Monochromatic aberrations of the human eye in a large population

Can uncompensated higher order aberration profile, or aberropia be responsible for subnormal best corrected vision and pseudo-amblyopia

BACKGROUND

Higher order aberrations (HOA) are components of wavefront distortion which cannot be corrected by conventional spectacle correction. Normally they constitute up to 15% of wavefront distortion in the ocular media. The HOA interact in a nonlinear method and tend to compensate each other in most conditions.

HYPOTHESES

We hypothesize that abnormally increased and uncompensated higher order aberration profile in certain cases may limit the amount of best corrected visual acuity to subnormal levels and produce a pseudo-ambylopia like picture. We term this entity as aberropia.

EVALUATION OF THE HYPOTHESIS

Higher order aberrations (HOA) have been proven to have supporting role in visual function in association with lower order aberrations. Normally HOA tend to compensate for each other and have an effect much less than what would be expected if they would have acted separately. This unique state of compensation may be lost in certain cases, for example, in patients who have undergone laser refractive surgery without consideration for HOA correction or in partial correction of a pathological eye like severe keratoconus. Occasionally investigators have noticed that patients with high induced aberrations after refractive surgery cannot achieve spectacle correction to get a 20/20 vision. Conversely, there is evidence for gain of vision after wavefront guided refractive surgery and phakic intraocular lens implantations in some cases which cannot be explained only by retinal image change.

CHALLENGES TO CONCLUSIVELY PROVE THE HYPOTHESES

With the current level of advancement in refractive surgery, we can correct lower order aberration to a near zero level. However it is not as easy to do the same with higher order aberrations because of variability in assessment, evolving laser beam profiles and factors associated with the surgery itself and wound healing. All the four can alter higher order aberrations.

IMPLICATIONS OF THE HYPOTHESES

Understanding of uncompensated higher order profiles leading to loss of BCVA, or aberropia, would be a paradigm shift in understanding of the role of higher order aberrations on visual function. With improvement in diagnostic and treatment methods, these patients with a subnormal vision, may be treated to achieve their maximum visual potential.

Statistical generation of normal and post-refractive surgery wavefronts

BACKGROUND

Wavefront sensors provide detailed information regarding the aberration structure of large populations of patients. Knowledge of the statistical distribution of the aberrations has several applications, including the development of ophthalmic devices. The statistical distribution aids in defining the required performance range of the device. Another application would be customised schematic eye models that incorporate likely patterns of aberrations found in a given subject population. These models can then be used to find the statistical distribution of image quality metrics based on metrics such as MTF and retinal spot size.

METHODS

Myopic and post-refractive surgical patient populations were analysed to determine the statistical properties of their ocular aberrations. A matrix method is developed that can be used to generate aberration coefficients that are consistent with each population.

RESULTS

Generated wavefronts have statistical properties similar to the respective populations and incorporate the correlations between aberration coefficients.

CONCLUSION

The matrix techniques illustrated here can be used to generate wavefronts that are consistent with various populations of interest to the ophthalmic community. Generation of wavefronts enables techniques such as Monte Carlo simulations to be performed that aid in the development of ophthalmic instrumentation and visual performance metrics.

Higher-Order Wavefront Aberrations for Populations of Young Emmetropes and Myopes

Purpose

To test the hypothesis that human eyes have a central tendency to be free of higher-order aberrations by analyzing wavefront aberrations for two young populations of respectively emmetropic and myopic subjects.

Methods

Both right and left eyes of 75 emmetropes and 196 myopes were measured for corneal wavefront aberration using a Humphrey corneal topographer and for the whole eye wavefront aberration using a WASCA wavefront sensor without pupil dilation. 35 Zernike aberration coefficients over a 6.0 mm pupil diameter were derived, and statistics of the higher-order terms (3^rd to 5^th orders) were tested.

Results

When signed Zernike aberrations of the right and left eyes were averaged together for the emmetropes, three higher-order modes (j=6, 12 and 13) were significantly different from zero in both the cornea and the whole eye (P<0.0005), and three additional terms (j=14, 15 and 17) were statistically non-zero for the whole eye. As the signs of y-axis asymmetrical terms in the left eye were flipped, three more terms in either the cornea (j=8, 18 and 19) or the whole eye (j=8, 10 and 20) became statistically non-zero. For the myopes, 8 corneal terms and 5 whole-eye terms were statistically non-zero when the two eyes were averaged together. As the signs flipped, the majority of the Zernike aberration terms were statistically different from zero.

Conclusions

Human eyes have systematical higher order aberrations in population, and factors that cause bilateral symmetry of wavefront aberrations between the right and left eyes made important contribution to the systematical aberrations.

Comparison of Control Algorithms for a MEMS-based Adaptive Optics Scanning Laser Ophthalmoscope

We compared four algorithms for controlling a MEMS deformable mirror of an adaptive optics (AO) scanning laser ophthalmoscope. Interferometer measurements of the static nonlinear response of the deformable mirror were used to form an equivalent linear model of the AO system so that the classic integrator plus wavefront reconstructor type controller can be implemented. The algorithms differ only in the design of the wavefront reconstructor. The comparisons were made for two eyes (two individuals) via a series of imaging sessions. All four controllers performed similarly according to estimated residual wavefront error not reflecting the actual image quality observed. A metric based on mean image intensity did consistently reflect the qualitative observations of retinal image quality. Based on this metric, the controller most effective for suppressing the least significant modes of the deformable mirror performed the best.

