Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor

Adaptive optics for studying visual function: a comprehensive review

Compared to most ophthalmic technologies, adaptive optics, or AO, is relatively young. The first working systems were presented in 1997 and, owing in part to its complexity, the development of AO systems has been relatively slow. Nevertheless, AO for vision science is coming of age and the scope of applications continues to increase. Applications of AO can be broadly split along two lines; for retinal imaging and for testing visual function. This review will focus on the applications of adaptive optics for testing visual function. Since this represents only a subset of the field of AO for ophthalmoscopy, it is possible to cite virtually every paper that has been published in the field to date. As such, this is a comprehensive review whose intent is to get all readers up to speed on the state of the art. More importantly, perhaps, this review will focus on the types of science that can be accomplished with AO with a view to future applications. The reference list alone is informative, since the reader will quickly discover that the community that is using AO for vision science is rather small. Looking at the dates for the cited papers, the reader will also discover that the field is rapidly expanding.

Imaging single cells in the living retina

A quarter century ago, we were limited to a macroscopic view of the retina inside the living eye. Since then, new imaging technologies, including confocal scanning laser ophthalmoscopy, optical coherence tomography, and adaptive optics fundus imaging, transformed the eye into a microscope in which individual cells can now be resolved noninvasively. These technologies have enabled a wide range of studies of the retina that were previously impossible.

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

PURPOSE

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

MATERIALS AND METHODS

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

RESULTS

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

CONCLUSION

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

Neural contrast sensitivity calculated from measured total contrast sensitivity and modulation transfer function

PURPOSE

To test the feasibility of calculating neural contrast sensitivity function (neural CSF) from conventionally measured total contrast sensitivity function (total CSF) and measured modulation transfer function (MTF). Neural CSF considers the retina and the brain, whereas total CSF considers the optical eye media, the retina and the brain together.

METHODS

We studied three groups comprising nine eyes each: one group with normal ocular optics but retinal alterations (mild diabetic retinopathy), one with altered ocular optics and normal retina (keratoconus), and a normal control group.

RESULTS

Total CSF in the keratoconus and retinopathy groups was significantly lower compared to the control group. Modulation transfer function for keratoconus was lower, and in the retinopathy group was similar to that of the control group. Calculated neural CSF in the diabetes mellitus group was lower than in the control group whereas in the keratoconus group it was similar to that of the control group, with overestimations for some keratoconus cases.

CONCLUSION

It is possible to calculate a meaningful neural CSF from measured total CSF and MTF data. The neural CSF represents a CSF adjusted for optical aberrations. This would allow comparison of the neural component of visual function in eyes with different optical aberrations.

Forward light scatter analysis of the eye in a spatially-resolved double-pass optical system

An optical analysis is developed to separate forward light scatter of the human eye from the conventional wavefront aberrations in a double pass optical system. To quantify the separate contributions made by these micro- and macro-aberrations, respectively, to the spot image blur in the Shark-Hartmann aberrometer, we develop a metric called radial variance for spot blur. We prove an additivity property for radial variance that allows us to distinguish between spot blurs from macro-aberrations and micro-aberrations. When the method is applied to tear break-up in the human eye, we find that micro-aberrations in the second pass accounts for about 87% of the double pass image blur in the Shack-Hartmann wavefront aberrometer under our experimental conditions.

Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials

Purpose

To propose and evaluate Complex Zernike polynomials (CZPs) to represent general wavefronts with non uniform intensity (amplitude) in free-from transmission pupils.

Methods

They consist of three stages: (1) theoretical formulation; (2) numerical implementation; and (3) two studies of the fidelity of the reconstruction obtained as a function of the number of Zernike modes used (36 or 91). In the first study, we generated complex wavefronts merging wave aberration data from a group of 11 eyes, with a generic Gaussian model of the Stiles-Crawford effective pupil transmission. In the second study we simulated the wavefront passing through different pupil stop shapes (annular, semicircular, elliptical and triangular).

Results

The reconstructions of the wave aberration (phase of the generalized pupil function) were always good, the reconstruction RMS error was of the order of 10⁻⁴ wave lengths, no matter the number of modes used. However, the reconstruction of the amplitude (effective transmission) was highly dependent of the number of modes used. In particular, a high number of modes is necessary to reconstruct sharp edges, due to their high frequency content.

Conclusions

CZPs provide a complete orthogonal basis able to represent generalized pupil functions (or complex wavefronts). This provides a unified general framework in contrast to the previous variety of ad oc solutions. Our results suggest that complex wavefronts require a higher number of CZP, but they seem especially well-suited for inhomogeneous beams, pupil apodization, etc.

