Comparison of the eye's wave-front aberration measured psychophysically and with the Shack-Hartmann wave-front sensor

The Influence of Accommodative Demand on Ocular Aberrations: A Study of Zernike Coefficients Repeatability and Variability

PURPOSE

To evaluate the repeatability of the Zernike coefficients in healthy eyes when monocular accommodation was stimulated at different vergences demands.

METHODS

A total of 36 right eyes from healthy volunteers were prospectively and consecutively recruited for this study. Wavefront aberrometry was conducted to objectively characterize the ocular optical quality during accommodation, from the individual's far point to a 5 D accommodation demand in steps of 0.5 D. The repeatability of Zernike coefficients up to the fourth order was assessed by calculating the within-eye repeatability (Sw), the coefficient of repeatability (CR), the coefficient of variation (CV), and the intraclass correlation coefficient (ICC) as an indicator of measurement reliability.

RESULTS

Correlation among repeated measurements showed high reliability (ICC > 0.513) for all parameters measured except some fourth-order Zernike coefficients, C(4, -4) (ICC < 0.766), C(4, -2) (ICC < 0.875), C(4, 2) (ICC < 0.778) and C(4, 4) (ICC < 0.811). Greater repeatability and less variability were obtained for high-order Zernike coefficients (CR < 0.154), although an increase in CR in the coefficients analyzed was observed with increasing accommodative demand. No clear trend was evident in CV; however, it was observed that the low-order Zernike coefficients exhibit lower CV (CV < 1.93) compared to the high-order Zernike coefficients (CV > 0).

CONCLUSIONS

The reliability of Zernike coefficients up to the fourth order in healthy young individuals demonstrated a strong consistency in measuring terms up to the fourth order, with more variability observed for high-order terms. The Zernike coefficients up to the third order exhibited the highest level of repeatability.

Fourier tools for the evaluation of refractive multifocal designs

This paper presents innovative tools and methodologies for the theoretical assessment of optical properties in refractive multifocal designs. Utilizing lens segmentation techniques and classical Fourier optics, these tools can be of help evaluating multifocal contact lenses, intraocular lenses, small aperture designs, and corneal inlays. As an example of their utility, this study presents the through-focus Visual Strehl ratios in the frequency domain of 12 multifocal contact lenses from four companies, derived from the sagittal power profiles obtained with a NIMO equipment (LAMBDA-X) for three base prescriptions (- 6.00 D, - 3.00 D, and + 1.00 D). The contact lenses are also assessed alongside higher-order aberrations obtained from 65 eyes, measured using a Wavefront Sciences Complete Ophthalmic Analysis System (AMO). Diameter variations, corresponding to individual pupil sizes (2.45-6.27 mm), were considered in the evaluation. These novel tools enable the theoretical evaluation of multifocal solutions without the need for prototypes. In the case examples presented, they differentiate between lenses tailored for different presbyopic age groups, offer guidance on optimizing hyperfocal distance in contact lens design, and underscore the relevance of the effective aperture effect. Notably, this paper introduces the pioneering conversion of sagittal powers of multifocal solutions into an equivalent wavefront and optical quality metric, with potential applications in myopia control assessments. The author hopes that readers recognize and utilize these tools to advance the field of refractive multifocality.

Ray tracing optimization: a new method for intraocular lens power calculation in regular and irregular corneas

To develop a novel algorithm based on ray tracing, simulated visual performance and through-focus optimization for an accurate intraocular lens (IOL) power calculation. Custom-developed algorithms for ray tracing optimization (RTO) were used to combine the natural corneal higher-order aberrations (HOAs) with multiple sphero-cylindrical corrections in 210 higher order statistical eye models for developing keratoconus. The magnitude of defocus and astigmatism producing the maximum Visual Strehl was considered as the optimal sphero-cylindrical target for IOL power calculation. Corneal astigmatism and the RMS HOAs ranged from - 0.64 ± 0.35D and 0.10 ± 0.04 μm (0-months) to - 3.15 ± 1.38D and 0.82 ± 0.47 μm (120-months). Defocus and astigmatism target was close to neutral for eyes with low amount of HOAs (0 and 12-months), where 91.66% of eyes agreed within ± 0.50D in IOL power calculation (RTO vs. SRK/T). However, corneas with higher amounts of HOAs presented greater visual improvement with an optimized target. In these eyes (24- to 120-months), only 18.05% of eyes agreed within ± 0.50D (RTO vs. SRK/T). The power difference exceeded 3D in 42.2% while the cylinder required adjustments larger than 3D in 18.4% of the cases. Certain amounts of lower and HOAs may interact favourably to improve visual performance, shifting therefore the refractive target for IOL power calculation.

Recent advances in measurement of monochromatic aberrations of human eyes

The field of aberrations of the human eye is moving rapidly, being driven by the desire to monitor and optimise vision following refractive surgery. It is important for ophthalmologists and optometrists to have an understanding of the magnitude of various aberrations and how these are likely to be affected by refractive surgery and other corrections. In this paper, I consider methods used to measure aberrations, the magnitude of aberrations in general populations and how these are affected by various factors (for example, age, refractive error, accommodation and refractive surgery) and how aberrations and their correction affect spatial visual performance.

Shack-Hartmann versus reverse Hartmann wavefront sensors: experimental results

With respect to the classical Shack-Hartmann (SH) wavefront sensor (WFS), the recently proposed reverse Hartmann (RH) sensor inverts the locations of the filtering and observation planes and forms a direct image of the pupil on a detector array. The slopes of the wavefront error (WFE) are then reconstructed by using a double Fourier transform algorithm. It turns out that the same algorithm can also be applied to the raw data acquired by SH sensors. This Letter presents the first, to the best of our knowledge, experimental results obtained with a simplified RH WFS and their comparison to those provided by a reference SH sensor, in both classical and double Fourier transform modes. They demonstrate that similar WFE measurement accuracy is achievable when using the three techniques, at least within the limit of our test bench that is estimated around $\lambda/10$λ/10 RMS.