Correction of ocular and atmospheric wavefronts: a comparison of the performance of various deformable mirrors

The main applications of adaptive optics are the correction of the effects of atmospheric turbulence on ground-based telescopes and the correction of ocular aberrations in retinal imaging and visual simulation. The requirements for the wavefront corrector, usually a deformable mirror, will depend on the statistics of the aberrations to be corrected; here we compare the spatial statistics of wavefront aberrations expected in these two applications. We also use measured influence functions and numerical simulations to compare the performance of eight commercially available deformable mirrors for these tasks. The performance is studied as a function of the size of the optical pupil relative to the actuated area of the mirrors and as a function of the number of modes corrected. In the ocular case it is found that, with the exception of segmented mirrors, the performance is greatly enhanced by having a ring of actuators outside the optical pupil, as this improves the correction of the pupil edge. The effect is much smaller in the case of Kolmogorov wavefronts. It is also found that a high Strehl ratio can be obtained in the ocular case with a relatively low number of actuators if the stroke is sufficient. Increasing the number of actuators has more importance in the Kolmogorov case, even for the relatively weak turbulence considered here.

Binocular correlation of ocular aberration dynamics

Fluctuations in accommodation have been shown to be correlated in the two eyes of the same subject. However, the dynamic correlation of higher-order aberrations in the frequency domain has not been studied previously. A binocular Shack-Hartmann wavefront sensor is used to measure the ocular wavefront aberrations concurrently in both eyes of six subjects at a sampling rate of 20.5 Hz. Coherence function analysis shows that the inter-ocular correlation between aberrations depends on subject, Zernike mode and frequency. For each subject, the coherence values are generally low across the resolvable frequency range (mean 0.11), indicating poor dynamic correlation between the aberrations of the two eyes. Further analysis showed that phase consistency dominates the coherence values. Monocular and binocular viewing conditions showed similar power spectral density functions.

Ultrahigh resolution optical coherence tomography and pancorrection for cellular imaging of the living human retina

Cellular in vivo visualization of the three dimensional architecture of individual human foveal cone photoreceptors is demonstrated by combining ultrahigh resolution optical coherence tomography and a novel adaptive optics modality. Isotropic resolution in the order of 2-3 microm, estimated from comparison with histology, is accomplished by employing an ultrabroad bandwidth Titanium:sapphire laser with 140 nm bandwidth and previous correction of chromatic and monochromatic ocular aberrations. The latter, referred to as pancorrection, is enabled by the simultaneous use of a specially designed lens and an electromagnetically driven deformable mirror with unprecedented stroke for correcting chromatic and monochromatic aberrations, respectively. The increase in imaging resolution allows for resolving structural details of distal elements of individual foveal cones: inner segment zones--myoids and ellipsoids--are differentiated from outer segments protruding into pigment epithelial processes in the retina. The presented technique has the potential to unveil photoreceptor development and pathogenesis as well as improved therapy monitoring of numerous retinal diseases.

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.

Changes in through-focus spatial visual performance with adaptive optics correction of monochromatic aberrations

We determined the influence of adaptive optics correction on through-focus illiterate-E visual acuity and through-focus contrast sensitivity under monochromatic conditions. In two subjects, adaptive optics improved high and low (12%) contrast in-focus visual acuity by 0.1 to 0.15logMAR, but resulted in more rapid and more symmetrical deterioration in visual acuity away from in-focus. In one subject, adaptive optics improved in-focus contrast sensitivity and resulted in more symmetrical and greater loss of contrast sensitivity about the peak sensitivity because of correction of higher-order aberrations. The results show that full correction of higher-order aberrations may worsen spatial visual performance in the presence of some defocus.

Wavefront-guided versus wavefront-optimized laser in situ keratomileusis: contralateral comparative study

PURPOSE

To compare the outcomes of wavefront-guided and wavefront-optimized treatment in fellow eyes of patients having laser in situ keratomileusis (LASIK) for myopia.

SETTING

Medical and Vision Research Foundation, Tamil Nadu, India.

METHODS

This prospective comparative study comprised 27 patients who had wavefront-guided LASIK in 1 eye and wavefront-optimized LASIK in the fellow eye. The Hansatome (Bausch & Lomb) was used to create a superior-hinged flap and the Allegretto laser (WaveLight Laser Technologie AG), for photoablation. The Allegretto wave analyzer was used to measure ocular wavefront aberrations and the Functional Acuity Contrast Test chart, to measure contrast sensitivity before and 1 month after LASIK. The refractive and visual outcomes and the changes in aberrations and contrast sensitivity were compared between the 2 treatment modalities.

RESULTS

One month postoperatively, 92% of eyes in the wavefront-guided group and 85% in the wavefront-optimized group had uncorrected visual acuity of 20/20 or better; 93% and 89%, respectively, had a postoperative spherical equivalent refraction of +/-0.50 diopter. The differences between groups were not statistically significant. Wavefront-guided LASIK induced less change in 18 of 22 higher-order Zernike terms than wavefront-optimized LASIK, with the change in positive spherical aberration the only statistically significant one (P= .01). Contrast sensitivity improved at the low and middle spatial frequencies (not statistically significant) and worsened significantly at high spatial frequencies after wavefront-guided LASIK; there was a statistically significant worsening at all spatial frequencies after wavefront-optimized LASIK.

