Statistical variation of aberration structure and image quality in a normal population of healthy eyes

Testing of Lagrange multiplier damped least-squares control algorithm for woofer-tweeter adaptive optics

A Lagrange multiplier-based damped least-squares control algorithm for woofer-tweeter (W-T) dual deformable-mirror (DM) adaptive optics (AO) is tested with a breadboard system. We show that the algorithm can complementarily command the two DMs to correct wavefront aberrations within a single optimization process: the woofer DM correcting the high-stroke, low-order aberrations, and the tweeter DM correcting the low-stroke, high-order aberrations. The optimal damping factor for a DM is found to be the median of the eigenvalue spectrum of the influence matrix of that DM. Wavefront control accuracy is maximized with the optimized control parameters. For the breadboard system, the residual wavefront error can be controlled to the precision of 0.03 μm in root mean square. The W-T dual-DM AO has applications in both ophthalmology and astronomy.

Investigation of the isoplanatic patch and wavefront aberration along the pupillary axis compared to the line of sight in the eye

Conventional optical systems usually provide best image quality on axis, while showing unavoidable gradual decrease in image quality towards the periphery of the field. The optical system of the human eye is not an exception. Within a limiting boundary the image quality can be considered invariant with field angle, and this region is known as the isoplanatic patch. We investigate the isoplanatic patch of eight healthy eyes and measure the wavefront aberration along the pupillary axis compared to the line of sight. The results are used to discuss methods of ocular aberration correction in wide-field retinal imaging with particular application to multi-conjugate adaptive optics systems.

Influence of age on peripheral ocular aberrations

PURPOSE

To compare peripheral lower and higher order aberrations across the horizontal (±40°) and inferior (-20°) visual fields in healthy groups of young and old emmetropes.

METHODS

We have measured off-axis aberrations in the groups of 30 younger (24 ± 3 years) and 30 older (58 ± 5 years) emmetropes. The aberrations of OD were measured using the COAS-HD VR Shack-Hartmann aberrometer in 10° steps to ±40° horizontally and -20° inferiorly in the visual field. The aberrations were quantified with Zernike polynomials for a 4 mm pupil diameter. The second-order aberration coefficients were converted to their respective refraction components (M, J45, and J180). Mixed between-within subjects, analysis of variance were used to determine whether there were significant differences in the refraction and aberration components for the between-subjects variable age and the within-subjects variable eccentricity.

RESULTS

Peripheral refraction components were similar in both age groups. Among the higher order coefficients, horizontal coma (C3) and spherical aberration (C4) varied mostly between the groups. Coma increased linearly with eccentricity, at a more rapid rate in the older group than in the younger group. Spherical aberration was more positive in the older group compared with the younger group. Higher order root mean square increased more rapidly with eccentricity in the older group.

CONCLUSIONS

Like the axial higher order aberrations, the peripheral higher order aberrations of emmetropes increase with age, particularly coma and spherical aberration.

Effects on vision with glare after correction of monochromatic wavefront aberrations

PURPOSE

To investigate effects of optical aberration correction on vision with glare.

METHODS

Correction of aberrations up to the 6th Zernike order (closed-loop correction) was compared with conventional spectacle correction in 42 healthy eyes. To create these corrections, an adaptive optics system including a thin-film transistor (TFT) monitor for displaying optotypes with additional glare sources was used. Employing both corrections, visual acuity and contrast sensitivity (CS) were tested alternately with and without glare. Disability glare was computed as the difference between log CS without and with glare. Individuals were also asked to rate subjectively the quality of three images displayed on the TFT monitor.

RESULTS

Significant improvements of CS without and with glare were found with the closed-loop correction (0.147 and 0.198 log CS, respectively), whereas no significant difference in visual acuity was found in either correction. Correlations were determined between reduction of total root-mean-square error and increase of CS with glare (Pearson correlation coefficient r=0.42) and decrease of disability glare (r=-0.33). Visual acuity was correlated with the visual Strehl ratio based on the optical transfer function (r=0.46). Subjective comparison of the images showed improvements more clearly. Depending on the image, in 57% to 78% of the eyes, closed-loop correction was rated better than spectacle correction. The subjective glare effect was reduced as well.

CONCLUSIONS

Investigation of vision with glare seems to be a reasonable additional test to evaluate the visual outcome of a customized correction.

Vision is adapted to the natural level of blur present in the retinal image

Background

The image formed by the eye's optics is inherently blurred by aberrations specific to an individual's eyes. We examined how visual coding is adapted to the optical quality of the eye.

Methods and Findings

We assessed the relationship between perceived blur and the retinal image blur resulting from high order aberrations in an individual's optics. Observers judged perceptual blur in a psychophysical two-alternative forced choice paradigm, on stimuli viewed through perfectly corrected optics (using a deformable mirror to compensate for the individual's aberrations). Realistic blur of different amounts and forms was computer simulated using real aberrations from a population. The blur levels perceived as best focused were close to the levels predicted by an individual's high order aberrations over a wide range of blur magnitudes, and were systematically biased when observers were instead adapted to the blur reproduced from a different observer's eye.

Conclusions

Our results provide strong evidence that spatial vision is calibrated for the specific blur levels present in each individual's retinal image and that this adaptation at least partly reflects how spatial sensitivity is normalized in the neural coding of blur.

