measurements. The high match subgroup had a higher correlation coefficient than the low match subgroup for refraction. Topographic cylinder and axis were not strongly correlated to wavefront refraction, but manifest axis was significantly correlated to topographic axis.

CONCLUSION

In 60 normal eyes, the Alcon LADARWave wavefront measurement was highly correlated with refraction, but less well with corneal topography.

Predicting and assessing visual performance with multizone bifocal contact lenses

PURPOSE

To investigate how bifocal contact lenses, when combined with the aberrations of the eye, will affect visual performance. Also, to investigate the relationship between the patient's predicted and actual visual benefit with bifocal contact lenses.

METHODS

The monochromatic aberrations of 16 subjects were measured and used to simulate visual quality with three bifocal contact lens designs. Actual and computed visual benefit was compared for an Acuvue bifocal contact lens in 5 of the 16 subjects.

RESULTS

Subjects were predicted to have either a bifocal response or an increase in depth of focus for all lens designs. Our subjects were predicted to have a decrease in visual benefit for distance viewing and a gain in visual benefit at near compared with not wearing a contact lens. We found a statistically significant association between our subjects' predicted and actual visual benefit with the Acuvue Bifocal contact lens (r = 0.685, p = 0.008).

CONCLUSIONS

Bifocal contact lens designs, when combined with the aberrations of the eye, will not always provide bifocal vision. Visual quality with a bifocal contact lens can be predicted based on a patient's ocular aberrations.

Effect of Higher-order Wavefront Aberrations on Binocular Summation

PURPOSE

To determine the effect of individual Zernike wavefront aberrations on binocular summation and binocular visual acuity.

METHODS

A 0.25-microm wavefront aberration of second, third and fourth order Zernike modes were introduced into a set of log minimum angle of resolution unit (logMAR) visual acuity charts convolved by CTView. Subjects were dilated and fitted with an artificial pupil of 3 mm. For each set of charts, right eye, left eye, and binocular acuity was measured. The gain in binocular visual acuity over monocular visual acuity was defined as binocular summation. The visual acuity lost binocularly reading aberrated charts was normalized for each subject and defined as the aberration induced loss in acuity.

RESULTS

Binocular summation was 10.0% (95% limits of agreement 8.8 to 11.1%) in the unaberrated state and ranged from 17.3 to 3.4% in the Zernike modes studied. Binocular summation was greatest in defocus followed by coma and astigmatism. The aberration induced loss in monocular and binocular acuity was higher for Zernike modes with low angular frequency compared to those with high angular frequency. Linear regression showed a significant relationship between aberration-induced loss of visual acuity and binocular summation.

CONCLUSIONS

A fixed amount of root mean square (RMS) aberration has a varied effect on binocular vision depending on the angular frequency and radial order of Zernike mode. Binocular vision has a positive effect in reducing the visual impact of aberrations as Zernike modes that suffer from the most loss of visual acuity also experience the greatest amounts of binocular summation.

Vision Improvement by Correcting Higher-order Aberrations With Phase Plates in Normal Eyes

PURPOSE

To psychophysically demonstrate vision improvement when correcting higher-order aberrations with phase plates in normal eyes.

METHODS

The wavefront aberrations of three nonsurgical normal eyes were measured with a Shack-Hartmann wavefront sensor. With these measured aberrations, phase plates were fabricated using a lathing technique. Theoretical improvement in retinal image quality was estimated by calculating the optical modulation transfer functions under the white light condition. Visual acuity measurements were also conducted to demonstrate improvement in visual performance after correcting higher-order aberrations with the phase plate. In this visual acuity measurement, a tumbling "E" with high (100%) and low (10%) contrast was used.

RESULTS

The phase plate reduced the higher-order root mean square (RMS) wavefront error from 0.39 +/- 0.09 to 0.15 +/- 0.02 microm (mean +/- standard deviation from three eyes) for a 6-mm pupil. With the phase plate, retinal image quality based on the volume of modulation transfer function under 60 cycles per degree (c/deg) was improved by a factor of 1.8 +/- 0.4 over that of the eyes with spherocylindrical correction only. Average improvement in visual acuity achieved by correcting the higher-order aberration was 0.23 lines with high-contrast letters and 1.12 lines with low-contrast letters. All subjects reported subjective improvement in image quality of the letter with the phase plate.

