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

Closed-loop adaptive optics in the human eye

We have developed a prototype apparatus for real-time closed-loop measurement and correction of aberrations in the human eye. The apparatus uses infrared light to measure the wave-front aberration at 25 Hz with a Hartmann-Shack sensor. Defocus is removed by a motorized optometer, and higher-order aberrations are corrected by a membrane deformable mirror. The device was first tested with an artificial eye. Correction of static aberrations takes approximately five iterations, making the system capable of following aberration changes at 5 Hz. This capability allows one to track most of the aberration dynamics in the eye. Results in living eyes showed effective closed-loop correction of aberrations, with a residual uncorrected wave front of 0.1microm for a 4.3-mm pupil diameter. Retinal images of a point source in different subjects with and without adaptive correction of aberrations were estimated in real time. The results demonstrate real-time closed-loop correction of aberration in the living eye. An application of this device is as electro-optic "spectacles" to improve vision.

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

An ideal correcting method, such as a customized contact lens, laser refractive surgery, or adaptive optics, that corrects higher-order aberrations as well as defocus and astigmatism could improve vision. The benefit achieved with this ideal method will be limited by decentration. To estimate the significance of this potential limitation we studied the effect on image quality expected when an ideal correcting method translates or rotates with respect to the eye's pupil. Actual wave aberrations were obtained from ten human eyes for a 7.3-mm pupil with a Shack-Hartmann sensor. We computed the residual aberrations that appear as a result of translation or rotation of an otherwise ideal correction. The model is valid for adaptive optics, contact lenses, and phase plates, but it constitutes only a first approximation to the laser refractive surgery case where tissue removal occurs. Calculations suggest that the typical decentrations will reduce only slightly the optical benefits expected from an ideal correcting method. For typical decentrations the ideal correcting method offers a benefit in modulation 2-4 times higher (1.5-2 times in white light) than with a standard correction of defocus and astigmatism. We obtained analytical expressions that show the impact of translation and rotation on individual Zernike terms. These calculations also reveal which aberrations are most beneficial to correct. We provided practical rules to implement a selective correction depending on the amount of decentration. An experimental study was performed with an aberrated artificial eye corrected with an adaptive optics system, validating the theoretical predictions. The results in a keratoconic subject, also corrected with adaptive optics, showed that important benefits are obtained despite decentrations in highly aberrated eyes.

Ocular optical aberrometer for clinical use

Higher-order optical errors of the human eye are often responsible for reduced visual acuity in spite of an optimal spherical or cylindrical refraction. These optical aberrations are of natural origin or can result from operations in the eye that involve optical structures. The ocular aberrometer presented is based on Tscherning's aberroscope. A collimated laser beam (532 nm, 10 mW) illuminates a mask with a regular matrix of holes which forms a bundle of thin parallel rays of 0.3 mm diameter. These rays are focused by a lens in front of the eye so that their intraocular focus point is located a certain distance in front of the retina, generating a corresponding pattern of light spots on it. According to the existing ocular optical errors, this spot pattern is more or less distorted in comparison to the mask matrix. For a 6 mm pupil diameter 68 retinal spots are plottable for assessment of the optical aberrations. The retinal spot pattern is imaged onto the sensor of a low-light charge coupled device video camera by indirect ophthalmoscopy. Deviations of all spots from their ideal regular positions are measured by means of a PC, and from these values the intraocular wave front aberration is computed in the form of the sum of Zernike polynomials up to sixth order.

Understanding refraction and accommodation through "retinal imaging" aberrometry: a case report

PURPOSE

A new form of aberrometry based on Tscherning optics has been proposed that captures the refraction and high-order aberrations of the eye with and without accommodation.

DESIGN

Experimental clinical optics study.

METHOD

A green neodymium:yttrium-aluminum-garnet laser grid pattern is projected into the eye and viewed on the retina through a narrow, collimated aperture of 1 mm. The resulting aberrated pattern is photographically recorded in a normal eye in the unaccommodated and accommodated state through a pharmacologically dilated pupil without cycloplegia.

MAIN OUTCOME MEASURES

Detection of pupil-dependent refraction and high-order optical aberration with and without accommodation.

RESULTS

Subtle pupil-dependent errors in refraction and high-order aberrations (spherical aberrations and coma) are demonstrated in the unaccommodated normal eye. Accommodation reveals slightly more spherical power through the central 3-mm zone than through a 6.5-mm pupil without significant increase in aberration.

CONCLUSIONS

Tscherning aberrometry based on 'retinal imaging' is useful in defining the refraction and optical aberrations in a normal eye. Accommodation increases spherical refractive power with only small aberration changes, including negative asphericity.

