Visual performance after correcting the monochromatic and chromatic aberrations of the eye

The development of technology to measure and correct the eye's higher-order aberrations, i.e., those beyond defocus and astigmatism, raises the issue of how much visual benefit can be obtained by providing such correction. We demonstrate improvements in contrast sensitivity and visual acuity in white light and in monochromatic light when adaptive optics corrects the eye's higher-order monochromatic aberrations. In white light, the contrast sensitivity and visual acuity when most monochromatic aberrations are corrected with a deformable mirror are somewhat higher than when defocus and astigmatism alone are corrected. Moreover, viewing conditions in which monochromatic aberrations are corrected and chromatic aberrations are avoided provides an even larger improvement in contrast sensitivity and visual acuity. These results are in reasonable agreement with the theoretical improvement calculated from the eye's optical modulation transfer function.     

Effect of aberrations and scatter on image resolution assessed by adaptive optics retinal section imaging

The effect of increased high-order wavefront aberrations on image resolution was investigated, and the performance of adaptive optics (AO) for correcting wavefront error in the presence of increased light scatter was assessed in a model eye. An AO section imaging system provided an oblique view of a model retina and incorporated a wavefront sensor and deformable mirror for measurement and compensation of wavefront aberrations. Image resolution was quantified by the width of a Lorentzian curve fitted to a laser line image. Wavefront aberrations were significantly reduced with AO, resulting in improvement of image resolution. In the model eye, image resolution was degraded with increased high-order wavefront aberrations (horizontal coma and spherical) and improved with AO correction of wavefront error in the presence of increased light scatter. The findings of the current study suggest that AO imaging systems can potentially improve image resolution in aging eyes with increased aberrations and scatter.     

Modeling the combined effect of static and varying phase distortions on the performance of adaptive optical systems

The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time-averaged Strehl ratio and the time-averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few percent for a range of representative residual wave-front errors. In these calculations, we combined static optical system aberrations and time-varying residual phase distortion characteristics of a deformable mirror fitting error, wave-front sensor noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini 8-Meter Telescopes Project. The overall Strehl ratios and OTF's that are due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio that is due to both errors is greater than approximately 0.1. For lower Strehl ratios, the products provide lower bounds on the actual values of the Strehl ratio and the OTF. The speckle transfer function is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.     

Compact multimodal adaptive-optics spectral-domain optical coherence tomography instrument for retinal imaging

We have developed a compact, multimodal instrument for simultaneous acquisition of en face quasi-confocal fundus images and adaptive-optics (AO) spectral-domain optical coherence tomography (SDOCT) cross-sectional images. The optical system including all AO and SDOCT components occupies a 60x60 cm breadboard that can be readily transported for clinical applications. The AO component combines a Hartmann-Shack wavefront sensor and a microelectromechanical systems-based deformable mirror to sense and correct ocular aberrations at 15 Hz with a maximum stroke of 4 microm. A broadband superluminescent diode source provides 4 mum depth resolution for SDOCT imaging. In human volunteer testing, we observed up to an 8 dB increase in OCT signal and a corresponding lateral resolution of <10 microm as a result of AO correction.     

Correcting ocular spherical aberration with soft contact lenses

Following aberroscopy, aspheric front surface soft contact lenses (SCLs) were custom-made to correct spherical refractive error and ocular spherical aberration (SA) of 18 myopic and five hypermetropic subjects (age, 20.5 +/- 5 yr). On-eye residual aberrations, logMAR visual acuity, and contrast sensitivity were compared with the best-correcting spectacle lens, an equally powered standard SCL, and an SCL designed to be aberration free in air. Custom-made and spherical SCLs reduced SA (p < 0.001; p < 0.05) but did not change total root-mean-square (rms) wave-front aberration (WFA). Aberration-free SCLs increased SA (p < 0.05), coma (p < 0.05), and total rms WFA. Visual acuity remained unchanged with any of the SCL types compared with the spectacle lens correction. Contrast sensitivity at 6 cycles/degree improved with the custom-made SCLs (p < 0.05). Increased coma with aspheric lens designs and uncorrected astigmatism limit the small possible visual benefit from correcting ocular SA with SCLs.     

