Theory and measurement of ocular chromatic aberration

Asymmetric wavefront aberrations and pupillary shapes induced by electrical stimulation of ciliary nerve in cats measured with compact wavefront aberrometer

To investigate the changes in the wavefront aberrations and pupillary shape in response to electrical stimulation of the branches of the ciliary nerves in cats. Seven eyes of seven cats were studied under general anesthesia. Trains of monophasic pulses (current, 0.1 to 1.0 mA; duration, 0.5 ms/phase; frequency, 5 to 40 Hz) were applied to the lateral or medial branch of the short ciliary nerve near the posterior pole of the eye. A pair of electrodes was hooked onto one or both branch of the short ciliary nerve. The electrodes were placed about 5 mm from the scleral surface. The wavefront aberrations were recorded continuously for 2 seconds before, 8 seconds during, and for 20 seconds after the electrical stimulation. The pupillary images were simultaneously recorded during the stimulation period. Both the wavefront aberrations and the pupillary images were obtained 10 times/sec with a custom-built wavefront aberrometer. The maximum accommodative amplitude was 1.19 diopters (D) produced by electrical stimulation of the short ciliary nerves. The latency of the accommodative changes was very short, and the accommodative level gradually increased up to 4 seconds and reached a plateau. When only one branch of the ciliary nerve was stimulated, the pupil dilated asymmetrically, and the oblique astigmatism and one of the asymmetrical wavefront terms was also altered. Our results showed that the wavefront aberrations and pupillary dilations can be measured simultaneously and serially with a compact wavefront aberrometer. The asymmetric pupil dilation and asymmetric changes of the wavefront aberrations suggest that each branch of the ciliary nerve innervates specific segments of the ciliary muscle and dilator muscle of the pupil.

Crystalline lens thickness determines the perceived chromatic difference in magnification

Since the origin of the high interindividual variability of the chromatic difference in retinal image magnification (CDM) in the human eye is not well understood, optical parameters that might determine its magnitude were studied in 21 healthy subjects with ages ranging from 21 to 58 years. Two psychophysical procedures were used to quantify CDM. They produced highly correlated results. First, a red and a blue square, presented on a black screen, had to be matched in size by the subjects with their right eyes. Second, a filled red and blue square, flickering on top of each other at 2 Hz, had to be adjusted in perceived brightness and then in size to minimize the impression of flicker. CDM varied widely among subjects from 0.0% to 3.6%. Biometric ocular parameters were measured with low coherence interferometry and crystalline lens tilt and decentration with a custom-built Purkinjemeter. Correlations were studied between CDM and corneal power, anterior chamber depth, lens thickness, lens tilt and lens decentration, and vitreous chamber depths. Lens thickness was found significantly correlated with CDM and accounted for 64% of its variance. Vertical lens tilt and decentration were also significantly correlated. It was also found that CDM increased by 3.5% per year, and part of this change can be attributed to the age-related increase in lens thickness.

On using isoluminant stimuli to separate magno- and parvocellular responses in psychophysical experiments-a few words of caution

Isoluminant (or equiluminant) color stimuli (i.e., those that contain variations only in chromaticity) have been employed in attempts to separate magno- and parvocellular responses in psychophysical and noninvasive electrophysiological experiments. The justification for this has been the assumption that magnocellular cells, unlike parvocellular neurons, do not respond to stimuli varying only in hue. However, several problems are associated with this notion: (1) under many conditions, magnocellular neurons are not fully silenced at isoluminance, and (2) in many circumstances, parvocellular responses are substantially reduced at isoluminance. To rely upon isoluminant stimuli to "bias" stimuli toward the parvocellular system also faces obstacles. Therefore, caution is required when attempting to use isoluminant color to separate magno- and parvocellular responses.

Imaging of the parafoveal capillary network in diabetes

The retinal vasculature is an extremely complex system that is adapted to support the metabolic demands of the retinal structures, but on the other hand maintain the optimal optical qualities of this tissue. Through histological studies and clinical studies using fluorescein angiography we have learned a lot about the retinal vasculature in its physiological state and in different diseases, but both of these study methods have serious limitations that limit their extensive application in healthy subjects or in patients with early disease. In this current review we will present early observations about the retinal vasculature from several novel noninvasive imaging modalities like adaptive optics SLO, retinal functional imager, adaptive optics OCT and Doppler OCT. Some of these instruments allow a more detailed in vivo examination of the retinal vasculature than fluorescein angiography without its potentially serious side effects, thus better allowing us to further study retinal vascular homeostasis in healthy subjects and to identify preclinical changes in early disease stages.

Visual function and cortical organization in carriers of blue cone monochromacy

Carriers of blue cone monochromacy have fewer cone photoreceptors than normal. Here we examine how this disruption at the level of the retina affects visual function and cortical organization in these individuals. Visual resolution and contrast sensitivity was measured at the preferred retinal locus of fixation and visual resolution was tested at two eccentric locations (2.5° and 8°) with spectacle correction only. Adaptive optics corrected resolution acuity and cone spacing were simultaneously measured at several locations within the central fovea with adaptive optics scanning laser ophthalmoscopy (AOSLO). Fixation stability was assessed by extracting eye motion data from AOSLO videos. Retinotopic mapping using fMRI was carried out to estimate the area of early cortical regions, including that of the foveal confluence. Without adaptive optics correction, BCM carriers appeared to have normal visual function, with normal contrast sensitivity and visual resolution, but with AO-correction, visual resolution was significantly worse than normal. This resolution deficit is not explained by cone loss alone and is suggestive of an associated loss of retinal ganglion cells. However, despite evidence suggesting a reduction in the number of retinal ganglion cells, retinotopic mapping showed no reduction in the cortical area of the foveal confluence. These results suggest that ganglion cell density may not govern the foveal overrepresentation in the cortex. We propose that it is not the number of afferents, but rather the content of the information relayed to the cortex from the retina across the visual field that governs cortical magnification, as under normal viewing conditions this information is similar in both BCM carriers and normal controls.