Dynamics of the eye's wave aberration

It is well known that the eye's optics exhibit temporal instability in the form of microfluctuations in focus; however, almost nothing is known of the temporal properties of the eye's other aberrations. We constructed a real-time Hartmann-Shack (HS) wave-front sensor to measure these dynamics at frequencies as high as 60 Hz. To reduce spatial inhomogeneities in the short-exposure HS images, we used a low-coherence source and a scanning system. HS images were collected on three normal subjects with natural and paralyzed accommodation. Average temporal power spectra were computed for the wave-front rms, the Seidel aberrations, and each of 32 Zernike coefficients. The results indicate the presence of fluctuations in all of the eye's aberration, not just defocus. Fluctuations in higher-order aberrations share similar spectra and bandwidths both within and between subjects, dropping at a rate of approximately 4 dB per octave in temporal frequency. The spectrum shape for higher-order aberrations is generally different from that for microfluctuations of accommodation. The origin of these measured fluctuations is not known, and both corneal/lenticular and retinal causes are considered. Under the assumption that they are purely corneal or lenticular, calculations suggest that a perfect adaptive optics system with a closed-loop bandwidth of 1-2 Hz could correct these aberrations well enough to achieve diffraction-limited imaging over a dilated pupil.

Polarization and retinal image quality estimates in the human eye

We have previously studied how polarization affects the double-pass estimates of the retinal image quality by using an imaging polarimeter [Opt. Lett. 24, 64 (1999)]. A series of 16 images for independent combinations of polarization states in the polarimeter were recorded to obtain the spatially resolved Mueller matrices of the eye. From these matrices, double-pass images of a point source for light with different combinations of incoming (first-pass) and outcoming (second-pass) polarization states were reconstructed and their corresponding modulation transfer functions were calculated. We found that the retinal image or, alternatively, the ocular aberrations, are nearly independent of the state of polarization of the incident light (in the first pass). This means that a significant improvement in the ocular optics by using a specific type of polarized light could not be achieved. However, quite different estimates of the retinal image quality are obtained for combinations of polarization states in both the first and the second passes in the double-pass apparatus.

Comparing laser ray tracing, the spatially resolved refractometer, and the Hartmann-Shack sensor to measure the ocular wave aberration

PURPOSE

To compare quantitatively three techniques to measure the optical aberrations of the human eye: laser ray tracing (LRT), the Hartmann-Shack wavefront sensor (H-S), and the spatially resolved refractometer (SRR). LRT and H-S are objective imaging techniques, whereas SRR is psychophysical.

METHODS

Wave aberrations were measured in two normal subjects with all three techniques implemented in two different laboratories.

RESULTS

We compared the experimental variability of the results obtained with each technique with the overall variability across the three methods. For the two subjects measured (RMS wavefront error 0.5 microm and 0.9 microm, respectively), we found a close agreement; the average standard deviation of the Zernike coefficients within a given method was 0.07 microm, whereas the average global standard deviation across techniques was 0.09 microm, which is only slightly higher.

CONCLUSIONS

There is a close match between the Zernike coefficients obtained by LRT, H-S, and SRR. Thus, all three techniques provide similar information concerning wave aberration when applied to normal human eyes. However, the methods are operationally different, and each has advantages and disadvantages depending on the particular application.

Measurement of parameters of polarization in the living human eye using imaging polarimetry

An imaging polarimeter using liquid-crystal variable retarders (Bueno, J. M., Artal, P. (1999). Double-pass imaging polarimetry in the human eye. Optics Letters, 24, 64-66) has been used to study the parameters of polarization in the living human eye. Retardation introduced by birefringent structures of the eye has been calculated by using a spatially resolved collection of Mueller matrices obtained from series of 16 double-pass retinal images. Results for images with a 2-mm pupil diameter show that although the retardation introduced by the eye in a double-pass varies among individuals, at the central cornea the slow axis is directed along the upper-temporal to lower-nasal line and the ellipticity is close to zero, which indicates the presence of linear birefringence. As pupil size increased, the measured retardation also increased, while ocular birefringence remained linear and azimuthal angle changed without a clear tendency.

The spherical aberration of the crystalline lens of the human eye

The in vivo spherical aberration of the lenses of 26 subjects was estimated from the measured total aberration of the eye and that predicted from the measured shape of the anterior corneal surface. Since it was only possible to estimate the aberration contribution from the posterior corneal surface, its value led to an uncertainty in the final aberration level of the lens. For all the subjects and for a wide range of possible aberration levels at the posterior corneal surface, the spherical aberration of the relaxed lens was found to be negative.

Multivariate analysis of refractive data: mathematics and statistics of spherocylinders

PURPOSE

To develop methods for multivariate statistical analysis of spherocylinders and to use these methods to compare autorefraction and manifest subjective refraction in 50 healthy eyes.

SETTING

Department of Ophthalmology, Arhus University Hospital, Arhus, Denmark.

METHODS

A method was developed to transform a spherocylinder to a suitable format as a spherical equivalent power (SEP) and 2 polar values, separated by an arch of 45 degrees, a so-called power-vector format. The accuracy of autorefraction was defined as the difference between autorefraction and manifest refraction, using the described power vector. These entities were subjected to multivariate analysis using the Hotelling T2 test. A method of graphic analysis was developed, using matrix algebra and computation of eigenvectors and eigenvalues.

RESULTS

For individual data, the variation was considerably larger for the SEP than for the astigmatism. For aggregate data, univariate, bivariate, and trivariate statistical analysis did not demonstrate significant average differences between the 2 refraction methods. No refractive components and no combinations of refractive components displayed significant mean differences.