CONCLUSION

The phase plate effectively corrected the higher-order aberrations in normal eyes. As a result, both retinal image quality and visual acuity especially with the low-contrast letters were improved. This study demonstrated the feasibility of correcting higher-order aberrations and improving vision with customized optics.

In vivo and in vitro repeatability of Hartmann-Shack aberrometry

PURPOSE

To assess the in vivo and in vitro repeatability of objective refraction and higher-order aberrations (HOAs) measured by a commercially available Hartmann-Shack wavefront sensor.

SETTING

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

METHODS

After pupil dilation of 40 myopic or myopic, astigmatic eyes of 20 patients, wavefront measurements were performed 6 times in each eye and in a test object provided by the manufacturer by 2 experienced examiners using a Hartmann-Shack wavefront sensor (Zywave, software version 3.21, Bausch & Lomb). The mean standard deviation (SD) and the coefficient of variation (CV) for sphere, cylinder, and each Zernike polynomial were computed for a 7.0 mm pupil diameter. Vector analysis was performed for the astigmatism. After the data were subdivided into 2 groups with 3 measurements in each, one measurement that best matched the subjective manifest refraction was chosen in each group and the difference between them was calculated.

RESULTS

The mean SD (CV) was 0.15 diopter (D) (7%) for the sphere value of the predicted phoropter refraction and 0.16 D (22%) for astigmatism. Thirty-two eyes had an axis deviation of at least 10 degrees. Vector analysis revealed a mean SD of 0.24@109.8. Other results for mean SD and mean CV were as follows: total in vivo higher-order RMS, 0.097 microm, 13.4%; sphere in myopic test device, 0.034 D, 0.65%; sphere in hyperopic test object, 0.035 D, 0.72%. The difference between the 2 best-matched refractions was significantly different from zero (0.11 D, P<.001). The CV was significantly higher for HOAs than for the 2nd-order aberrations (defocus and astigmatism).

CONCLUSIONS

Repeatability of Hartmann-Shack aberrometry by the Zywave wavefront sensor was not satisfactory, particularly for small amounts of HOAs. Under these conditions, aberrometry measurements should be repeated several times and outliers should be excluded in calculating the means.

The prospects for super-acuity: limits to visual performance after correction of monochromatic ocular aberration

It has recently been suggested that correction of the monochromatic aberration of the eye could lead to substantial improvements in visual acuity and contrast sensitivity function. After consideration of the best-corrected visual acuity of normal eyes, the optical and neural limits to visual performance are reviewed. It is concluded that, even if current problems with the accuracy of the suggested techniques of aberration correction, through corneal excimer laser ablation or customised contact lenses, can be overcome, changes in monochromatic ocular aberration over time, the continuing presence of chromatic aberration, errors of focus associated with lags and leads in accommodation, and other factors, are likely to result in only minor improvements in the high-contrast acuity performance of most normal eyes being produced by attempted aberration control. Significant gains in contrast sensitivity might, however, be achievable, particularly under mesopic and scotopic conditions when the pupil is large, provided that correct focus can be maintained. In the immediate future, reduction of the high levels of aberration that are currently found in eyes that have undergone refractive surgery and in some abnormal eyes should bring useful benefits.

Ocular higher-order aberrations in individuals screened for refractive surgery

PURPOSE

To explore the distribution of ocular higher-order aberrations (HOAs, 3rd to 6th orders) in the population, evaluate the symmetry of ocular aberrations between right and left eyes in each subject using a Hartmann-Shack wavefront sensor, and study the differences in aberration as a function of age.

SETTING

Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA.