Chromatic aberration in heterocentric astigmatic systems including the eye

PURPOSE

There is inconsistency in the literature in the definitions of longitudinal and transverse chromatic aberration, and there appear to be no definitions that make allowance for astigmatism and heterocentricity. The purpose is to propose definitions of longitudinal and transverse chromatic aberration that hold for systems which, like the typical eye, may be heterocentric and astigmatic and to develop the associated optics.

METHODS

Common definitions of longitudinal and transverse chromatic aberration based on Gaussian optics are generalized naturally in terms of linear optics to accommodate heterocentricity and astigmatism.

CONCLUSIONS

The definitions offered here apply to systems in general, including the visual optical system of the eye, and hold for homocentric stigmatic systems in particular. Care is advocated in the use of the terms longitudinal and transverse chromatic aberration.

Adaptive optics scanning laser ophthalmoscope-based microperimetry

PURPOSE

To develop and test the application of an adaptive optics scanning laser ophthalmoscope (AOSLO) with eye tracking for high-resolution microperimetric testing.

METHODS

An AOSLO was used to conduct simultaneous high-resolution retinal imaging and visual function testing in six normal subjects. Visual sensitivity was measured at test locations between the fovea and 5.0° eccentricity via an increment threshold approach using a 40-trial, yes-no adaptive Bayesian staircase procedure (QUEST). A high-speed eye tracking algorithm enabled real-time video stabilization and the delivery of diffraction-limited Goldmann I-sized stimuli (diameter = 6.5 arc min = ∼32 μm; λ = 680 nm) to targeted retinal loci for 200 ms. Test locations were selected either manually by the examiner or automatically using Fourier-based image registration. Cone spacing was assessed at each test location and sensitivity was plotted against retinal eccentricity. Finally, a 4.2 arc min stimulus was used to probe the angioscotoma associated with a blood vessel located at 2.5° eccentricity.

RESULTS

Visual sensitivity decreases with eccentricity at a rate of -1.32 dB/deg (R = 0.60). The vertical and horizontal errors of the targeted stimulus delivery algorithm averaged 0.81 and 0.89 arc min (∼4 μm), respectively. Based on a predetermined exclusion criterion, the stimulus was successfully delivered to its targeted location in 90.1% of all trials. Automated recovery of test locations afforded the repeat testing of the same set of cones over a period of 3 months. Thresholds measured over a parafoveal blood vessel were 1.96 times higher (p < 0.05; one-tailed t-test) than those measured in directly adjacent retina.

CONCLUSIONS

AOSLO-based microperimetry has the potential to test visual sensitivity with fine retinotopic precision. Automated recovery of previously tested locations allows these measures to be tracked longitudinally. This approach can be implemented by researchers interested in establishing the functional correlates of photoreceptor mosaic structure in patients with retinal disease.

Measurement and correction of transverse chromatic offsets for multi-wavelength retinal microscopy in the living eye

A special challenge arises when pursuing multi-wavelength imaging of retinal tissue in vivo, because the eye's optics must be used as the main focusing elements, and they introduce significant chromatic dispersion. Here we present an image-based method to measure and correct for the eye's transverse chromatic aberrations rapidly, non-invasively, and with high precision. We validate the technique against hyperacute psychophysical performance and the standard chromatic human eye model. In vivo correction of chromatic dispersion will enable confocal multi-wavelength images of the living retina to be aligned, and allow targeted chromatic stimulation of the photoreceptor mosaic to be performed accurately with sub-cellular resolution.

Near-infrared light photoacoustic ophthalmoscopy

We achieved photoacoustic ophthalmoscopy (PAOM) imaging of the retina with near-infrared (NIR) light illumination. A PAOM imaging system with dual-wavelength illumination at 1064 nm and 532 nm was built. We compared in vivo imaging results of both albino and pigmented rat eyes at the two wavelengths. The results show that the bulk optical absorption of the retinal pigment epithelium (RPE) is only slightly higher than that of the retinal vessels at 532 nm while it becomes more than an order of magnitude higher than that of the retinal vessels at 1064 nm. These studies suggest that although visible light illumination is suitable for imaging both the retinal vessels and the RPE, NIR light illumination, being more comfortable to the eye, is better suited for RPE melanin related investigations and diagnoses.

Object frequency characteristics of visual acuity

PURPOSE

To examine the extent to which visual acuity (VA) for broadband optotypes is scale invariant by determining whether the same object frequencies mediate VA for individuals with different levels of VA.

METHODS

LogMAR (minimum angle of resolution) VA for briefly presented tumbling E's was measured in 10 visually normal individuals and in five patients with VA loss. The E's were either unblurred or blurred with Gaussian low-pass filters that had cutoff frequencies spanning a 1.2-log unit range. The data were fit with a standard equivalent intrinsic blur model to estimate each subject's unblurred VA (MAR(0) in minutes of arc) and equivalent intrinsic blur (σ(int) in minutes of arc). From these estimates, the high-frequency cutoff of the band of retinal frequencies (cpd(crit) in cycles per degree) and object frequencies (cpl(crit) in cycles per letter) mediating VA were derived.