CONCLUSIONS

The study confirmed our clinical experience that the astigmatism derived from autorefraction is nearly identical to manifest refraction, while the sphere needs some adjustment. In groups of healthy eyes, autorefraction can be used as a substitute for manifest refraction. Statistical analysis of spherocylinders, including evaluation of refractive procedures, can be performed in an exact manner with multivariate statistics.

Monochromatic aberrations and characteristics of retinal image quality

BACKGROUND: Patients use a wide variety of terms to describe the characteristics of their vision. These descriptions encompass the effects of their eyes' monochromatic aberrations. METHODS: To illustrate the effect of monochromatic aberrations on the quality of the retinal image, we mathematically reconstructed the image falling on the retina. This has been achieved by combining the properties of various scenes with the optical characteristics of the eye. RESULTS: The effects of some common monochromatic aberrations are illustrated. We also show examples of the retinal image characteristics for two eyes, one with a decentred corneal apex and a second with a decentred refractive surgery ablation. CONCLUSIONS: The image reconstruction technique provides a powerful tool for investigating the quality of the retinal image. It provides the capacity for clinicians to better understand a patient's visual performance. The image reconstruction technique can also broaden our knowledge of the effects of various forms of aberrations on retinal image quality for complex real-world scenes.

Preoperative Simulation of Outcomes Using Adaptive Optics

Measurements of the wavefront of light reflected from the retina of the human eye can be used to determine optical aberrations of the human eye for large pupils. An instrument based on the Hartmann-Shack principle was developed. The wavefront is refracted by a microlens array and detected by a CCD camera. In first clinical studies human volunteer eyes and preoperative and postoperative refractive surgical patient eyes have been examined. An adaptive optical closed loop system has been devised for preoperative simulation of refractive outcomes of aberration free refractive surgical procedures.

Slit Skiascopic-guided Ablation Using the Nidek Laser

PURPOSE

To present the approach of using a scanning slit refractometer (the ARK 10000) in conjunction with a corneal topography system to guide customized corneal ablation. This diagnostic system is coupled with the Nidek EC-5000 system which combines scanning slit and a scanning small area ablation (1.0 mm) to perform a customized ablation.

METHODS

The ARK 10000 diagnostic system which contains a scanning slit refractometer is described. Information generated from the ARK 10000 wavefront sensor and corneal topography system can be coupled to the new Nidek EC-5000 excimer laser system, which combines the larger area of scanning slit ablation with the small area (1.0 mm) ablation.

RESULTS

The Nidek ARK 10000 diagnostic system captures wavefront information using a retinoscopic system which is converted into a refractive power map. This is different from other autorefraction systems in that it has four sensors at different diameters of the cornea and captures 1440 points in 0.4 seconds. This map is used in conjunction with corneal topography-captured simultaneously. This information is then combined to perform a customized ablation using the new Nidek EC-5000 system.

CONCLUSIONS

The ARK 10000 diagnostic system represents a different approach to customized ablation in that it combines a corneal topography system with a wavefront system and a larger treatment area of the traditional scanning slit ablation with a new small area ablation treatment for greater efficiency.

Adaptive Optics Ophthalmoscopy

Retinal images in the human eye are normally degraded because we are forced to use the optical system of the human eye--which is fraught with aberrations--as the objective lens. The recent application of adaptive optics technology to measure and compensate for these aberrations has produced retinal images in human eyes with unprecedented resolution. The adaptive optics ophthalmoscope is used to take pictures of photoreceptors and capillaries and to study spectral and angular tuning properties of individual photoreceptors. Application of adaptive optics technology for ophthalmoscopy promises continued progress toward understanding the basic properties of the living human retina and also for clinical applications.

Principles of Ray Tracing Aberrometry

PURPOSE

Of all transforms of an eye, aberrations are significant when higher visual acuity is to be achieved. Ray tracing aberrometry developed by the Institute of Biomedical Engineering (Kiev) and first tested at the Vardinoyannion Eye Institute of Crete is a promising technique for eye refraction aberration and refraction mapping.

METHODS

The technique uses measurement of the position of a thin laser beam projected onto the retina. The beam is directed into the eye parallel to the visual axis. Each entrance point provides its own projection on the retina. A set of entrance points forms a set of projections. From these data, a refraction map is reconstructed as well as a point spread function of the eye. The total time of scanning over the whole aperture of the eye is within 10 to 20 ms and depends on the number of test points at the eye entrance, as well as on the number of independent measurements in each point. Configuration of the scanning pattern can be chosen by the operator. It may contain 60 to 400 points, each checked 1 to 5 times.

RESULTS

Preliminary studies showed high reproducibility of results. Twenty pseudophakic eyes were subjected to 30 consecutive measurements each. Ninety-five percent of all measured values were within +/-0.20 D of declination from the mean.

CONCLUSIONS

Ray tracing aberrometry is a flexible technology for eye investigation. It can be adapted to any laser technique of vision correction Its further development should be oriented on laser-linked applications of the refraction driven refractive surgery.