CONCLUSION

Although both wavefront-guided and wavefront-optimized LASIK gave excellent refractive correction results, the former induced less higher-order aberrations and was associated with better contrast sensitivity.

The effect of optical zone decentration on lower- and higher-order aberrations after photorefractive keratectomy in a cat model

PURPOSE

To simulate the effects of decentration on lower- and higher-order aberrations (LOAs and HOAs) and optical quality, by using measured wavefront error (WFE) data from a cat photorefractive keratectomy (PRK) model.

METHODS

WFE differences were obtained from five cats' eyes 19 +/-7 weeks after spherical myopic PRK for -6 D (three eyes) and -10 D (two eyes). Ablation-centered WFEs were computed for a 9.0 mm pupil. A computer model was used to simulate decentration of a 6-mm subaperture in 100-microm steps over a circular area of 3000 microm diameter, relative to the measured WFE difference. Changes in LOA, HOA, and image quality (visual Strehl ratio based on the optical transfer function; VSOTF) were computed for simulated decentrations over 3.5 and 6.0 mm.

RESULTS

Decentration resulted in undercorrection of sphere and induction of astigmatism; among the HOAs, decentration mainly induced coma. Decentration effects were distributed asymmetrically. Decentrations >1000 microm led to an undercorrection of sphere and cylinder of >0.5 D. Computational simulation of LOA/HOA interaction did not alter threshold values. For image quality (decrease of best-corrected VSOTF by >0.2 log units), the corresponding thresholds were lower. The amount of spherical aberration induced by the centered treatment significantly influenced the decentration tolerance of LOAs and log best corrected VSOTF.

CONCLUSIONS

Modeling decentration with real WFE changes showed irregularities of decentration effects for rotationally symmetric treatments. The main aberrations induced by decentration were defocus, astigmatism, and coma. Treatments that induced more spherical aberration were less tolerant of decentration.

[Application of wavefront analysis in clinical and scientific settings. From irregular astigmatism to aberrations of a higher order--Part II: examples]

In recent years, wavefront analysis has ceased to be purely a laboratory application and emerged as a method used in ophthalmological diagnosis. This development has been promoted mainly by the widespread use of wavefront-guided LASIK (laser in situ keratomileusis). However, aberrometry is still not a common diagnostic technique, and for many ophthalmologists interpretation of the results is difficult. The second part of this serial paper reviews findings that are relevant for the ophthalmological community and highlights current scientific applications in this area.

Calculations and Measurements of the Visual Benefit of Correcting the Higher-order Aberrations Using Adaptive Optics Technology

Purpose

Our goal was to examine the accuracy of metrics, calculated using a numerical eye model including the measurement of the monochromatic aberrations of the eye, to predict the contrast sensitivity (CS) and visual acuity (VA) visual benefits (VB) of correcting higher-order aberrations (HO).

Methods

We measured, on the right eyes of 25 subjects (10 myopes and 15 emmetropes) aged 21 to 56 years, the 16 c/deg CS and high-contrast VA in two conditions of aberration corrections: (i) when correcting only the defocus and astigmatism terms and (ii) when dynamically correcting all the monochromatic aberration terms up to the 5^th order. The measured VB was defined as the ratio of the performances between these two conditions of aberration corrections.

Results

We measured a VB of 1.25 and 1.64 respectively in term of VA and CS. We did not find any influence of age on the VB and no statistical significant difference between the myopic and emmetropic group. The contrast sensitivity VB was well correlated (r²=0.79) with the ratio of the modulation transfer functions calculated at 16 c/deg in both conditions of aberrations corrections (i.e. MTF_{16c/deg HO}/MTF_{16c/deg SC}). The levels of correlation between various metrics and measured visual acuity VB were lower (r²=0.30 in the better case), however the averaged VB was correctly predicted by the ratio of the intersections between the MTF and a typically neural contrast threshold function.

Conclusions

Metrics based on wave aberration measurements are able to predict the impact of monochromatic aberrations on CS.

Association between Offset of the Pupil Center from the Corneal Vertex and Wavefront Aberration

Purpose

To investigate the influence of offsets of the pupil center from the corneal vertex on wavefront aberrations in the anterior cornea and the whole eye.

Methods

Both right and left eyes of 103 subjects were measured for the wavefront aberrations in the anterior cornea, along with the offset of the pupil center relative to the corneal vertex, using a Humphrey corneal topographer, and for the wavefront aberration in the whole eye using a WASCA wavefront sensor. Correlations of the pupil center offsets with the Zernike aberrations were tested.

Results

X-axis shift of the pupil center from the corneal vertex was significantly correlated to horizontal coma for both the right (r = 0.54, P<0.0001) and left eyes (r=0.48, P<0.0001) in the cornea, but was weakly correlated to the coma in the whole eye (r=0.17, P=0.04 for OD; and r=0.17, P=0.05 for OS). Significant but weak correlations with the x-axis pupil center shift were also found for several other Zernike aberrations, including the oblique astigmatism, vertical trefoil and secondary astigmatism. Very few Zernike aberrations were significantly correlated to y-axis pupil center shift. Most Zernike aberrations were significantly correlated between the right and left eyes to produce bilateral symmetry in the cornea and the whole eye.