RESULTS

LogMAR(0) was related linearly to log σ(int) with a slope of 1.47, which is steeper than that predicted by scale invariance. Log cpd(crit) was related linearly to logMAR(0) by a slope of -0.64, which is shallower than that predicted by scale invariance. This lack of scale invariance is due to a linear relationship between log cpl(crit) and logMAR(0) that had a slope of 0.36.

CONCLUSIONS

The overall pattern of results is not consistent with the expectation of scale invariance underlying the MAR scale. Optotypes that conform to the expectations of scale invariance are needed to improve vision assessment and to provide equivalency of VA defined in terms of MAR and cpd.

Pascal's ring, cardinal points, and refractive compensation

Pascal's ring is a hexagon each of whose corners represents one of the six cardinal points of an optical system and whose sides represent relationships of relative axial position of the cardinal points. Changes to the ring represent the axial displacements of the cardinal points of the visual optical system of an eye that are caused when a spectacle lens compensates for the ametropia. Pascal's schema was described some 70 years ago with little theoretical justification. The purpose of this paper is to derive expressions for the axial locations of the cardinal points of a compound system consisting of an optical instrument and a visual optical system and for the shift caused by the instrument, and to provide theoretical justification for Pascal's schema. The cardinal points are treated not as separate entities but in a unified manner as special cases of an infinite class of special points. Expressions are derived using Gaussian optics. The results are specialized for the case of the eye's ametropia compensated by optical instruments in general and by spectacle lenses in particular. Pascal's schema is shown to be broadly correct although some modification is necessary for the effects on the incident cardinal points especially for the myopic eye.

Contributions of optical and non-optical blur to variation in visual acuity

PURPOSE

To determine the relative contributions of optical and non-optical sources of intrinsic blur to variations in visual acuity (VA) among normally sighted subjects.

METHODS

Best-corrected VA of 16 normally sighted subjects was measured using briefly presented (59 ms) tumbling E optotypes that were either unblurred or blurred through convolution with Gaussian functions of different widths. A standard model of intrinsic blur was used to estimate each subject's equivalent intrinsic blur (σint) and VA for the unblurred tumbling E (MAR0). For 14 subjects, a radially averaged optical point spread function due to higher-order aberrations was derived by Shack-Hartmann aberrometry and fit with a Gaussian function. The standard deviation of the best-fit Gaussian function defined optical blur (σopt). An index of non-optical blur (η) was defined as 1 - σopt/σint. A control experiment was conducted on five subjects to evaluate the effect of stimulus duration on MAR0 and σint. RESULTS.: The logarithm of the minimum angle of resolution (logMAR₀) for the briefly presented E was correlated significantly with log σint (r = 0.95, p < 0.01), consistent with previous work. However, logMAR₀ was not correlated significantly with log σopt (r = 0.46, p = 0.11). For subjects with logMAR₀ equivalent to ~20/20 or better, logMAR₀ was independent of log η, whereas for subjects with larger logMAR₀ values, logMAR₀ was proportional to log η. The control experiment showed a statistically significant effect of stimulus duration on logMAR₀ (p < 0.01) but a non-significant effect on σint (p = 0.13).

CONCLUSIONS

The relative contributions of optical and non-optical blur to VA varied among the subjects and were related to the subject's VA. Evaluating optical and non-optical blur may be useful for predicting changes in VA following procedures that improve the optics of the eye in patients with both optical and non-optical sources of VA loss.

Wavelength adjustment using an eye model from aberrometry data

We developed a method to convert aberrometry data obtained in one wavelength to the corresponding data in another wavelength using an eye model. A single map of aberrometry data is used to construct a free-form one-surface eye model. A general algorithm for the surface construction is described and implemented for real aberrometry data. Our method can handle varying conjugate distances of the measurement plane of the aberrometer and can also manage the chief ray prism that may be present. The algorithm is validated with the aid of an artificial plastic eye. The wavefronts in different wavelengths are compared through the Zernike analysis not only for lower-order aberrations, but also for higher-order aberrations. The results show that the changes of the Zernike aberration coefficients due to wavelengths are non-uniform. The defocus term has the highest effect from wavelength changes, which is consistent with the previous literature. Our method is compared with two approximate semi-analytical algorithms. The wavelength adjustments from a multi-surface eye model are contrasted with our method. We prove analytically that the conventional method of wavelength adjustment is based on paraxial analysis. In addition, we provide a method of finding the chief ray using back-projection in some cases and discuss different meanings of prism.

Design of a trichromatic cone array

Cones with peak sensitivity to light at long (L), medium (M) and short (S) wavelengths are unequal in number on the human retina: S cones are rare (<10%) while increasing in fraction from center to periphery, and the L/M cone proportions are highly variable between individuals. What optical properties of the eye, and statistical properties of natural scenes, might drive this organization? We found that the spatial-chromatic structure of natural scenes was largely symmetric between the L, M and S sensitivity bands. Given this symmetry, short wavelength attenuation by ocular media gave L/M cones a modest signal-to-noise advantage, which was amplified, especially in the denser central retina, by long-wavelength accommodation of the lens. Meanwhile, total information represented by the cone mosaic remained relatively insensitive to L/M proportions. Thus, the observed cone array design along with a long-wavelength accommodated lens provides a selective advantage: it is maximally informative.