Creating effective focus cues in multi-plane 3D displays

Focus cues are incorrect in conventional stereoscopic displays. This causes a dissociation of vergence and accommodation, which leads to visual fatigue and perceptual distortions. Multi-plane displays can minimize these problems by creating nearly correct focus cues. But to create the appearance of continuous depth in a multi-plane display, one needs to use depth-weighted blending: i.e., distribute light intensity between adjacent planes. Akeley et al. [ACM Trans. Graph. 23, 804 (2004)] and Liu and Hua [Opt. Express 18, 11562 (2009)] described rather different rules for depth-weighted blending. We examined the effectiveness of those and other rules using a model of a typical human eye and biologically plausible metrics for image quality. We find that the linear blending rule proposed by Akeley and colleagues [ACM Trans. Graph. 23, 804 (2004)] is the best solution for natural stimuli.

Six just-noticeable differences in retinal image quality in 1 line of visual acuity: toward quantification of happy versus unhappy patients with 20/20 acuity

PURPOSE

To determine the number of just-noticeable differences in wavefront blur necessary to induce a 1-line loss of corrected distance visual acuity (CDVA).

SETTING

Visual Optics Institute, College of Optometry, University of Houston, Houston, Texas, USA.

DESIGN

Evidence-based manuscript.

METHODS

The 3.0 mm wavefront error of a well-corrected average eye was scaled to yield 9 small steps of blur quantified in units of log visual Strehl (logVS). For each logVS value, 10 unique 3-line acuity charts were generated. Using a temporal forced-choice paradigm, subjects compared each test chart to a reference acuity chart and indicated which chart was blurrier. The difference between 80% and 50% on the psychometric function defined a just-noticeable difference. The CDVA was measured up to fifth-letter miss for several aberrated logMAR charts for 6 logVS values. The number of just-noticeable differences necessary to lose 1 line of acuity was defined as the change in logVS necessary to lose 1 line of acuity divided by the 1 just-noticeable difference in logVS.

RESULTS

Linear regression showed that logVS = -2.98 × (logMAR acuity) - 0.31 (R(2) = 0.961). The mean just-noticeable difference was 0.049 logVS ± 0.012 (SD), resulting in a mean of 6.1 just-noticeable differences per line of logMAR acuity.

CONCLUSIONS

The retinal image quality metric logVS was highly correlated with logMAR acuity. The 6 just-noticeable differences in logVS before 1 line of acuity was lost may provide an objective explanation for the distinction between patients with 20/20 CDVA who are happy and patients with 20/20 CDVA who are unhappy and other aberration-related clinical complaints when acuity is near normal.

Chromatic and wavefront aberrations: L-, M- and S-cone stimulation with typical and extreme retinal image quality

The first physiological process influencing visual perception is the optics of the eye. The retinal image is affected by diffraction at the pupil and several kinds of optical imperfections. A model of the eye (Thibos & Bradley, 1999), which takes account of pupil aperture, chromatic aberration and wavefront aberrations, was used to determine wavelength-dependent point-spread functions, which can be convolved with any stimulus specified by its spectral distribution of light at each point. The resulting retinal spectral distribution of light was used to determine the spatial distribution of stimulation for each cone type (S, M and L). In addition, individual differences in retinal-image quality were assessed using a statistical model (Thibos, Bradley, & Hong, 2002) for population values of Zernike coefficients, which characterize imperfections of the eye's optics. The median and relatively extreme (5th and 95th percentile) modulation transfer functions (MTFs) for the S, M and L cones were determined for equal-energy-spectrum (EES) 'white' light. The typical MTF for S cones was more similar to the MTF for L and M cones after taking wavefront aberrations into account but even with aberrations the S-cone MTF typically was below the M- or L-cone MTF by a factor of at least 10 (one log unit). More generally, the model presented here provides a technique for estimating retinal image quality for the S, M and L cones for any stimulus presented to the eye. The model is applied to some informative examples.

Optical and biometric characteristics of anisomyopia in human adults

PURPOSE

To investigate the role of higher order optical aberrations and thus retinal image degradation in the development of myopia, through the characterization of anisomyopia in human adults in terms of their optical and biometric characteristics.

METHODS

The following data were collected from both eyes of 15 young adult anisometropic myopes and 16 isometropic myopes: subjective and objective refractive errors, corneal power and shape, monochromatic optical aberrations, anterior chamber depth, lens thickness, vitreous chamber depth, and best corrected visual acuity. Monochromatic aberrations were analyzed in terms of their higher order components, and further analyzed in terms of 31 optical quality metrics. Interocular differences for the two groups (anisomyopes vs isomyopes) were compared and the relationship between measured ocular parameters and refractive errors also analyzed across all eyes.

RESULTS

As expected, anisomyopes and isomyopes differed significantly in terms of interocular differences in vitreous chamber depth, axial length and refractive error. However, interocular differences in other optical properties showed no significant intergroup differences. Overall, higher myopia was associated with deeper anterior and vitreous chambers, higher astigmatism, more prolate corneas, and more positive spherical aberration. Other measured optical and biometric parameters were not significantly correlated with spherical refractive error, although some optical quality metrics and corneal astigmatism were significantly correlated with refractive astigmatism.

CONCLUSIONS

An optical cause for anisomyopia related to increased higher order aberrations is not supported by our data. Corneal shape changes and increased astigmatism in more myopic eyes may be a by-product of the increased anterior chamber growth in these eyes; likewise, the increased positive spherical aberration in more myopic eyes may be a product of myopic eye growth.