Modal estimation of wavefront phase from slopes over elliptical pupils

PURPOSE

Measuring the off-axis optical quality of the eye with a Shack-Hartmann wavefront sensor requires methods for reconstructing wavefront from the gradient data defined within an elliptical pupil. Such methods for modal estimation of wavefront aberrations are sensitive to pupil shape.

METHODS

We develop a conceptual framework that reconciles two published, but apparently dissimilar, methods for reconstruction over an elliptical pupil based on Zernike analysis. Our unified treatment shows that the two methods have different interpretations but the vectors of Zernike coefficients they produce are related linearly. Two novel methods based on Fourier series are also introduced for a model of gradient sensors based on Southwell geometry.

RESULTS

All four methods were evaluated numerically with three test-cases: a defocus wavefront (1), a spherocylindrical wavefront (2), and a random-generated wavefront (3). Under noise-free conditions, all four methods reconstructed the tested wavefronts accurately. The reconstruction error is negligible at the level of numerical computation. Furthermore, the Monte-Carlo simulation with test case 2 revealed small differences in sensitivity to noise between the two Zernike methods but no difference between the two Fourier methods. Because of the smoothing effects, the two Zernike-based methods are more robust to noise than are the two Fourier methods. However, Fourier methods are computationally faster.

CONCLUSIONS

All four modal methods are validated methods to reconstruct wavefronts from the gradients over the elliptical pupil. The choice of these methods is application dependent.

Adaptive optics wide-field microscopy using direct wavefront sensing

We report a technique for measuring and correcting the wavefront aberrations introduced by a biological sample using a Shack-Hartmann wavefront sensor, a fluorescent reference source, and a deformable mirror. The reference source and sample fluorescence are at different wavelengths to separate wavefront measurement and sample imaging. The measurement and correction at one wavelength improves the resolving power at a different wavelength, enabling the structure of the sample to be resolved.

Optical properties of the mouse eye

The Shack-Hartmann wavefront sensor (SHWS) spots upon which ocular aberration measurements depend have poor quality in mice due to light reflected from multiple retinal layers. We have designed and implemented a SHWS that can favor light from a specific retinal layer and measured monochromatic aberrations in 20 eyes from 10 anesthetized C57BL/6J mice. Using this instrument, we show that mice are myopic, not hyperopic as is frequently reported. We have also measured longitudinal chromatic aberration (LCA) of the mouse eye and found that it follows predictions of the water-filled schematic mouse eye. Results indicate that the optical quality of the mouse eye assessed by measurement of its aberrations is remarkably good, better for retinal imaging than the human eye. The dilated mouse eye has a much larger numerical aperture (NA) than that of the dilated human eye (0.5 NA vs. 0.2 NA), but it has a similar amount of root mean square (RMS) higher order aberrations compared to the dilated human eye. These measurements predict that adaptive optics based on this method of wavefront sensing will provide improvements in retinal image quality and potentially two times higher lateral resolution than that in the human eye.

Wavefront sensing with critical sampling

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

Measurement of ocular aberrations in downward gaze using a modified clinical aberrometer

Changes in corneal optics have been measured after downward gaze. However, ocular aberrations during downward gaze have not been previously measured. A commercial Shack-Hartmann aberrometer (COAS-HD) was modified by adding a relay lens system and a rotatable beam splitter to allow on-axis aberration measurements in primary gaze and downward gaze with binocular fixation. Measurements with the modified aberrometer (COAS-HD relay system) in primary and downward gaze were validated against a conventional aberrometer. In human eyes, there were significant changes (p<0.05) in defocus C(2,0), primary astigmatism C(2,2) and vertical coma C(3,-1) in downward gaze (25 degrees) compared to primary gaze, indicating the potential influence of biomechanical forces on the optics of the eye in downward gaze. To demonstrate a further clinical application of this modified aberrometer, we measured ocular aberrations when wearing a progressive addition lens (PAL) in primary gaze (0 degree), 15 degrees downward gaze and 25 degrees downward gaze.

New testing software for quantifying discrimination capacity in subjects with ocular pathologies

We develop a new visual test, designed as software for quantifying discrimination capacity under low-illumination conditions. This is an important task in the presence of visual disturbances, such as those perceived by subjects with some ocular pathologies. For this purpose, we propose a visual-disturbance index, checking the test with two groups of observers having different ocular pathologies: a group with unilateral keratitis and another group affected with age-related macular degeneration (ARMD). To compare the test results to objective data, we use a double-pass device to measure the Strehl ratio, a parameter that quantifies the retinal-image quality, taking into account aberrations, retinal reflection, and intraocular scattering working jointly. Diseased eyes present higher disturbance indexes and a lower Strehl ratio compared to their healthy fellow eyes, registering a significant descending correlation between the disturbance index and the Strehl ratio. The lower the Strehl ratio is, the higher the disturbance index for the eyes studied. Therefore, in keratitis and ARMD eyes, our results demonstrate a deterioration in the retinal-image quality and a lower discrimination capacity to peripheral stimuli, reducing visual performance. The test presented here could be useful for the study and time course in different eye diseases, especially those involving an increase in scattered light or alterations in the ocular media, as shown in this work.