METHODS

Ocular HOAs were examined across a 6.0 mm pupil in 532 eyes of 306 subjects (mean age 41 years +/- 10 [SD] [range 20 to 71 years]; mean WaveScan spherical equivalent -3.39 +/- 2.84 diopters [D] [range -11.56 to 7.60 D]) using the WaveScan system (Visx, Inc.). Zernike coefficients and root-mean-square (RMS) values of HOAs, spherical aberration (SA, Z(4)(0) and Z(6)(0)), and coma (Z(3)(-1), Z(3)(1), Z(5)(-1), and Z(5)(1)) were analyzed. Correlation analysis was performed to assess the association between ocular HOAs and age and investigate the aberration symmetry between right and left eyes.

RESULTS

For individual terms, the highest mean absolute values were for 4th-order SA (Z(4)(0)), 3rd-order coma, and trefoil terms. The mean RMS values of HOA, SA, and coma were 0.305 +/- 0.095 microm, 0.128 +/- 0.074 microm, and 0.170 +/- 0.089 microm, respectively. Moderate to high correlations were found between the right and left eyes for HOA, SA, and coma (Pearson correlation coefficient = 0.601, 0.776, and 0.511, respectively; all P<.001). Thirteen of the 22 Zernike terms (59%) were significantly correlated across eyes (Bonferroni correction, P'<.05/22). Higher-order aberrations, SA, and coma were weakly correlated with age (r = 0.317, 0.273, and 0.176, respectively; all P<.002).

CONCLUSION

Wavefront aberrations varied widely among subjects and increased slightly with age. A moderate to high degree of mirror symmetry existed between right and left eyes.

Optical aberrations of the human anterior cornea

PURPOSE

(1). To investigate the distribution of anterior corneal higher-order aberrations (HOAs, 3rd to 6th orders) in the population; (2). to evaluate the symmetry of anterior corneal aberrations between right and left eyes of individuals; and (3). to study the variations in anterior corneal aberrations with aging.

SETTING

Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA.

METHODS

Using the CTView program (Sarver and Associates, Inc.), corneal HOAs were computed from the central 6.0 mm zone of the corneal topographic maps (Humphrey Atlas, Carl Zeiss, Inc.) of 228 eyes of 134 subjects (mean age 50 years +/- 17 (SD); range 20 to 79 years; manifest spherical equivalent between -3.0 and +3.0 diopters [D]). Correlation analysis was performed to investigate the aberration symmetry between the right and left eyes and to assess the association between anterior corneal HOAs and age.

RESULTS

There was wide individual variability in aberrations with ranges of individual Zernike terms from -0.579 to +0.572 microm. The mean coefficient of the 4th-order spherical aberration (SA) (Z(4)(0)) was 0.280 +/- 0.086 microm and was positive in all corneas. The mean root-mean-square (RMS) values were 0.479 +/- 0.124 microm for HOA, 0.281 +/- 0.086 microm for SA (Z(4)(0)and Z(6)(0)), and 0.248 +/- 0.135 microm for coma (Z(3)(-1), Z(3)(1), Z(5)(-1), and Z(5)(1)). Moderate to high correlations were found between right and left eyes for HOA, SA, and coma (Pearson r = 0.565, 0.751, and 0.565, respectively; all P<.001); 8 of the 9 Zernike terms in the 3rd and 4th orders were significantly correlated between eyes (Bonferroni correction P'<.05/22). Higher-order aberration RMS and coma RMS increased with aging (r = 0.434 and 0.290, respectively; both P<.001); SA RMS was not correlated with change in age (r = 0.034).

CONCLUSION

Anterior corneal wavefront aberrations varied greatly among subjects and increased slightly with aging. All corneas had positive 4th-order SAs, and the values did not change with aging. A moderate to high degree of mirror symmetry existed between right and left eyes.

Separate effects of the microkeratome incision and laser ablation on the eye's wave aberration

PURPOSE

To study the optical changes induced by the microkeratome cut, the subsequent laser ablation, and the biomechanical healing response of the cornea in normal laser in situ keratomileusis (LASIK) eyes.

DESIGN

Prospective randomized clinical trial.

METHODS

A Hansatome microkeratome was used to cut a corneal flap in one eye (study eye) of 17 normal myopic patients and a subsequent laser ablation was performed 2 months after this initial microkeratome incision. Control eyes received conventional LASIK treatments at the latter time point. The wave aberration of both the study and contralateral control eyes were measured over a 6-mm pupil with a Shack-Hartmann wavefront sensor for all preoperative, postflap cut, and postablation visits.