Advances in refractive surgery: 1975 to the present

PURPOSE

To review the major advances in the field of refractive surgery occurring over the past 25 years.

METHODS

Literature review.

RESULTS

The major developments in refractive surgery over the past 25 years are reviewed.

CONCLUSIONS

The past 25 years have witnessed great changes in refractive surgery. As a result of advancements in technology, instrumentation, and technique, we have seen improvements in the treatment of all types of ametropias. In this article, we review some of the successes and failures of the past quarter-century.

Visual Benefit of Correcting Higher Order Aberrations of the Eye

There is currently considerable debate concerning the visual impact of correcting the higher order aberrations of the eye. We describe new measurements of a large population of human eyes and compute the visual benefit of correcting higher order aberrations. We also describe the increase in contrast sensitivity when higher order aberrations are corrected with an adaptive optics system. All these results suggest that many, though not all, observers with normal vision would receive worthwhile improvements in spatial vision from customized vision correction, at least over a range of viewing distances and particularly when the pupils are large. Keratoconic patients or patients suffering from spherical aberration as a result of laser refractive surgery as it is presently performed would especially benefit. These results encourage the development of methods to correct higher order aberrations.

Theoretical limits to visual performance

Wavefront sensors and scanning laser technology are enabling the correction of the aberrations of the eye. The effects of aberrations on visual performance are reviewed, and the theoretical limit of visual performance is predicted to understand the ultimate endpoint of these new technologies. A schematic eye model that incorporates diffraction, chromatic aberration, photopic response, the Stiles-Crawford effect, and pupil size is ray-traced to determine its limiting optical properties. These properties are compared to the detection requirements of the retina and brain to determine the theoretical limit of foveal vision. The theoretical limits on foveal vision are found to be between 20/12 and 20/5, depending on pupil diameter. It is concluded that emerging refractive surgery technologies may provide substantial increases in visual performance.

Analysis of the performance of the Hartmann-Shack sensor in the human eye

A description of a Hartmann-Shack sensor to measure the aberrations of the human eye is presented. We performed an analysis of the accuracy and limitations of the sensor using experimental results and computer simulations. We compared the ocular modulation transfer function obtained from simultaneously recorded double-pass and Hartmann-Shack images. The following factors affecting the sensor performance were evaluated: the statistical accuracy, the number of modes used to reconstruct the wave front, the size of the microlenses, and the exposure time.

Laser Ray Tracing versus Hartmann-Shack sensor for measuring optical aberrations in the human eye

A comparison and validation study of Laser Ray Tracing (LRT) and Hartmann-Shack wave-front-sensor (to be referred to as H-S) methods was carried out on both artificial and human eyes. The aim of this work was double. First, we wanted to verify experimentally the equivalence of single- and double-pass measurements for both H-S and LRT. This interest is due to the impossibility of making single-pass measurements in human eyes. In addition, we wanted to validate the LRT technique by comparing it with the H-S wave-front sensor, currently used in many physiological optics laboratories. Comparison of the different methods and configurations carried out in the artificial eye yielded basically the same results in all cases, which means a reciprocal validation of both LRT and H-S, in either single- or double-pass configurations. Other aspects, such as robustness against speckle noise or the influence of the size of the entrance (H-S) or exit (LRT) pupil were studied as well. As a global reference, the point-spread function (PSF) of the artificial eye was recorded directly on a CCD camera and compared with simulated PSF's computed from the experimental aberration data. We also applied these two methods to real eyes (double pass), finding again a close match between the resulting aberration coefficients and also between the standard errors for two normal subjects. However, for one myopic eye with an especially low optical quality (RMS wave-front error >2 microm) and asymmetric aberrations, the array of spots recorded with the H-S sensor was highly distorted and too difficult to analyze.

Monochromatic aberrations in the accommodated human eye

The wave-front aberration of the human eye was measured for eight subjects using a spatially resolved refractometer (a psychophysical ray-tracing test). The eyes were undilated and presented with accommodative stimuli varying from 0 to -6 diopters. Monochromatic wave-front aberrations tend to increase with increasing levels of accommodation, although there are substantial individual variations in the actual change in the wave-front aberration. While spherical aberration always decreased with increasing accommodation, it did not change from positive to negative for every observer. The direction and amount of change in fourth order aberrations varied between observers. Aberrations with orders higher than fourth are at a minimum near the resting state of accommodation. The accommodation induced change in wavefront aberration was not strongly related to the total amount of aberration in the eight eyes studied.

Position and displacement sensing with shack-hartmann wave-front sensors

The use of a Shack-Hartmann wave-front sensor as a position-sensing device is proposed and demonstrated. The coordinates of a pointlike object are determined from the modal Zernike coefficients of the wave fronts emitted by the object and detected by the sensor. The position of the luminous centroid of a moderately extended incoherent flat object can also be measured with this device. Experimental results with off-the-shelf CCD cameras and conventional relay optics as well as inexpensive diffractive microlens arrays show that axial positioning accuracies of 74 microm rms at 300 mm and angular accuracies of 4.3 microrad rms can easily be achieved.