Unbiased estimation of refractive state of aberrated eyes

We seek unbiased methods for estimating the target vergence required to maximize visual acuity based on wavefront aberration measurements. Experiments were designed to minimize the impact of confounding factors that have hampered previous research. Objective wavefront refractions and subjective acuity refractions were obtained for the same monochromatic wavelength. Accommodation and pupil fluctuations were eliminated by cycloplegia. Unbiased subjective refractions that maximize visual acuity for high contrast letters were performed with a computer controlled forced choice staircase procedure, using 0.125 diopter steps of defocus. All experiments were performed for two pupil diameters (3mm and 6mm). As reported in the literature, subjective refractive error does not change appreciably when the pupil dilates. For 3mm pupils most metrics yielded objective refractions that were about 0.1D more hyperopic than subjective acuity refractions. When pupil diameter increased to 6mm, this bias changed in the myopic direction and the variability between metrics also increased. These inaccuracies were small compared to the precision of the measurements, which implies that most metrics provided unbiased estimates of refractive state for medium and large pupils. Thus a variety of image quality metrics may be used to determine ocular refractive state for monochromatic (635nm) light, thereby achieving accurate results without the need for empirical correction factors.

Aspheric Optical Zones in hyperopia with the SCHWIND AMARIS

Purpose

To evaluate the corneal Functional Optical Zone (FOZ) and the Effective Optical Zone (EOZ) of the ablation, among eyes that underwent LASEK/Epi-LASEK treatments for hyperopic astigmatism.

Methods

Twenty LASEK/Epi-LASEK treatments with mean defocus +2.21 ± 1.28 D performed using the SCHWIND AMARIS were retrospectively evaluated at 6-month follow-up. In all cases pre-/post-operative Corneal-Wavefront analyses using the Keratron-Scout (OPTIKON2000) were performed. FOZ-values were evaluated from the Root-Mean-Square of High-Order Wave-Aberration (RMSho), whereas EOZ-values were evaluated from the changes of Root-Mean-Square of High-Order Wave-Aberration (ΔRMSho) and Root-Mean-Square of the change of High-Order Wave-Aberration (RMS(ΔHOAb)). Correlations of FOZ and EOZ with Planned Optical Zone (POZ) and Defocus correction (SEq) were analyzed using a bilinear function.

Results

At six-month, defocus was −0.04 ± 0.44 D, ninety percent eyes were within ± 0.50 D from emmetropia. Mean RMSho increased 0.18 ± 0.22 μm, SphAb −0.30 ± 0.18 μm, and Coma 0.07 ± 0.18 μm 6-month after treatment (6-mm diameter). Mean FOZPre was 7.40 ± 1.48 mm, mean POZ was 6.76 ± 0.22 mm, whereas mean FOZPost was 5.53 ± 1.18 mm (significantly smaller, p < 0.0001; bilinear correlation p < 0.005), mean EOZΔRMSho 6.47 ± 1.17 mm (bilinear correlation p < 0.005), EOZRMS(ΔHOAb) 5.67 ± 1.23 mm (significantly smaller, p < 0.0005; bilinear correlation p < 0.05). EOZ positively correlates with POZ and declines steadily with SEq. A treatment of +3 D in 6.50-mm POZ results in 5.75-mm EOZ (7.75-mm NPOZ), treatments in 7.00-mm POZ result in about 6.25-mm EOZ (8.25-mm nomogrammed POZ).

Conclusions

FOZPost was significantly smaller than FOZPre. EOZΔRMSho was similar to POZ, whereas EOZRMS(ΔHOAb) was significantly smaller. Differences were larger for smaller POZ or larger Defocus. SEq up to +2 D result in EOZ, at least, as large as POZ. For SEq higher than +2 D, a nomogram for OZ can be applied.

Adapting to blur produced by ocular high-order aberrations

The perceived focus of an image can be strongly biased by prior adaptation to a blurred or sharpened image. We examined whether these adaptation effects can occur for the natural patterns of retinal image blur produced by high-order aberrations (HOAs) in the optics of the eye. Focus judgments were measured for 4 subjects to estimate in a forced choice procedure (sharp/blurred) their neutral point after adaptation to different levels of blur produced by scaled increases or decreases in their HOAs. The optical blur was simulated by convolution of the PSFs from the 4 different HOA patterns, with Zernike coefficients (excluding tilt, defocus, and astigmatism) multiplied by a factor between 0 (diffraction limited) and 2 (double amount of natural blur). Observers viewed the images through an Adaptive Optics system that corrected their aberrations and made settings under neutral adaptation to a gray field or after adapting to 5 different blur levels. All subjects adapted to changes in the level of blur imposed by HOA regardless of which observer's HOA was used to generate the stimuli, with the perceived neutral point proportional to the amount of blur in the adapting image.

Peripheral aberration measurements: elliptical pupil transformation and variations in horizontal coma across the visual field

BACKGROUND

The aim was to determine the critical eccentricity at which two methods of elaborating peripheral wavefront measurements are significantly different and to characterise horizontal coma in healthy young adults.

METHODS

Peripheral aberrations were determined for 20 observers for central and eight peripheral gaze positions up to 20° using an IRX-3 aberrometer. In one subject, additional measurements up to 40° were obtained. Two definitions of stretching coefficients were compared. The raw empirical data were compared with theoretical modelling.

RESULTS

For both 3.5 mm and 6.0 mm pupils, no significant differences were observed between recalculated and non-recalculated elliptical pupils for both methods (p > 0.05) up to 20° eccentricity. For eccentricities greater than 20° and up to 40°, significant differences between circular and elliptical pupils at some eccentricities were apparent, which corresponded to theoretical models. Wide individual variations in horizontal coma across the peripheral field were observed.