Fresnel diffraction analysis of Ronchi and reverse Hartmann tests

This paper presents a Fresnel diffraction analysis of classical Ronchi and reverse Hartmann tests. Simplified analytical expressions of the intensity patterns observed by the camera are established, allowing quantitative measurements of the wavefront slopes of the tested optical system. The wavefronts are then reconstructed from their slopes using a double Fourier transform algorithm. The optimization of the operational parameters of the system is discussed in view of different quality criteria, including relative pupil shear and contrast factors in both monochromatic and polychromatic light. Practical examples of applications are studied with the help of numerical simulations, demonstrating that measurement accuracies better than λ/100 RMS are achievable on properly dimensioned systems. Finally, the technique is also applicable to wavefront sensing in adaptive optics systems.

Mechanisms, imaging and structure of tear film breakup

Tear film breakup (BU) is an important aspect of dry eye disease, as a cause of ocular aberrations, irritation and ocular surface inflammation and disorder. Additionally, measurement of breakup time (BUT) is a common clinical test for dry eye. The current definition of BUT is subjective; here, a more objective concept of "touchdown" - the moment when the lipid layer touches down on the corneal surface - is proposed as an aid to understanding processes in early and late stages of BU development. Models of BU have generally been based on the assumption that a single mechanism is involved. In this review, it is emphasized that BU does not have a single explanation but it is the end result of multiple processes. A three-way classification of BU is proposed - "immediate," "lid-associated," and "evaporative." Five different types of imaging systems are described, which have been used to help elucidate the processes involved in BU and BUT; a new method, "high resolution chromaticity images," is presented. Three directions of tear flow - evaporation, osmotic flow out of the ocular surface, and "tangential flow" along the ocular surface - determine tear film thinning between blinks, leading to BU. Ten factors involved in BU and BUT, both before and after touchdown, are discussed. Future directions of research on BU are proposed.

Aberrometry Repeatability and Agreement with Autorefraction

SIGNIFICANCE

Commercially available aberrometers are essential to clinical studies evaluating refractive error and image quality. The Discovery System (Innovative Visual Systems, Elmhurst, IL) is a promising clinical instrument that allows investigators to export aberration data for research and analysis purposes. An assessment of the Discovery System's performance is essential to the interpretation of the data obtained.

PURPOSE

The aims of this study were to determine the between-visit repeatability of refractive error and higher-order aberration measurements with the Discovery System and to examine between-instrument agreement of refractive error measurements with the Discovery System and Grand Seiko WAM-5500 open-field autorefractor (Grand Seiko Co., Hiroshima, Japan).

METHODS

Cycloplegic refractive error values from the Discovery System (over a 3-mm pupil) and the Grand Seiko autorefractor were converted to power vectors (M, J0, and J45), and averaged. Zernike coefficients were also calculated by the Discovery System over a 6-mm pupil through the sixth radial order. Between-visit repeatability and agreement were evaluated using Bland-Altman difference-versus-mean plots. A t-test compared each mean difference (bias) to zero, and the 95% limits of agreement were calculated.

RESULTS

Twenty-five young adults with a mean (±SD) cycloplegic spherical-equivalent refractive error of -2.91 ± 1.85 diopters (D) (range, -6.96 to +0.74 D) were enrolled. There were no significant between-visit differences with the Discovery System for M, J0, J45, third- through sixth-order root mean square (RMS), higher-order RMS, or spherical aberration (all P > .30), and the repeatability for defocus and higher-order RMS were ±0.31 D and ±0.095 μm, respectively, for a 6-mm pupil. At a 3-mm pupil, the Discovery System, on average, measured slightly more positive values than the Grand Seiko for M (0.28 D), J0 (0.11 D), and J45 (0.12 D; all P < .005).

CONCLUSIONS

The Discovery System was very repeatable and would be an appropriate instrument to measure cycloplegic refractive error and higher-order aberration changes in adults. Small differences in refractive error were found between the Discovery System and Grand Seiko.

Longitudinal chromatic aberration of the human eye in the visible and near infrared from wavefront sensing, double-pass and psychophysics

Longitudinal Chromatic Aberration (LCA) influences the optical quality of the eye. However, the reported LCA varies across studies, likely associated to differences in the measurement techniques. We present LCA measured in subjects using wavefront sensing, double-pass retinal images, and psychophysical methods with a custom-developed polychromatic Adaptive Optics system in a wide spectral range (450-950 nm), with control of subjects' natural aberrations. LCA measured psychophysically was significantly higher than that from reflectometric techniques (1.51 D vs 1.00 D in the 488-700 nm range). Ours results indicate that the presence of natural aberrations is not the cause for the discrepancies across techniques.

Scale and spatial distribution of aberrations associated with tear breakup

PURPOSE

We examined the spatial correlation between tear breakup (TBU) and the associated optical anomalies on multiple spatial scales.

METHODS

Five subjects refrained from blinking while the time course and patterns of TBU were sequentially observed using fluorescein, retroillumination, and Shack-Hartmann (SH) aberrometry. Wavefront error maps were developed using Zernike polynomials, as well as local zonal analysis of measured wavefront slopes. The difference between these maps reveals the presence of very high-order aberrations missed by standard modal fitting methods. Size of SH spots was also quantified to estimate optical perturbations on a microscopic scale. The spatial correlation between TBU and optical aberrations was also computed.

RESULTS

Degradation of the tear film increased wavefront aberrations over all spatial scales measured. Consistent with tear thinning, blink suppression induced an irregular pattern of phase advances in regions of TBU. SH spot size also increased in regions of TBU, which indicates the presence of optical aberrations on a scale smaller than individual lenslets.