RESULTS

The eye's higher order aberrations had a small, but significant increase (P =.03) of approximately 30% 2 months after cutting a flap. No systematic changes were observed in nearly all Zernike coefficients from their preoperative levels at 2 months postflap cut. A significant difference between the study and control eyes was observed for one trefoil mode, Z(3)(3) (P =.04).

CONCLUSIONS

There was a wide variation in the response of individual Zernike modes across patients after cutting a flap. The majority of spherical aberration induced by the LASIK procedure seems to be due to the laser ablation and not the microkeratome cut. In addition, the total and higher order root mean square of wavefront errors were nearly identical for both the study and control eyes 3-months after the laser ablation, indicating that a procedure in which the incision and the ablation are separated in time to better control aberrations does not compromise the outcome of a conventional LASIK treatment.

Validation of a clinical Shack-Hartmann aberrometer

PURPOSE

To validate the accuracy, tolerance, and repeatability of the complete ophthalmic analysis system aberrometer (COAS, Wavefront Sciences Inc.) with model eyes and normal human eyes.

METHOD

Model eyes were constructed from six polymethyl methacrylate, single-surface lenses with known characteristics. Accuracy of second-order aberrations was verified by measuring defocus and astigmatism induced by series of spherical and cylindrical trial lenses. Accuracy of higher-order aberrations was evaluated by comparing ray-tracing predictions with measured spherical aberration and coma of the aspheric model eyes. Tolerance to axial and lateral misalignment was measured by controlled displacements of the model eye relative to the aberrometer. Repeatability was tested on the same model eyes with repeated measurements taken within 1 s or within half an hour with realignment between each trial. Analyses were based on a 5-mm pupil diameter.

RESULTS

Defocus and astigmatism were accurately measured within the working range of the instrument automatic focus adjustment (e.g., measured defocus was within +/-0.25 diopters over a -6.50 to +3.00 D range of refractive error). Accuracy of spherical aberration and coma agreed closely with theoretical predictions (e.g., for all six aspheric models, the mean absolute difference between predicted and measured Z(4)0 was 0.007 microm). Axial displacements over the range +/-2.5 mm had little effect on measurements for myopic and emmetropic model eyes. Also, lateral displacements over the range +/-1.5 mm did not produce significant coma. The standard deviations of repeated measurements of higher-order root mean square on model eyes were <1% of the mean with repeated measures within 1 s and 10% of the mean for five individual measurements with realignment in between each. Tolerance to small lateral displacements was also observed for human eyes.

CONCLUSION

The complete ophthalmic analysis system aberrometer can measure second-, third-, and fourth-order aberrations accurately and repeatedly on model eyes.

Hartmann-Shack technique and refraction across the horizontal visual field

We compared refractions across the horizontal visual field, based on different analyses of wave aberration obtained with a Hartmann-Shack instrument. The wave aberrations had been determined for 6-mm-diameter pupils up to at least the sixth Zernike order in five normal subjects [J. Opt. Soc. Am. A 19, 2180 (2002)]. The polynomials were converted into refractions based on 6-mm pupils and second-order Zernike aberrations (6 mm/2nd order), 3-mm pupils and second-order aberrations (3 mm/2nd order), 1-mm pupils and second-order aberrations (1 mm/2nd order), and 6-mm pupils with both second- and fourth-order aberrations (6 mm/4th order). The 3-mm/2nd-order and 6-mm/2nd-order refractions differed by as much as 0.9 D in mean sphere on axis, but the differences reduced markedly toward the edges of the visual field. The cylindrical differences between these two analyses were small at the center of the visual field (<0.3 D) but increased into the periphery to be greater than 1.0 D for some subjects. Much smaller differences in mean sphere and cylinder were found when 3-mm/2nd-order refractions and either the 1-mm/2nd-order refractions or the 6-mm/4th-order refractions were compared. The results suggest that, for determining refractions based on wave aberration data with large pupils, similar results occur by either restricting the analysis to second-order Zernike aberrations with a smaller pupil such as 3 mm or using both second- and fourth-order Zernike aberrations. Since subjective refraction is largely independent of the pupil size under photopic conditions, objective refractions based on either of these analyses may be the most useful.