Conclusions

The results suggest that offset of the pupil center from the corneal vertex plays an important role in determining horizontal coma and few other Zernike aberrations. Factors controlling bilateral symmetry of the wavefront aberrations between the two eyes could make important contributions to wavefront aberrations in the human eye.

Use of adaptive optics to determine the optimal ocular spherical aberration

PURPOSE

To explore the impact of spherical aberration (SA) on contrast sensitivity using an adaptive optics vision simulator to determine the optimal amount of SA to include in customized corrections of wavefront aberrations.

SETTING

Laboratorio de Optica, Universidad de Murcia, Murcia, Spain, and AMO Groningen BV, Groningen, The Netherlands.

METHODS

An adaptive optics vision simulator consisting of a wavefront sensor, a 97-segmented deformable mirror to induce and correct aberrations of the eye, and a visual testing path was constructed for this study. The deformable mirror allows the effective ocular wavefront aberration to be manipulated and the resulting visual performance to be measured simultaneously. Subjective measurements of contrast sensitivity at 15 cycles per degree were performed with a 4.8 mm pupil in 5 subjects with different levels of naturally occurring SA. Contrast sensitivity was measured when SA values of -0.09 microm, 0.0 microm, 0.09 microm, and 0.182 microm were induced when the other natural aberrations of the eye were present, when the aberrations were corrected, and at defocus values of +/-0.25 diopter (D) and +/-0.50 D.

RESULTS

Subjects experienced peak contrast sensitivity performance with varying levels of SA when their natural aberrations were present; however, average contrast performance peaked at 0 mum of SA. When all higher-order aberrations were corrected, all 5 subjects' peak performance occurred at 0 microm of SA.

CONCLUSIONS

The adaptive optics vision simulator reduced the root-mean-square wavefront aberration of the eye by up to a factor of 4 and allowed noninvasive testing of the visual performance resulting from any ocular wavefront aberration introduced by customized correction procedures. This study showed that, on average, contrast performance peaked when SA was completely corrected.

Ocular aberrations in barn owl eyes

Optical quality in barn owl eyes is presented in terms of measuring the ocular wavefront aberrations with a standard Tscherning-type wavefront aberrometer under natural viewing conditions. While accommodative state was uncontrolled, all eyes were focused within 0.4D with respect to the plane of the aberrometer. Total RMS wavefront error was between 0.06 and 0.15 microm (mean: 0.10 microm, STD: 0.03 microm, defocus cancelled) for a 6 mm pupil. The results suggest that image quality in barn owl eyes is excellent.

Wave aberrations in rhesus monkeys with vision-induced ametropias

The purpose of this study was to investigate the relationship between refractive errors and high-order aberrations in infant rhesus monkeys. Specifically, we compared the monochromatic wave aberrations measured with a Shack-Hartman wavefront sensor between normal monkeys and monkeys with vision-induced refractive errors. Shortly after birth, both normal monkeys and treated monkeys reared with optically induced defocus or form deprivation showed a decrease in the magnitude of high-order aberrations with age. However, the decrease in aberrations was typically smaller in the treated animals. Thus, at the end of the lens-rearing period, higher than normal amounts of aberrations were observed in treated eyes, both hyperopic and myopic eyes and treated eyes that developed astigmatism, but not spherical ametropias. The total RMS wavefront error increased with the degree of spherical refractive error, but was not correlated with the degree of astigmatism. Both myopic and hyperopic treated eyes showed elevated amounts of coma and trefoil and the degree of trefoil increased with the degree of spherical ametropia. Myopic eyes also exhibited a much higher prevalence of positive spherical aberration than normal or treated hyperopic eyes. Following the onset of unrestricted vision, the amount of high-order aberrations decreased in the treated monkeys that also recovered from the experimentally induced refractive errors. Our results demonstrate that high-order aberrations are influenced by visual experience in young primates and that the increase in high-order aberrations in our treated monkeys appears to be an optical byproduct of the vision-induced alterations in ocular growth that underlie changes in refractive error. The results from our study suggest that the higher amounts of wave aberrations observed in ametropic humans are likely to be a consequence, rather than a cause, of abnormal refractive development.

Optical Quality of the Eye Degraded by Time-Varying Wavefront Aberrations with Tear Film Dynamics

PURPOSE

Wavefront aberrations (WFAs) of the eye vary with time because of the tear film dynamics. We investigated, using a simulation method, the variation of optical quality with time-varying wavefront measurements of 13 eyes with different refractions.

METHODS

WFAs of 13 normal eyes of 13 subjects were measured every second for 10 s. First, we simulated WFAs with conventional corneal laser refractive surgery by subtracting the second-order aberrations of the least aberrated measurement from measured consecutive WFAs. Second, we simulated customized refractive surgery by subtracting the second- to sixth-order aberrations of the least aberrated measurement from measured consecutive WFAs. We calculated Strehl ratios and retinal images from these corrected consecutive WFAs.

RESULTS

In one eye, the root mean square (RMS) values of WFAs with a second-order correction were sometimes smaller than those of WFAs with a second- to sixth-order correction, when these were compared at the same time point after a blink. However, in the other 12 eyes, the RMS values with second- to sixth-order corrections were smaller than those with only a second-order correction. In eight eyes, the Strehl ratios with second- to sixth-order corrections were larger than those with second-order corrections. In the remaining five eyes, Strehl ratios with second- to sixth-order corrections were sometimes smaller than those with second-order corrections.

