Effect of rotation and translation on the expected benefit of an ideal method to correct the eye's higher-order aberrations

Treatment-induced shifts of ocular reference axes used for measurement centration

PURPOSE

To determine the shifts of the main corneal reference points in dependence of the chosen centration axis for the treatment.

SETTING

Federal Institute of Technology Zurich, Institute of Biomedical Engineering, Zurich, Switzerland.

METHODS

Computer simulations were performed on several variants of the Gullstrand-Emsley schematic eye, which was modified by an off-axis fovea. Refractive corrections were simulated by centering Munnerlyn's formula on each of the 4 corneal reference points determined in the preoperative eye: the optical axis, the line of sight, the visual axis, and the first corneal reflex. Subsequently, the postoperative locations of these axes were determined and compared with the preoperative values.

RESULTS

The postoperative line of sight was found to depend least on the choice of the preoperative centration axis for both myopic and hyperopic treatments. It undergoes a maximum movement of 0.040 mm when centering a +5 diopter correction on the preoperative line of sight, whereas the corneal reflex, which is used for centering most topography systems, can move by more than 0.10 mm.

CONCLUSIONS

Centration of the correction on the preoperative line of sight enabled good comparability between preoperative and postoperative measurements that use the line of sight as a reference axis. Yet, centration of the treatment on the preoperative line of sight does not ensure comparability between preoperative and postoperative measurements that use the corneal reflex as a reference axis such as most corneal topography systems. Axis shifts might lead to misinterpretation of data such as a wrong diagnosis of a decentered ablation or changes in the Zernike representation.

Aberrations induced in wavefront-guided laser refractive surgery due to shifts between natural and dilated pupil center locations

PURPOSE

To determine the aberrations induced in wavefront-guided laser refractive surgery due to shifts in pupil center location from when aberrations are measured preoperatively (over a dilated pupil) to when they are corrected surgically (over a natural pupil).

SETTING

Center for Visual Science and Department of Ophthalmology, University of Rochester, Rochester, New York, USA.

METHODS

Shifts in pupil center were measured between dilated phenylephrine hydrochloride (Neo-Synephrine [2.5%]) and nonpharmacological mesopic conditions in 65 myopic eyes treated with wavefront-guided laser in situ keratomileusis (Technolas 217z, Bausch & Lomb). Each patient's preoperative and 6-month postoperative wave aberrations were measured over the dilated pupil. Aberrations theoretically induced by decentration of a wavefront-guided ablation were calculated and compared with those measured 6 months postoperatively (6.0 mm pupil).

RESULTS

The mean magnitude of pupil center shift was 0.29 mm +/- 0.141 (SD) and usually occurred in the inferonasal direction as the pupil dilated. Depending on the magnitude of shift, the fraction of the higher-order postoperative root-mean-square wavefront error that could be due theoretically to pupil center decentrations was highly variable (mean 0.26 +/- 0.20 mm). There was little correlation between the calculated and 6-month postoperative wavefronts, most likely because pupil center decentrations are only 1 of several potential sources of postoperative aberrations.

CONCLUSIONS

Measuring aberrations over a Neo-Synephrine-dilated pupil and treating them over an undilated pupil typically resulted in a shift of the wavefront-guided ablation in the superotemporal direction and an induction of higher-order aberrations. Methods referencing the aberration measurement and treatment with respect to a fixed feature on the eye will reduce the potential for inducing aberrations due to shifts in pupil center.

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.

Iris-Based Cyclotorsional Image Alignment Method for Wavefront Registration

In refractive surgery, especially wavefront-guided refractive surgery, correct registration of the treatment to the cornea is of paramount importance. The specificity of the custom ablation formula requires that the ablation be applied to the cornea only when it has been precisely aligned with the mapped area. If, however, the eye has rotated between measurement and ablation, and this cyclotorsion is not compensated for, the rotational misalignment could impair the effectiveness of the refractive surgery. To achieve precise registration, a noninvasive method for torsional rotational alignment of the captured wavefront image to the patient's eyes at surgery has been developed. This method applies a common coordinate system to the wavefront and the eye. Video cameras on the laser and wavefront devices precisely establish the spatial relationship between the optics of the eye and the natural features of the iris, enabling the surgeon to identify and compensate for cyclotorsional eye motion, whatever its cause.