Human color perception arises by comparing the signals from cones with peak sensitivities, at long (L), medium (M) and short (S) wavelengths. In dichromats, a characteristic distribution of S and M cones supports blue-yellow color vision: a few S and mostly M. When L cones are added, allowing red-green color vision, the S proportion remains low, increasing slowly with increasing retinal eccentricity, but the L/M proportion can vary 5-fold without affecting red-green color perception. We offer a unified explanation of these striking facts. First, we find that the spatial-chromatic statistics of natural scenes are largely symmetric between the L, M and S sensitivity bands. Thus, attenuation of blue light in the optical media, and chromatic aberration after long-wavelength accommodation of the lens, can give L/M cones an advantage. Quantitatively, information transmission by the cone array is maximized when the S proportion is low but increasing slowly with retinal eccentricity, accompanied by a lens accommodated to red light. After including blur by the lens, the optimum depends weakly on the red/green ratio, allowing large variations without loss of function. This explains the basic layout of the cone mosaic: for the resources invested, the organization maximizes information.

Effects of ocular transverse chromatic aberration on near foveal letter recognition

Transverse chromatic aberration (TCA) smears retinal images of peripheral stimuli. In reading, text information is extracted from both foveal and near fovea, where TCA magnitude is relatively small and variable. The present study investigated whether TCA significantly affects near foveal letter identification. Subjects were briefly presented a string of five letters centered one degree of visual angle to the left or right of fixation. They indicated whether the middle letter was the same as a comparison letter subsequently presented. Letter strings were rendered with a reddish fringe on the left edge of each letter and a bluish fringe on the right edge, consistent with expected left periphery TCA, or with the opposite fringe consistent with expected right periphery TCA. Effect of the color fringing on letter recognition was measured by comparing the response accuracy for fringed and non-fringed stimuli. Effects of lateral interference were examined by manipulating inter-letter spacing and similarity of neighboring letters. Results demonstrated significantly improved response accuracy with the color fringe opposite to the expected TCA, but decreased accuracy when consistent with it. Narrower letter spacing exacerbated the effect of the color fringe, whereas letter similarity did not. Our results suggest that TCA significantly reduces the ability to recognize letters in the near fovea by impeding recognition of individual letters and by enhancing lateral interference between letters.

Dual-conjugate adaptive optics for wide-field high-resolution retinal imaging

We present analysis and preliminary laboratory testing of a real-time dual-conjugate adaptive optics (DCAO) instrument for ophthalmology that will enable wide-field high resolution imaging of the retina in vivo. The setup comprises five retinal guide stars (GS) and two deformable mirrors (DM), one conjugate to the pupil and one conjugate to a plane close to the retina. The DCAO instrument has a closed-loop wavefront sensing wavelength of 834 nm and an imaging wavelength of 575 nm. It incorporates an array of collimator lenses to spatially filter the light from all guide stars using one adjustable iris, and images the Hartmann patterns of multiple reference sources on a single detector. Zemax simulations were performed at 834 nm and 575 nm with the Navarro 99 and the Liou- Brennan eye models. Two correction alternatives were evaluated; conventional single conjugate AO (SCAO, using one GS and a pupil DM) and DCAO (using multiple GS and two DM). Zemax simulations at 575 nm based on the Navarro 99 eye model show that the diameter of the corrected field of view for diffraction-limited imaging (Strehl >or= 0.8) increases from 1.5 deg with SCAO to 6.5 deg using DCAO. The increase for the less stringent condition of a wavefront error of 1 rad or less (Strehl >or= 0.37) is from 3 deg with SCAO to approximately 7.4 deg using DCAO. Corresponding results for the Liou-Brennan eye model are 3.1 deg (SCAO) and 8.2 deg (DCAO) for Strehl >or= 0.8, and 4.8 deg (SCAO) and 9.6 deg (DCAO) for Strehl >or= 0.37. Potential gain in corrected field of view with DCAO is confirmed both by laboratory experiments on a model eye and by preliminary in vivo imaging of a human eye.

The Optical Design of the Human Eye: a Critical Review

Cornea, lens and eye models are analyzed and compared to experimental findings to assess properties and eventually unveil optical design principles involved in the structure and function of the optical system of the eye. Models and data often show good match but also some paradoxes. The optical design seems to correspond to a wide angle lens. Compared to conventional optical systems, the eye presents a poor optical quality on axis, but a relatively good quality off-axis, thus yielding higher homogeneity for a wide visual field. This seems the result of an intriguing combination of the symmetry design principle with a total lack of rotational symmetry, decentrations and misalignments of the optical surfaces.

Calculation of retinal image quality for polychromatic light

Although the retinal image is typically polychromatic, few studies have examined polychromatic image quality in the human eye. We begin with a conceptual framework including the formulation of a psychophysical linking hypothesis that underlies the utility of image quality metrics based on the polychromatic point-spread function. We then outline strategies for computing polychromatic point-spread functions of the eye when monochromatic aberrations are known for only a single wavelength. Implementation problems and solutions for this strategy are described. Polychromatic image quality is largely unaffected by wavelength-dependent diffraction and higher-order chromatic aberration. However, accuracy is found to depend critically upon spectral sampling. Using typical aberrations from the Indiana Aberration Study, we assessed through-focus image quality for model eyes with and without chromatic aberrations using a polychromatic metric called the visual Strehl ratio. In the presence of typical levels of monochromatic aberrations, the effect of longitudinal chromatic aberration is greatly reduced. The effect of typical levels of transverse chromatic aberration is virtually eliminated in the presence of longitudinal chromatic aberration and monochromatic aberrations. Clinical value and limitations of the method are discussed.

