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

Stability of the retinal image under normal viewing conditions and the implications for neural adaptation

Previous studies have demonstrated that the visual system adapts to the specific aberration pattern of an individual's eye. Alterations to this pattern can lead to reduced visual performance, even when the Root Mean Square (RMS) of the wavefront error remains constant. However, it is well-established that ocular aberrations are dynamic and can change with factors such as pupil size and accommodation. This raises an intriguing question: can the neural system adapt to continuously changing aberration patterns? To address this question, we measured the ocular aberrations in four subjects under various natural viewing conditions, which included changes in accommodative state and pupil size. We subsequently computed the associated Point Spread Functions (PSFs). For each subject, we examined the stability in the orientation of the PSFs and analyzed the cross-correlation between different PSFs. These findings were then compared to the characteristics of a distribution featuring PSF shapes akin to random variations. Our results indicate that the changes observed in the PSFs are not substantial enough to produce a PSF shape distribution resembling random variations. This lends support to the notion that neural adaptation is indeed a viable mechanism even in response to continuously changing aberration patterns.

Digital ocular swept source optical coherence aberrometry

Ocular aberrometry is an essential technique in vision science and ophthalmology. We demonstrate how a phase-sensitive single mode fiber-based swept source optical coherence tomography (SS-OCT) setup can be employed for quantitative ocular aberrometry with digital adaptive optics (DAO). The system records the volumetric point spread function at the retina in a de-scanning geometry using a guide star pencil beam. Succeeding test-retest repeatability assessment with defocus and astigmatism analysis on a model eye within ± 3 D dynamic range, the feasibility of technique is demonstrated in-vivo at a B-scan rate of >1 kHz in comparison with a commercially available aberrometer.

Higher order aberrations of the eye: Part one

This article is the first in a series of two articles that provide a comprehensive literature review of higher order aberrations (HOAs) of the eye. The present article mainly explains the general principles of such HOAs as well as HOAs of importance, and the measuring apparatus used to measure HOAs of the eye. The second article in the series discusses factors contributing to variable results in measurements of HOAs of the eye.Keywords: Higher order aberrations; wavefront aberrations; aberrometer

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.

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.

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.

Ocular aberrations up to the infrared range: from 632.8 to 1070 nm

Ocular aberrations were measured by using a Hartmann-Shack wavefront sensor in the visible and infrared portions of the spectrum. In the latter, wavelengths 1030, 1050 and 1070 nm were used for the first time for the study of the optical quality of the eye. In this spectral range the retinal photoreceptors barely respond, so the radiation is virtually invisible for the subject. The results were confronted with those obtained by the same system at 780 and 632.8 nm. Monochromatic aberrations were found to be similar from the visible to the infrared. Longitudinal chromatic aberration was experimentally obtained, being approximately 1 D from 632.8 to 1070 nm. The feasibility of using the infrared for studying the eye was demonstrated. The employment of the infrared has an enormous potential for the better understanding of the impact and influence of the aberrations in vision with adaptive optics. It allows for measuring and controlling aberrations whilst the subject might eventually perform visual tests, with no interference from the beacon light.

Representing the retinal line spread shape with mathematical functions

OBJECTIVE

To report a mathematical function that characterizes the double-pass line spread function (LSF) of the human eye. Determining analytical functions that represent the double-pass LSF is important because it allows modeling the optical performance of the eye.

METHODS

Optical section retinal images, generated in normal human eyes using a modified slit-lamp biomicroscope, were analyzed to derive the double-pass LSF by plotting the intensity distribution of laser light reflected/ scattered from the vitreoretinal interface. Three mathematical functions (Lorentzian, Gaussian, exponential) were fitted to the double-pass LSF and the root mean square error (RMSE) was calculated to provide a measure of the goodness of fit.

RESULTS

The Lorentzian function provided the best representation of the double-pass LSF of normal human eyes. The full width at half maximum (FWHM) of the Lorentzian fitted curve was positively correlated with age, indicating that the double-pass LSF broadens with age. Furthermore, the goodness of fit of the Lorentzian function was significantly better in younger subjects as compared with older subjects, suggesting that the fitted function to the double-pass LSF may vary according to age.

CONCLUSION

The results demonstrate an age-related change in the double-pass LSF width and the goodness of fit of the Lorentzian function.