CONCLUSIONS

In a simulation, the correction of time-invariant higher order aberrations usually reduced RMS values, but it did not always result in higher Strehl ratios than those obtained with only second-order corrections.

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.

Requirements for discrete actuator and segmented wavefront correctors for aberration compensation in two large populations of human eyes

Numerous types of wavefront correctors have been employed in adaptive optics (AO) systems for correcting the ocular wavefront aberration. While all have improved image quality, none have yielded diffraction-limited imaging for large pupils (>/=6 mm), where the aberrations are most severe and the benefit of AO the greatest. To this end, we modeled the performance of discrete actuator, segmented piston-only, and segmented piston/tip/tilt wavefront correctors in conjunction with wavefront aberrations measured on normal human eyes in two large populations. The wavefront error was found to be as large as 53 microm, depending heavily on the pupil diameter (2-7.5 mm) and the particular refractive state. The required actuator number for diffraction-limited imaging was determined for three pupil sizes (4.5, 6, and 7.5 mm), three second-order aberration states, and four imaging wavelengths (0.4, 0.6, 0.8, and 1.0 microm). The number across the pupil varied from only a few actuators in the discrete case to greater than 100 for the piston-only corrector. The results presented will help guide the development of wavefront correctors for the next generation of ophthalmic instrumentation.

A review of astigmatism and its possible genesis

Astigmatism is a refractive condition encountered commonly in clinical practice. This review presents an overview of research that has been carried out examining various aspects of this refractive error. We examine the components of astigmatism and the research into the prevalence and natural course of astigmatic refractive errors throughout life. The prevalence of astigmatism in various ethnic groups and diseases and syndromes is also discussed. We highlight the extensive investigations that have been conducted into the possible aetiology of astigmatism, however, no single model or theory of the development of astigmatism has been proven conclusively. Theories of the development of astigmatism based on genetics, extraocular muscle tension, visual feedback and eyelid pressure are considered. Observations and evidence from the literature supporting and contradicting these hypotheses are presented. Recent advances in technology such as wavefront sensors and videokeratoscopes have led to an increased understanding of ocular astigmatism and with continued improvements in technology, our knowledge of astigmatism and its genesis should continue to grow.

Comparison of higher-order aberrations between eyes with natural supervision and highly myopic eyes in Koreans

Purpose

To describe the characteristics and investigate the differences of higher-order aberrations (HOAs) between the eyes with a natural, uncorrected visual acuity (UCVA) of 20/12 and eyes with highly myopic eyes in Korean adults.

Methods

Thirty-one eyes of 20 subjects with UCVA of 20/12 (Group 1) and 54 eyes of 36 myopic patients with greater than -6 diopters (Group 2) were analyzed for type and magnitude of HOAs across a 6.0 mm pupil. HOAs were measured by Wavescan (VISX, Santa Clara, CA, USA) in natural scotopic conditions and were presented as root-mean-square (RMS:µm) in Belle aberration maps.

Results

The mean spherical equivalent (SE) of manifest refraction was -0.15±0.25 D (range: +0.37 to -0.50 D) in Group 1 and -7.25±0.78 D (range: -6.00 to -9.25 D) in Group 2. The total root-mean-square (RMS) values of HOAs for Group 1 and Group 2 were 0.28±0.09 µm and 0.27±0.087 µm, respectively (P>0.05). The mean values of coma, trefoil, and spherical aberration were 0.14±0.091 µm, 0.14±0.089 µm, 0.091±0.059 µm in Group 1 and 0.16±0.077 µm, 0.14±0.073 µm, 0.082±0.059 µm in Group 2, respectively.

Conclusions

This study helped establish ocular aberration standards for those with natural supervision and those with highly myopic eyes among Koreans. Individuals with natural supervision had significant amounts of HOAs, and there was no significant difference in the amount of HOAs between the two groups. The index of higher-order aberrations may not be a perfect predictor of the amount of refractive error.

Characterizing the wave aberration in eyes with keratoconus or penetrating keratoplasty using a high-dynamic range wavefront sensor

PURPOSE

The purpose of this study was to characterize aberrations in 2 populations of eyes, namely those with keratoconus (KC) and those having undergone penetrating keratoplasty (PK), using a large-dynamic range Shack-Hartmann wavefront sensor.

DESIGN

Prospective comparative case series.

PARTICIPANTS

Twenty-one people with ocular pathologic features (either KC or PK) were recruited for this study. A previously compiled population of 190 people with no pathologic features other than refractive error was used as a means for comparison.

METHODS

Thirty-three abnormal eyes (19 with KC and 14 PK) were measured using a high-dynamic range wavefront sensor, and Zernike coefficients were computed over a 6-mm pupil. The data then were used to characterize the populations by themselves, as well as to compare them with the population of normal eyes.

MAIN OUTCOME MEASURES

Root mean square (RMS) higher-order aberration (HOA), percent of higher-order or total aberration variance, and magnitude of individual Zernike modes (in micrometers). Visual benefit of correcting higher-order aberrations was used when comparing pathologic and normal populations.