Effect of laser in situ keratomileusis on vision analyzed using preoperative optical quality

PURPOSE

To evaluate the effect on vision of laser in situ keratomileusis (LASIK) based on preoperative optical quality.

SETTING

Universitat Politècnica de Catalunya, Terrassa, and Barcelona Institute of Ocular Microsurgery, Barcelona, Spain.

DESIGN

Comparative case series.

METHODS

The relative change in optical quality and visual acuity were evaluated in eyes that had LASIK for myopia. The optical quality was assessed before and 3 months after surgery using parameters provided by a double-pass system. Patients were classified into 4 groups by preoperative optical quality: low (Group 1), moderate (Group 2), high (Group 3), and very high (Group 4).

RESULTS

The study evaluated 25 patients (50 eyes). The optical quality parameters improved postoperatively in Group 1 and Group 2, with the improvement ranging from 15% to 21% and from 13% to 17%, respectively. The preoperative and postoperative optical quality in Group 3 was similar. The optical quality in Group 4 worsened significantly by percentages ranging from -20% to -26%. Although visual acuity had the same trend, there were no statistically significant changes.

CONCLUSION

The changes in optical quality after LASIK surgery depended on the patient's preoperative optical quality; visual acuity showed the same trend, although no change was significant.

Intrasubject repeatability of internal aberrometry obtained with a new integrated aberrometer

PURPOSE

To evaluate the intrasubject repeatability of the internal aberrometry obtained with a new integrated aberrometer in a sample of normal eyes to assess its clinical usefulness.

METHODS

Twenty-six healthy eyes of 26 participants, aged 20 to 50 years, were included in the study. All eyes achieved corrected distance visual acuity of 1.0 (Snellen decimal notation) and did not undergo previous ocular surgeries. Three consecutive measurements of internal aberrations were obtained with the KR-1W system (Topcon Corp) by an experienced examiner. Intrasubject repeatability for 4- and 6-mm pupils was evaluated by the within-subject standard deviation (S(w)) and intraclass correlation coefficient (ICC).

RESULTS

Low values of S(w) and values of ICC close to 1 were found for the 4-mm pupil astigmatism and for several aberrometric coefficients: primary spherical aberration and higher order, third order, and trefoil root-mean-square (RMS). Significant correlations of the S(w) for the 4-mm pupil higher order aberrations RMS with the magnitude of different aberrometric coefficients were found (r≥0.611, P<.01). In addition, tetrafoil RMS for 4-mm pupils correlated significantly with the S(w) for some higher order errors (r≥0.675, P<.01). Significantly larger values of S(w) for 6-mm pupils were found for trefoil (P<.01) and secondary astigmatism RMS (P=.02).

CONCLUSIONS

The KR-1W provided repeatable measurements of internal astigmatism and some higher order aberrations, although consistency of such measurements appears to be limited by the level of aberration.

Optical quality and intraocular scattering in a healthy young population

BACKGROUND

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

METHODS

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

RESULTS

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

CONCLUSION

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

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

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

Theoretical analysis of wavefront aberration from treatment decentration with oblique incidence after conventional laser refractive surgery

Analysis of induced wavefront aberration after refractive surgery is important in the design of vision correction and the development of visual correction technology. Based on a mathematical model of the anterior corneal surface, the influence of treatment decentration on induced wavefront aberrations was studied by considering oblique incidence. The results revealed that significant coma was induced from the treatment translation, and it was nearly proportional to the translation or corrected refraction of vision correction. The induced aberrations from the lateral translation correlated with the angle formed by the position vector and the astigmatism axis of myopia astigmatism correction. The induced spherical aberration did not relate to a lateral translation of the center of the pupil, but was determined only by the corrected refraction. Additionally, no significant higher-order aberrations were induced from eye cyclotorsion for pure myopia or myopia astigmatism correction. Oblique incidence played an important role in the impact of treatment decentration on the induced aberrations in refractive surgery. The induced coma without considering the oblique incidence was obviously larger than that with it. In order to achieve the best postoperative visual performance, the effect of oblique incidence in refractive surgery should be taken into account, and treatment decentration should be minimized by all means, particularly for high myopia.