CONCLUSIONS

The optical signature of TBU caused by blink suppression is a combination of wavefront aberrations on macroscopic and microscopic scales due to non-uniform tear film thinning and possible exposure of a rough epithelial surface. Localized optical defects correspond temporally and spatially with TBU revealed by fluorescein and retroillumination. In addition to gross wavefront aberrations, scatter develops in areas of TBU that will further contribute to image degradation and visual disturbances after TBU.

Noniterative boundary-artifact-free wavefront reconstruction from its derivatives

Wavefront sensors are usually based on measuring the wavefront derivatives. The most commonly used approach to quantitatively reconstruct the wavefront uses discrete Fourier transform, which leads to artifacts when phase objects are located at the image borders. We propose here a simple approach to avoid these artifacts based on the duplication and antisymmetrization of the derivatives data, in the derivative direction, before integration. This approach completely erases the border effects by creating continuity and differentiability at the edge of the image. We finally compare this corrected approach to the literature on model images and quantitative phase images of biological microscopic samples, and discuss the effects of the artifacts on the particular application of dry mass measurements.

Quantitative surface normal measurement by a wavefront camera

A compact wavefront camera that allows users to quantitatively measure the intensity and wavefront at a remote object plane is reported. The camera is built from a chip-scale wavefront sensor that we previously developed. By measuring the wavefront of the image and calibrating the wavefront relationship between the image and object planes, the wavefront at the object plane can be computed and the surface normal of the object can be derived. We built a prototype camera and calibrated the wavefront relationship. In a proof-of-concept experiment, a set of concave mirrors with different focal lengths (50-200 mm), were imaged. The results agree well with their expected values. To demonstrate the application of the camera, we applied this method to measure the deformation of a microfluidic channel under pressure.

Problems testing diffractive intraocular lenses with Shack-Hartmann sensors

Shack-Hartmann wavefront sensors have found widespread application for testing ocular aberrations. These sensors provide an accurate map of the wavefront emerging from an eye in most cases. However, there is a growing class of patients with diffractive intraocular lenses that will potentially be measured incorrectly with Shack-Hartmann devices. We explore the pitfalls of measuring diffractive lenses with this technology.

Design and validation of a scanning Shack Hartmann aberrometer for measurements of the eye over a wide field of view

Peripheral vision and off-axis aberrations not only play an important role in daily visual tasks but may also influence eye growth and refractive development. Thus it is important to measure off-axis wavefront aberrations of human eyes objectively. To achieve efficient measurement, we incorporated a double-pass scanning system with a Shack Hartmann wavefront sensor (SHWS) to develop a scanning Shack Hartmann aberrometer (SSHA). The prototype SSHA successfully measured the off-axis wavefront aberrations over +/- 15 degree visual field within 7 seconds. In two validation experiments with a wide angle model eye, it measured change in defocus aberration accurately (<0.02microm, 4mm pupil) and precisely (<0.03microm, 4mm pupil). A preliminary experiment with a human subject suggests its feasibility in clinical applications.

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.

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.

Clinical Ocular Wavefront Analyzers

PURPOSE

To provide a summary of the methods used by clinical wavefront analyzers and their historical, current, and future applications.

METHODS

Review of the literature and authors' experience with the various devices.

RESULTS

A wide range of clinical wavefront aberrometers, which use different principles, are available to clinicians and researchers.

CONCLUSIONS

Applications of wavefront analyzers in vision sciences range from assessment of refractive error, refractive surgery planning, evaluation of outcomes, optimization of contact lenses and IOL designs, evaluation of pathology relating to optical performance of the eye, and evaluation of accommodation alterations.

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.

Operator-induced errors in Hartmann-Shack wavefront sensing: Model eye study

PURPOSE

To evaluate the effects of instrument realignment and angular misalignment during the clinical determination of wavefront aberrations by simulation in model eyes.

SETTING

Aston Academy of Life Sciences, Aston University, Birmingham, United Kingdom.

METHODS

Six model eyes were examined with wavefront-aberration-supported cornea ablation (WASCA) (Carl Zeiss Meditec) in 4 sessions of 10 measurements each: sessions 1 and 2, consecutive repeated measures without realignment; session 3, realignment of the instrument between readings; session 4, measurements without realignment but with the model eye shifted 6 degrees angularly. Intersession repeatability and the effects of realignment and misalignment were obtained by comparing the measurements in the various sessions for coma, spherical aberration, and higher-order aberrations (HOAs).

RESULTS

The mean differences between the 2 sessions without realignment of the instrument were 0.020 microm +/- 0.076 (SD) for Z(3)(-1)(P = .551), 0.009 +/- 0.139 microm for Z(3)(1)(P = .877), 0.004 +/- 0.037 microm for Z(4)(0) (P = .820), and 0.005 +/- 0.01 microm for HO root mean square (RMS) (P = .301). Differences between the nonrealigned and realigned instruments were -0.017 +/- 0.026 microm for Z(3)(-1)(P = .159), 0.009 +/- 0.028 microm for Z(3)(1) (P = .475), 0.007 +/- 0.014 microm for Z(4)(0)(P = .296), and 0.002 +/- 0.007 microm for HO RMS (P = 0.529; differences between centered and misaligned instruments were -0.355 +/- 0.149 microm for Z(3)(-1) (P = .002), 0.007 +/- 0.034 microm for Z(3)(1)(P = .620), -0.005 +/- 0.081 microm for Z(4)(0)(P = .885), and 0.012 +/- 0.020 microm for HO RMS (P = .195). Realignment increased the standard deviation by a factor of 3 compared with the first session without realignment.

CONCLUSIONS

Repeatability of the WASCA was excellent in all situations tested. Realignment substantially increased the variance of the measurements. Angular misalignment can result in significant errors, particularly in the determination of coma. These findings are important when assessing highly aberrated eyes during follow-up or before surgery.

Normal-eye Zernike coefficients and root-mean-square wavefront errors

PURPOSE

To compare aberrometry measurements from multiple sites and compute mean Zernike coefficients and root-mean-square (RMS) values for the entire data pool to serve as a reference set for normal, healthy adult eyes.