RESULTS

The keratoconic eyes exhibited 2.24 microm of HOA RMS on average. Vertical coma accounted for 53+/-32% (mean+/-standard deviation [SD]) of the HOA variance and was the most dominant higher-order aberration. The PK subjects had an average higher-order RMS of 2.25 microm, and trefoil dominated in this population with an average HOA variance contribution of 38+/-23% (mean+/-SD). The KC and PK higher-order aberrations represented 16+/-20% and 16+/-13% (mean+/-SD) of the total aberration variance, whereas the ratio was only 1+/-1% in the normal population. A visual benefit calculation on 15 KC eyes and 14 PK eyes yielded a result of 4.4+/-2.0 and 6.0+/-1.5 (mean+/-SD), respectively, whereas the normal population had a visual benefit of only 2.1+/-0.4.

CONCLUSIONS

Eyes with KC and PK have higher-order aberrations that are approximately 5.5 times more than what is typical in normal eyes. Vertical coma is the dominant higher-order aberration in people with KC, whereas PK eyes are dominated by trefoil, spherical aberration, and coma. Correcting these aberrations may provide substantial improvements in vision beyond what is possible with conventional correction methods.

[The influence of phenylephrine and tropicamide on higher order monochromatic aberrations]

BACKGROUND

For wave-front guided corneal surgery, measuring higher order monochromatic aberrations in mydriasis is needed. However, a potential influence of mydriatic drugs on such aberrations could distort the ablation profile.

METHOD

Wave-front analysis was carried out on 20 (tropicamide) and 19 (phenylephrine) eyes after dark adaptation, followed by measurement after the instillation of the mydriatics one after another.

RESULTS

Phenylephrine had no significant influence on the wave-front; neither sphere nor RMS data differed from those taken after dark adaptation. After instilling tropicamide, significant changes in Z(2) (0) and, in parallel, also of the sphere were found. The RMS showed no significant difference, only the spherical aberration Z(4) (0) was reduced by an average of 0.035 microm.

CONCLUSION

The wave-front changes individually through the mydriasis due to phenylephrine and tropicamide. In the case of tropicamide, the deviation is statistically significant. Therefore, abandonment of these mydriatics before refractive surgery can be recommended, as can the use physiological pupil dilatation. Because of its lower influence, phenylephrine should be the first choice if dimout effects no adequate mydriasis.

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.

High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors

Adaptive optics scanning laser ophthalmoscopes have been used to produce noninvasive views of the human retina. However, the range of aberration compensation has been limited by the choice of deformable mirror technology. We demonstrate that the use of dual deformable mirrors can effectively compensate large aberrations in the human eye while maintaining the quality of the retinal imagery. We verified experimentally that the use of dual deformable mirrors improved the dynamic range for correction of the wavefront aberrations compared with the use of the micro-electro-mechanical-system mirror alone and improved the quality of the wavefront correction compared with the use of the bimorph mirror alone. We also demonstrated that the large-stroke bimorph deformable mirror improved the capability for axial sectioning with the confocal imaging system by providing an easier way to move the focus axially through different layers of the retina.

Spherical aberration and depth of focus in eyes implanted with aspheric and spherical intraocular lenses: a prospective randomized study

PURPOSE

To compare distance-corrected, near, and intermediate visual acuities as a measurement of depth of focus and spherical aberration of eyes implanted with aspheric and spherical intraocular lenses (IOLs).

DESIGN

Randomized prospective study.

PARTICIPANTS

One hundred twenty eyes of 60 patients with bilateral cataract implanted with 3 IOL models (AcrySof IQ, AcrySof SN60AT [Alcon Laboratories, Fort Worth, TX], and Sensar AR40 [Allergan Surgical, Irvine, CA]).

METHODS

Pupil diameter was analyzed by using a Colvard pupillometer (OASIS Medical, Inc., Glendora, CA) under photopic, mesopic, and scotopic conditions. Distance (6 m), intermediate (1 m), and near (0.33 m) visual acuities were measured with distance correction in place 90 days after surgery. Wavefront analysis (LadarWave; Alcon Laboratories) was performed using 5-mm and measured photopic pupil diameter at 30 and 90 days after surgery.

MAIN OUTCOME MEASURES

To evaluate spherical aberration and depth of focus (by means of distance-corrected near and intermediate visual acuity) in patients implanted with aspheric and spherical IOLs.

RESULTS

Photopic pupil sizes in each group were similar at 30 days after surgery. At 90 days after surgery, mean logarithm of the minimum angle of resolution distance-corrected near visual acuity (+/-standard deviation [SD]) was 0.50+/-0.20 in the AcrySof IQ group, 0.38+/-0.17 in the AcrySof SN60AT group, and 0.45+/-0.16 in Sensar AR40 group. Mean spherical aberration values (+/-SD) were 0.03+/-0.05 microm in the AcrySof IQ group, 0.24+/-0.04 microm in the AcrySof SN60AT group, and 0.14+/-0.07 microm in the Sensar AR40 group. The AcrySof IQ group showed a statistically significant lower induction of spherical aberration and worse distance-corrected near visual acuity. The AcrySof SN60AT group showed statistically significant higher mean spherical aberration values and better distance-corrected near and intermediate visual acuity.

CONCLUSIONS

The reduction of total spherical aberration after aspheric IOL implantation may degrade distance-corrected near and intermediate visual acuity.