Calibration and precompensation of noncommon path aberrations for extreme adaptive optics

Noncommon path aberrations (NCPAs) are one of the main limitations of an extreme adaptive optics (AO) system. NCPAs prevent extreme AO systems from achieving their ultimate performance. These static aberrations are unseen by the wavefront sensor and therefore are not corrected in closed loop. We present experimental results validating what we believe to be new procedures of measurement and precompensation of the NCPAs on the AO bench at ONERA (Office National d'Etudes et de Recherches Aérospatiales). The measurement procedure is based on refined algorithms of phase diversity. The precompensation procedure makes use of a pseudo-closed-loop scheme to overcome the AO wavefront-sensor-model uncertainties. Strehl ratio obtained in the images reaches 98.7% at 632.8 nm. This result allows us to be confident of achieving the challenging performance required for direct observation of extrasolar planets.     

Open-loop control of liquid-crystal spatial light modulators for vertical atmospheric turbulence wavefront correction

We present an open-loop adaptive optics (AO) system based on two liquid-crystal spatial light modulators (LCSLMs) that profit from high precision wavefront generation and good repeatability. A wide optical bandwidth of 300 nm is designed for the system, and a new open-loop optical layout is invented to conveniently switch between the open and closed loop. The corresponding control algorithm is introduced with a loop frequency (the reciprocal of the total time delay of a correction loop) of 103 Hz. The system was mounted onto a 2.16 m telescope for vertical atmospheric turbulence correction. The full width at half-maximum of the image of the star α Boo reached 0.636 arc sec after the open-loop correction, while it was 2.12 arc sec before the correction. The result indicates that the open-loop AO system based on LCSLMs potentially has the ability to be used for general astronomical applications.     

Adaptive optics and vision

It has long been recognised that the optical quality of the human eye is far from diffraction limited. This affects our visual acuity and severely limits the resolution at which images of the living retina can be obtained. Adaptive optics is a technique that can correct for the eye's aberrations and provide diffraction limited resolution. The origins of the technique lie in astronomy, but it was successfully adapted to the human eye just over 10 years ago. Since then there have been rapid developments in the field of adaptive optics and vision science. In vivo images of the retina can now be routinely achieved with unprecedented resolution. Sophisticated experiments can be performed to gain a deeper knowledge of the interaction of neural retinal architecture and visual perception. This article presents the theory behind adaptive optics for the human eye and reviews the developments in this field to date.     

Characterization and closed-loop performance of a liquid mirror adaptive optical system

A deformable mirror based on the principle of total internal reflection of light from an electrostatically deformed liquid-air interface was realized and used to perform closed-loop adaptive optical (AO) correction on a collimated laser beam aberrated by a rotating phase disk. Equations describing the resonant and oscillatory behavior of the liquid system were obtained and applied to the system under consideration. Characterization of the mirror included open- and closed-loop frequency responses, determination of rise times, the damping times of the liquid, and the influence of liquid surface motion in the absence of external optical aberrations. The performance of the AO system was determined for static and dynamic aberrations for various sets of system parameters. The predictions of the general expressions were compared to the results of the experimental realization and were found to be in good agreement.     

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

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

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.     

Peripheral refractive errors in myopic,emmetropic, and hyperopic young subjects

To gain more insight into the relationship between foveal and peripheral refractive errors in humans, spheres, cylinders, and their axes were binocularly measured across the visual field in myopic, emmetropic, and hyperopic groups of young subjects. Both automated infrared photorefraction (the "PowerRefractor"; www. plusoptix.de) and a double-pass technique were used because the PowerRefractor provided extensive data from the central 44 deg of the visual field in a very convenient and fast way. Two-dimensional maps for the average cross cylinders and spherical equivalents, as well as for the axes of the power meridians of the cylinders, were created. A small amount of lower-field myopia was detected with a significant vertical gradient in spherical equivalents. In the central visual field there was little difference among the three refractive groups. The established double-pass technique provided complementary data also from the far periphery. At 45 deg eccentricity the double-pass technique revealed relatively more hyperopic spherical equivalents in myopic subjects than in emmetropic subjects [+/-2.73 +/- 2.85 D relative to the fovea, p < 0.01 (+/- standard deviation)] and more myopic spherical equivalents in hyperopic subjects (-3.84 +/- 2.86 D relative to the fovea, p < 0.01). Owing to the pronounced peripheral astigmatism, spherical equivalents (refractions with respect to the plane of the circle of least confusion) became myopic relative to the fovea in all three groups. The finding of general peripheral myopia was unexpected. Its possible roles in foveal refractive development are discussed.     