Generalized ray-transfer matrix for an optical element having an arbitrary wavefront aberration

A generalized ray-transfer matrix for describing the action of an optical element having an arbitrary wavefront aberration is obtained. In this generalized ray-transfer matrix, the action of the aberrated optical element is represented by the product of radial ray-transfer matrices and tangential ray-transfer matrices. The refraction angle of an incident ray is calculated from the gradient of the wavefront aberration at the point of incidence, and the radial and tangential ray-transfer matrices directly use the gradient as a matrix component. To show the validity of the generalized ray-transfer matrix, intercept heights from a spot diagram are calculated with the generalized ray-transfer matrix and compared with those calculated with commercial ray-tracing software.

Design and fabrication of a freeform phase plate for high-order ocular aberration correction

In recent years it has become possible to measure and in some instances to correct the high-order aberrations of human eyes. We have investigated the correction of wavefront error of human eyes by using phase plates designed to compensate for that error. The wavefront aberrations of the four eyes of two subjects were experimentally determined, and compensating phase plates were machined with an ultraprecision diamond-turning machine equipped with four independent axes. A slow-tool servo freeform trajectory was developed for the machine tool path. The machined phase-correction plates were measured and compared with the original design values to validate the process. The position of the phase-plate relative to the pupil is discussed. The practical utility of this mode of aberration correction was investigated with visual acuity testing. The results are consistent with the potential benefit of aberration correction but also underscore the critical positioning requirements of this mode of aberration correction. This process is described in detail from optical measurements, through machining process design and development, to final results.

Surgeon offsets and dynamic eye movements in laser refractive surgery

PURPOSE

To determine the amount of static and dynamic pupil decentrations that occur during laser refractive surgery.

SETTING

The Center of Visual Science and the Department of Ophthalmology, University of Rochester, Rochester, New York, USA.

METHODS

The surgeon's accuracy in aligning the pupil center with the laser center axis was measured when engaging the eye-tracker in 17 eyes receiving conventional laser in situ keratomileusis (LASIK) procedures (Technolas 217z; Bausch & Lomb). Eye movements were measured subsequently during the treatment in 10 eyes using a pupil camera operating at 50 Hz. Temporal power spectra were calculated from the eye movement measurements.

RESULTS

The mean pupil misalignment by the surgeon at the beginning of the procedure was 206.1 microm +/- 80.99 (SD) (with respect to the laser center). The laser center was typically misaligned below (inferiorly) and to the left (nasally and temporally in left and right eyes, respectively) of the pupil [corrected] center. Small amounts of cyclotorsion were observed during the ablation (<2 degrees). The mean magnitude of dynamic pupil decentration from the laser center during treatment was 227.0 +/- 44.07 microm. The mean standard deviation of eye movements was 65.7 +/- 25.64 microm. Temporal power spectra calculated from the horizontal and vertical changes in eye position during the ablation were similar. Ninety-five percent of the total power of the eye movements was contained in temporal frequencies up to 1 Hz, on average, in both directions.

CONCLUSIONS

Most eye movements during LASIK are slow drifts in fixation. An eye-tracker with a 1.4 Hz closed-loop bandwidth could compensate for most eye movements in conventional or customized ablations.

Ocular Cyclotorsion During Customized Laser Ablation

PURPOSE

To compare the measured difference and degree of cyclotorsion in eyes undergoing customized laser ablation between the time of wavefront measurement and laser refractive surgery.