Higher Order Ocular Aberrations After Cycloplegic and Non-cycloplegic Pupil Dilation

PURPOSE

Clinical aberrometry is commonly undertaken with the use of mydriatic agents, however there is no literature available on whether aberrometry results obtained under cycloplegia differ from those obtained without cycloplegia.

METHODS

Higher order aberrations were measured over a 6-mm pupil with a Bausch and Lomb Technolas Zywave Aberrometer on the right eyes of 31 young subjects (average age 19.7 +/- 1.7 years; 5 females, 16 males). Two measurement conditions were used for each subject: 1) topical installation of 3 drops 1% cyclopentolate hydrochloride; and 2) topical installation of 1 drop 2.5% phenylephrine hydrochloride, prior to aberrometry measurements.

RESULTS

For higher order aberrations (3rd to 5th order), average root mean square (RMS) after phenylephrine measurement (0.3852 microm) was significantly lower than after cyclopentolate (0.4259 microm). A small but statistically significant difference was found between the two conditions for average vertical and horizontal coma and, to a lesser extent, horizontal 5th order aberrations. Repeatability RMS, a measure of test-retest measurement repeatability, was similar for the two conditions at 0.15 microm, and significantly lower than the average RMS for the difference between the two conditions (residual RMS) of 0.22 microm.

CONCLUSIONS

The difference between cycloplegic and non-cycloplegic aberration measurements has implications for surgical correction of higher order aberrations.

Measuring of ocular wavefront aberration in large pupils using OPD-scan

Wavefront analysis using a scanning slit refractometer (the OPD-Scan) was evaluated in both artificial and human eyes, in comparison with the Hartmann-Shack wavefront sensor (H-S) currently often used. Comparison of different methods and configurations carried out in the artificial eyes yielded basically the same results in moderate refractive error cases. There was a closer match between the RMS (root mean square) wavefront error obtained by OPD-Scan and H-S in the 6 mm pupils than in the 4 mm pupils of the same normal human eyes. Although OPD-Scan employs a different approach in determining aberration, the aberration value is similar to that of H-S, especially in large pupils.

Simplified mathematics for customized refractive surgery

PURPOSE

To describe a simple mathematical approach to customized corneal refractive surgery or customized intraocular lens (IOL) design that allows "hypervision" and to investigate the accuracy limits.

SETTING

University eye hospital, Mainz, Germany.

METHODS

Corneal shape and at least 1 IOL surface are approximated by the well-known Cartesian conic section curves (ellipsoid, paraboloid, or hyperboloid). They are characterized by only 2 parameters, the vertex radius and the numerical eccentricity. Residual refraction errors for this approximation are calculated by numerical ray tracing. These errors can be displayed as a 2-dimensional refraction map across the pupil or by blurring the image of a Landolt ring superimposed on the retinal receptor grid, giving an overall impression of the visual outcome.

RESULTS

If the eye is made emmetropic for paraxial rays and if the numerical eccentricities of the cornea and lens are appropriately fitted to each other, the residual refractive errors are small enough to allow hypervision. Visual acuity of at least 2.0 (20/10) appears to be possible, particularly for mesopic pupil diameters. However, customized optics may have limited application due to their sensitivity to misalignment errors such as decentrations or rotations.

CONCLUSIONS

The mathematical approach described by Descartes 350 years ago is adequate to calculate hypervision optics for the human eye. The availability of suitable mathematical tools should, however, not be viewed with too much optimism as long as the accuracy of the implementation in surgical procedures is limited.

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.

Wide-field compensation of monochromatic eye aberrations: expected performance and design trade-offs

The optical quality of the human eye varies across the visual field. Hence an exact compensation of the eye aberration for a given field point can give rise to a less-than-optimum compensation in neighboring field regions. We have studied some aspects of this problem and present here an approach to design wide-field (< 10 degrees) optically thin correcting elements, e.g., phase plates, deformable mirrors, and liquid-crystal displays. Their expected performance is assessed using actual eye aberration data. Particular attention is given to the design of elements providing a minimum averaged rms residual aberration and those providing a nearly uniform rms residual aberration across a given field.