CONCLUSIONS

The data suggest that for eyes with average levels of aberrations, the elliptical transformation is of no practical importance for eccentricities up to 20°. In some cases the slope of horizontal coma was reversed compared with previous findings in normal eyes.

Integrated adaptive optics optical coherence tomography and adaptive optics scanning laser ophthalmoscope system for simultaneous cellular resolution in vivo retinal imaging

We describe an ultrahigh-resolution (UHR) retinal imaging system that combines adaptive optics Fourier-domain optical coherence tomography (AO-OCT) with an adaptive optics scanning laser ophthalmoscope (AO-SLO) to allow simultaneous data acquisition by the two modalities. The AO-SLO subsystem was integrated into the previously described AO-UHR OCT instrument with minimal changes to the latter. This was done in order to ensure optimal performance and image quality of the AO- UHR OCT. In this design both imaging modalities share most of the optical components including a common AO-subsystem and vertical scanner. One of the benefits of combining Fd-OCT with SLO includes automatic co-registration between two acquisition channels for direct comparison between retinal structures imaged by both modalities (e.g., photoreceptor mosaics or microvasculature maps). Because of differences in the detection scheme of the two systems, this dual imaging modality instrument can provide insight into retinal morphology and potentially function, that could not be accessed easily by a single system. In this paper we describe details of the components and parameters of the combined instrument, including incorporation of a novel membrane magnetic deformable mirror with increased stroke and actuator count used as a single wavefront corrector. We also discuss laser safety calculations for this multimodal system. Finally, retinal images acquired in vivo with this system are presented.

Reflective afocal broadband adaptive optics scanning ophthalmoscope

A broadband adaptive optics scanning ophthalmoscope (BAOSO) consisting of four afocal telescopes, formed by pairs of off-axis spherical mirrors in a non-planar arrangement, is presented. The non-planar folding of the telescopes is used to simultaneously reduce pupil and image plane astigmatism. The former improves the adaptive optics performance by reducing the root-mean-square (RMS) of the wavefront and the beam wandering due to optical scanning. The latter provides diffraction limited performance over a 3 diopter (D) vergence range. This vergence range allows for the use of any broadband light source(s) in the 450-850 nm wavelength range to simultaneously image any combination of retinal layers. Imaging modalities that could benefit from such a large vergence range are optical coherence tomography (OCT), multi- and hyper-spectral imaging, single- and multi-photon fluorescence. The benefits of the non-planar telescopes in the BAOSO are illustrated by resolving the human foveal photoreceptor mosaic in reflectance using two different superluminescent diodes with 680 and 796 nm peak wavelengths, reaching the eye with a vergence of 0.76 D relative to each other.

Depth of focus and visual acuity with primary and secondary spherical aberration

It is known that the depth of focus (DOF) of the human eye can be affected by the higher order aberrations. We estimated the optimal combinations of primary and secondary Zernike spherical aberration to expand the DOF and evaluated their efficiency in real eyes using an adaptive optics system. The ratio between increased DOF and loss of visual acuity was used as the performance indicator. The results indicate that primary or secondary spherical aberration alone shows similar effectiveness in extending the DOF. However, combinations of primary and secondary spherical aberration with different signs provide better efficiency for expanding the DOF. This finding suggests that the optimal combinations of primary and secondary spherical aberration may be useful in the design of optical presbyopic corrections.

Cellular-resolution in vivo imaging of the feline retina using adaptive optics: preliminary results

PURPOSE

To perform cellular-level in vivo imaging of the feline retina using an adaptive optics flood illumination fundus camera (AO FIFC) designed for the human eye.

MATERIALS AND METHODS

Cellular-level images were obtained from three eyes of two normal sedated cats. Ocular aberrations were corrected using an AO system based on a 52-acuator electromagnetic deformable mirror and a 1024 lenslet Hartmann-Shack sensor (both Imagine Eyes, Orsay, France). A square 3°×3° area of the ocular fundus was flood-illuminated by a pulsed LED emitting at 850 nm and imaged onto a low-noise, high-resolution CCD camera. The animal's pupils were dilated and the effective pupil size was set to 7.5 mm. Conjunctival atraumatic clips were used to avoid eyeball movements and eyelid closure. The cornea was artificially hydrated throughout the experiments. Each acquisition consisted of 20 consecutive images, out of which 10 were numerically averaged to produce an enhanced final image.

RESULTS

The total amount of ocular aberrations was greatly reduced by the AO correction, from 2.4 to 0.21 microns root mean square on average. The resulting images presented white dots distributed at a density similar to that of cone photoreceptors and they allowed us to visualize small blood vessels and nerve fiber bundles at a higher resolution than classically obtained with conventional fundus photography.

CONCLUSION

Retinal imaging with cellular resolution was feasible in cats under sedation using an AO FIFC designed for human eyes without any optical modification. The AO FIFC technology could find new applications in clinical, pharmacological, and toxicological investigations.

Comparison of higher order aberration profiles between normal and amblyopic eyes in children with idiopathic amblyopia

AIM

To evaluate the higher order aberrations and resultant bilateral wavefront patterns in paediatric patients with idiopathic amblyopia.

MATERIAL AND METHODS

  In this cross sectional observational trial, seventeen consecutive patients of previously diagnosed idiopathic amblyopia underwent wavefront analysis on Zyoptix platform (Bausch and Lomb, Rochester, NY, USA).