METHODS

The degree of cyclotorsion was measured in 1019 consecutive eyes of 732 patients who underwent wavefront-guided corneal ablation for the treatment of myopia with or without astigmatism with the Alcon LADARVision excimer laser. Prior to obtaining the wavefront measurement, the horizontal axis of each eye was marked. Cyclotorsional alignment was measured on the supine patient prior to beginning the laser.

RESULTS

The predominant trend was for excyclotorsion. The total range of torsion in degrees was 0.5 degrees to 17.5 degrees (mean: 4.05 +/- 2.9 degrees). Cyclotorsion > 2 degrees occurred in 68% of all eyes. In the right eyes, 83% excyclotorted, 14% incyclotorted, and 3% displayed no torsion. In the left eyes, 62% excyclotorted, 34% incyclotorted, and 4% exhibited no torsion. In a subset of 112 patients undergoing simultaneous bilateral surgery, 46% displayed bilateral excyclotorsion and 1.7% displayed bilateral incyclotorsion.

CONCLUSIONS

In this study, the majority of eyes had a low to moderate amount of cyclotorsion observed with the change of orientation from seated to supine position. Excyclotorsion was the predominant pattern. Proper registration prior to wavefront-guided corneal ablation is essential for proper correction of astigmatism and higher order aberrations to achieve optimal visual outcomes.

Changes in Wavefront Aberration With Pharmaceutical Dilating Agents

PURPOSE

Finding the best way to capture the wavefronts of small pupils for refractive surgery has become a more pressing issue as the general population ages. This study explores whether pharmaceutical dilation impacts wavefront measurement and pupil centroid.

METHODS

Baseline measurements were performed on 32 eyes using the VISX WaveScan Wavefront system. Pupils were dark adapted. One drop of 0.05% tropicamide was placed in each eye, and wavefront measurements were conducted at 10, 20, and 30 minutes. One drop each of 0.5% tropicamide and 2.5% phenylephrine were administered after the measurements. Wavefronts were captured again 30 minutes after the last eye drop. All patients returned for repeated procedures. Wavefront analysis was performed using the same pupillary area as the smallest capture from the same visit. Pupil center shift was taken into account.

RESULTS

Mean patient age was 40 +/- 12 years (range: 20 to 59 years). Mean dark-adapted pupil was 6.40 +/- 1.17 mm. Pupil centers shifted randomly after pharmacological dilation compared to the dark-adapted condition. Pupil centers of 45% of the population shifted by > or = 0.2 mm. Repeatability coefficients were established for the wavefront measurements. After controlling for pupil diameter and pupil center, total high order aberrations root-mean-square (RMS) had changed significantly in 18% of the population. The diluted tropicamide formula, which caused less dilation effect, also induced less high order aberration RMS change.

CONCLUSIONS

Pharmaceutical dilation agents cause random shifts of the pupil centroid from the dark-adapted pupil condition and could induce changes in wavefront measurements. Caution is required when resorting to dilation to obtain a wavefront measurement of smaller pupils.

From Wavefront Device to Laser: An Alignment Method for Complete Registration of the Ablation to the Cornea

PURPOSE

When customized laser refractive surgery is based on a wavefront measurement, correct registration of the laser ablation to the prescribed treatment area is vital. If the treatment is not ablated exactly where it was measured, the error could negate some benefits of the procedure. Currently, treatments are aligned to the pupil center, which has been shown to shift between measurement and treatment. This article describes an alignment method that uses an image-based coordinate system to compensate for shifts of the pupil center as well as cyclorotation.

METHODS

Images of patients' eyes were taken during wavefront measurements and again when patients were in position for surgery. An image-processing method, which matches multiple ocular landmarks in both image sets, was used to align the laser beam to the ablation target.

RESULTS

Analyses of the data collected from both instruments suggest that alignment errors caused by movement of the pupil center and cyclorotation could be significantly reduced by using the proposed alignment method.