Use of retroillumination to visualize optical aberrations caused by tear film break-up

PURPOSE

The aim of the current study was to develop quantitative methods to assess optical aberrations caused by tear film disruption.

METHODS

We used standard fluorescein imaging (FL) and a novel retroillumination (RI) method to image tear film disruption in 12 eyes. Using a clinical slit lamp biomicroscope, we alternated between widefield blue and narrow-beam white light to obtain an interleaved series of FL and RI images of the time course and pattern of tear film break-up. We developed an optical analysis that indicates that the RI image should be proportional to the spatial derivative of the FL image. Intensity fluctuations in the RI images are due to thickness changes in the tear film, whereas intensity fluctuations in FL images are directly determined by tear film thickness.

RESULTS

As predicted by optical analysis of RI, the spatial distribution of gaps in the tear film seen with fluorescein appeared as pairs of light and dark contours in the RI images, and a precise correspondence between the spatial derivative of the FL image (slope) and the RI image was found. Both methods showed a gradual spreading of the tear disruption during blink suppression that varied tremendously among eyes in both time and spatial pattern. Resumption of normal blinking did not produce an immediate reconstitution of the normal tear film, and areas of tear break-up created during blink suppression remained abnormal for up to several minutes of normal blinking.

CONCLUSIONS

Our analysis indicates that both FL and RI have the potential to quantify optical changes occurring during tear break-up. These results support an interpretation of RI as an intensity-based method for mapping the highly irregular optical aberrations of the eye produced by tear film disruption.

Effect of Beam Size on the Expected Benefit of Customized Laser Refractive Surgery

PURPOSE

Customized laser surgery attempts to correct higher order aberrations, as well as defocus and astigmatism. The success of such a procedure depends on using a laser beam that is small enough to produce fine ablation profiles needed to correct higher order aberrations.

METHODS

Wave aberrations were obtained from a population of 109 normal eyes and 4 keratoconic eyes using a Shack-Hartmann wavefront sensor. We considered a theoretical customized ablation in each eye, performed with beams of 0.5, 1.0, 1.5, and 2.0 mm in diameter. We then calculated the residual aberrations remaining in the eye for the different beam sizes. Retinal image quality was estimated by means of the modulation transfer function (MTF), computed from the residual aberrations. Fourier analysis was used to study spatial filtering of each beam size.

RESULTS

The laser beam acts like a spatial filter, smoothing the finest features in the ablation profile. The quality of the correction declines steadily when the beam size increases. A beam of 2 mm is capable of correcting defocus and astigmatism. Beam diameters of 1 mm or less may effectively correct aberrations up to fifth order.

CONCLUSION

Large diameter laser beams decrease the ability to correct higher order aberrations. A top-hat laser beam of 1 mm (Gaussian with FWHM of 0.76 mm) is small enough to produce a customized ablation for typical human eyes.

Relationship between refractive error and monochromatic aberrations of the eye

PURPOSE

To examine the relationship between ametropia and optical aberrations in a population of 200 normal human eyes with refractive errors spanning the range from +5.00 to -10.00 D.

METHODS

Using a reduced-eye model of ametropia, we tested the hypothesis that the optical system of the eye is uncorrelated with the degree of ametropia. These predictions were evaluated experimentally with a Shack-Hartmann aberrometer that measured the monochromatic aberrations across the central 6 mm of the dilated pupil in well-corrected, cyclopleged eyes.

RESULTS

Optical theory predicted, and control experiments on a model eye verified, that Shack-Hartmann measurements of spherical aberration will vary with axial elongation of the eye even if the dioptric components of the eye are fixed. Contrary to these predictions, spherical aberration was not significantly different from emmetropic eyes. Root mean square of third-order aberrations, fourth-order aberrations, and total higher aberrations (third to 10th) in myopic and hyperopic eyes were also uncorrelated with refractive error. Astigmatic eyes tended to have larger total higher-order aberrations than nonastigmatic eyes.