RESULTS

The mean age was 9 ± 3 years. There was no significant difference in comparison with means for the Zernike coefficients between normal and amblyopic eye. However, interrelation between Zernike coefficients, which is responsible for their interaction leading to difference in visual function, was different between amblyopic and fellow eyes. This was noticed using stepwise regression analysis. Predicting variables and R(2) (r squared) values for each Zernike polynomial were calculated. The sets of significantly predicting coefficients were different in most patients, with only seven common pairs and 42 dissimilar dependent-predictor sets. Maximum difference in the R-squared values between amblyopic and normal (fellow) eyes was seen with coma-like and trefoil-like aberrations (third order and fifth order terms).

CONCLUSION

It seems a strong possibility that a subset of 'idiopathic' amblyopia may be associated with loss of symmetry in wavefront patterns of the two eyes.

Clinical validation of point-source corneal topography in keratoplasty

PURPOSE

To validate the clinical performance of point-source corneal topography (PCT) in postpenetrating keratoplasty (PKP) eyes and to compare it with conventional Placido-based topography.

METHODS

Corneal elevation maps of the anterior corneal surface were obtained from 20 post-PKP corneas using PCT (VU topographer, prototype; VU University Medical Center, Amsterdam, The Netherlands) and Placido-based topography (Keratron, Optikon 2000, Rome, Italy). Corneal surface parameters are calculated in terms of radius and asphericity. Corneal aberrations were characterized using standard Zernike convention. An artificial surface with quadrafoil feature (SUMIPRO, Almelo, The Netherlands) was measured and used as a reference to assess instrument performance compared with the gold standard.

RESULTS

The differences (mean ± std of PCT - Placido) found between the two types of topographers in measurements of post-PKP eyes are 0.02 ± 0.21 mm (p=0.64) for radius of curvature, 0.14 ± 0.49 (p=0.23) for asphericity, -0.19 ± 1.67 μm (p=0.61) for corneal astigmatism, -0.25 ± 1.34 μm (p=0.41) for corneal coma, 0.23 ± 0.82 μm (p=0.23) for corneal trefoil, and 0.15 ± 0.28 μm (p=0.02) for corneal quadrafoil. The PCT measured the artificial surface more accurate (rms error 0.16 μm; 0.12 eq. Dpt.) than the Placido-based topographer (rms error 1.50 μm; 1.15 eq. Dpt.).

CONCLUSIONS

PCT is more accurate than Placido-based topography in measuring quadrafoil aberration.

Inherent ocular spherical aberration and multifocal contact lens optical performance

PURPOSE

The role of inherent spherical aberration (SA) in the optical performance of presbyopic eyes corrected with simultaneous vision multifocal contact lenses was investigated.

METHODS

Presbyopic schematic eyes were modeled with partial accommodative function to represent 45- and 55-year olds and were further classified into five categories based on their magnitude of inherent SA. Two representative ametropic models of each category were corrected with four multifocal contact lens iterations. High-add designs were used to correct 55-year olds, whereas low-add designs served 45-year ones. The overall performances were gauged in terms of visual Strehl ratio and area under through-focus modulation transfer function.

RESULTS

The root mean square error of higher order aberrations of the eye and correcting lens combination were significantly different (p < 0.05) within the five inherent SA models, for all pupils and accommodative states. Area under through-focus modulation transfer function at all three spatial frequencies tested was found to be significantly different (p < 0.05) within the five SA models. Visual Strehl ratio measures were also different but statistically insignificant. Eyes having the same refractive prescriptions but diverse levels of inherent SA perform differently even when corrected with identical multifocal designs, and the performance is dependent on pupil size and level of residual accommodation. Overall, the distinct performances within the five SA models were optically relevant for pupils ∼4 mm and greater. Among the designs investigated, the low-add multizone iteration demonstrated performance relatively independent of the inherent SA because of the favorable interactions of defocus with primary, secondary, and tertiary SA.

CONCLUSIONS

These findings confirm that the coupling of ocular SA and correcting lens aberrations contributes to the multifocal functionality.

Subjective blur limits for higher order aberrations

PURPOSE

We compared subjective blur limits for defocus and the higher-order aberrations of coma, trefoil, and spherical aberration.

METHODS

Spherical aberration was presented in both Zernike and Seidel forms. Black letter targets (0.1, 0.35, and 0.6 logMAR) on white backgrounds were blurred using an adaptive optics system for six subjects under cycloplegia with 5 mm artificial pupils. Three blur criteria of just noticeable, just troublesome, and just objectionable were used.

RESULTS

When expressed as wave aberration coefficients, the just noticeable blur limits for coma and trefoil were similar to those for defocus, whereas the just noticeable limits for Zernike spherical aberration and Seidel spherical aberration (the latter given as an "rms equivalent") were considerably smaller and larger, respectively, than defocus limits.

CONCLUSIONS

Blur limits increased more quickly for the higher order aberrations than for defocus as the criterion changed from just noticeable to just troublesome and then to just objectionable.

Wavefront sensing with critical sampling

Different types of nonredundant sampling patterns are shown to guarantee completeness of the basis formed by the sampled partial derivatives of Zernike polynomials, commonly used to reconstruct the wavefront from its slopes (wavefront sensing). In the ideal noise-free case, this enables one to recover double the number of modes J than sampling points I (critical sampling J=2I). With real data, noise amplification makes the optimal number of modes lower I<J<2I. Our computer simulations show that optimized nonredundant sampling provides a significant improvement of wavefront reconstructions, with the number of modes recovered about 2.5 higher than with standard sampling patterns.