Clinical Ocular Wavefront Analyzers

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Monochromatic ocular wave aberrations in young monkeys

High-order monochromatic aberrations could potentially influence vision-dependent refractive development in a variety of ways. As a first step in understanding the effects of wave aberration on refractive development, we characterized the maturational changes that take place in the high-order aberrations of infant rhesus monkey eyes. Specifically, we compared the monochromatic wave aberrations of infant and adolescent animals and measured the longitudinal changes in the high-order aberrations of infant monkeys during the early period when emmetropization takes place. Our main findings were that (1) adolescent monkey eyes have excellent optical quality, exhibiting total RMS errors that were slightly better than those for adult human eyes that have the same numerical aperture and (2) shortly after birth, infant rhesus monkeys exhibited relatively larger magnitudes of high-order aberrations predominately spherical aberration, coma, and trefoil, which decreased rapidly to assume adolescent values by about 200 days of age. The results demonstrate that rhesus monkey eyes are a good model for studying the contribution of individual ocular components to the eye's overall aberration structure, the mechanisms responsible for the improvements in optical quality that occur during early ocular development, and the effects of high-order aberrations on ocular growth and emmetropization.

A Method for Differentiating Ocular Higher-Order Aberrations From Light Scatter Applied to Retinitis Pigmentosa

PURPOSE

The purpose of this study is to report a method for differentiating ocular higher-order aberrations and intraocular light scatter based on a deconvolution technique.

METHODS

An optical system was used to image a laser slit on the retina and also to perform Shack-Hartmann wavefront sensing. From the laser slit image, the line spread function, incorporating both ocular higher-order aberrations and light scatter, was derived. The laser slit image was deconvolved with a point spread function obtained from the Shack-Hartmann image. The area under the line spread function that was derived from the laser slit image after deconvolution provided a measurement of intraocular light scatter. The deconvolution technique was applied to images obtained in a group of 13 patients (mean age +/- 1 standard deviation: 42 +/- 12 years) with retinitis pigmentosa (RP), a retinal disease in which, by clinical examination, changes in the lens of the eye can be manifested. Measurements were compared with those obtained from 20 visually normal control subjects (mean age +/- 1 standard deviation: 43 +/- 17 years).

RESULTS

Combined higher-order aberrations and light scatter, measured as the area under the line spread function derived from the laser slit image, were increased significantly in the patients with RP as compared with the control subjects (p = 0.004). Ocular higher-order aberrations obtained from the Shack-Hartmann images were higher in the patients with RP than in the control subjects (p = 0.05). Intraocular light scatter derived from the deconvolved laser slit image was significantly higher in the patients with RP than in the control subjects (p = 0.009). Minimizing the contribution of ocular higher-order aberrations by deconvolution reduced the area under the line spread function in the control subjects and patients with RP, denoting an improvement in retinal image quality.

CONCLUSIONS

A method for differentiating ocular higher-order aberrations and intraocular light scatter based on deconvolution was developed that may be useful for determining the level of improvement in retinal image quality that can be anticipated by the application of adaptive optics to aging and diseased human eyes.

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

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

Study of the tear topography dynamics using a lateral shearing interferometer

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

Measurements of Ocular Aberrations and Light Scatter in Healthy Subjects

PURPOSE

To report and validate an optical imaging system that provides measurements of higher order ocular aberrations and light scatter in human eyes.

METHODS

An optical imaging system has been established that provides for combined measurements of ocular aberrations and light scatter. A laser beam was expanded and focused to a point on the retina by the optics of the eye. Wavefront sensing was performed with a Shack-Hartmann aberrometer to determine the wavefront aberration function and calculate the point spread function, giving information on ocular aberrations. A cylindrical lens was placed in the path of the incident laser beam path, and the line spread function was derived from the laser slit, giving information on combined ocular aberrations and light scatter. A relative index for ocular light scatter was determined by subtracting the area under the two line spread functions. Measurements were performed in one eye of 20 normal healthy subjects. The subjects' ages ranged between 21 and 78 years, and the average for all the eyes was 43 +/- 17 years (mean +/- SD).

RESULTS

Higher order ocular aberrations were correlated with subjects' ages (r = 0.6; p = 0.01; N = 20). Combined higher order ocular aberrations and light scatter were correlated with age (r = 0.7; p = 0.0002; N = 20). Light scatter was correlated with age (r = 0.6; p = 0.002; N = 20).

CONCLUSIONS

A method was established to measure age-related changes in ocular higher order aberrations and light scatter. Differentiating the contribution of ocular aberrations and light scatter to the retinal image quality has potential value for anticipating the outcome of procedures that attempt to compensate for ocular aberrations and for providing information on factors that degrade the optical performance of the eye in health and disease.

Degree of polarization as an objective method of estimating scattering

A new method of determining objectively the amount of scattered light in an optical system has been developed. It is based on measuring the degree of polarization of the light in images formed after a double pass through the system. A dual apparatus composed of a modified double-pass imaging polarimeter and a wave-front sensor was used to measure polarization properties and aberrations of the system under test. We studied the accuracy of the procedure in a system that included a lanthanum-modified lead zirconate titanate (PLZT) ceramic plate able to generate variable amounts of scattered light as a function of the applied voltage. Changes in the voltage applied to the ceramics plate modified significantly the scattering contribution while hardly altering the wave-front aberration. The degree of polarization was well correlated with the level of scattering in the system as determined by direct-intensity measurements at the tails of the double-pass images. This indicates that this polarimetric parameter provides accurate relative estimates of the amount of scattering generated in a system. The technique can be used in a number of applications, for example, to determine objectively the amount of scattered light in the human eye.