CONCLUSIONS

Because the pupil center undergoes significant movement with changes in lighting conditions, it is unsuitable as the sole alignment point for custom ablations. Several reference points are necessary to compensate for changing pupil size as well as the cyclotorsional eye position changes that occur between wavefront measurement and laser procedure. By providing multiple points for alignment, the registration method described herein increases safety and effectiveness of wavefront-based laser vision correction.

Variable aberration generators using rotated Zernike plates

The rotational properties of Zernike polynomials allow for an easy generation of variable amounts of aberration using two rotated phase plates, each one encoding one or several Zernike modes. This effect may be used to build variable aberration generators useful for calibrating different kinds of aberrometer.

Cyclotorsional eye movements during a simulated PRK procedure

PURPOSE

Eye alignment is a serious concern when performing corneal surface ablation. Although several excimer lasers monitor horizontal and vertical movements, little is known about the potential impact of cyclotorsional movements. Dynamic cyclotorsions have been measured on 10 emmetropic subjects during a simulated PRK treatment.

METHODS

Cyclotorsional eye movements were measured using a 3D videoculographic system (SMI) in 10 emmetropic subjects in upright and supine position. The subjects were wearing an eyelid speculum and were asked to fixate on a 1 degrees red spot. The fixation target was either in focus or optically degraded by electronic filters. Data were collected at the University Eye Clinic, Torino, Italy, and the different setting measurements were compared using Student's t-test for paired data.

RESULTS

Cyclotorsions were significantly higher when subjects were fixating an optically degraded stimulus (upright: P=0.04; supine: P=0.0002). The cyclotorsional movements ranged from -13 to 17 degrees. A significant difference in eye orientation was present when changing from the upright to the supine position (P=0.03). Even when correcting for this positional error, significantly higher cyclotorsional movements were detected in the supine position (in focus: P=0.0043; optically degraded: P=0.0008). The torsional range was from -14.85 to 14.55 degrees.

CONCLUSIONS

The high range of cyclotorsional eye movements during a simulated PRK procedure suggests that 3D tracking could improve surface ablation results when treating high astigmatism or when wavefront guided.

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.

Simulation of Eye-tracker Latency, Spot Size, and Ablation Pulse Depth on the Correction of Higher Order Wavefront Aberrations With Scanning Spot Laser Systems

PURPOSE

The aim of this theoretical work was to investigate the robustness of scanning spot laser treatments with different laser spot diameters and peak ablation depths in case of incomplete compensation of eye movements due to eye-tracker latency.

METHODS

Scanning spot corrections of 3rd to 5th Zernike order wavefront errors were numerically simulated. Measured eye-movement data were used to calculate the positioning error of each laser shot assuming eye-tracker latencies of 0, 5, 30, and 100 ms, and for the case of no eye tracking. The single spot ablation depth ranged from 0.25 to 1.0 microm and the spot diameter from 250 to 1000 microm. The quality of the ablation was rated by the postoperative surface variance and the Strehl intensity ratio, which was calculated after a low-pass filter was applied to simulate epithelial surface smoothing.

RESULTS

Treatments performed with nearly ideal eye tracking (latency approximately 0) provide the best results with a small laser spot (0.25 mm) and a small ablation depth (250 microm). However, combinations of a large spot diameter (1000 microm) and a small ablation depth per pulse (0.25 microm) yield the better results for latencies above a certain threshold to be determined specifically. Treatments performed with tracker latencies in the order of 100 ms yield similar results as treatments done completely without eye-movement compensation. CONCWSIONS: Reduction of spot diameter was shown to make the correction more susceptible to eye movement induced error. A smaller spot size is only beneficial when eye movement is neutralized with a tracking system with a latency <5 ms.

Stroke amplifier for deformable mirrors

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

Alignment in Customized Laser in situ Keratomileusis

PURPOSE

To identify fundamentals of beam alignment in customized laser in situ keratomileusis (LASIK) with a special focus on the Nidek NAVEX system.