A proposed regression analysis-based method for assessment of higher order aberration interrelationships in ocular wavefront sets from apparently similar origins

PURPOSE

To analyze the interrelations and difference in higher order aberration patterns in ocular wavefront sets with similar measures of central tendency and apparently similar origins.

METHODS

This theoretical simulation and assessment study was performed at the cornea and refractive surgery services of a tertiary care, teaching hospital. A sample data set of myopic candidates was used to create distribution patterns of signed and absolute values. Histograms and quantile-to-quantile (Q-Q) plots were used to analyze the pattern. Regression models were used for interocular comparison between fellow eyes without enantiomeric considerations, to create a subtle difference in interrelation, but not in the overall mean of absolute values. The values were represented in the form of R-squared values and slope of the regression line.

RESULTS

The Q-Q plots suggested large deviations from normal values in analyzing the absolute values. Regression plots were used to find out the Zernike modes that predicted other modes, and the ones with the highest R-square values were compared between data sets. This revealed differences in the interrelationship of various Zernike modes from each other, which could have been missed in measures of central tendency.

CONCLUSIONS

The proposed regression analysis-based model could pick up subtle differences in the higher order aberration patterns and interrelation, which would have been ignored in measures of central tendency. Large multicentric pooled data could be used and stratified according to age and racial variations to establish the limits of normal ranges based on this model.

Influence of ocular longitudinal chromatic aberration on the selection of aspheric intraocular lenses

Polychromatic defocus could affect the optimal residual spherical aberration that could yield the best image quality for patients with intraocular lenses (IOLs). Modulation transfer functions (MTFs) were generated using a model that included polychromatic defocus. The maximum MTF volume occurred at + 0.05 μm of overall ocular spherical aberration. For 3 case studies, the optimal overall ocular spherical aberration was ~0.05 μm more positive with the contribution of polychromatic defocus than without it. Overall, the model indicated that image quality was usually best when IOLs allowed overall ocular spherical aberration that was slightly positive, rather than strongly positive, zero, or negative.

Optical quality and intraocular scattering in a healthy young population

BACKGROUND

We objectively assessed the optical quality and intraocular scattering by means of parameters provided by a clinical double-pass system in healthy young subjects and thereby we obtained new reference data for clinical diagnosis. We calculated normal values of neural contrast sensitivity function (nCSF) from the measured modulation transfer function (MTF) and the contrast sensitivity function (CSF).

METHODS

Eligible subjects were healthy adults aged from 18 to 30 years with a logMAR visual acuity (VA) of 0.0 or better and normal values of CSF. Optical quality measurements for a 4.0 mm pupil were performed using the Optical Quality Analysis System (OQAS) based on the double-pass technique. The following parameters were analysed: the modulation transfer function cutoff frequency (MTF(cutoff)), the Strehl(2D) ratio, the OQAS values (OV) at 100, 20 and nine per cent contrasts and the objective scatter index (OSI).

RESULTS

A total of 178 volunteers responded to the call, of whom 181 eyes were finally part of the study taking into account the criteria for inclusion. The values for the optical quality parameters were: 44.54 ± 7.14 cpd (MTF(cutoff)), 0.27 ± 0.06 (Strehl(2D) ratio), 1.48 ± 0.24 (OV(100%)), 1.58 ± 0.32 (OV(20%)), 1.64 ± 0.39 (OV(9%)), and 0.38 ± 0.19 (OSI). The nCSF calculated was 1.76 ± 0.21 (3 cpd), 2.13 ± 0.23 (6 cpd), 2.01 ± 0.28 (12 cpd) and 1.86 ± 0.33 (18 cpd).

CONCLUSION

The normal values provided can be a useful tool for discriminating healthy eyes from early abnormal ones in which the optical quality or sensory function is impaired.

System design considerations to improve isoplanatism for adaptive optics retinal imaging

Adaptive optics (AO) retinal images are limited by anisoplanatism; wavefront shape varies across the field of view such that only a limited area can achieve diffraction-limited image quality at one time. We explored three alternative AO modalities designed to reduce this effect, drawn from work in astronomy. Optical design analysis and computer modeling was undertaken to predict the benefit of each modality for various schematic eyes and various complexities of the imaging system. Off-axis performance was found to be limited by system parameters and not by the eye itself, due to the inherent off-axis characteristics of the eye's gradient index lens. This rendered the alternative AO modalities ineffectual compared with conventional AO but did suggest several methods by which anisoplanatism may be reduced by altering the design of conventional AO systems. Several of these design possibilities were explored with further modeling. The best-performing method involved the replacement of system lenses with gradient index versions inspired by the human eye lens. Mirror-based relay optics also demonstrated good off-axis performance, but their advantage was lost in regions of the system suffering from uncorrected higher-order aberration. Incorporating "off-the-plane" beam deviations ameliorated this loss substantially. In this work we also show, to our knowledge for the first time, that the ideal location of a single AO corrector need not lie in the pupil plane.

Adaptive optics binocular visual simulator to study stereopsis in the presence of aberrations

A binocular adaptive optics visual simulator has been devised for the study of stereopsis and of binocular vision in general. The apparatus is capable of manipulating the aberrations of each eye separately while subjects perform visual tests. The correcting device is a liquid-crystal-on-silicon spatial light modulator permitting the control of aberrations in the two eyes of the observer simultaneously in open loop. The apparatus can be operated as an electro-optical binocular phoropter with two micro-displays projecting different scenes to each eye. Stereo-acuity tests (three-needle test and random-dot stereograms) have been programmed for exploring the performance of the instrument. As an example, stereo-acuity has been measured in two subjects in the presence of defocus and/or trefoil, showing a complex relationship between the eye's optical quality and stereopsis. This instrument might serve for a better understanding of the relationship of binocular vision and stereopsis performance and the eye's aberrations.