From Scattering to Wavefronts-What's in Between?

PURPOSE

Some optical errors are too localized and random to be detected by commercial wavefront devices and Zernike polynomial expression. We looked beyond aberrations defined by Zernike expression to discuss implications of fine irregularities associated with highly aberrated corneal surfaces and complex surface roughness that can lead to light scattering.

METHODS

Most fine irregularities are related to postoperative surface roughness, complexities of corneal ablation, and the laser in situ keratomileusis (LASIK) flap. These can be characterized mathematically by a random function that includes local surface tilts, the correlation radius of irregularities (Ic), surface roughness, and other terms. The Kirchoff method of scatter analysis characterizes fine surface irregularities by replacing each point on the surface with a tangential plane, allowing it to be governed by Snellen and Fresnel laws.

RESULTS

The joint action of the continuum of microbeams defines a complex point spread function that can be expressed by the Strehl ratio. Small, highly irregular steep central islands and flap striae may not be adequately detected by Zernike expression and may have a surface irregularity diameter of 0.1 to 2.0 mm and height of 10 to 20 microm that results in a reduced Strehl ratio below 0.8. Laser ablation inhomogeneities may have dimensions of 1 to 10 microm, resulting in a root mean square tilt value approaching 1.0 and a Strehl ratio below 0.5.

CONCLUSION

Corneal surface irregularities after laser vision correction may induce significant optical aberrations and distortions apart from classical wavefront or scattering errors. As these may not be detected by commercial wavefront devices, and yet contribute to the degradation of optical performance, alternate techniques should be evaluated to detect and describe these surface irregularities.

Aberro-polariscope for the human eye

We have developed an aberro-polariscope that simultaneously measures spatially resolved polarization properties and wave-front aberration in a living human eye. The setup consists of an infrared Hartmann-Shack sensor that incorporates a polariscope. A series of four Hartmann-Shack images corresponding to independent polarization states were recorded. The corresponding wave-front aberration was computed from each image. Moreover, from each set of four images spatially resolved (over the pupil plane) parameters of polarization were also determined. This instrument allows useful information on both the optical and the biomechanical properties of the eye to be obtained.

Scatter and its implications for the measurement of optical image quality in human eyes

PURPOSE

To investigate the effect of scatter on measurements of wavefront aberrations and point-spread functions in a model eye.

METHODS

The wavefront aberrations of a model eye were measured using Hartmann-Shack wavefront sensing and crossed-cylinder aberroscope techniques and compared with its measured point-spread function in the presence of scattering media of different concentrations.

RESULTS

The point-spread functions became broader as the concentration increased. Forward light scatter on both the light path into the eye and the light path out of the eye contributed to this broadening of the point-spread function. Neither the crossed-cylinder aberroscope nor wavefront sensing, which, respectively, measure the ocular wavefront aberrations for light entering the eye and leaving the eye, were affected by the scatter.

CONCLUSION

We predict that by minimizing the contribution of the forward light scatter from one or other of these light paths by manipulating the size of the entrance and exit pupils, it should be possible to objectively assess narrow-angle forward light scatter in the eye by measuring and removing any confounding effect from wavefront aberration.

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

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

Ocular wave-front aberration statistics in a normal young population

Monochromatic ocular aberrations in 108 eyes of a normal young population (n=59) were studied. The wave-front aberration were obtained under natural conditions using a near-infrared Shack-Hartmann wave-front sensor. For this population and a 5 mm pupil, more than 99% of the root-mean square wave-front error is contained in the first four orders of a Zernike expansion and about 91% corresponds only to the second order. Comparison of wave-fronts aberrations from right and left eye in 35 subjects, showed a good correlation between most of the second- and third-order terms and a slight (but not clear) tendency for mirror symmetry between eyes.

Effect of the polarization on ocular wave aberration measurements

Measurement of the eye's wave aberrations has become fairly standard in recent years. However, most studies have not taken into account the possible influence of the polarization state of light on the wave aberration measurements. The birefringence properties of the eye's optical components, in particular corneal birefringence, can be expected to have an effect on the wave aberration estimates obtained under different states of polarization for the measurement light. In the work described, we used a psychophysical aberrometer (the spatially resolved refractometer) to measure the effect of changes in the polarization state of the illumination light on the eye's wave aberration estimates obtained in a single pass. We find, contrary to our initial expectation, that the polarization state of the measurement light has little influence on the measured wave aberration. For each subject, the differences in wave aberrations across polarization states were of the same order as the variability in aberrations across consecutive estimates of the wave front for the same polarization conditions.