CONCLUSIONS

We conclude that a reduced-eye model of myopia assuming fixed optical parameters and variable axial length is not tenable.

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.

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.

Wavefront-guided versus standard laser in situ keratomileusis to correct low to moderate myopia

To evaluate the 6-month refractive outcomes of wavefront-guided laser in situ keratomileusis (LASIK) (Zyoptix, Bausch & Lomb) versus standard LASIK (PlanoScan, Bausch & Lomb). Department of Ophthalmology, University Hospital Maastricht, Maastricht, The Netherlands. In a prospective randomized study, 12 patients with myopia had Zyoptix wavefront-guided LASIK in 1 eye and PlanoScan LASIK in the contralateral eye. The safety, efficacy, predictability, stability, optical zone size, and ablation depth were evaluated. The mean preoperative spherical equivalent (SE) of the subjective manifest refraction was -3.88 diopters (D) +/- 1.92 (SD) (Zyoptix) and -4.35 +/- 2.11 D (PlanoScan). Six months postoperatively, 8% of PlanoScan patients and 16% of Zyoptix patients gained at least 2 lines of best corrected visual acuity; the safety index was 1.12 in the Zyoptix group and 1.08 in the PlanoScan group. An SE of +/-1.00 D and +/-0.50 D was achieved by 100% and 92%, respectively, in both groups. There were 2 undercorrections in the Zyoptix group and 1 undercorrection in the PlanoScan group. In the Zyoptix group, 100% had a UCVA of 20/40 and 67% of 20/20 and in the PlanoScan group, 100% and 83%, respectively. The efficacy index was 0.87 and 0.93 in the Zyoptix group and PlanoScan group, respectively. The mean optical zone 6 months postoperatively was 6.16 +/- 0.34 mm in the PlanoScan group and 6.23 +/- 0.41 mm in the Zyoptix group (P =.67). The ablation depth per diopter of defocus equivalent was 13.5 +/- 4.6 microm/D and 8.6 +/- 4.4 microm/D, respectively (P =.01).An excellent safety index was achieved with the Zyoptix and PlanoScan treatments. The efficacy index was marginally lower for Zyoptix treatments as a result of 2 undercorrections. The ablation depth in the Zyoptix group per diopter of defocus equivalent was significantly lower than in the PlanoScan group. Further refinements in defining the ablation algorithms may increase the efficacy index.

Scaling Zernike expansion coefficients to different pupil sizes

Recent developments in technologies to correct aberrations in the eye have fostered extensive research in wave-front sensing of the eye, resulting in many reports of Zernike expansions of wave-front errors of the eye. For different reports of Zernike expansions, to be compared, the same pupil diameter is required. Since no standard pupil size has been established for reporting these results, a technique for converting Zernike expansion coefficients from one pupil size to another is needed. This investigation derives relationships between the Zernike expansion coefficients for two different pupil sizes.

A statistical model of the aberration structure of normal, well-corrected eyes

A statistical model of the wavefront aberration function of the normal, well-corrected eye was constructed based on normative data from 200 eyes which show that, apart from spherical aberration, the higher-order aberrations of the human eye tend to be randomly distributed about a mean value of zero. The vector of Zernike aberration coefficients describing the aberration function for any individual eye was modelled as a multivariate, Gaussian, random variable with known mean, variance and covariance. The model was verified by analysing the statistical properties of 1000 virtual eyes generated by the model. Potential applications of the model include computer simulation of individual variation in aberration structure, retinal image quality, visual performance, benefit of novel designs of ophthalmic lenses, or outcome of refractive surgery.

Aberration Generation by Contact Lenses With Aspheric and Asymmetric Surfaces

PURPOSE

We explored the potential of aberration correction in the human eye by using a new generation of soft contact lenses with aspheric and asymmetric surfaces.

METHODS

Soft contact lens samples were designed with one asymmetrical surface (front) and one spherical (back) to produce predetermined amounts of desired pure defocus, astigmatism, trefoil, coma, and spherical aberration. Contact lens wavefront aberrations were measured ex vivo using a Fizeau-Tolanski interferometer and compared with the in vivo wavefronts obtained by subtracting the aberrations of the eye with and without the contact lenses. These second set of measurements were obtained using a Shack-Hartmann sensor.