METHODS

Analysis of Nidek specifications and recommendations for beam alignment with regard to a critical case example are presented. The potential impact of misalignment (tilt and defocus) is calculated. Cyclotorsional error evaluation in a normal LASIK population was performed by video image comparison. Potential problems of infrared-based eyetracking systems are discussed.

RESULTS

The laser beam should be aligned with reference to the line of sight (LOS) when customized segmental laser ablation is applied. Only in cases with significant offset between the LOS and the visual axis it is recommended not to use segmental ablation and to manually align the beam toward the visual axis. Eye drift (tilt) as well as defocus should be avoided since undercorrection and irregular astigmatism can result. Almost 30% of eyes in a normal LASIK population showed a torsional error of 5 degrees to 10 degrees (9% more than 10 degrees) on video-based image comparison. Eye-trackers not only are defined by take-up speed and latency, but also by their sensibility (picking the real center of the pupil) and robustness (keeping it tracked during surgery). Errors due to parallax and reflex effects can systematically influence the performance of an eyetracker.

CONCLUSION

Correct alignment is difficult to achieve but is of fundamental importance in customized LASIK. Strict standardization and further improvement in the alignment strategy is necessary to achieve more consistent results in customized LASIK.

Wavefront-customized intraocular lenses

PURPOSE OF REVIEW

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

RECENT FINDINGS

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

SUMMARY

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

Limitations of Pupil Tracking in Refractive Surgery: Systematic Error in Determination of Corneal Locations

PURPOSE

The goal of this investigation was to show the theoretical limitations of pupil tracking in refractive surgery. The parallax error associated with localizing corneal positions by tracking the subjacent entrance pupil center was quantified.

METHODS

Optical ray-tracing in a schematic model eye was performed to determine the geometric parallax error. The calculations required several assumptions regarding ocular geometry, eye movements, and eye tracker position. Various parameter combinations were evaluated to assess the potential range of error to be expected in clinical practice.

RESULTS

Tracking error can amount to 30% (or more for eye trackers mounted closer than 500 mm to the eye) of the detected lateral shift. Thus, if the eye tracker registers a lateral shift of the entrance pupil of 0.2 mm away from the tracking reference axis, the point of interest located on the cornea would essentially be 0.26 mm away from this reference axis. A laser pulse fired at that moment would be systematically displaced by 60 microm. Our results depended on geometric parameters of the eye and the tracking device. Based on conservative assumptions regarding these geometric parameters, partial compensation could be realized by adding a certain percentage to the modulus of each eye tracker reading.

CONCLUSIONS

The fact that corneal displacement was generally underestimated by up to 30% of the measured entrance pupil shift demonstrates the severity of the parallax effect.

Validation of a combined corneal topographer and aberrometer based on Shack-Hartmann wave-front sensing

A corneal aberrometer based on Shack-Hartmann wave-front sensing was developed and validated by using calibrated aspheric surfaces. The aberrometer was found to accurately measure corneal reflective aberrations, from which corneal topography and corneal refractive aberrations were derived. Measurements of reflective aberrations correlated well with theory (R2 = 0.964 to 0.994). The sag error root mean square (RMS) was small, ranging from 0.1 to 0.17 microm for four of the five calibrated surfaces with the fifth at 0.36 microm as a result of residual defocus. Measured refractive aberrations matched with theory and whole-eye aberrometry to within a small fraction of a wavelength. Measurements on three human corneas revealed very large refractive astigmatism (0.65-1.2 microm) and appreciable levels of trefoil (0.08-0.47 microm), coma (0.14-0.19 microm), and spherical aberration (0.18-0.25 microm). The mean values of these aberrations were significantly larger than the RMS in repeated measurements.

Wavefront-optimized ablation profiles

PURPOSE

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

SETTING

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Cyclotorsional eye motion occurring between wavefront measurement and refractive surgery

PURPOSE

To quantify the cyclorotation occurring between wavefront measurement and laser refractive surgery.

SETTING

LaserVue Eye Center Ophthalmic Clinic, Santa Rosa, California, USA.