Changes of the eye optics after iris constriction☆

Purpose

To evaluate the possible change in the optics of the human eye after iris constriction.

Methods

Ocular aberrations were measured under natural viewing conditions in 26 eyes. The measured eyes fixated on a dim target while the contralateral eye was either occluded (so the measured eye had a large pupil) or highly illuminated (so the measured eye had a small pupil). The measured eyes fixated to a dim target placed 0.5 D beyond the subject’s far point. Zernike values obtained in both situations were compared within the same pupil diameter corresponding to the one obtained under the high illumination condition.

Results

Significant variation in some aberration coefficients were found between the two illumination conditions. Specially, spherical aberration (SA) increased significantly after pupil miosis (P = .0017). The mean increase of SA measured was 0.018 microns, for a 3-mm pupil. Mean values of other ocular aberrations also vary significantly after pupil miosis (changes were larger than the standard deviation of the repeated measurements). A mean paraxial hyperopic shift of one third of diopter was found after iris constriction.

Conclusion

Iris constriction slightly modifies the optics of the eye. The small hyperopic shift of the best image plane after iris constriction may be explained by a change in the lens shape and/or position.

Wavefront aberration measurements and corrections through thick tissue using fluorescent microsphere reference beacons

We present a new method to directly measure and correct the aberrations introduced when imaging through thick biological tissue. A Shack-Hartmann wavefront sensor is used to directly measure the wavefront error induced by a Drosophila embryo. The wavefront measurements are taken by seeding the embryo with fluorescent microspheres used as "artificial guide-stars." The wavefront error is corrected in ten millisecond steps by applying the inverse to the wavefront error on a micro-electro-mechanical deformable mirror in the image path of the microscope. The results show that this new approach is capable of improving the Strehl ratio by 2 times on average and as high as 10 times when imaging through 100 microm of tissue. The results also show that the isoplanatic half-width is approximately 19 microm resulting in a corrected field of view 38 microm in diameter around the guide-star.

Centroid displacement statistics of the eye aberration

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

Applications of adaptive optics scanning laser ophthalmoscopy

Adaptive optics (AO) describes a set of tools to correct or control aberrations in any optical system. In the eye, AO allows for precise control of the ocular aberrations. If used to correct aberrations over a large pupil, for example, cellular level resolution in retinal images can be achieved. AO systems have been demonstrated for advanced ophthalmoscopy as well as for testing and/or improving vision. In fact, AO can be integrated to any ophthalmic instrument where the optics of the eye is involved, with a scope of applications ranging from phoropters to optical coherence tomography systems. In this article, I discuss the applications and advantages of using AO in a specific system, the AO scanning laser ophthalmoscope. Since the Borish award was, in part, awarded to me because of this effort, I felt it appropriate to select this as the topic for this article. Furthermore, users of AO scanning laser ophthalmoscope continue to appreciate the benefits of the technology, some of which were not anticipated at the time of development, and so it is time to revisit this topic and summarize them in a single article.

High-resolution retinal imaging through open-loop adaptive optics

Using the liquid crystal spatial light modulator (LC-SLM) as the wavefront corrector, an open-loop adaptive optics (AO) system for fundus imaging in vivo is constructed. Compared with the LC-SLM closed-loop AO system, the light energy efficiency is increased by a factor of 2, which is helpful for the safety of fundus illumination in vivo. In our experiment, the subjective accommodation method is used to precorrect the defocus aberration, and three subjects with different myopia 0, -3, and -5 D are tested. Although the residual wavefront error after correction cannot to detected, the fundus images adequately demonstrate that the imaging system reaches the resolution of a single photoreceptor cell through the open-loop correction. Without dilating and cyclopleging the eye, the continuous imaging for 8 s is recorded for one of the subjects.

Optics of human eye: 400 years of exploration from Galileo's time

We present a brief historical background and a description of the main features of the eye's optical properties: the eye is a simple, but rather optimized, optical instrument. It is only since Galileo's time that the importance of the eye as a part of different optical instruments has driven a continuous scientific exploration of ocular optics. In the past decade, the use of wavefront sensing technology allowed us to complete our understating of eye optics as a robust aplanatic system.

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.

Aspheric Optical Zones: The Effective Optical Zone with the SCHWIND AMARIS

PURPOSE

To evaluate the effective optical zone (the part of the ablation that receives full correction) among eyes that underwent laser epithelial keratomileusis (LASEK)/epi-LASEK treatments for myopic astigmatism.