Comparison of sorting algorithms to increase the range of Hartmann-Shack aberrometry

Recently many software-based approaches have been suggested for improving the range and accuracy of Hartmann-Shack aberrometry. We compare the performance of four representative algorithms, with a focus on aberrometry for the human eye. Algorithms vary in complexity from the simplistic traditional approach to iterative spline extrapolation based on prior spot measurements. Range is assessed for a variety of aberration types in isolation using computer modeling, and also for complex wavefront shapes using a real adaptive optics system. The effects of common sources of error for ocular wavefront sensing are explored. The results show that the simplest possible iterative algorithm produces comparable range and robustness compared to the more complicated algorithms, while keeping processing time minimal to afford real-time analysis.

Effects of accommodation training on accommodation and depth of focus in an eye implanted with a crystalens intraocular lens

PURPOSE

To investigate objective measures of the effects of accommodative training of a pseudophakic eye implanted with a Crystalens AT-52SE (eyeonics Inc) intraocular lens (IOL) on reading performance, accommodation, and depth of focus.

METHODS

Objective dynamic measures of accommodation, pupil size, and depth of focus were quantified from wavefront measures before and after 1 week of accommodative training that began 29 months after implantation of an accommodating IOL in one patient. Depth of focus was estimated from 50% cut-off of peak performance levels for defocus curves that were computed from the image quality metric VSOTF based on ocular wavefront aberrations.

RESULTS

The patient reported improved near vision reading performance after completing the training procedure. After training, there was a shift in conjugate focus in the hyperopic direction, yet the depth of focus increased significantly for near objects. Simulated retinal images and the calculated modulation transfer function of the eye both demonstrated improved quality for near vision after training.

CONCLUSIONS

The subjective report of improved near vision after training was correlated with improvement of objective measures. Depth of focus increased for near objects with attempts to accommodate after training. This change was linked to increases in aberrations and pupil size and occurred despite the conjugate focus shifting in the hyperopic direction. These results demonstrate that accommodative training may be useful in improving near vision in patients with accommodating IOLs.

Adaptation to astigmatic blur

Adapting to blurred or sharpened images alters the perceived focus of subsequently viewed images. We examined whether these adaptation effects could arise from actual sphero-cylindrical refractive errors, by testing aftereffects in images simulating second-order astigmatism. Image blur was varied from negative (vertical) through isotropic to positive (horizontal) astigmatism while maintaining constant blur strength. A 2AFC staircase was used to estimate the stimulus that appeared isotropically blurred before or after adapting to images with astigmatism. Adaptation to horizontal blur caused isotropically blurred images to appear vertically biased and vice versa, shifting the perceived isotropic point toward the adapting level. Aftereffects were similar for different types of images and showed partial selectivity so that strongest effects generally occurred when testing and adapting images were the same. Further experiments explored whether the adaptation depended more strongly on the blurring or "fuzziness" in the images vs. the apparent "figural" changes introduced by the blur, by comparing how the aftereffects transfer across changes in size or orientation. Our results suggest that strong selective adaptation can occur for different lower order aberrations of the eye and that these may be at least partly driven by the apparent figural changes that blurring introduces into the retinal image.

Correlation among ocular spherical aberration, corneal spherical aberration, and corneal asphericity before and after LASIK for myopic astigmatism with the SCHWIND AMARIS platform

PURPOSE

To determine the spherical wave aberration of the human eye based on corneal topography.

METHODS

Based on the pre- and postoperative status of 146 consecutive eyes (median patient age 36 years), the correlations between spherical aberration and asphericity and between corneal and ocular spherical aberrations were determined using simple linear regression methods. The asphericity (Q) values for which spherical aberration equals zero as well as the reference Q values for which corneal spherical aberration equals ocular spherical aberration have been determined. Patients underwent LASIK using the AMARIS excimer laser platform (SCHWIND eye-tech-solutions). All ablations were based on aspheric aberration-neutral profiles.

RESULTS

Corneal and ocular spherical aberrations correlate well with Q value and the value p · R(-3) in patients before and after LASIK for myopic astigmatism. A Q value of -0.19 to -0.27 can provide zero ocular spherical aberration in patients before and after LASIK for myopic astigmatism. Ocular spherical aberration is induced at a rate of half the induced corneal spherical aberration. A reference Q value of -0.12 to +0.01 can provide corneal spherical aberration equal to ocular spherical aberration in patients before and after LASIK for myopic astigmatism.

CONCLUSIONS

Ocular and corneal wave aberrations are two different concepts that are not interchangeable. As for spherical aberration, a simple static model with a reference cornea deviating from a Cartesian oval can provide a 2:1 correspondence between corneal and ocular spherical aberration.

A non-stationary model for simulating the dynamics of ocular aberrations

The time-evolution of ocular aberrations has been the subject of many studies, but so far there has been little discussion involving the modelling of the underlying temporal statistics. This paper presents a non-stationary modelling approach based on a coloured-noise generator, which can be applied to ocular aberration dynamics. The model parameters are computed from measured ocular aberration data. A custom-built aberrometer based on a Shack-Hartmann sensor was used for measurement. We present simulations based on our modelling approach, and validate them through comparison to real data. This work could be useful in areas such as the testing of ophthalmic devices and the development of improved algorithms for laser refractive surgery.