SETTING

Northeastern State University, Tahlequah, Oklahoma, USA.

METHODS

Data were collected from 10 laboratories that measured higher-order aberrations (HOAs) in normal, healthy adult eyes using Shack-Hartmann aberrometry (2560 eyes of 1433 subjects). Signed Zernike coefficients were scaled to pupil diameters of 6.0 mm, 5.0 mm, 4.0 mm, and 3.0 mm and corrected to a common wavelength of 550 nm. The mean signed and absolute Zernike coefficients across data sets were compared. Then, the following were computed: overall mean values for signed and absolute Zernike coefficients; polar Zernike magnitudes and RMS values for coma-like aberrations (Z(3)(+/-1) and Z(5)(+/-1) combined); spherical-like aberrations (Z(4)(0) and Z(6)(0) combined); and 3rd-, 4th-, 5th-, and 6th-order, and higher-order aberrations (orders 3 to 6).

RESULTS

The different data sets showed good agreement for Zernike coefficients values across most higher-order modes, with greater variability for Z(4)(0) and Z(3)(-1). The most prominent modes and their mean absolute values (6.0-mm pupil) were, respectively, Z(3)(-1) and 0.14 microm, Z(4)(0) and 0.13 microm, and Z(3)(-3) and 0.11 microm. The mean total higher-order RMS was 0.33 microm.

CONCLUSIONS

There was a general consensus for the magnitude of HOAs expected in normal adult human eyes. At least 90% of the sample had aberrations less than double the mean values reported here. These values can serve as a set of reference norms.

A New Wavefront Sensor With Polar Symmetry: Quantitative Comparisons With a Shack-Hartmann Wavefront Sensor

PURPOSE

A novel wavefront sensor has been developed. It follows the same principle of the Shack-Hartmann wavefront sensor in that it is based on slope information. However, it has a different symmetry, which may offer benefits in terms of application.

METHODS

The new wavefront sensor consists of a set of donut-shaped acrylic lenses with a charge coupled device located at the focal plane. From detection of shift in the radial direction, radial slopes are computed for 2880 points. Theoretical computations for higher order aberrations and lower order aberrations were implemented for the Shack-Hartmann wavefront sensor and the new wavefront sensor, and practical measurements were conducted on several sphere-cylinder trial lenses.

RESULTS

The overall mean value of root mean square error (RMSE) (in microns) for theoretical computations was 0.03 for the Shack-Hartmann wavefront sensor and 0.02 for the new wavefront sensor. The mean value of RMSE for lower order aberrations (1-5) was 0.01 and 0.00003, and for higher order aberrations was 0.02 and 0.02, for the Shack-Hartmann and new wavefront sensors, respectively. For practical measurements (sphere, cylinder, axis), the standard deviation was 0.04 diopters (D), 0.04 D, and 4 degrees for the new wavefront sensor and 0.02 D, 0.02 D, and 5 degrees for the Shack-Hartmann wavefront sensor.

CONCLUSIONS

Precision of the new wavefront sensor when measuring astigmatic and spherical surfaces is compatible with the Shack-Hartmann wavefront sensor. Centration with this new sensor is an absolute process using the center of the entrance pupil, which is where the line of site passes. This wavefront sensor, similar to the Shack-Hartmann sensor, does not eliminate the possibility of tilt. For more conclusive and statistically valid data, in vivo measurements are needed.

Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity

PURPOSE

The purpose of this study is to determine the ability of single-value metrics of retinal image quality of the eye to predict visual performance as measured by high (HC) and low (LC) -contrast acuity at photopic (P) and mesopic (M) light levels in eyes with 20/17 and better visual acuity.

METHODS

Forty-nine normal subjects in good health ranging in age from 21.8 to 62.6 with 20/17 or better monocular high-contrast logarithm of the minimum angle of resolution (logMAR) acuity served as subjects. Wavefront error through the 10th Zernike radial order over a 7-mm pupil was measured on each test eye using a custom-built Shack/Hartmann wavefront sensor. For each eye, 31 different single-value retinal image quality metrics were calculated. Visual acuity was measured using HC (95%) and LC (11%) logMAR at photopic (270 cd/m) and mesopic (0.75 cd/m) light levels. To determine the ability of each metric of retinal image quality to predict each type of logMAR acuity (P HC, P LC, M HC, and M LC), each acuity measure was regressed against each optical quality metric.

RESULTS

The ability of the metrics of retinal image quality to predict logMAR acuity improved as luminance and/or contrast is lowered. The best retinal image quality metric (logPFSc) accounted for 2.6%, 15.1%, 27.6%, and 40.0% of the variance in P HC, P LC, M HC, and M LC logMAR acuity, respectively.

CONCLUSIONS

In eyes with 20/17 and better P HC acuity, P HC logMAR acuity is insensitive to variations in retinal image quality compared with M LC logMAR acuity. Retinal image quality becomes increasingly predictive of logMAR acuity as contrast and/or luminance is decreased. Everyday life requires individuals to function over a large range of contrast and luminance levels. Clinically, the impact of retinal image quality as a function of luminance and contrast is readily measurable in a time-efficient manner with M LC logMAR acuity charts.

A New Calibration Set of Phase Plates for Ocular Aberrometers

PURPOSE

To manufacture and test a set of phase plates for the calibration of ocular aberrometers and apply it to the calibration of an ocular laser ray tracing aberrometer.

METHODS

The set of phase plates is made by a greyscale single-mask photosculpture in photoresist method. Each plate induces a given amount of a particular aberration (Zernike) mode. The set contains two subsets: 1) pure Zernike modes to test the accuracy among different orders (from 3rd to 7th, approximately 0.3 to 0.4 microm); and 2) plates having different amounts of the same mode, 3rd order coma ranging from 0.11 to 0.47 microm. After manufacturing, the plates were tested twice, as a crosscheck, measuring the aberration pattern of each plate with a Mach-Zehnder interferometer and a single-pass Hartmann-Shack wavefront sensor. The set was then applied to the calibration of an ocular double-pass laser ray tracing aberrometer.