A new approach to the study of ocular chromatic aberrations

We measured the ocular wavefront aberration at six different visible wavelengths (between 450 and 650 nm) in three subjects, using a spatially resolved refractometer. In this technique, the angular deviation of light rays entering the pupil at different locations is measured with respect to a target viewed through a centered pupil. Fits of the data at each wavelength to Zernike polynomials were used to estimate the change of defocus with wavelength (longitudinal chromatic aberration, LCA) and the wavelength-dependence of the ocular aberrations. Measured LCA was in good agreement with the literature. In most cases the wavefront aberration increased slightly with wavelength. The angular deviations from the reference stimulus measured using a magenta filter allowed us to estimate the achromatic axis and both optical and perceived transverse chromatic aberration (TCA), (including the effect of aberrations and Stiles-Crawford effect). The amount of TCA varied markedly across subjects, and between eyes of the same subject. Finally, we used the results from these experiments to compute the image quality of the eye in polychromatic light.

Effect of aging on the monochromatic aberrations of the human eye

We measured the contrast sensitivity (CS) of a group of older subjects through natural pupils and compared the results with those from a group of younger subjects. We also measured each subject's monochromatic ocular wave-front aberrations using a crossed-cylinder aberroscope and calculated their modulation transfer functions (MTF's) and root-mean-squared (RMS) wave-front aberrations for fixed pupil diameters of 4 mm and 6 mm and for a natural pupil diameter. The CS at a natural pupil diameter and the MTF computed for a fixed pupil diameter were found to be significantly poorer for the older group than for the younger group. However, the older group showed very similar MTF's and significantly smaller RMS wave-front aberrations compared with the younger group at their natural pupil diameters, owing to the effects of age-related miosis. These results suggest that although monochromatic ocular wave-front aberrations for a given pupil size increase with age, the reduction in CS with age is not due to this increase.

Off-axis aberrations of a wide-angle schematic eye model

A schematic eye model based on anatomical data, which had been previously designed to reproduce image quality on axis, has been transformed into a wide-angle model by simply adding a spherical image surface that plays the role of the retina. This model captures the main features of the wide-angle optical design of the human eye with minimum complexity: four conic optical surfaces plus a spherical image surface. Seidel aberrations (spherical aberration, coma, astigmatism, field curvature, and distortion), longitudinal and transverse chromatic aberrations, and overall monochromatic spot diagrams have been computed for this eye model and for field angles ranging from 0 degree to 60 degrees by both finite and third-order ray tracing. The modulation transfer function for each field angle has been computed as well. In each case our results have been compared with average experimental data found in the literature, showing a reasonably good agreement. The agreement between the model and experimental data is better off axis, mainly at moderate (10 degrees-40 degrees) field angles, than on axis. The model has been applied to simulate a variety of experimental methods in which image aberrations are estimated from measurements taken in the object space. Our results suggest that for some types of aberration, these methods may yield biased estimates.

Measurement of the eye's near infrared wave-front aberration using the objective crossed-cylinder aberroscope technique

We used the crossed-cylinder aberroscope technique to obtain the near infrared (784 nm) wave-front aberration of the human eye. We compared the results with those obtained under the same conditions using red light (633 nm). Other than the greater retinal scattering of the near infrared light, third- and fourth-order wave-front aberrations are similar in both wavelengths. Values of the calculated near infrared point spread function show a typical half-height width of around 2 arcmin, which is in good agreement with previous work.

Influence of optical aberrations on laser-induced plasma formation in water and their consequences for intraocular photodisruption

The influence of spherical aberrations on laser-induced plasma formation in water by 6-ns Nd:YAG laser pulses was investigated for focusing angles that are used in intraocular microsurgery. Waveform distortions of 5.5lambda and 18.5lambda between the optical axis and the 1/e(2) irradiance values of the laser beam were introduced by replacement of laser achromats in the delivery system by planoconvex lenses. Aberrations of 18.5lambda increased the energy threshold for plasma formation by a factor of 8.5 compared with the optimized system. The actual irradiance threshold for optical breakdown was determined from the threshold energy in the optimized system and the spot size measured with a knife-edge technique. For aberrations of 18.5lambda the irradiance threshold was 48 times larger than the actual threshold when it was calculated by use of the diffraction-limited spot size but was 35 times smaller when it was calculated by use of the measured spot size. The latter discrepancy is probably due to hot spots in the focal region of the aberrated laser beam. Hence the determination of the optical-breakdown threshold in the presence of aberrations leads to highly erroneous results. In the presence of aberrations the plasmas are as much as 3 times longer and the transmitted energy is 17-20 times higher than without aberrations. Aberrations can thus strongly compromise the precision and the safety of intraocular microsurgery. They can further account for a major part of the differences in the breakdown-threshold and the plasma-transmission values reported in previous investigations.

Double-pass imaging polarimetry in the human eye

A Mueller-matrix imaging polarimeter was developed to measure spatially resolved polarization properties in the living human eye. The apparatus is a double-pass setup that incorporates two liquid-crystal variable retarders and a slow-scan CCD camera in the recording stage. Series of 16 images for the combinations of independent polarization states in the first and second passages were recorded for two experimental conditions: with the camera conjugated either with the retina or with the eye's pupil plane. Spatially resolved collections of Mueller matrices and the degree of polarization were calculated from those images for both retinal and pupil planes.