METHODS

The pupil camera of the Visx WaveScan wavefront device was used to obtain images of 51 eyes (26 patients) from 5 to 20 minutes before refractive laser surgery. Additionally, an infrared camera was mounted on the Visx Star S3 ActiveTrak excimer laser system to obtain another image immediately before the laser was fired. After surgery, the 2 sets of images were compared to determine the amount of cyclotorsion between the measurement and surgery.

RESULTS

Cyclorotation of individual eyes was as high as 9.5 degrees. The mean was approximately 2.0 degrees for each eye. Binocular excyclotorsion was the predominant trend, affecting 19 of 24 patients.

CONCLUSIONS

A low to moderate amount of cyclotorsion was observed in the transition from seated to supine position. Comparison of eye position at the time of measurement to eye position at the time of surgery can be used to adjust the laser ablation algorithm to compensate for this rotational displacement.

Maximum permissible torsional misalignment in aberration-sensing and wavefront-guided corneal ablation

PURPOSE

To determine the maximum permissible torsional misalignment in wavefront-guided refractive surgery.

SETTING

University of Zurich, Department of Ophthalmology, Zurich, Switzerland.

METHODS

The effect of torsionally misaligned ablations on the optical outcome was simulated using measured wavefront aberration patterns (2nd to 6th orders) in 130 normally aberrated eyes. The calculations were done for 3.0 mm, 5.0 mm, and 7.0 mm pupils. The optical quality of the simulated correction was rated by the root-mean-square residual wavefront error.

RESULTS

The required accuracy of torsional alignment is higher for the correction of higher-order aberrations than for cylindrical treatments only. To improve the optical performance to the level of the best 10% of a normal, untreated population, ablation would have to occur within a tolerance range of 4.0 degrees for 7.0 mm pupils.

CONCLUSIONS

The tolerance range for torisional alignment in wavefront-guided higher-order corrections depends on the amount of original optical error in each eye. Rough centration based on the surgeon's judgment may not be accurate enough to achieve significantly improved optical quality in a high percentage of treated eyes.

Simulated optical performance of custom wavefront soft contact lenses for keratoconus

PURPOSE

Outstanding improvements in vision can theoretically be expected using contact lenses that correct monochromatic aberrations of the eye. Imperfections in such correction inherent to contact lenses are lens flexure, translation, rotation, and tear layer effects. The effects of pupil size and accommodation on ocular aberration may cause further difficulties. The purpose of this study was to evaluate whether nonaxisymmetric soft contact lenses could efficiently compensate for higher-order aberrations induced by keratoconus and to what extent rotation and translation of the lens would degrade this perfect correction.

METHODS

Height topography data of nine moderate to severe keratoconus corneas were obtained using the Maastricht Shape Topographer. Three-dimensional ray tracing was applied to each elevation topography to calculate aberrations in the form of a phase error mapping. The effect of a nonaxisymmetric soft contact lens tailored to the corneal aberrations was simulated by adding an opposite phase error mapping that would theoretically compensate all corneal-induced optical aberrations of the keratoconus eyes. Translation (0.25, 0.5, 0.75, and 1.0 mm) and rotation (2.5 degrees, 5.0 degrees, 7.5 degrees, and 10 degrees ) mismatches were introduced. The modulation transfer function (MTF) of each eye with each displaced correction and with various pupil sizes (3, 5, and 7 mm) was deduced from the residual phase error mapping. A single performance criterion (mtfA) was calculated as the area under the MTF over a limited spatial frequency range (5 to 15 periods per degree). Finally, the ratio (RmtfA) of corrected mtfA over uncorrected mtfA provided an estimate of the global enhancement in contrast sensitivity with the customized lens.

RESULTS

The contrast improvement ratios RmtfA with perfectly located lenses were for an average pupil size of 4.5 mm between 6.5 and 200. For small translation errors (0.25 mm), RmtfA ranged between 2 and 7. The largest lens translation tested (1 mm) often resulted in poorer performance than without correction (RmtfA <1). More than threefold improvements were achieved with any of the angular errors experimented. RmtfA values showed significant variations for pupil diameters between 3 and 7 mm.