RESULTS

Close agreement was found between the three types of measurement. The maximum difference between Hartmann-Shack and laser ray tracing measurements was 0.032 microm (ie, approximately lambda/20, half of the typical measuring error in human eyes). This permitted detection of a small bias in the ocular laser ray tracing aberrometer.

CONCLUSIONS

The calibration set may be a powerful tool for the assessment of accuracy and reliability in ocular aberrometry. It discovered a small bias, which is almost impossible to detect when working with human eyes or trial lenses. This type of calibration tool is especially important in clinical environments.

The placido wavefront sensor and preliminary measurement on a mechanical eye

PURPOSE

The hardware and software of a novel wavefront sensor was developed (The sensor presented here is patent pending.). It has the same principal of the Hartmann-Shack (HS) and other sensors that are based on slope information for recovery of wavefront surface, but a different symmetry, and does not use individual microlenses. This polar symmetry might offer differences during practical measurements that may add value to current and well-established "gold standard" techniques.

METHODS

The sensor consists of a set of concentric "half-donut" surfaces (longitudinally sectioned toroids) molded on an acrylic surface with a CCD located at the focal plane. When illuminated with a plane wavefront, it focuses a symmetric pattern of concentric discs on the CCD plane; for a distorted wavefront, a nonsymmetric disc pattern is formed (similar to images of a placido-based videokeratographer). From detection of shift in the radial direction, radial slopes are computed for a maximum of 2880 points, and the traditional least-squares procedure is used to fit these partial derivatives to a set of 15 conventional OSA-VSIA Zernike polynomials. Theoretical computations for several synthetic surfaces containing low-order aberration (LOA) and high-order aberration (HOA) were implemented for both the HS and the new sensor.

RESULTS

Root mean square error (RMSE) in microns when theoretical data was taken as control, for HS sensor and new sensor, was 0.02 and 0.00003 for LOA (defocus, astigmatism) and 0.07 and 0.06 for HOA (coma, spherical, and higher terms), respectively. After this, practical preliminary measurements on a mechanical eye with a 5-mm pupil and 10 different defocus aberrations ranging from -5 D to 5 D, in steps of 1 D, were compared between sensors. RMSE for difference in measurements for HS and new sensor for sphere, cylinder, and axis, was 0.13 D, 0.07 D, and 11. Measurements were taken only on defocus aberrations. Qualitative images for astigmatism are shown.

DISCUSSION

Although practical in vivo tests were not conducted in this first study, we also discuss certain possible alignment differences that may arise as a result of the different symmetry of the new sensor. To take any conclusive assumption regarding the accuracy and/or precision of this new sensor, when compared with other well-established sensors, statistically significant in vivo measurements will need to be conducted.

High-speed Shack-Hartmann wavefront sensor design with commercial off-the-shelf optics

Several trade-offs relevant to the design of a two-dimensional high-speed Shack-Hartmann wavefront sensor are presented. Also outlined are some simple preliminary experiments that can be used to establish critical design specifications not already known. These specifications include angular uncertainty, maximum measurable wavefront tilt, and spatial resolution. A generic design procedure is then introduced to enable the adaptation of a limited selection of CCD cameras and lenslet arrays to the desired design specifications by use of commercial off-the-shelf optics. Although initially developed to aid in the design of high-speed (i.e., megahertz-frame-rate) Shack-Hartmann wavefront sensors, our method also works when used for slower CCD cameras. A design example of our procedure is provided.

Clinical comparison of 6 aberrometers Part 2: Statistical comparison in a test group

PURPOSE

To compare and mutually validate the measurements of 6 aberrometers: the Visual Function Analyzer (Tracey), the OPD-Scan (ARK-10000, Nidek), the Zywave (Bausch & Lomb), the WASCA (Carl Zeiss Meditec), the MultiSpot Hartmann-Shack device, and the Allegretto Wave Analyzer.

SETTING

University Hospital Antwerp, Antwerp, Belgium.

METHODS

This prospective study was conducted on a group of 44 healthy eyes with refractions ranging from -5.25 diopters (D) to +5.25 D (cylinder 0 to -2 D). For each aberrometer and each eye, the averaged Zernike data were used to calculate various kinds of root-mean-square (RMS). These parameters, together with the refractive parameters, were then analyzed with a repeated-measures analysis of variance (ANOVA) test, complemented by paired t tests. A similar analysis was done for the comparison of the variances of these parameters.

RESULTS

The aberrometers gave comparable values for all studied parameters with the following exceptions: The OPD-Scan underestimated the polynomials describing 4- and 5-fold symmetries, and the Visual Function Analyzer slightly overestimated the astigmatism terms. The 3rd-order radial RMS value was different for each device, as well as the RMS in the central 2.0 mm zone. The WASCA presented the lowest variance.

CONCLUSION

These results suggest that in healthy eyes, all aberrometers produced globally similar results but they may vary in some details.

Influences of reference plane and direction of measurement on eye aberration measurement

We explored effects of measurement conditions on wave aberration estimates for uncorrected, axially myopic model eyes. Wave aberrations were initially referenced to either the anterior corneal pole or the natural entrance pupil of symmetrical eye models, with rays traced into the eye from infinity (into the eye) to simulate normal vision, into the eye from infinity and then back out of the eye from the retinal intercepts (into/out of the eye), or out of the eye from the retinal fovea (out of the eye). The into-the-eye and out-of-the-eye ray traces gave increases in spherical aberration as myopia increased, but the into/out-of-the-eye ray trace showed little variation in spherical aberration. Reference plane choice also affected spherical aberration. Corresponding residual aberrations were calculated after the models had been optically corrected, either by placing the object or image plane at the paraxial far point or by modifying corneas to simulate laser ablation corrections. Correcting aberrations by ablation was more complete if the original aberrations were referenced to the cornea rather than to the entrance pupil. For eyes corrected by spectacle lenses, failure to allow for effects of pupil magnification on apparent entrance pupil diameter produced larger changes in measured aberrations. The general findings regarding choice of reference plane and direction of measurement were found to be equally applicable to eyes that lacked rotational symmetry.