Retinal image quality in the human eye as a function of the accommodation

The changes in the retinal image quality with accommodation in the human eye were studied by using a near-infrared double-pass apparatus. A slightly better modulation transfer function (MTF) in the unaccommodated eye with respect to the accommodated eye was found when using an artificial pupil with a fixed diameter. The technique allows the estimation of the MTF of the accommodated eye discounting the effect of the accommodative defocus error. Most of the reduction found in the MTF with accommodation could be explained in terms of the accommodative defocusing error. However, the shape of the retinal images clearly changes with accommodation, indicating that other aberrations are also altered with accommodation. In general, the double-pass image for the accommodated eye tends to be more symmetric than that of the unaccommodated eye. This is probably due to either a decrease in the amount of coma-like aberrations with accommodation or to an increase of other symmetric aberrations, such as defocus or spherical aberration, that hide the asymmetries present in the retinal image of the unaccommodated eye.

Generation of third-order spherical and coma aberrations by use of radically symmetrical fourth-order lenses

We have extended the method of Alvarez [J. Am. Optom. Assoc. 49, 24 (1978)] to generate a variable magnitude of third-order spherical and/or coma aberration by using a combination of fourth-order plates with a magnification system. The technique, based on the crossed-cylinder aberroscope, is used to measure the wave-front aberration generated by the plates. The method has been applied to correct the third-order spherical aberration generated by an artificial eye as well as the coma produced by a progressive addition ophthalmic lens. The simplicity of the method and its relatively low cost make it attractive for partial correction of the aberrations of the eye.

Predicting the effects of optical defocus on human contrast sensitivity

We used diffraction modulation transfer functions and model eyes to predict the effect of defocus on the contrast sensitivity function (CSF) and compared these predictions with previously published experimental data. Using the principle that optically induced changes in the modulation transfer function should be paralleled by identical changes in the CSF, we used the modulation transfer function calculations with the best-focus CSF measurements to predict the defocused CSF. An aberration-free model predicted the effects of defocus well when the CSF was measured with small pupils (e.g., 2 mm) but not with larger pupils (6-8 mm). When the model included average aberrations, prediction of the defocused CSF with large pupils was better but remained inaccurate, failing, in particular, to reflect differences between individual subjects. Inclusion of measured aberrations for individual subjects provided accurate predictions in the shape of the monochromatic CSF of two of three subjects with hyperopic defocus and good predictions of the polychromatic CSF of two subjects with hyperopic defocus. Prediction of the effects of myopic defocus by use of measured individual aberrations of one subject were less successful. Hence a diffraction optics model can provide good predictions of the effects of defocus on the human CSF, given that one has knowledge of the individual ocular aberrations. These predictions are dependent on the quality of the aberration measurements.

Optimal corneal ablation for eyes with arbitrary Hartmann-Shack aberrations

New technologies for accurately measuring corneal shape and full eye aberrations are now available. An algorithm that uses these technologies to predict the amount of ablation needed to produce a corneal surface that optimally focuses light is developed. It is found that knowledge of the aberrations is far more important than knowledge of corneal shape. Neglect of corneal shape information introduces an error of less than approximately 0.05 micron in the optimal ablation depth. Neglect of the aberrations is a different story. Small changes in the aberration structure, such as going from the optimal ablation to a spherical ablation, introduce ablation changes of greater than 10 microns. It is argued that there are many occasions when less ablation can lead to improved image quality.

Measurement of the wave-front aberration of the eye by a fast psychophysical procedure

We used a fast psychophysical procedure to determine the wave-front aberrations of the human eye in vivo. We measured the angular deviation of light rays entering the eye at different pupillary locations by aligning an image of a point source entering the pupil at different locations to the image of a fixation cross entering the pupil at a fixed location. We fitted the data to a Zernike series to reconstruct the wave-front aberrations of the pupil. With this technique the repeatability of the measurement of the individual coefficients was 0.019 micron. The standard deviation of the overall wave-height estimation across the pupil is less than 0.3 micron. Since this technique does not require the administration of pharmacological agents to dilate the pupil, we were able to measure the changes in the aberrations of the eye during accommodation. We found that administration of even a mild dilating agent causes a change in the aberration structure of the eye.

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

The Shack-Hartmann wave-front sensor offers many theoretical advantages over other methods for measuring aberrations of the eye; therefore it is essential that its accuracy be thoroughly tested. We assessed the accuracy of a Shack-Hartmann sensor by directly comparing its measured wave-front aberration function with that obtained by the Smirnov psychophysical method for the same eyes. Wave-front profiles measured by the two methods agreed closely in terms of shape and magnitude with rms differences of approximately lambda/2 and approximately lambda/6 (5.6-mm pupil) for two eyes. Primary spherical aberration was dominant in these profiles, and, in one subject, secondary coma was opposite in sign to primary coma, thereby canceling its effect. Discovery of an unusual, subtle wave-front anomaly in one individual further demonstrated the accuracy and sensitivity of the Shack-Hartmann wave-front sensor for measuring the optical quality of the human eye.