A wavelength tunable wavefront sensor for the human eye

We have designed and assembled an instrument for objective measurement of the eye's wave aberrations for different wavelengths with no modifications in the measurement path. The system consists of a Hartmann-Shack wave-front sensor and a Xe-white-light lamp in combination with a set of interference filters used to sequentially select the measurement wavelength. To show the capabilities of the system and its reliability for measuring at different wavelengths, the ocular aberrations were measured in three subjects at 440, 488, 532, 633 and 694 nm, basically covering the whole visible spectrum. Even for the shortest wavelengths, the illumination level was always several orders of magnitude below the safety limits. The longitudinal chromatic aberration estimates and the wavelength dependence of coma and spherical aberration, as examples of higher-order aberration terms, were compared to the predictions of a chromatic eye model, with good agreement. To our knowledge, this is the first report of a device to objectively determine the spectral fluctuations in the ocular wavefront.

Chromatic tuning of contour-shape mechanisms revealed through the shape-frequency and shape-amplitude after-effects

We investigated whether contour-shape processing mechanisms are selective for color direction using the shape-frequency and shape-amplitude after-effects, or SFAE and SAAE [Gheorghiu, E. & Kingdom, F. A. A. (2006). Luminance-contrast properties of contour-shape processing revealed through the shape-frequency after-effect. Vision Research, 46(21), 3603-3615. Gheorghiu, E. & Kingdom, F. A. A. (2007). The spatial feature underlying the shape-frequency and shape-amplitude after-effects. Vision Research, 47(6), 834-844]. All contours were defined along the 'red-green', 'blue-yellow' and 'luminance' axes of cardinal color space. Adapting and test contours were defined along the same or along opposite polarities within a cardinal axis, and along the same or along different cardinal axes. We found (i) little transfer of the after-effects across different within-axis polarities, for all cardinal axes and for both even-symmetric and odd-symmetric contours; (ii) little transfer between the red-green and blue-yellow cardinal axes; (iii) little transfer between the chromatic and luminance cardinal directions for the SAAE; (iv) large transfer between the chromatic and luminance cardinal directions for the SFAE. We conclude that contour-shape mechanisms are selective for within-cardinal axis polarity and for the chromatic axes within the isoluminant plane. However for certain types of contour-shape processing they are poorly selective along the chromatic versus luminance dimension. Overall our results suggest that contour-shape encoding mechanisms are selective for color direction and that color is important for contour-shape processing.

Wide-angle chromatic aberration corrector for the human eye

The human eye is affected by large chromatic aberration. This may limit vision and makes it difficult to see fine retinal details in ophthalmoscopy. We designed and built a two-triplet system for correcting the average longitudinal chromatic aberration of the eye while keeping a reasonably wide field of view. Measurements in real eyes were conducted to examine the level and optical quality of the correction. We also performed some tests to evaluate the effect of the corrector on visual performance.

Chromatic aberration and the roles of double-opponent and color-luminance neurons in color vision

How does the visual cortex encode color? I summarize a theory in which cortical double-opponent color neurons perform a role in color constancy and a complementary set of color-luminance neurons function to selectively correct for color fringes induced by chromatic aberration in the eye. The theory may help to resolve an ongoing debate concerning the functional properties of cortical receptive fields involved in color coding.

Multi-wavelength imaging with the adaptive optics scanning laser Ophthalmoscope

The adaptive optics scanning laser ophthalmoscope has been fitted with three light sources of different wavelengths to allow simultaneous or separate imaging with one, two or three wavelength combinations. The source wavelengths used are 532 nm, 658 nm and 840 nm. Typically the instrument is used in dual-frame mode, performing imaging at 840 nm and precisely coincident retinal stimulation in one of the visible wavelengths. Instrument set-up and single-detector image capture are described. Simultaneous multi-wavelength imaging in the living human retina is demonstrated. The chromatic aberrations of the human eye lead to lateral and axial shifts, as well as magnification differences in the image, from one wavelength to another. Measurement of these chromatic effects is described for instrument characterization purposes.

Cone contributions to signals for accommodation and the relationship to refractive error

The accommodation response is sensitive to the chromatic properties of the stimulus, a sensitivity presumed to be related to making use of the longitudinal chromatic aberration of the eye to decode the sign of the defocus. Thus, the relative sensitivity to the long- (L) and middle-wavelength (M) cones may influence accommodation and may also be related to an individual's refractive error. Accommodation was measured continuously while subjects viewed a sine wave grating (2.2c/d) that had different cone contrast ratios. Seven conditions tested loci that form a circle with equal vector length (0.27) at 0, 22.5, 45, 67.5, 90, 120, 145 deg. An eighth condition produced an empty field stimulus (CIE (x,y) co-ordinates (0.4554, 0.3835)). Each of the gratings moved at 0.2 Hz sinusoidally between 1.00 D and 3.00 D for 40s, while the effects of longitudinal chromatic aberration were neutralized with an achromatizing lens. Both the mean level of accommodation and the gain of the accommodative response, to sinusoidal movements of the stimulus, depended on the relative L and M cone sensitivity: Individuals more sensitive to L-cone stimulation showed a higher level of accommodation (p=0.01; F=12.05; ANOVA) and dynamic gain was higher for gratings with relatively more L-cone contrast. Refractive error showed a similar correlation: More myopic individuals showed a higher mean level of accommodation (p<0.01; F=11.42; ANOVA) and showed higher gain for gratings with relatively more L-cone than M-cone contrast (p=0.01; F=10.83 ANOVA). If luminance contrast is maximized by accommodation, long wavelengths will be imaged behind the photoreceptors. Individuals in whom luminance is dominated by L-cones may maximize luminance contrast both by accommodating more, as shown here, and by increased ocular elongation, resulting in myopia, possibly explaining the correlations reported here among relative L/M-cone sensitivity, refractive error and accommodation.