Dihedral representations and statistical geometric optics. I. Spherocylindrical lenses

The linear 2-dim irreducible representations of the dihedral groups (Dn) are interpreted as classical linear operators of geometrical optics. It is shown that the 2-dim irreducible representation of D4 is simply the refractive group described by Campbell [Optom. Vision Sci. 74, 381 (1997)]. The dihedral Fourier-inverse mechanism is introduced and shown to provide a systematic connection between the standard refractive data and their vector space representation, as proposed by Thibos et al. [Vision Sci. Appl. 2, 14 (1994)].

Evaluation of a clinical aberrometer for lower-order accuracy and repeatability, higher-order repeatability, and instrument myopia

BACKGROUND

Refractive surgery has stimulated the development of aberrometers, which are instruments that measure higher-order aberrations. The purpose of this study was to test one clinical aberrometer, the Complete Ophthalmic Analysis System (COAS), for its accuracy, repeatability, and instrument myopia for measuring sphere and astigmatism and its repeatability for measuring higher-order aberrations.

METHODS

Aberrations of 56 normal eyes (28 subjects) were measured with and without cycloplegia using a COAS, a conventional autorefractor and by subjective refraction. We evaluated lower-order accuracy (sphere and astigmatism) of the COAS and autorefractor by comparing that data with that of subjective refraction. We also tested COAS lower- and higher-order repeatability for 5 measurements taken in less than 1 minute. We evaluated instrument myopia by comparing cycloplegic and noncycloplegic measurements of the same eye. Data were analyzed for a 5.0-mm-diameter pupil.

RESULTS

Mean COAS spherical error was between -0.1 and +0.4 diopters (D), depending on cycloplegia and the kind of sphere power computation selected. Cylinder power errors were less than 0.1 D. COAS repeatability coefficients were better than 0.25 D, and instrument myopia was less than 0.4 D. These were comparable with those of autorefraction. Higher-order repeatability was sufficient to allow reliable measurement of normal third-order aberrations and spherical aberration.

CONCLUSIONS

Accuracy, repeatability, and instrument myopia of the COAS are similar to those of a conventional autorefractor. Accuracy and repeatability are also similar to those of subjective refraction. Like an autorefractor, the COAS provides instantaneous, objective measurements of sphere and astigmatism, but it also measures higher-order aberrations. We found that it is capable of reliably measuring problematic higher-order aberrations and is therefore a valuable asset for modern clinical eye care.

Wavefront technology: Past, present and future

After outlining what is meant by wavefront aberration, the history of the field of wavefront technology is sketched and methods for measuring ocular wavefront aberration are briefly described. The variations in aberration of the normal eye with the individual and their pupil size, accommodation and age are summarised. Potential contact lens applications are outlined, including the design and on-eye performance of single-vision lenses, lenses for presbyopes and keratoconics, orthokeratology, tear film studies, and the design and performance of customised contact lenses intended to minimise residual lens-eye wavefront error.

Double lateral shearing interferometer for the quantitative measurement of tear film topography

A lateral shearing interferometer designed and built for the study of the precorneal tear film topography dynamics and its effect on visual performance is presented. Simple data processing algorithms are discussed and tested on data illustrating different tear topography features: postblink tear undulation, tear breakup, eyelid-produced bumps and ridges, bubbles, and rough precontact lens tear surfaces.

A Test Eye for Wavefront Eye Refractors

PURPOSE

A multi-site study was conducted to test feasibility of a modified automatic refractor style test eye as a test device for wavefront refractors of various types and to determine whether a) they could be measured and b) when measurements could be made, to see if they were similar. This study did not attempt to assess which instrument most accurately measures the aberrations of the test eye or human eye.

METHODS

Three automatic refractor style test eyes were modified for use as test devices for wavefront refractors. One had a simple spherical front surface, and two had additional aberrations added. The test eyes and holder were circulated to 11 test sites where attempts were made to measure them with eight different wave-front refractor systems.

RESULTS

Eight (100%) of the eight wavefront refractor systems tested successfully measured the test eyes. The systems did not give similar results for the same test eye. In some cases, coma was reported where none was present. Differences in reported defocus values reflect different approaches for compensating for the dispersion of the eye. A corneal topography system could measure and recognize the aberrations of the test eyes as well as the wavefront refractor systems tested. Interferometry, on the other hand, did not prove to be a successful method to assess the surface of the test eyes.

CONCLUSIONS

The test eye design may be used as a test device for wavefront refractor systems. This type of test eye can detect systematic differences between various wavefront refractors and can serve as a useful calibration and comparison tool.

Study of the tear topography dynamics using a lateral shearing interferometer

The dynamics of the pre-corneal tear film topography are studied on 21 subjects with a purpose-built lateral shearing interferometer. Interesting tear topography features such as post-blink undulation, break-up, eyelid-produced bumps/ridges, bubbles and rough pre-contact lens tear surfaces were recorded. Using the calculated tear topography maps, the effects of the tear dynamics in visual performance, refractive surgery and ophthalmic adaptive optics are discussed in terms of wavefront RMS. The potential of lateral shearing interferometry for clinical applications such as dry eye diagnosis and contact lens performance studies is illustrated by the recorded topography features such as post-blink undulation, break-up, eyelid-produced bumps/ridges, bubbles and rough tear surfaces in front of contact lenses.

Accuracy and Reproducibility of Zywave, Tracey, and Experimental Aberrometers

PURPOSE

To compare the accuracy and verify the reliability of different commercial and experimental prototypes of aberrometers using a small group of normal subjects with low myopia.