Estimates of the ocular wave aberration from pairs of double-pass retinal images

We apply a computational technique to retrieve the wave aberration of the eye from the point-spread function obtained from pairs of double-pass retinal images. The method consists of an adapted pyramidal version of a nonlinear least-squares fitting procedure to a wave aberration expressed as an expansion in Zernike polynomials. Although the procedure provides accurate estimates of the wave aberration, it presents several drawbacks that are discussed in detail. In particular, since a great deal of computational time is necessary to retrieve a single wave aberration, this technique is not useful for real-time applications. We present results of wave aberrations in five normal subjects in the fovea for a 4-mm-pupil diameter. In every case there is a clear presence of comalike aberrations, while the third-order spherical aberration is usually smaller than previous estimates. The root-mean-square error in the retrieved wave aberration, when defocus and astigmatism were corrected, ranges from 0.24 to 0.5 wavelength. The particular values of the aberration coefficients present a large intersubject variability.

Monochromatic aberrations and point-spread functions of the human eye across the visual field

The monochromatic aberrations of the human eye along the temporal meridian are studied by a novel laser ray-tracing method. It consists of delivering a narrow laser pencil into the eye through a given point on the pupil and recording the aerial image of the retinal spot with a CCD camera. The relative displacement of this image is proportional to the geometrical aberration of the ray (laser pencil) at the retina. We scanned the pupils of four observers in steps of 1 mm (effective diameter, 6.7 mm) and for five field angles (0 degree, 5 degrees, 10 degrees, 20 degrees, and 40 degrees). In addition, the aerial image for each chief ray is a low-pass-filtered version of the retinal point-spread function corresponding to a fully dilated pupil. The resulting spot diagrams, displaying the distribution of ray aberrations, are highly correlated with these point-spread functions. We have estimated the wave-front error by fitting Zernike polynomials (up to the fifth order). Despite the large variation found among observers, the overall rms wave-front error is relatively homogeneous. At the fovea, the average rms value was 1.49 microns when the second-order terms (defocus and astigmatism) were considered; this was reduced to 0.45 micron when the second-order terms were ignored. The rms values increase slowly, in a roughly linear fashion with eccentricity, such that at 40 degrees they are approximately double. These results are consistent with previous findings on the off-axis optical quality of the eye.

Correction of the aberrations in the human eye with a liquid-crystal spatial light modulator: limits to performance

We evaluated the performance of a liquid-crystal spatial light modulator for static correction of the aberrations in the human eye. By applying phase-retrieval techniques to pairs of double-pass images we first estimated the wave aberration of the eye to be corrected. Then we introduced the opposite phase map in the modulator, which was placed in a plane conjugated with the eye's pupil, and we recorded double-pass images of a point source before and after correction of the aberrations. In a slightly aberrated artificial eye a clear improvement was obtained after correction, and, although diffraction-limited performance was not achieved, the results were close to the theoretical predictions. In the two living eyes that we studied some benefit also appeared in the correction, but the performance was worse than that expected. We evaluated possible explanations for the relatively poor performance that was obtained in the human eye: an incorrect estimate of the ocular aberration, the limited spatial resolution of the modulator, and the dynamic changes in the ocular aberrations. Based on the results in the artificial eye, the first problem was not considered to be a major source of error. However, we showed that the spatial resolution of the liquid-crystal spatial light modulator limits the maximum correction to be attained. In addition, the changes in the ocular optics over time also impose a limit in the performance of static corrections.

Corneal Aberrations and Visual Performance After Radial Keratotomy

BACKGROUND

Refractive surgery and videokeratography have allowed us to study the effects on visual performance of relatively large changes in corneal aberration structure induced by surgical changes in corneal shape.

METHODS

We quantified in one eye of nine normal and 23 radial keratotomy patients, the area under the log contrast sensitivity function (AULCSF) and corneal first surface wavefront variance for two artificial pupil sizes (3 and 7 mm). Contrast sensitivity was measured with sine-wave gratings at six spacial frequencies. Wavefront variance was derived from videokeratographs using Zernike polynomials.

RESULTS

For normals eyes there were no significant changes over time. For eyes that had radial keratotomy, there were significant pupil size-dependent changes. For the 3 mm pupil, there were significant surgery-induced changes in the corneal wavefront variance which became large (approximately 30 times preoperative values) at 7 mm. Significant correlated changes in AULCSF for the 7 mm pupil but not for the 3 mm pupil occurred immediately following surgery and remained.

CONCLUSIONS

Radial keratotomy, like photorefractive keratectomy, shifts the distribution of aberrations from third order dominance (coma-like aberrations) to fourth order dominance (spherical-like aberrations). Radial keratotomy-induced aberrations and loss in contrast sensitivity are reduced with increasing clear zone diameter. Radial keratotomy induces an increase in the optical aberrations of the eye and the increase for large pupils (7 mm) but not small (3 mm) is correlated to a decrease in contrast sensitivity.