Blue-Yellow Signals Are Enhanced by Spatiotemporal Luminance Contrast in Macaque V1

We measured the color tuning of a population of S-cone-driven V1 neurons in awake, fixating monkeys. Analysis of randomly chosen color stimuli that were effective in evoking action potentials showed that these neurons received opposite sign input from the S cones and a combination of L and M cones. Surprisingly, these cells also responded to LM cone contrast irrespective of polarity, a nonlinear sensitivity that was masked by conventional linear analysis methods. Taken together, these observations can be summarized in a nonlinear model that combines nonopponent and opponent signals such that luminance contrast enhances color processing. These findings indicate that important aspects of the cortical representation of color cannot be described by classical linear analysis, and reveal a possible neural correlate of perceptual color-luminance interactions.

Accommodation with and without short-wavelength-sensitive cones and chromatic aberration

Accommodation was monitored while observers (23) viewed a square-wave grating (2.2 cycles/deg; 0.53 contrast) in a Badal optometer. The grating moved sinusoidally (0.2 Hz) to provide a stimulus between -1.00 D and -3.00 D during trials lasting 40.96 s. There were three illumination conditions: 1. Monochromatic 550 nm light to stimulate long-wavelength-sensitive cones (L-cones) and medium-wavelength-sensitive cones (M-cones) without chromatic aberration; 2. Monochromatic 550 nm light+420 nm light to stimulate long-, medium- and short-wavelength-sensitive cones (S-cones) with longitudinal chromatic aberration (LCA); 3. Monochromatic 550 nm light+420 nm light to stimulate L-, M- and S-cones viewed through an achromatizing lens. In the presence of LCA mean dynamic gain decreased (p=0.0003; ANOVA) and mean accommodation level was reduced (p=0.001; ANOVA). The reduction in gain and increased lag of accommodation in the presence of LCA could result from a blue-yellow chromatic signal or from a larger depth-of-focus.

Small foveal targets for studies of accommodation and the Stiles–Crawford effect

The properties of small monochromatic targets as accommodative stimuli are not well understood. We used a dynamic optometer to record accommodation responses to monochromatic disc targets (1.0-27.3 min arc) and to a Maltese cross. Accommodation responded adequately to points as small as 13.6 min arc. The response to these small targets is relevant to the question of whether the Stiles-Crawford (SC) effect could provide a stimulus to accommodation. Previous studies have used pupil apodizing filters to neutralise the natural SC function and so determine how visual performance or accommodation is influenced by the SC effect. However, these filters cannot correct for known inhomogeneities in the SC function across the retina for extended targets. Therefore, we calculated the SC function inhomogeneities across the retinal image of a smaller 13.6-min arc target. Unfortunately, even this small target is too large to permit a homogenous SC function across its extent. Alternatives to the apodizing filter approach are discussed.

Accommodation responses to stimuli in cone contrast space

The aim was to identify the cone contributions and pathways for reflex accommodation. Twelve illumination conditions were used to test specified locations in cone-contrast space. Accommodation was monitored continuously in a Badal optometer while the grating stimulus (2.2 c/d sine-wave; 0.27 modulation) moved sinusoidally (0.195 Hz) towards and away from the eye from a mean position of 2.00 D (+/-1.00 D). Mean accommodation level and dynamic gain and phase at 0.195 Hz were calculated. Mean accommodation level varied significantly when the long- and middle-wavelength cone contrast ratio was altered in both the luminance and chromatic quadrants of cone-contrast space. This experiment indicates that L- and M-cones contribute to luminance and chromatic signals that produce the accommodation response, most likely through magno-cellular and parvo-cellular pathways, respectively. The L:M cone weighting to the luminance pathway that mediates accommodation is 1.63:1. The amplitude and direction of the response depends on changes in chromatic contrast and luminance contrast signals that result from longitudinal chromatic aberration and defocus of the image.

Whole Eye Wavefront Aberrations in Mexican Male Subjects

PURPOSE

To analyze the characteristics, incidence, and appearance of wavefront aberrations in undilated, normal, unoperated eyes.

METHODS

Eighty-eight eyes of 44 healthy male Mexican subjects (mean age 25.32 years, range 18 to 36 yr) were divided into three groups based on uncorrected visual acuity of greater than or equal to 20/20, 20/30, or 20/40. UCVA measurements were obtained using an Acuity Max computer screen chart. Wavefront aberrations were measured with the Nidek OPD-Scan ARK 10000, Ver. 1.11b. All measurements were carried out at the same center by the same technician during a single session, following manufacturer instructions. Background illumination was 3 Lux.

RESULTS

Wavefront aberration measurements for each group were statistically analyzed using StatView; an average eye was characterized and the resulting aberrations were simulated using MATLAB. We obtained wavefront aberration maps for the 20/20 undilated normal unoperated eyes for total, low, and high order aberration coefficients. Wavefront maps for right eyes were practically the same as those for left eyes. Higher aberrations did not contribute substantially to total wavefront analysis.

CONCLUSIONS

Average aberrations of this "normal eye" will be used as criteria to decide the necessity of wavefront-guided ablation in our facilities. We will focus on the nearly zero average of high order aberrations in this normal whole eye as a reference to be matched.