METHODS

Twenty LASEK/epi-LASEK treatments with a mean spherical equivalent refraction (SE) of -5.49±2.35 diopters (D) performed using the SCHWIND AMARIS system were retrospectively evaluated at 6-month follow-up. In all cases, pre- and postoperative corneal wavefront analyses were performed with the Keratron Scout (OPTIKON 2000). Effective optical zone values were evaluated from the changes of root-mean-square (RMS) of higher order wavefront aberration (ΔRMSho), spherical aberration (ΔSphAb), and RMS of the change of higher order wavefront aberration (RMS[ΔHOAb]). Correlations of effective optical zone with planned optical zone and SE correction were analyzed using a bilinear function as well as calculations of the isometric lines for which effective optical zone equals planned optical zone and of the nomogram planned optical zone to achieve an intended effective optical zone.

RESULTS

At 6 months, SE was -0.05±0.43 D, with 90% of eyes within ±0.50 D. Mean higher order wavefront aberration RMS increased 0.12 μm, spherical aberration 0.09 μm, and coma 0.04 μm after treatment (6-mm diameter). Mean planned optical zone was 6.76±0.25 mm, whereas mean EOZ(ΔRMSho) was 6.74±0.66 mm (bilinear correlation P<.005), EOZ(ΔSphAb) was 6.83±0.58 mm (bilinear correlation P<.0001), and EOZ(RMS(ΔHOAb)) was 6.42±0.58 mm (significantly smaller, P<.05; bilinear correlation P<.0005).

CONCLUSIONS

The EOZ(ΔRMSho) and EOZ(ΔSphAb) were similar to the planned optical zone, whereas EOZ(RMS(ΔHOAb)) was significantly smaller. Differences between effective optical zone and planned optical zone were larger for smaller planned optical zone or larger SE corrections. Planned optical zones >6.75 mm result in effective optical zones at least as large as planned optical zones. For optical zones <6.75 mm, a nomogram should be applied.

Pupil tracking with a Hartmann-Shack wavefront sensor

We present the theoretical background and experimental validation of a pupil tracking method based on measurement of the irradiance centroid of Hartmann-Shack aberrometric images. The experimental setup consists of a Hartmann-Shack (HS) sensor forming over the same camera the images of the eye's pupil and the aberrometric image. The calibration is made by comparing the controlled displacements induced to an artificial eye with the displacements estimated from the centroid of the pupil and of the HS focal plane. The pupil image is also used for validation of the method when operating with human eyes. The experimental results after calibration show a root mean square error of 10.45 mum for the artificial eye and 27, 10, and 6 mum rms for human eyes tested using Hartmann-Shack images, with signal-to-noise ratios of 6, 8, and 11, respectively. The performance of the method is similar to conventional commercial eye trackers. It avoids the need for using separate tracking devices and their associated synchronization problems. This technique can also be used to reprocess present and stored sets of Hartmann-Shack aberrometric images to estimate the ocular movements that occurred during the measurement runs, and, if convenient, to correct the measured aberrations from their influence.

Spherical aberration and other higher-order aberrations in the human eye: from summary wave-front analysis data to optical variables relevant to visual perception

Wave-front analysis data from the human eye are commonly presented using the aberration coefficient c(4)(0) (primary spherical aberration) together with an overall measure of all higher-order aberrations. If groups of subjects are compared, however, the relevance of an observed difference cannot easily be assessed from these summary aberration measures. A method was developed for estimating various optical variables relevant to visual perception from summary wave-front analysis data. These variables were the myopic shift (the difference in the optimal focus between high and low spatial frequencies, a threat to the simultaneous in-focus viewing of fine and coarse patterns), the depth-of-focus (at 8 cpd), and the modulation transfer at high (16 cpd; reading small print) and low (4 cpd; edge detection) spatial frequencies. The depth-of-focus was defined in two ways: using a relative measure (the full width at half-height of the through-focus curve) and an absolute measure (the range where the through-focus curve exceeds a predefined modulation transfer value). The method was shown to be accurate by using previously published contrast sensitivity data and wave-front analysis data. The applicability of the method was illustrated by applying the method to wave-front analysis measurements performed in pseudophakic patients with aspheric and spherical intraocular lenses.

Shack-Hartmann wavefront sensor with large dynamic range

A new spot centroid detection algorithm for a Shack-Hartmann wavefront sensor (SHWFS) is experimentally investigated. The algorithm is a kind of dynamic tracking algorithm that tracks and calculates the corresponding spot centroid of the current spot map based on the spot centroid of the previous spot map, according to the strong correlation of the wavefront slope and the centroid of the corresponding spot between temporally adjacent SHWFS measurements. That is, for adjacent measurements, the spot centroid movement will usually fall within some range. Using the algorithm, the dynamic range of an SHWFS can be expanded by a factor of three in the measurement of tilt aberration compared with the conventional algorithm, more than 1.3 times in the measurement of defocus aberration, and more than 2 times in the measurement of the mixture of spherical aberration plus coma aberration. The algorithm is applied in our SHWFS to measure the distorted wavefront of the human eye. The experimental results of the adaptive optics (AO) system for retina imaging are presented to prove its feasibility for highly aberrated eyes.