RESULTS

We found that an aberration-free contact lens sample induced in the eye a small amount of residual aberration. We obtained a good match between the ex vivo and in vivo wavefront measurements for most of the samples of the contact lenses.

CONCLUSIONS

The aberrations generated by soft contact lenses on the eye were predictable. Rotations and translations of the contact lenses with respect to correct position on the eye were, however, the main limitation for precise correction of the ocular aberrations.

High order wave aberration of eyes

This paper is concerned with the means and distribution of the wavefront variances and their root mean squares (RMS) of normal eyes, as measured by various techniques and computed for various pupil sizes. Using data from a subjective crossed cylinder aberroscope [Howland and Howland J. Opt. Soc. Am. A 67(1977)1508] it was found that the logarithms of the wavefront variances are approximately normally distributed. A comparison of data from this subjective study with that of six other studies using a variety of techniques of wavefront measurement showed that the relationship between RMS wavefront deviations of high order aberrations (third order polynomial terms and above) obeyed the relationship: log (RMS) (microm) = -1.918 +/- 0.048 SE + 3.023 +/- 0.111 x log (pupil radius) (mm), with R2 = 0.971.

Liquid-crystal adaptive optics based on feedback interferometry for high-resolution retinal imaging

A novel, to our knowledge, adaptive optical imaging system for high-resolution retinal imaging is described. The system is based on a feedback interferometer, in which two-dimensional output fringe intensity from a Mach-Zehnder interferometer with large radial shear is fed back, with the help of a video projector connected with a CCD camera, to an optically addressed phase-only liquid-crystal spatial light modulator. Experiments to verify the system performance have been conducted by use of an artificial eye consisting of a lens, an aberration plate, and a resolution test target. We observed that an image of the test target (mimicking a retina) blurred by the aberration plate (mimicking ocular aberrations) was successfully restored immediately after our adaptive optics system was activated.

Ocular wave-front aberration statistics in a normal young population

Monochromatic ocular aberrations in 108 eyes of a normal young population (n=59) were studied. The wave-front aberration were obtained under natural conditions using a near-infrared Shack-Hartmann wave-front sensor. For this population and a 5 mm pupil, more than 99% of the root-mean square wave-front error is contained in the first four orders of a Zernike expansion and about 91% corresponds only to the second order. Comparison of wave-fronts aberrations from right and left eye in 35 subjects, showed a good correlation between most of the second- and third-order terms and a slight (but not clear) tendency for mirror symmetry between 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.

Imperfect optics may be the eye's defence against chromatic blur

The optics of the eye cause different wavelengths of light to be differentially focused at the retina. This phenomenon is due to longitudinal chromatic aberration, a wavelength-dependent change in refractive power. Retinal image quality may consequently vary for the different classes of cone photoreceptors, cells tuned to absorb bands of different wavelengths. For instance, it has been assumed that when the eye is focused for mid-spectral wavelengths near the peak sensitivities of long- (L) and middle- (M) wavelength-sensitive cones, short-wavelength (bluish) light is so blurred that it cannot contribute to and may even impair spatial vision. These optical effects have been proposed to explain the function of the macular pigment, which selectively absorbs short-wavelength light, and the sparsity of short-wavelength-sensitive (S) cones. However, such explanations have ignored the effect of monochromatic wave aberrations present in real eyes. Here we show that, when these effects are taken into account, short wavelengths are not as blurred as previously thought, that the potential image quality for S cones is comparable to that for L and M cones, and that macular pigment has no significant function in improving the retinal image.

Adaptive optics scanning laser ophthalmoscopy

We present the first scanning laser ophthalmoscope that uses adaptive optics to measure and correct the high order aberrations of the human eye. Adaptive optics increases both lateral and axial resolution, permitting axial sectioning of retinal tissue in vivo. The instrument is used to visualize photoreceptors, nerve fibers and flow of white blood cells in retinal capillaries.

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.

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.