METHODS

Three different devices were used to measure the wavefront aberration of five normal myopic eyes: 1) Zywave--commercial aberrometer based on a Hartmann-Shack wavefront sensor; 2) Tracey--commercial system based on the laser ray tracing principle; and 3) an experimental laboratory laser ray tracing instrument working at two different wavelengths (532 and 786 nm). A series of five measurements were taken for each subject. Pupil diameter and alignment were controlled. All wave aberration maps were reduced to a common 6.5-mm pupil diameter, and then the mean and standard deviation were computed for the series, as well as the global average and standard deviation for each subject.

RESULTS

Despite several important differences among devices and sessions, the results obtained with the different devices were equivalent. The main difference found between aberrometers was due to the longitudinal chromatic aberration caused by the use of different wavelengths. The signal-to-noise ratio estimated from the raw data was moderate, 12, but could be improved by a factor of 2 by discarding those measurements with a higher deviation from the mean and averaging the remaining data, which was the approach implemented in the Zywave instrument.

CONCLUSION

The aberrometers tested were reliable in normal eyes with low myopia. Aberrometry is a robust but noisy technique. Accuracy is limited by noise and other sources of variability, including the size and alignment of the pupil. These conclusions might not apply to eyes with large aberrations.

Variability of wavefront aberration measurements in small pupil sizes using a clinical Shack-Hartmann aberrometer

BACKGROUND

Recently, instruments for the measurement of wavefront aberration in the living human eye have been widely available for clinical applications. Despite the extensive background experience on wavefront sensing for research purposes, the information derived from such instrumentation in a clinical setting should not be considered a priori precise. We report on the variability of such an instrument at two different pupil sizes.

METHODS

A clinical aberrometer (COAS Wavefront Scienses, Ltd) based on the Shack-Hartmann principle was employed in this study. Fifty consecutive measurements were performed on each right eye of four subjects. We compared the variance of individual Zernike expansion coefficients as determined by the aberrometer with the variance of coefficients calculated using a mathematical method for scaling the expansion coefficients to reconstruct wavefront aberration for a reduced-size pupil.

RESULTS

Wavefront aberration exhibits a marked variance of the order of 0.45 microns near the edge of the pupil whereas the central part appears to be measured more consistently. Dispersion of Zernike expansion coefficients was lower when calculated by the scaling method for a pupil diameter of 3 mm as compared to the one introduced when only the central 3 mm of the Shack - Hartmann image was evaluated. Signal-to-noise ratio was lower for higher order aberrations than for low order coefficients corresponding to the sphero-cylindrical error. For each subject a number of Zernike expansion coefficients was below noise level and should not be considered trustworthy.

CONCLUSION

Wavefront aberration data used in clinical care should not be extracted from a single measurement, which represents only a static snapshot of a dynamically changing aberration pattern. This observation must be taken into account in order to prevent ambiguous conclusions in clinical practice and especially in refractive surgery.

Validation of a clinical Shack-Hartmann aberrometer

PURPOSE

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

METHOD

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

RESULTS

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

CONCLUSION

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

Hartmann-Shack technique and refraction across the horizontal visual field

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

Evaluation of refractive error measurements of the Wavescan Wavefront system and the Tracey Wavefront aberrometer

PURPOSE

To evaluate the accuracy and repeatability of the WaveScan WavePrint system and the Tracey wavefront aberrometer in measuring refractive errors in phakic eyes.

SETTING

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

METHODS

Using subjective manifest refraction (MR) as the standard, the spherical equivalent (SE), sphere, and cylinder were compared to values measured by WaveScan and Tracey devices in virgin eyes and eyes that had had corneal refractive surgery. Astigmatism was evaluated using vector analysis. The accuracy of the WaveScan and Tracey devices was assessed by 95% limits of agreement (95% LA), and repeatability was analyzed by 2 standard deviations (SDs) and intraclass correlation coefficients (ICCs).

RESULTS

The mean differences in SE, sphere, and cylinder between MR and WaveScan were -0.26 diopter (D), -0.12 D, and -0.28 D, respectively, and between MR and Tracey, -0.21 D, -0.01 D, and -0.40 D, respectively. The 95% LA for SE, sphere, and cylinder were -1.09 to 0.57 D, -1.14 to 0.89 D, and -0.95 to 0.40 D, respectively, for WaveScan and -1.37 to 0.95 D, -1.27 to 1.26 D, and -1.16 to 0.35 D, respectively, for Tracey. Vector analysis revealed mean differences of -0.47 +0.07 x 9 degrees between MR and WaveScan and of -0.53 +0.27 x 12 between MR and Tracey. The 2 SDs for SE, sphere, and cylinder were 0.26 D, 0.29 D, and 0.16 D, respectively, for WaveScan and 0.31 D, 0.36 D, and 0.33 D, respectively, for Tracey. The ICCs for SE, sphere, and cylinder were 0.993, 0.992, and 0.902, respectively, for WaveScan and 0.994, 0.992, and 0.764, respectively, for Tracey. The Tracey device measured all eyes evaluated; the WaveScan could not measure 14% of normal eyes and 50% of post laser in situ keratomileusis eyes.

CONCLUSIONS

Using MR as the standard, refractive errors measured by the WaveScan and Tracey devices were reliable and reproducible. However, the Tracey device was more robust in its ability to obtain measurements in normal and postoperative eyes.

Repeatability of ocular wavefront measurement

PURPOSE

To assess the repeatability of measurements of ocular aberrations using wavefront sensing in a small group of observers and to assess the potential effect of measurement error on custom corneal correction due to this variability.

METHOD

A Shack-Hartmann wavefront sensor was used to measure the ocular wavefront in nine eyes. Head position was stabilized using a dental bite bar, and the pupil was centred using a cathode ray tube monitor and circular grating. Twenty Shack-Hartmann images were collected for each measurement. Each observer had three sets of measurements taken; the first and the second after careful alignment and the final after regrasping the bite bar in the same position as for the second measurement, but without pupil realignment. The modulation transfer functions for each set were calculated, and the effect of best-aligned custom treatments on the modulation transfer function was estimated.