Corneal Refractive Therapy with Different Lens Materials, Part 2: Effect of Oxygen Transmissibility on Corneal Shape and Optical Characteristics

PURPOSE

To compare the effects of two different oxygen transmissible (Dk/t) lenses on corneal shape and optical performance after one night of corneal refractive therapy (CRT(R)) for myopia.

METHODS

Twenty myopic subjects were fit with Menicon Z (MZ) (Dk/t = 90.6, Paragon CRT(R) lenses) on one eye and an Equalens II (EII) CRT lens (Dk/t = 47.2) on the contralateral eye (eye randomized). Corneal topography, refractive error and aberrations were measured before lens insertion (baseline), and the following day after overnight lens wear, on lens removal and 1, 3, 6, 12 h later. Root mean square wavefront errors were measured using 4.5 mm pupils.

RESULTS

Averaged over position and time, the horizontal corneal curvature was statistically different between the MZ and EII lens-wearing eyes (p = 0.011). The central cornea flattened similarly (p = 0.886) and the mid-periphery steepened in both eyes (p = 0.061) from baseline. The EII lens-wearing eyes were steeper in the mid-periphery than the MZ eyes immediately after lens removal and at the 1-h visit (p < or = 0.032). Central corneal flattening and mid-peripheral corneal steepening regressed over time (all p < 0.001) but did not recover to baseline by 12 h (all p < 0.004). Myopia was reduced equally by 0.84 +/- 0.83 D for the MZ-lens wearing eyes and 0.84 +/- 0.87 D for the EII eyes (p = 0.969). Coma increased from baseline 1.85X (0.056 +/- 0.081 microm) for the MZ-lens wearing eyes and 1.72X (0.048 +/- 0.084 microm) for the EII eyes (both p < 0.001). Spherical aberration increased from baseline 4.55X (0.101 +/- 0.077 microm) for the MZ-lens wearing eyes and 4.31X (0.085 +/- 0.076 microm) for the EII eyes (both p < 0.001), but there were no differences between the MZ and EII eyes (all p > or = 0.308). Coma and spherical aberration did not return to baseline by 12 h (both p < or = 0.007).

CONCLUSIONS

After one night of CRT lens wear, changes in corneal shape were slightly different, with more mid-peripheral steepening in the EII eyes compared to the MZ eyes. Change in central corneal curvature and optical performance were similar in both eyes.

Theoretical Comparison of Aberration-correcting Customized and Aspheric Intraocular Lenses

PURPOSE

To assess the performance and optical limitations of standard, aspheric, and wavefront-customized intraocular lenses (IOLs) using clinically verified pseudophakic eye models.

METHODS

White light pseudophakic eye models were constructed from physical measurements performed on 46 individual cataract patients and subsequently verified using the clinically measured contrast sensitivity function (CSF) and wavefront aberration of pseudophakic patients implanted with two different types of IOLs. These models are then used to design IOLs that correct the astigmatism and higher order aberrations of each individual eye model's cornea and to investigate how this correction would affect visual benefit, subjective tolerance to lens misalignment (tilt, decentration, and rotation), and depth of field.

RESULTS

Physiological eye models and clinical outcomes show similar levels of higher order aberration and contrast improvement. Customized correction of ocular wavefront aberrations with an IOL results in contrast improvements on the order of 200% over the control and the Tecnis IOLs. The customized lenses can be, on average, decentered by as much as 0.8 mm, tilted > 10 degrees , and rotated as much as 15 degrees before their polychromatic modulation transfer function at 8 cycles/degree is less than that of the Tecnis or spherical control lens. Correction of wavefront aberration results in a narrower through focus curve but better out of focus performance for +/- 0.50 diopters.

CONCLUSIONS

The use of realistic eye models that include higher order aberrations and chromatic aberrations are important when determining the impact of new IOL designs. Customized IOLs show the potential to improve visual performance.

Defining subclinical keratoconus using corneal first-surface higher-order aberrations

PURPOSE

To describe corneal higher-order wavefront aberrations of clinically inconspicuous fellow eyes in patients with early keratoconus (KC).

DESIGN

Prospective comparative case series, conducted at a university eye hospital outpatient clinic.

METHODS

Twenty-three eyes (group 1) were newly diagnosed with KC; 10 eyes (group 2) were asymptomatic fellow eyes that showed neither major topographic anomaly nor clinical signs of KC; 127 healthy eyes of 74 patients served as negative controls (group 3). A seventh-order Zernike decomposition of first-surface aberrations was performed. Single Zernike coefficients, higher-order aberration root mean square (HOA RMS) values, the Z3 index and the output values of discriminant analysis D(13) (with input from groups 1 and 3) and D(23) (groups 2 and 3) were assessed for their usefulness to discriminate between clinically normal fellow eyes, KC eyes and controls by plotting receiver-operating characteristic (ROC) curves.

RESULTS

There were significant differences between group 1 and group 3 for 11 Zernike coefficients, Z3, total HOA RMS, coma RMS and third-order RMS. Group 2 and 3 showed significant differences only for the coefficients Z(3)(-1) and Z(5)(-1). Z(3)(-1), D(13), and D(23) discriminated between groups 1 and 3 with maximum sensitivity and specificity. For discrimination between groups 2 and 3, D(23) turned out to be the best parameter (A(z) ROC = 0.98), followed by Z(3)(-1) (A(z) ROC = 0.96).