Super-resolution pupil filtering for visual performance enhancement using adaptive optics

Ocular aberration correction can significantly improve visual function of the human eye. However, even under ideal aberration correction conditions, pupil diffraction restricts the resolution of retinal images. Pupil filtering is a simple super-resolution (SR) method that can overcome this diffraction barrier. In this study, a 145-element piezoelectric deformable mirror was used as a pupil phase filter because of its programmability and high fitting accuracy. Continuous phase-only filters were designed based on Zernike polynomial series and fitted through closed-loop adaptive optics. SR results were validated using double-pass point spread function images. Contrast sensitivity was further assessed to verify the SR effect on visual function. An F-test was conducted for nested models to statistically compare different CSFs. These results indicated CSFs for the proposed SR filter were significantly higher than the diffraction correction (p < 0.05). As such, the proposed filter design could provide useful guidance for supernormal vision optical correction of the human eye.     

Impact of Zernike-fit error on simulated high- and low-contrast acuity in keratoconus: implications for using Zernike-based corrections

This study examines the extent to which a Zernike-based optical correction can restore acuity in keratoconus as a function of disease severity and contrast level. Increasingly complete Zernike corrections in the presence of Zernike-fit error were simulated. Acuity for keratoconic eyes with <60 D maximum corneal power reached 20/13 with a fifth-order Zernike correction under high-contrast conditions and exhibited a loss of 0.1 logMAR (minimum angle of resolution) (from 20/32 to 20/40) for low-contrast conditions. Acuity for keratoconic eyes with >60 D maximum corneal power approached 20/13 with sixth-tenth-order corrections under high-contrast conditions but did not return to similar levels with a tenth-order correction for low-contrast conditions. The results suggest that fit error affects visual performance for more difficult tasks and that restoring high-contrast acuity (20/16 or better) using a fifth-order Zernike correction is not limited by Zernike=fit error for over 88% of keratoconus cases.     

Statistical properties of the Strehl ratio as a function of pupil diameter and level of adaptive optics correction following atmospheric propagation

The propagation of an optical beam through atmospheric turbulence produces wave-front aberrations that can reduce the power incident on an illuminated target or degrade the image of a distant target. The purpose of the work described here was to determine by computer simulation the statistical properties of the normalized on-axis intensity--defined as (D/r0)2 SR--as a function of D/r0 and the level of adaptive optics (AO) correction, where D is the telescope diameter, r0 is the Fried coherence diameter, and SR is the Strehl ratio. Plots were generated of (D/r0)2 (SR) and sigmaSR/(SR), where (SR) and sigma(SR) are the mean and standard deviation, respectively, of the SR versus D/r0 for a wide range of both modal and zonal AO correction. The level of modal correction was characterized by the number of Zernike radial modes that were corrected. The amount of zonal AO correction was quantified by the number of actuators on the deformable mirror and the resolution of the Hartmann wave-front sensor. These results can be used to determine the optimum telescope diameter, in units of r0, as a function of the AO design. For the zonal AO model, we found that maximum on-axis intensity was achieved when the telescope diameter was sized so that the actuator spacing was equal to approximately 2r0. For modal correction, we found that the optimum value of D/r0 (maximum mean on-axis intensity) was equal to 1.79Nr + 2.86, where Nr is the highest Zernike radial mode corrected.     

Wavefront-guided correction of ocular aberrations: are phase plate and refractive surgery solutions equal?