Changes of ocular aberrations with gaze

The dependence of the ocular aberrations on gaze has been studied in three eyes using a fast-acquisition, Hartmann-Shack wavefront sensor. Although there were some trends in the change of some aberration terms with gaze, the changes of most Zernike coefficients were smaller than their variability at each individual gaze position, due to the combined effects of microfluctuations of accommodation, eye movements, tear film dynamics, and measurement noise. For our particular experimental dataset, the confidence level at which the null hypothesis (i.e. that the aberrations do not change significantly with gaze) can be rejected is very low. Further advances in the study of the dependence of eye aberrations with gaze will require a tighter control of the sources of aberration variability at each individual gaze position.

The SCHWIND AMARIS Total-Tech Laser as An All-Rounder in Refractive Surgery

PURPOSE

To describe and argument an overview of the main features and unique technical points of AMARIS Total-Tech Laser, coupled with patient outcomes supporting the decision to perform LASIK treatments with maximised outcomes.

SETTINGS

Dr. M.C. Arbelaez, Muscat Eye Laser Center, Muscat, Sultanate of Oman.

METHODS

The findings collected during 18-month experience using SCHWIND AMARIS Total-Tech Laser have been reviewed to provide arguments for supporting the decision to perform LASIK treatments with maximised outcomes. For updated clinical outcomes, the last 100 myopic astigmatism treatments, the last 100 hyperopic astigmatism treatments, the last 30 ocular-wavefront-guided treatments, and the last 30 corneal-wavefront-guided treatments, all with 6-month follow-up, were included. For all those, LDV femtosecond system was used to prepare the flaps, and AMARIS flying spot system was used to perform ablations. Clinical outcomes were evaluated in terms of predictability, refractive outcome, safety, wavefront aberration, and contrast sensitivity.

RESULTS

6-month postoperatively, mean defocus was -0.14+/-0.31D and astigmatism 0.25+/-0.37D. 70+/- eyes were within +/-0.25D of emmetropia. 43+/- eyes gained lines of best spectacle-corrected visual acuity. For Aberration-Free treatments, none of the aberration metrics changed from pre- to postoperative values in a clinically relevant amount. For ocular-wavefront-guided treatments, the surgery did not change coma or spherical aberration, and reduced trefoil (p<0.005). For corneal-wavefront-guided treatments, the trefoil, coma, and spherical aberrations, as well as the total root-mean-square values of higher order aberration, were significantly reduced (p<.05) when the pre-existing aberrations were greater than the repeatability and the biological noise.

CONCLUSIONS

Although this review does not allow for evidence-based conclusions, following our strategy, LASIK results were excellent. LASIK surgery with AMARIS system yield excellent outcomes. Refractions were reduced to subclinical values with no induction of High-Order-Aberrations. Neither adverse events nor complications were observed.

Wavefront measurements of phase plates combining a point-diffraction interferometer and a Hartmann-Shack sensor

A dual setup composed of a point diffraction interferometer (PDI) and a Hartmann-Shack (HS) wavefront sensor was built to compare the estimates of wavefront aberrations provided by the two different and complementary techniques when applied to different phase plates. Results show that under the same experimental and fitting conditions both techniques provide similar information concerning the wavefront aberration map. When taking into account all Zernike terms up to 6th order, the maximum difference in root-mean-square wavefront error was 0.08 microm, and this reduced up to 0.03 microm when excluding lower-order terms. The effects of the pupil size and the order of the Zernike expansion used to reconstruct the wavefront were evaluated. The combination of the two techniques can accurately measure complicated phase profiles, combining the robustness of the HS and the higher resolution and dynamic range of the PDI.

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.

Direct and inverse discrete Zernike transform

An invertible discrete Zernike transform, DZT is proposed and implemented. Three types of non-redundant samplings, random, hybrid (perturbed deterministic) and deterministic (spiral) are shown to provide completeness of the resulting sampled Zernike polynomial expansion. When completeness is guaranteed, then we can obtain an orthonormal basis, and hence the inversion only requires transposition of the matrix formed by the basis vectors (modes). The discrete Zernike modes are given for different sampling patterns and number of samples. The DZT has been implemented showing better performance, numerical stability and robustness than the standard Zernike expansion in numerical simulations. Non-redundant (critical) sampling along with an invertible transformation can be useful in a wide variety of applications.