CONCLUSIONS

Clinically normal fellow eyes of eyes with early KC showed significant differences of first-surface aberrations compared to normal eyes and could therefore be considered as eyes with subclinical KC.

Effect of third-order aberrations on dynamic accommodation

We investigate the potential for the third-order aberrations coma and trefoil to provide a signed cue to accommodation. It is first demonstrated theoretically (with some assumptions) that the point spread function is insensitive to the sign of spherical defocus in the presence of odd-order aberrations. In an experimental investigation, the accommodation response to a sinusoidal change in vergence (1-3D, 0.2Hz) of a monochromatic stimulus was obtained with a dynamic infrared optometer. Measurements were obtained in 10 young visually normal individuals with and without custom contact lenses that induced low and high values of r.m.s. trefoil (0.25, 1.03 microm) and coma (0.34, 0.94 microm). Despite variation between subjects, we did not find any statistically significant increase or decrease in the accommodative gain for low levels of trefoil and coma, although effects approached or reached significance for the high levels of trefoil and coma. Theoretical and experimental results indicate that the presence of Zernike third-order aberrations on the eye does not seem to play a crucial role in the dynamics of the accommodation response.

The Genetic Effect on Refractive Error and Anterior Corneal Aberration: Twin Eye Study

PURPOSE

To investigate the role of heredity in determining refractive variables, anterior corneal curvature, and anterior corneal aberrations.

METHODS

Thirty-three monozygotic and 10 dizygotic twin pairs were enrolled in this study. Corneal curvature, corneal astigmatism, and corneal topography were obtained from computerized videokeratoscope. The CTView program was used to compute anterior corneal aberrations from corneal height data of the videokeratoscope. Correlation analysis was performed to investigate the symmetry of the refractive error, corneal curvature, corneal astigmatism, and anterior corneal aberrations between right and left eyes of each twin pair. Heritability (h2) of these parameters was also calculated.

RESULTS

Positive correlations were noted between right and left eyes for spherical power, total astigmatism, mean corneal curvature, and corneal astigmatism. In monozygotic twins, vertical coma, secondary vertical coma, spherical aberration, and secondary spherical aberration were moderately correlated. In dizygotic twins, vertical coma, secondary horizontal coma, and spherical aberration were moderately correlated. In unrelated controls, secondary vertical coma, secondary horizontal coma, and secondary spherical aberration were moderately correlated. Root-mean-square (RMS) of higher order aberrations (3rd to 6th orders), RMS of spherical aberration, and RMS of coma were moderately correlated between right and left eyes in all three groups. Heritability of spherical aberration, RMS of spherical aberration, and corneal astigmatism (h2 = 0.56, 0.44, and 0.46) were greater than those of refractive power, corneal curvature, and other higher order aberrations.

CONCLUSIONS

These results suggest that corneal astigmatism and spherical aberration possess a greater genetic predisposition than those of other refractive errors and higher order aberrations.

Long-term optical quality of the photoablated cornea

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

Three-dimensional relationship between high-order root-mean-square wavefront error, pupil diameter, and aging

We report root-mean-square (RMS) wavefront error (WFE) for individual aberrations and cumulative high-order (HO) RMS WFE for the normal human eye as a function of age by decade and pupil diameter in 1 mm steps from 3 to 7 mm and determine the relationship among HO RMS WFE, mean age for each decade of life, and luminance for physiologic pupil diameters. Subjects included 146 healthy individuals from 20 to 80 years of age. Ocular aberration was measured on the preferred eye of each subject (for a total of 146 eyes through dilated pupils; computed for 3, 4, 5, 6, and 7 mm pupils; and described with a tenth-radial-order normalized Zernike expansion. We found that HO RMS WFE increases faster with increasing pupil diameter for any given age and pupil diameter than it does with increasing age alone. A planar function accounts for 99% of the variance in the 3-D space defined by mean log HO RMS WFE, mean age for each decade of life, and pupil diameter. When physiologic pupil diameters are used to estimate HO RMS WFE as a function of luminance and age, at low luminance (9 cd/m2) HO RMS WFE decreases with increasing age. This normative data set details (1) the 3-D relationship between HO RMS WFE and age for fixed pupil diameters and (2) the 3-D relationship among HO RMS WFE, age, and luminance for physiologic pupil diameters.

Characterization of a bimorph deformable mirror using stroboscopic phase-shifting interferometry

The static and dynamic characteristics of a bimorph deformable mirror (DM) for use in an adaptive optics system are described. The DM is a 35-actuator device composed of two disks of lead magnesium niobate (PMN), an electrostrictive ceramic that produces a mechanical strain in response to an imposed electric field. A custom stroboscopic phase-shifting interferometer was developed to measure the deformation of the mirror in response to applied voltage. The ability of the mirror to replicate optical aberrations described by the Zernike polynomials was tested as a measure of the mirror's static performance. The natural frequencies of the DM were measured up to 20 kHz using both stroboscopic interferometry as well as a commercial laser Doppler vibrometer (LDV). Interferometric measurements of the DM surface profile were analyzed by fitting the surface with mode-shapes predicted using classical plate theory for an elastically supported disk. The measured natural frequencies were found to be in good agreement with the predictions of the theoretical model.