Wavefront-guided laser eye surgery has been recently introduced and holds the promise of correcting not only defocus and astigmatism in patients but also higher-order aberrations. Research is just beginning on the implementation of wavefront-guided methods in optical solutions, such as phase-plate-based spectacles, as alternatives to surgery. We investigate the theoretical differences between the implementation of wavefront-guided surgical and phase plate corrections. The residual aberrations of 43 model eyes are calculated after simulated refractive surgery and also after a phase plate is placed in front of the untreated eye. In each case, the current wavefront-guided paradigm that applies a direct map of the ocular aberrations to the correction zone is used. The simulation results demonstrate that an ablation map that is a Zernike fit of a direct transform of the ocular wavefront phase error is not as efficient in correcting refractive errors of sphere, cylinder, spherical aberration, and coma as when the same Zernike coefficients are applied to a phase plate, with statistically significant improvements from 2% to 6%.     

Relationship between acuity for gratings and for tumbling-E letters in peripheral vision.

Earlier studies have reported that grating resolution is sampling-limited in peripheral vision but that letter acuity is generally poorer than grating acuity. These results suggest that peripheral resolution of objects with rich Fourier spectra may be limited by some factor other than neural sampling. To examine this suggestion we formulated and tested the hypothesis that letter acuity in the periphery is sampling-limited, just as it is for extended and truncated gratings. We tested this hypothesis with improved methodology to avoid the confounding factors of target similarity, alphabet size, individual variation, peripheral refractive error, and stimulus size. Acuity was measured for an orientation-discrimination task (horizontal versus vertical) for a three-bar resolution target and for a block-E letter in which all strokes have the same length. We confirmed previous reports in the literature that acuity for these targets is worse than for extended sinusoidal gratings. To account for these results quantitatively, we used difference-spectrum analysis to identify those frequency components of the targets that might form a basis for performing the visual discrimination task. We find that discrimination performance for the three-bar targets and the block-E letters can be accounted for by a sampling-limited model, provided that the limited number of cycles that are present in the characteristic frequency of the stimulus is taken into account. Quantitative differences in acuity for discriminating other letter pairs (e.g., right versus left letters E or characters with short central strokes) could not be attributed to undersampling of either the characteristic frequency or the frequency of maximum energy in the difference spectrum. These results suggest additional tests of the sampling theory of visual resolution, which are the subject of a companion paper.     

Influence of Stiles-Crawford apodization on visual acuity

The Stiles-Crawford effect (SCE) of the first kind has often been considered to be important to spatial visual performance in that it ameliorates the influence of defocus and aberrations. We investigated the influence of SCE apodization on visual acuity as a function of defocus (out to +/-2 D) in four subjects. We used optical filters, conjugate with the eye's entrance pupil, that neutralized or doubled the existing SCE. With an illiterate-E task, the influence of the SCE was more noticeable for myopic defocus than for hypermetropic defocus, was generally more noticeable for high-contrast than for low-contrast letters, and increased with increase in pupil size. The greatest influence on visual acuity of neutralizing the SCE, across the subjects and range of conditions, was deterioration of 0.06 (4-mm pupil), 0.16 (6-mm pupil), and 0.29 log unit (7.6-mm pupil).     

Resolution of synthetic-aperture imaging through turbulence

A theory is developed for the resolution of an optical synthetic-aperture imaging system viewing an object through an inhomogeneous refractive medium. The inhomogeneities of the propagation medium create errors in the phase history data with resultant space-variant image effects, including geometric distortions and broadening of the impulse response or point-spread function. I relate the intensity-impulse response to the usual wave structure function. I determine the modulation transfer function for synthetic apertures of any size and exposure time, valid whenever the optical bandwidth is small compared with the carrier frequency, and derive the resolution for monostatic and bistatic synthetic apertures, valid whenever the real sampling aperture is small compared with the medium's coherence length. The results take the same form as the well-known turbulence-limited resolution of incoherent, real-aperture imaging with short exposure. Turbulence-limited synthetic-aperture resolution is somewhat better than incoherent real-aperture resolution under the same conditions. Autofocus processing improves synthetic-aperture resolution beyond this limit, and adaptive correction of higher-order phase history errors would improve it further.