The role of short-wavelength sensitive cones and chromatic aberration in the response to stationary and step accommodation stimuli

The aim of the experiment was to test for a contribution from short-wavelength sensitive cones to the static and step accommodation response, to compare responses from short and long- plus middle-wavelength sensitive cone types, and to examine the contribution of a signal from longitudinal chromatic aberration to the accommodation response. Accommodation was monitored continuously (eight subjects) to a square-wave grating (2.2 c/d; 0.57 contrast) in a Badal optometer. The grating stepped (1.00 D) randomly towards or away from the eye from a starting position of 2.00 D. Five illumination conditions were used to isolate cone responses, and combine them with or without longitudinal chromatic aberration. Accuracy of the response before the step, step amplitude, latencies and time-constants, were compared between conditions using single factor ANOVA and t-test comparisons. Both S-cones and LM-cones mediated static and step accommodation responses. S-cone contrast drives "static" accommodation for near, but the S-cone response is too slow to influence step dynamics when LM-cones participate.

Color constancy and the functional significance of McCollough effects

A central problem in visual perception concerns how humans perceive stable and uniform object colors despite variable lighting conditions (i.e. color constancy). One solution is to 'discount' variations in lighting across object surfaces by encoding color contrasts, and utilize this information to 'fill in' properties of the entire object surface. Implicit in this solution is the caveat that the color contrasts defining object boundaries must be distinguished from the spurious color fringes that occur naturally along luminance-defined edges in the retinal image (i.e. optical chromatic aberration). In the present paper, we propose that the neural machinery underlying color constancy is complemented by an 'error-correction' procedure which compensates for chromatic aberration, and suggest that error-correction may be linked functionally to the experimentally induced illusory colored aftereffects known as McCollough effects (MEs). To test these proposals, we develop a neural network model which incorporates many of the receptive-field (RF) profiles of neurons in primate color vision. The model is composed of two parallel processing streams which encode complementary sets of stimulus features: one stream encodes color contrasts to facilitate filling-in and color constancy; the other stream selectively encodes (spurious) color fringes at luminance boundaries, and learns to inhibit the filling-in of these colors within the first stream. Computer simulations of the model illustrate how complementary color-spatial interactions between error-correction and filling-in operations (a) facilitate color constancy, (b) reveal functional links between color constancy and the ME, and (c) reconcile previously reported anomalies in the local (edge) and global (spreading) properties of the ME. We discuss the broader implications of these findings by considering the complementary functional roles performed by RFs mediating color-spatial interactions in the primate visual system.

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

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

Artifacts in spatiochromatic stimuli due to variations in preretinal absorption and axial chromatic aberration: implications for color physiology

The spatiochromatic receptive-field structure of neurons in the macaque visual system has been studied almost exclusively with stimuli based on the human foveal cone fundamentals of Smith and Pokorny [Vision Res. 15, 161 (1975)] and generated on cathode ray tube displays. In the current study the artifacts evoked by cone-isolating, spatially structured stimuli due to variations in the eye's preretinal absorption characteristics and axial chromatic aberration are quantified. In addition, the luminance artifacts evoked by nominally isoluminant sinusoidal grating stimuli due to the same factors are quantified. The results indicate that the spatiochromatic stimuli commonly employed to map receptive fields of neurons at eccentricities > 10 deg are especially prone to artifacts and that these artifacts are maximal for the high-contrast S-cone-isolating stimuli that are often used. On the basis of these simulations, a method is introduced that improves spatiochromatic receptive-field estimates by compensating for response contributions from the incompletely silenced cone mosaics during cone-isolating stimulation.

Interaction between aberrations to improve or reduce visual performance

PURPOSE

To investigate how pairs of Zernike modes interact to increase or decrease visual acuity.

SETTING

Visual Optics Institute, College of Optometry, University of Houston, Houston, Texas, USA.

METHODS

Subjects read aberrated and unaberrated visual acuity charts 3 times. Each aberrated chart was produced by convolving an aberrated point-spread function with an unaberrated acuity chart. Point-spread functions were defined by 4 pairs of Zernike modes. For each pair, 9 combinations were used, ranging from all aberration being loaded into the first mode to all aberration being loaded into the second mode. The root mean square (RMS) wavefront error always totaled 0.25 microm (6.0 mm pupil), a level similar to the aberration induced by traditional flying small-spot laser refractive surgeries.

RESULTS

For all conditions (except the unaberrated charts), visual acuity decreased. Acuity varied significantly depending on which modes were mixed and the relative contribution of each mode. Modes 2 radial orders apart and having the same sign and angular frequency tended to combine to increase visual acuity. Modes within the same radial order tended to combine to decrease acuity.

CONCLUSIONS

For low levels of aberration, the RMS wavefront error is not a good predictor of visual acuity. Clinically, it is important to define how aberrations interact to optimize visual performance. New metrics of optical/neural performance that correlate better with clinical measures of visual performance need to be adopted or developed, as well as new clinically viable measures of visual performance that are sensitive to subtle changes in optical performance.

Bayesian model of Snellen visual acuity

A Bayesian model of Snellen visual acuity (VA) has been developed that, as far as we know, is the first one that includes the three main stages of VA: (1) optical degradations, (2) neural image representation and contrast thresholding, and (3) character recognition. The retinal image of a Snellen test chart is obtained from experimental wave-aberration data. Then a subband image decomposition with a set of visual channels tuned to different spatial frequencies and orientations is applied to the retinal image, as in standard computational models of early cortical image representation. A neural threshold is applied to the contrast responses to include the effect of the neural contrast sensitivity. The resulting image representation is the base of a Bayesian pattern-recognition method robust to the presence of optical aberrations. The model is applied to images containing sets of letter optotypes at different scales, and the number of correct answers is obtained at each scale; the final output is the decimal Snellen VA. The model has no free parameters to adjust. The main input data are the eye's optical aberrations, and standard values are used for all other parameters, including the Stiles-Crawford effect, visual channels, and neural contrast threshold, when no subject specific values are available. When aberrations are large, Snellen VA involving pattern recognition differs from grating acuity, which is based on a simpler detection (or orientation-discrimination) task and hence is basically unaffected by phase distortions introduced by the optical transfer function. A preliminary test of the model in one subject produced close agreement between actual measurements and predicted VA values. Two examples are also included: (1) application of the method to the prediction of the VAin refractive-surgery patients and (2) simulation of the VA attainable by correcting ocular aberrations.