The oblique effect has an optical component: orientation-specific contrast thresholds after correction of high-order aberrations

Most of the high-order aberrations of the eye are not circularly symmetric. Hence, while it is well known that human vision is subject to cortically based orientation preference in cell tuning, the optics of the eye might also introduce some orientational anisotropy. We tested this idea by measuring contrast sensitivity at different orientations of sine-wave gratings when viewing through a closed-loop adaptive optics phoropter. Under aberration-corrected conditions, mean contrast sensitivity improved for all observers by a factor of 1.8× to 5×. The detectability of some orientations improved more than others. As expected, this orientation-specific effect varied between individuals. The sensitivity benefits were accurately predicted from MTF model simulations, demonstrating that the observed effects reflected the individual's pattern of high-order aberrations. In one observer, the orientation-specific effects were substantial: an improvement of 8× at one orientation and 2× in another orientation. The experiments confirm that, for conditions that are not diffraction limited, the optics of the eye introduce rotational asymmetry to the luminance distribution on the retina and that this impacts vision, inducing orientational anisotropy. These results suggest that the traditional view of meridional anisotropy having an entirely neural origin may be true for diffraction-limited pupils but that viewing through larger pupils introduces an additional orientation-specific optical component to this phenomenon.

Forward ray tracing for image projection prediction and surface reconstruction in the evaluation of corneal topography systems

A forward ray tracing (FRT) model is presented to determine the exact image projection in a general corneal topography system. Consequently, the skew ray error in Placido-based topography is demonstrated. A quantitative analysis comparing FRT-based algorithms and Placido-based algorithms in reconstructing the front surface of the cornea shows that arc step algorithms are more sensitive to noise (imprecise). Furthermore, they are less accurate in determining corneal aberrations particularly the quadrafoil aberration. On the other hand, FRT-based algorithms are more accurate and more precise showing that point to point corneal topography is superior compared to its Placido-based counterpart.

Ocular wavefront aberrations in the common marmoset Callithrix jacchus: effects of age and refractive error

The common marmoset, Callithrix jacchus, is a primate model for emmetropization studies. The refractive development of the marmoset eye depends on visual experience, so knowledge of the optical quality of the eye is valuable. We report on the wavefront aberrations of the marmoset eye, measured with a clinical Hartmann-Shack aberrometer (COAS, AMO Wavefront Sciences). Aberrations were measured on both eyes of 23 marmosets whose ages ranged from 18 to 452 days. Twenty-one of the subjects were members of studies of emmetropization and accommodation, and two were untreated normal subjects. Eleven of the 21 experimental subjects had worn monocular diffusers and 10 had worn binocular spectacle lenses of equal power. Monocular deprivation or lens rearing began at about 45 days of age and ended at about 108 days of age. All refractions and aberration measures were performed while the eyes were cyclopleged; most aberration measures were made while subjects were awake, but some control measurements were performed under anesthesia. Wavefront error was expressed as a seventh-order Zernike polynomial expansion, using the Optical Society of America's naming convention. Aberrations in young marmosets decreased up to about 100 days of age, after which the higher-order RMS aberration leveled off to about 0.10 μm over a 3 mm diameter pupil. Higher-order aberrations were 1.8 times greater when the subjects were under general anesthesia than when they were awake. Young marmoset eyes were characterized by negative spherical aberration. Form-deprived eyes of the monocular deprivation animals had greater wavefront aberrations than their fellow untreated eyes, particularly for asymmetric aberrations in the odd-numbered Zernike orders. Both lens-treated and form-deprived eyes showed similar significant increases in Z3(-3) trefoil aberration, suggesting the increase in trefoil may be related to factors that do not involve visual feedback.

Physical human model eye and methods of its use to analyse optical performance of soft contact lenses

A bench-top physical model eye that closely replicates both anatomical and optical properties of an average human eye was designed and constructed. The cornea was sourced from a flouro-polymer with refractive index (RI) of 1.376 and crystalline lenses were made of Boston RGP polymers, EO and Equalens II, with an equivalent RI of 1.429 and 1.423 respectively. These materials served to make crystalline lens components of different age groups and accommodative states. De-Ionized water, with RI of 1.334 represented both aqueous and vitreous humor. The complementary metal-oxide sensor of a PixelLink digital camera with a resolution of 5MP and a 2.2 microm pixel pitch, hosted on a motor-base, served as the 'acting' retina. The translation and rotary functions of the motor-base facilitated the simulation of different states of ametropia and assessment of peripheral visual function, respectively. We validated one of its configurations to suit normal viewing conditions and results from the on and off-axis optical quality measurements are presented. As a demonstration of potential practical uses, several corrective soft contact lenses were placed on the model eye and their optical performance evaluated.

Centroid displacement statistics of the eye aberration

We discuss a method for the study of the spatial statistics of the ocular aberrations, based on the direct use of the Hartmann-Shack centroid displacements, avoiding the wavefront reconstruction step. Centroid diagrams are introduced as a helpful aid to visualize basic properties of the aberration datasets, and slope-related second-order statistical functions are applied to check the compatibility between the experimental data and different models for the aberration statistics. Preliminary results suggest that no single power-law spectrum (e.g., Kolmogorov's) is able to represent the whole range of spatial statistics of individual eye fluctuations and that more elaborated models, including at least the contribution of a relevant defocus fluctuation term, are required. This centroid-based approach allows for an easier intercomparison of results between laboratories and avoids the bias and information loss associated with the estimation of a reduced number of Zernike coefficients from a much wider slope data set.