Systematic errors analysis for a large dynamic range aberrometer based on aberration theory

In Ref. 1, it was demonstrated that the significant systematic errors of a type of large dynamic range aberrometer are strongly related to the power error (defocus) in the input wavefront. In this paper, a generalized theoretical analysis based on vector aberration theory is presented, and local shift errors of the SH spot pattern as a function of the lenslet position and the local wavefront tilt over the corresponding lenslet are derived. Three special cases, a spherical wavefront, a crossed cylindrical wavefront, and a cylindrical wavefront, are analyzed and the possibly affected Zernike terms in the wavefront reconstruction are investigated. The simulation and experimental results are illustrated to verify the theoretical predictions.

Systematic error of a large dynamic range aberrometer

Shack-Hartmann aberrometers are routinely used for measuring ocular aberrations. In one configuration, the intermediate images of the Shack-Hartmann spots formed by the lenslet array are relayed by an imaging lens onto a sensor. A systematic introduction of spherical aberration that is strongly related to the power error (defocus) of the incident wavefront is observed in this configuration. We found that the largest component of this error is induced by the pupil aberration of the imaging relay lens. Some simulations and experimental results are demonstrated.

Excimer laser correction of moderate to high astigmatism with a non-wavefront-guided aberration-free ablation profile: Six-month results

PURPOSE

To evaluate the postoperative clinical outcomes and higher-order aberrations (HOAs) in eyes with astigmatism greater than 2.00 diopters (D) that had laser in situ keratomileusis (LASIK) using a non-wavefront-guided aberration-free ablation profile.

SETTINGS

Private practice.

METHODS

This retrospective study evaluated the 6-month results of LASIK for astigmatism greater than 2.00 D. Standard examinations and preoperative and postoperative wavefront analyses were performed. Aspheric treatments with a non-wavefront-guided ablation profile were planned using software integrated into the Amaris flying-spot excimer laser system, which was used to perform the ablations. The LASIK flaps were created using an LDV femtosecond laser. Clinical outcomes were predictability, refractive outcomes, safety, efficacy, and wavefront aberration.

RESULTS

At 6 months, 84% of the 50 eyes evaluated achieved 20/20 or better uncorrected distance visual acuity (UDVA) and 40% achieved 20/16 or better UDVA. Forty-four percent of eyes were within +/-0.25 D of the attempted astigmatic correction, and 78% were within +/-0.50 D. The mean SE was -0.12 D +/- 0.25 (SD) and the mean astigmatism, 0.50 +/- 0.26 D. Corrected distance visual acuity (CDVA) improved in 36% of eyes; 4% of eyes lost 1 line of CDVA. The predictability slope for astigmatism was 0.97 and the intercept, -0.15 D. There were no clinically relevant changes in any aberration metric from preoperatively to postoperatively.

CONCLUSIONS

Excimer laser LASIK using a non-wavefront-guided aberration-free ablation profile yielded excellent visual outcomes. The preoperative astigmatism was reduced to subclinical values with no clinically relevant induction of HOA.

Population distribution of wavefront aberrations in the peripheral human eye

We present a population study of peripheral wavefront aberrations in large off-axis angles in terms of Zernike coefficients. A laboratory Hartmann-Shack sensor was used to assess the aberrations in 0 degrees, 20 degrees, and 30 degrees in the nasal visual field of 43 normal eyes. The elliptical pupil meant that the quantification could be done in different ways. The three approaches used were (1) over a circular aperture encircling the pupil, (2) over a stretched version of the elliptical pupil, and (3) over a circular aperture within the pupil (MATLAB conversion code given). Astigmatism (c(2)(2)) increased quadratically and coma (c(3)(1)) linearly with the horizontal viewing angle, whereas spherical aberration (c(4)(0)) decreased slightly toward the periphery. There was no correlation between defocus and angle, although some trends were found when the subjects were divided into groups depending on refractive error. When comparing results of different studies it has to be kept in mind that the coefficients differ depending on how the elliptical pupil is taken into consideration.

Correlation of aberrometry, contrast sensitivity, and subjective symptoms with quality of vision after LASIK

PURPOSE

To compare which parameter category (wavefront data, psychophysical data, or subjective symptoms) predicts best subjective quality of vision after LASIK.