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

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

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

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

Investigating sources of variability of monochromatic and transverse chromatic aberrations across eyes

Schematic eye models have typically been used to explain the average monochromatic and chromatic imaging properties of the eye. Both monochromatic aberrations and transverse chromatic aberration are known to vary widely across subjects. However, to our knowledge, the ability of schematic eye models to predict these individual variations has not been tested experimentally. We used a spatially resolved refractometer to measure the monochromatic aberrations and the optical transverse chromatic aberration (oTCA) in a group of 15 eyes. By recording the 1st and 4th Purkinje images for five directions of gaze, we also estimated the tilt, misalignment of ocular surfaces (front surface of the cornea and back surface of the lens) and off-axis position of the fovea (angle alpha), as well as pupil centration. We conclude that, contrary to expectations none of those factors are major contributors to the variability in monochromatic aberrations and oTCA in this group of eyes. Simulations show that corneal curvature and corneal conicity are also unlikely to account for the observed relation between monochromatic aberrations and oTCA. Our results suggest an important contribution of corneal irregularities to those aberrations.

Monochromatic aberrations of the human eye in a large population

From both a fundamental and a clinical point of view, it is necessary to know the distribution of the eye's aberrations in the normal population and to be able to describe them as efficiently as possible. We used a modified Hartmann-Shack wave-front sensor to measure the monochromatic wave aberration of both eyes for 109 normal human subjects across a 5.7-mm pupil. We analyzed the distribution of the eye's aberrations in the population and found that most Zernike modes are relatively uncorrelated with each other across the population. A principal components analysis was applied to our wave-aberration measurements with the resulting principal components providing only a slightly more compact description of the population data than Zernike modes. This indicates that Zernike modes are efficient basis functions for describing the eye's wave aberration. Even though there appears to be a random variation in the eye's aberrations from subject to subject, many aberrations in the left eye were found to be significantly correlated with their counterparts in the right eye.

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.

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.

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.

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.

Corneal wave aberration from videokeratography: accuracy and limitations of the procedure

A procedure to calculate the wave aberration of the human cornea from its surface shape measured by videokeratography is presented. The wave aberration was calculated as the difference in optical path between the marginal rays and the chief ray refracted at the surface, for both on- and off-axis objects. The corneal shape elevation map was obtained from videokeratography and fitted to a Zernike polynomial expansion through a Gram-Schmidt orthogonalization. The wave aberration was obtained also as a Zernike polynomial representation. The accuracy of the procedure was analyzed. For calibrated reference surface elevations, a root-mean-square error (RMSE) of 1 to 2 microm for an aperture 4-6 mm in diameter was obtained, and the RMSE associated with the experimental errors and with the fitting method was 0.2 microm. The procedure permits estimation of the corneal wave aberration from videokeratoscopic data with an accuracy of 0.05-0.2 microm for a pupil 4-6 mm in diameter, rendering the method adequate for many applications.

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.

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.

Apodization by the Stiles-Crawford effect moderates the visual impact of retinal image defocus

Previous optical modeling of the human eye with large pupils has predicted a larger impact of defocus on the human contrast sensitivity function and modulation transfer function than is observed experimentally. Theory predicts that aberrations and the Stiles-Crawford effect (SCE) should both lead to increased depth of focus, resulting in higher contrast sensitivities and veridical (not phase-reversed) perception over a larger range of spatial frequencies in defocused retinal images. Using a wave optics model, we examine these predictions quantitatively and compare them with psychophysical experiments that measure the effect of defocus on contrast sensitivity and perceived phase reversals. We find that SCE apodization has its biggest effect on defocused image quality when defocus and spherical aberration have the same sign. A model including typical amounts of spherical aberration and pupil apodization provides a dramatically improved prediction of the effects of defocus on contrast sensitivity with large pupils. The SCE can significantly improve defocused image quality and defocused vision, particularly for tasks that require veridical phase perception.

Contributions of the cornea and the lens to the aberrations of the human eye

The relative contributions of optical aberrations of the cornea and the crystalline lens to the final image quality of the human eye were studied. The aberrations of the entire eye were obtained from pairs of double-pass retinal images, and the aberrations of the cornea were obtained from videokeratographic data. Third-order spherical aberration and coma were significantly larger for the cornea than for the complete eye, indicating a significant role of the lens in compensating for corneal aberrations. In a second experiment retinal images were recorded in an eye before and after we neutralized the aberrations of the cornea by having the subjects wear swimming goggles filled with saline water, providing a direct estimate of the optical performance of the crystalline lens.

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.