CONCLUSIONS

Three-dimensional aberration-customized soft contact lenses may drastically improve visual performance in patients with keratoconus. However, such lenses should be well positioned on the cornea. In particular, translation errors should not exceed 0.5 mm. Angular errors appeared to be less critical. It is further questioned whether the visual system is able to adapt to variations in optical performance of the correction in situ due to lens positioning and pupil size.

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

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

System for the design, manufacture, and testing of custom lenses with known amounts of high-order aberrations

Now that excimer laser systems can be programmed to correct complex aberrations of the eye on the basis of wave-front measurements, a method is needed to test the accuracy of the system from measurement through treatment. A closed-loop test method was developed to ensure that treatment plans generated by a wavefront measuring system were accurately transferred to and executed by the excimer laser. A surface was analytically defined, and a Shack-Hartmann-based wave-front system was used to formulate a treatment plan, which was downloaded to an excimer laser system. A plastic lens was ablated by the laser and then returned to the wave-front device, where it was measured and compared with the analytically defined wave-front surface. The two surfaces agreed up to 6th-order Zernike terms, validating the accuracy of the system.

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.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Simplified mathematics for customized refractive surgery

PURPOSE

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

SETTING

University eye hospital, Mainz, Germany.

METHODS

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

RESULTS

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

CONCLUSIONS

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

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.

Maximum permissible lateral decentration in aberration-sensing and wavefront-guided corneal ablation

PURPOSE

To investigate the lateral alignment accuracy needed in wavefront-guided refractive surgery to improve the ocular optics to a desired level in a percentage of normally aberrated eyes.

SETTING

Department of Ophthalmology, University of Zurich, Zurich, Switzerland.

METHODS

The effect of laterally misaligned ablations on the optical outcome was simulated using measured wavefront aberration patterns from 130 normal eyes. The calculations were done for 3.0 mm, 5.0 mm, and 7.0 mm pupils. The optical quality of the simulated correction was rated by means of the root-mean-square residual wavefront error.

RESULTS

To achieve the diffraction limit in 95% of the normal eyes with a 7.0 mm pupil, a lateral alignment accuracy of 0.07 mm or better was required. An accuracy of 0.2 mm was sufficient to reach the same goal with a 3.0 mm pupil.

CONCLUSION

Procedures must be developed to ensure that the ablation is within a tolerance range based on each eye's original optical error. Rough centration based on the surgeon's judgment might not be accurate enough to achieve significantly improved optical quality in a high percentage of treated eyes.

Aberration Generation by Contact Lenses With Aspheric and Asymmetric Surfaces

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

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

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

Spherical and irregular aberrations are important for the optimal performance of the human eye

Contrast sensitivity measured psychophysically at different levels of defocus can be used to evaluate the eye optics. Possible parameters of spherical and irregular aberrations, e.g. relative modulation transfer (RMT), myopic shift, and depth of focus, can be determined from these measurements. The present paper compares measured results of RMT, myopic shift, and depth of focus with the theoretical results found in the two eye models described by Jansonius and Kooijman (1998). The RMT data in the present study agree with those found in other studies, e.g. Campbell and Green (1965) and Jansonius and Kooijman (1997). A new theoretical eye model using a spherical aberration intermediate between those of the eye models described by Jansonius and Kooijman (1998) and an irregular aberration with a typical S.D. of 0.3-0.5 D could adequately explain the measured RMT, myopic shift, and depth of focus data. Both spherical and irregular aberrations increased the depth of focus, but decreased the modulation transfer (MT) at high spatial frequencies at optimum focus. These aberrations, therefore, play an important role in the balance between acuity and depth of focus.

Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes

We calculated the impact of higher-order aberrations on retinal image quality and the magnitude of the visual benefit expected from their correction in a large population of human eyes. Wave aberrations for both eyes of 109 normal subjects and 4 keratoconic patients were measured for 3-, 4-, and 5.7-mm pupils with a Shack-Hartmann sensor. Retinal image quality was estimated by means of the modulation transfer function (MTF) in white light. The visual benefit was calculated as the ratio of the MTF when the monochromatic higher-order aberrations are corrected to the MTF corresponding to the best correction of defocus and astigmatism. On average, the impact of the higher-order aberrations for a 5.7-mm pupil in normal eyes is similar to an equivalent defocus of approximately 0.3 D. The average visual benefit for normal eyes at 16 c/deg is approximately 2.5 for a 5.7-mm pupil and is negligible for small pupils (1.25 for a 3-mm pupil). The benefit varies greatly among eyes, with some normal eyes showing almost no benefit and others a benefit higher than 4 at 16 c/deg across a 5.7-mm pupil. The benefit for keratoconic eyes is much larger. The benefit at 16 c/deg is 12 and 3 for 5.7- and 3-mm pupils, respectively, averaged across four keratoconics. These theoretical benefits could be realized in normal viewing conditions but only under specific conditions.

Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes

We calculated the impact of higher-order aberrations on retinal image quality and the magnitude of the visual benefit expected from their correction in a large population of human eyes. Wave aberrations for both eyes of 109 normal subjects and 4 keratoconic patients were measured for 3-, 4-, and 5.7-mm pupils with a Shack-Hartmann sensor. Retinal image quality was estimated by means of the modulation transfer function (MTF) in white light. The visual benefit was calculated as the ratio of the MTF when the monochromatic higher-order aberrations are corrected to the MTF corresponding to the best correction of defocus and astigmatism. On average, the impact of the higher-order aberrations for a 5.7-mm pupil in normal eyes is similar to an equivalent defocus of approximately 0.3 D. The average visual benefit for normal eyes at 16 c/deg is approximately 2.5 for a 5.7-mm pupil and is negligible for small pupils (1.25 for a 3-mm pupil). The benefit varies greatly among eyes, with some normal eyes showing almost no benefit and others a benefit higher than 4 at 16 c/deg across a 5.7-mm pupil. The benefit for keratoconic eyes is much larger. The benefit at 16 c/deg is 12 and 3 for 5.7- and 3-mm pupils, respectively, averaged across four keratoconics. These theoretical benefits could be realized in normal viewing conditions but only under specific conditions.

Method for optimizing the correction of the eye's higher-order aberrations in the presence of decentrations

The use of a correcting element to compensate for higher-order aberrations in an optical system often requires accurate alignment of the correcting element. This is not always possible, as in the case of a contact lens on the eye. We propose a method consisting of partial correction of every aberration term to minimize the average variance of the residual wave-front aberration produced by Gaussian decentrations (translations and rotations). Analytical expressions to estimate the fraction of every aberration term that should be corrected for a given amount of decentration are derived. To demonstrate the application of this method, three examples are used to compare performance with total and with partial correction. The partial correction is more robust and always yields some benefit regardless of the amount of decentration.

On-eye evaluation of optical performance of rigid and soft contact lenses

A Shack-Hartmann aberrometer was used to assess the optical performances of eyes corrected with rigid or soft contact lenses compared with spectacles. Metrics of optical quality derived from the measured wave aberrations were consistent with the subjective rating of visual clarity by subjects. Optical aberration analysis illustrated the differences in aberration structures of eyes wearing different optical corrections. For our subjects, correction with a rigid gas-permeable lens yielded significantly better optical quality than did the soft contact lens or spectacle lens. This was due to a reduction in the eye's asymmetric (odd-order) aberrations and a reduction in the amount of the eye's positive spherical aberration. These observations can be explained by theoretical calculations of the aberrations of the eye plus lens optical system. We conclude that aberrometry provides a better understanding of the optical effects of contact lenses in situ and could be useful for optimizing future designs of contact lenses.