RESULTS

There were highly statistically significant differences in a large number of Zernike modes between the three sets of measurements. The modulation transfer functions calculated for the residual wavefronts after aligned custom treatment were below the diffraction limit. The root mean square wavefront errors were consistently better for the residual wavefronts obtained using the realigned data than using data taken without pupil realignment.

CONCLUSIONS

Sequential measurement of ocular aberrations shows statistically significant differences in a large number of Zernike modes. If aberrations determined by a single measurement are to be used in a custom correction, the resulting modulation transfer function is likely to remain below the diffraction limit. Pupil realignment is critical in reduction of the residual root mean square wavefront values to a minimum.

Measurement of refractive errors in young myopes using the COAS Shack-Hartmann aberrometer

PURPOSE

To evaluate the Complete Ophthalmic Analysis System (COAS; WaveFront Science) for accuracy, repeatability, and instrument myopia when measuring myopic refractive errors.

METHODS

We measured the refractive errors of 20 myopic subjects (+0.25 to -10 D sphere; 0 to -1.75 D cylinder) with a COAS, a phoropter, and a Nidek ARK-2000 autorefractor. Measurements were made for right and left eyes, with and without cycloplegia, and data were analyzed for large and small pupils. We used the phoropter refraction as our estimate of the true refractive error, so accuracy was defined as the difference between phoropter refraction and that of the COAS and autorefractor. Differences and means were computed using power vectors, and accuracy was summarized in terms of mean vector and mean spherocylindrical power errors. To assess repeatability, we computed the mean vector deviation for each of five measurements from the mean power vector and computed a coefficient of repeatability. Instrument myopia was defined as the difference between cycloplegic and noncycloplegic refractions for the same eyes.

RESULTS

Without cycloplegia, both the COAS and autorefractor had mean power vector errors of 0.3 to 0.4 D. Cycloplegia improved autorefractor accuracy by 0.1 D, but COAS accuracy remained the same. For large pupils, COAS accuracy was best when Zernike mode Z4(0) (primary spherical aberration) was included in the computation of sphere power. COAS repeatability was slightly better than autorefraction repeatability. Mean instrument myopia for the COAS was not significantly different from zero.

CONCLUSIONS

When measuring myopes, COAS accuracy, repeatability, and instrument myopia were similar to those of the autorefractor. Error margins for both were better than the accuracy of subjective refraction. We conclude that in addition to its capability to measure higher-order aberrations, the COAS can be used as a reliable, accurate autorefractor.

Relationship between refractive error and monochromatic aberrations of the eye

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Comparison of monochromatic ocular aberrations measured with an objective cross-cylinder aberroscope and a Shack-Hartmann aberrometer

Repeated measures of wavefront aberrations were taken along the line-of-sight of seven eyes using two instruments: an objective, cross-cylinder aberroscope (OA) and a Shack-Hartmann (SH) aberrometer. Both instruments were implemented on the same optical table to facilitate interleaved measurements on the same eyes under similar experimental conditions. Variability of repeated measures of individual coefficients tended to be much greater for OA data than for SH data. Although Zernike coefficients obtained from a single measurement were generally larger when measured with the OA than with the SH, the averages across five trials were often smaller for the OA. The Zernike coefficients obtained from the two instruments were not significantly correlated. Radial modulation-transfer functions and point-spread functions derived from the two sets of measurements were similar for some subjects, but not all. When average Zernike coefficients were used to determine optical quality, the OA indicated superior optics in some eyes, but the reverse trend was true if Zernike coefficients from individual trials were used. Possible reasons for discrepancies between the OA and SH measurements include difference in sampling density, quality of data images, alignment errors, and temporal fluctuations. Multivariate statistical analysis indicated that the SH aberrometer discriminated between subjects much better than did the objective aberroscope.

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

A Shack-Hartmann aberrometer was used to measure the monochromatic aberration structure along the primary line of sight of 200 cyclopleged, normal, healthy eyes from 100 individuals. Sphero-cylindrical refractive errors were corrected with ophthalmic spectacle lenses based on the results of a subjective refraction performed immediately prior to experimentation. Zernike expansions of the experimental wave-front aberration functions were used to determine aberration coefficients for a series of pupil diameters. The residual Zernike coefficients for defocus were not zero but varied systematically with pupil diameter and with the Zernike coefficient for spherical aberration in a way that maximizes visual acuity. We infer from these results that subjective best focus occurs when the area of the central, aberration-free region of the pupil is maximized. We found that the population averages of Zernike coefficients were nearly zero for all of the higher-order modes except spherical aberration. This result indicates that a hypothetical average eye representing the central tendency of the population is nearly free of aberrations, suggesting the possible influence of an emmetropization process or evolutionary pressure. However, for any individual eye the aberration coefficients were rarely zero for any Zernike mode. To first approximation, wave-front error fell exponentially with Zernike order and increased linearly with pupil area. On average, the total wave-front variance produced by higher-order aberrations was less than the wave-front variance of residual defocus and astigmatism. For example, the average amount of higher-order aberrations present for a 7.5-mm pupil was equivalent to the wave-front error produced by less than 1/4 diopter (D) of defocus. The largest pupil for which an eye may be considered diffraction-limited was 1.22 mm on average. Correlation of aberrations from the left and right eyes indicated the presence of significant bilateral symmetry. No evidence was found of a universal anatomical feature responsible for third-order optical aberrations. Using the Marechal criterion, we conclude that correction of the 12 largest principal components, or 14 largest Zernike modes, would be required to achieve diffraction-limited performance on average for a 6-mm pupil. Different methods of computing population averages provided upper and lower limits to the mean optical transfer function and mean point-spread function for our population of eyes.