Design of array illuminators operating under spherical illumination

The effect of the form of the illuminating wave on array illuminators is investigated. Attention is focused on spherical illumination, and relevant parameters such as spot size and compression ratio are discussed. In addition, a general approach is presented to designing a Talbot array illuminator that operates under spherical illumination. It is shown how spherical illumination can be used as a degree of freedom, and an example of application in the field of human eye aberration correction is given.

Reconstruction of the point-spread function of the human eye from two double-pass retinal images by phase-retrieval algorithms

In the double-pass technique used to measure the optical performance of the eye, the double-pass image is the cross correlation of the input spread function with the output spread function [J. Opt. Soc. Am. A 12, 195 (1995)]. When entrance and exit pupil sizes are equal, the information on the point-spread function is lost from the double-pass image, although the modulation transfer function of the eye is obtained. A modification of the double-pass technique that uses unequal-sized entrance and exit pupils allows a low-resolution version of the ocular point-spread function to be recorded [J. Opt. Soc. Am. A 12, 2358 (1995)]. We propose the combined use of these two double-pass measurements as input in a phase-retrieval procedure to reconstruct the ocular point-spread function. We use an adapted version of the iterative Fourier-transform algorithm consisting of two steps. In the first step, error-reduction iterations with expanding weighting functions in the Fourier domain yield an estimation of the phase that serves as an initial guess for the second step, which consists of cycles of hybrid input-output iterations. We tested the robustness and limitations of the retrieval algorithm by using simulated data with and without noise. We then applied the procedure to reconstruct the point-spread function from actual measurements of double-pass retinal images in the living eye.

Supernormal vision and high-resolution retinal imaging through adaptive optics

Even when corrected with the best spectacles or contact lenses, normal human eyes still suffer from monochromatic aberrations that blur vision when the pupil is large. We have successfully corrected these aberrations using adaptive optics, providing normal eyes with supernormal optical quality. Contrast sensitivity to fine spatial patterns was increased when observers viewed stimuli through adaptive optics. The eye's aberrations also limit the resolution of images of the retina, a limit that has existed since the invention of the ophthalmoscope. We have constructed a fundus camera equipped with adaptive optics that provides unprecedented resolution, allowing the imaging of microscopic structures the size of single cells in the living human retina.

Aberrations and retinal image quality of the normal human eye

We have constructed a wave-front sensor to measure the irregular as well as the classical aberrations of the eye, providing a more complete description of the eye's aberrations than has previously been possible. We show that the wave-front sensor provides repeatable and accurate measurements of the eye's wave aberration. The modulation transfer function of the eye computed from the wave-front sensor is in fair, though not complete, agreement with that obtained under similar conditions on the same observers by use of the double-pass and the interferometric techniques. Irregular aberrations, i.e., those beyond defocus, astigmatism, coma, and spherical aberration, do not have a large effect on retinal image quality in normal eyes when the pupil is small (3 mm). However, they play a substantial role when the pupil is large (7.3-mm), reducing visual performance and the resolution of images of the living retina. Although the pattern of aberrations varies from subject to subject, aberrations, including irregular ones, are correlated in left and right eyes of the same subject, indicating that they are not random defects.

Refractive Surgery, Optical Aberrations, and Visual Performance

Visual optics is taking on new clinical significance. Given that current refractive procedures can and do induce large amounts of higher order ocular aberration that often affects the patient's daily visual function and quality of life, we can no longer relegate the considerations of ocular aberrations to academic discussions. Instead, we need to move toward minimizing (not increasing) the eye's aberrations at the same time we are correcting the eye's spherical and cylindrical refractive error. These are exciting times in refractive surgery, which need to be tempered by the fact that after all the research, clinical, and marketing dust settles, the level to which we improve the quality of the retinal image will be guided by the trade-off between cost and the improvement in the quality of life that refractive surgery offers.

Monocular diplopia caused by ocular aberrations and hyperopic defocus

As a single aperture, approximately monofocal optical system, the human eye generally creates a single image on the retina. However, the literature contains many reports of perceptual monocular diplopia. While it is easy to understand how distortion may produce monocular diplopia, its reported high incidence in normal eyes is less easily understood. We examine a model which ascribes monocular diplopia to an interaction between defocus and ocular spherical aberration. Using a psychophysical hyperacuity-based alignment procedure we measured the transverse aberration function in 0.5 mm steps horizontally across the pupil in the eyes of three cyclopleged subjects. Ocular transverse aberration functions were derived with best refraction and with simulated myopia and hyperopia. Monocular diplopia was also measured under the same conditions. All three subjects showed significant, but different, degrees of positive spherical aberration. The measured ocular transverse aberration functions were predictably modified by the hyperopic and myopic defocus. Hyperopic defocus combined with positive (myopic) spherical aberration changes a monotonic transverse aberration function with a single inflection point into a biphasic function with two inflection points. The locations of the inflections predict the presence and magnitude of the perceived diplopia. These experimental results confirm Verhoeff's (1900) hypothesis for the ocular cause of monocular diplopia.