METHODS

Twenty-eight eyes (15 patients) were included. Twenty-three eyes (12 patients) underwent uneventful LASIK; 5 eyes (3 patients) were symptomatic eyes treated with myopic LASIK elsewhere. Mean preoperative spherical equivalent refraction was -4.79+/-1.92 diopters (D) (range: -1.63 to -7.13 D); mean patient age was 36.6+/-7.4 years (range: 18 to 48 years). All examinations were performed 1 month postoperatively. The wavefront error was described with Zernike polynomials (6-mm pupil). Psychophysical tests included high-contrast visual acuity and contrast sensitivity with and without glare at 167 cd/m(-2), 1.67 cd/m(-2), and 0.167 cd/m(-2) with best spectacle correction. Correspondingly, overall subjective quality of vision and frequency of visual symptoms (glare, halos, starbursts, ghosting, blur) were assessed for three lighting conditions (photopic, high-mesopic, and low-mesopic) using a questionnaire with a visual analog scale. For each parameter category and each lighting condition, a multiple stepwise backwards regression model with the overall quality of vision item value as dependent was applied.

RESULTS

Under all lighting conditions, subjective symptom scores predicted subjective quality of vision best (adjusted R2=0.83-0.92) with blur as the main predictor throughout all conditions. Psychophysical tests did not significantly predict postoperative subjective quality of vision. The adjusted R2 for the Zernike coefficients was highest for low-mesopic (0.56) and lowest for photopic conditions (0.31).

CONCLUSIONS

Different parameter categories for the description of optical quality did not predict subjective quality of vision after LASIK equally. Subjective symptom scores had the highest predictability, whereas psychophysical tests with spectacle correction had no predictability. The latter probably do not reflect all dimensions of subjective quality of vision.

Contrast sensitivity evaluation of aspheric and spherical intraocular lenses 2 years after implantation

PURPOSE

To compare the quality of vision with aspheric and spherical intraocular lenses (IOLs) in pseudophakic patients after long-term follow-up.

METHODS

Two hundred eyes of 100 patients with bilateral cataracts were randomly assigned to receive spherical (Acrysof SN60AT [Alcon Laboratories Inc] or Sensar AR40e [Advanced Medical Optics Inc]) or aspheric IOLs (Acrysof SN60WF [Alcon] or Tecnis Z9000 [Advanced Medical Optics]). Ophthalmologic examination, including best spectacle-corrected visual acuity (BSCVA), pupil size, ocular dominance, contrast sensitivity under mesopic and photopic conditions, and wavefront analysis, was performed 2 months and 1 and 2 years after surgery.

RESULTS

No statistically significant differences among the four groups in terms of age, pupil diameter, postoperative BSCVA, comeal spherical aberration, and posterior capsular opacification were noted. At all followup examinations, contrast sensitivity results showed no significant differences between the two aspheric IOLs at all spatial frequencies. Under photopic conditions, significant differences (P<.05) between spherical and aspheric IOLs were detected for spatial frequencies of 12 and 18 cycles per degree (cpd) at 2 months and 2 years and 12 cpd at 1 year. Under mesopic conditions, significant differences (P<.05) were detected between spherical and aspheric IOLs for all spatial frequencies at 2 months; all spatial frequencies except 18 cpd at 1 year; and spatial frequencies of 3, 12, and 18 cpd at 2 years. In addition, aspheric IOLs had statistical reductions in total spherical aberration at all follow-up examinations (P<.01).

CONCLUSIONS

This study confirms that implantation of a modified aspheric IOL improves functional visual performance at 2 years postoperative.

Validation of a Hartmann-Moiré wavefront sensor with large dynamic range

Our goal was to validate the accuracy, repeatability, sensitivity, and dynamic range of a Hartmann-Moiré (HM) wavefront sensor (PixelOptics, Inc.) designed for ophthalmic applications.

METHODS

Testing apparatus injected a 4 mm diameter monochromatic (532 nm) beam of light into the wavefront sensor for measurement. Controlled amounts of defocus and astigmatism were introduced into the beam with calibrated spherical (-20D to + 18D) and cylindrical (-8D to + 8D) lenses. Repeatability was assessed with three repeated measurements within a 2-minute period.

RESULTS

Correlation coefficients between mean wavefront measurements (n = 3) and expected wavefront vergence for both sphere and cylinder lenses were >0.999. For spherical lenses, the sensor was accurate to within 0.1D over the range from -20D to + 18D. For cylindrical lenses, the sensor was accurate to within 0.1D over the range from -8D to + 8D. The primary limitation to demonstrating an even larger dynamic range was the increasingly critical requirements for optical alignment. Sensitivity to small changes of vergence was constant over the instrument's full dynamic range. Repeatability of measurements for fixed condition was within 0.01D.

CONCLUSION

The Hartmann-Moiré wavefront sensor measures defocus and astigmatism accurately and repeatedly with good sensitivity over a large dynamic range required for ophthalmic applications.