Primary Multipoint (Segmental) Custom Ablation

PURPOSE

We present our experience in resolving visual symptoms in refractive patients undergoing primary multipoint (segmental) custom ablation.

METHODS

Twelve eyes with mixed myopic astigmatism underwent evaluation and primary treatment by multipoint (segmental) custom ablation for the correction of refractive errors and visual symptoms using the Nidek NAVEX platform.

RESULTS

Twelve eyes showed resolution of visual symptoms following diagnosis and treatment with MCA using the NAVEX platform. No patient lost two or more lines of best spectacle-corrected visual acuity. The postoperative root mean square of higher order aberrations did not change in a predictable or reproducible fashion.

CONCLUSION

Multipoint (segmental) custom ablation with the Nidek NAVEX system was safe and effective for correcting mixed myopic astigmatism and for resolving visual symptoms in selected refractive surgery candidates. Small changes in the root mean square of higher order aberration values were not always reflected in a patient's subjective assessment of vision quality.

Visual acuity as a function of Zernike mode and level of root mean square error

BACKGROUND

The coefficients of normalized Zernike expansion are orthogonal and reflect the relative contribution of each mode to the total root mean square (RMS) wavefront error. The relationship between the level of RMS wavefront error within a mode and its effect on visual performance is unknown.

PURPOSE

To determine for various levels of RMS wavefront error how each mode of the normalized Zernike expansion for the second, third, and fourth orders affect high- and low-contrast acuity.

METHODS

Three healthy optimally corrected cyclopleged subjects read aberrated and unaberrated high- and low-contrast logarithm of the minimum angle of resolution acuity charts monocularly through a 3-mm artificial pupil. Acuity was defined by the total number of letters read correctly up to the fifth miss. Aberrated and unaberrated charts were generated using a program called CTView. Six levels of RMS wavefront error were used (0.00, 0.05, 0.10, 0.15, 0.20, and 0.25 microm). Each level of RMS error was loaded into each mode of the second, third, and fourth radial orders individually for a total of 72 charts. Data were normalized by subject, and the normalized data were averaged across subjects.

RESULTS

Across modes and within each mode as the level of RMS wavefront error increased above 0.05 microm of RMS wavefront error, visual acuity decreased in a linear fashion. Slopes of the linear fits varied depending on the mode. Modes near the center of the Zernike pyramid had steeper slopes than those near the edge.

CONCLUSIONS

Increasing the RMS error within any single mode of the normalized Zernike expansion decreases visual acuity in a linear fashion. The slope of the best fitting linear equation varies with Zernike mode. Slopes near the center of the Zernike pyramid are steeper than those near the edge. Although the normalized Zernike expansion parcels RMS error orthogonally, the resulting effects on visual performance as measured by visual acuity are not orthogonal. New metrics of the combined effects of the optical and the neural transfer functions that are predictive of visual performance need to be developed.

Preneural limitations on letter identification in central and peripheral vision

We created a sequential ideal-observer model that could address the question, How much of letter identification performance and its change with eccentricity can be accounted for by preneural factors? The ideal-observer model takes into account preneural factors including the stimulus rendering properties of a CRT display, the optical imaging quality of the eye, and photon capture and sampling characteristics of the cones. We validated the formulation of the model by comparing its performance on simple psychophysical tasks with that of previous sequential ideal-observer models. The model was used to study properties of the image rendering of letters. For example, the model's identification of high-resolution letters (i.e., many pixels per letter), but not low-resolution letters, is largely immune to changes in pixel width. We compared human and ideal-observer letter-identification acuity for the lowercase alphabet at 0 degrees, 5 degrees, and 20 retinal eccentricity. Acuity of the ideal observer for high-contrast letters is approximately seven times better than that of the human observers at 0 degrees. Acuity decreased with eccentricity more rapidly for human observers than for the ideal observer such that the thresholds differed by a factor of 50 at 20 degrees. A decrease in stimulus duration from 100 to 33 ms resulted in no decrease in relative threshold size between the human and ideal observers at all eccentricities, indicating that humans effectively integrate stimulus information over this range. Decreasing contrast from 75% to 25%, however, reduced the difference in acuities twofold at all eccentricities between humans and the ideal-observer model, consistent with the presence a compressive nonlinearity only in the human observers. The gap between human and ideal acuity in central vision means that there are substantial limitations in human letter recognition beyond the stage of photoreceptor sampling. The increasing performance gap between human and ideal-observer performance with eccentricity implicates an increasing role of neural limitations with eccentricity in limiting human letter identification.

Standards for Reporting the Optical Aberrations of Eyes

In response to a perceived need in the vision community, an OSA taskforce was formed at the 1999 topical meeting on vision science and its applications (VSIA-99) and charged with developing consensus recommendations on definitions, conventions, and standards for reporting of optical aberrations of human eyes. Progress reports were presented at the 1999 OSA annual meeting and at VSIA-2000 by the chairs of three taskforce subcommittees on (1) reference axes, (2) describing functions, and (3) model eyes.

Are All Aberrations Equal?

PURPOSE

To determine for a fixed RMS error (25 microm, over a 6-mm pupil) how each mode of the normalized Zernike polynomial (second through the fourth radial order) affects high and low contrast logMAR visual acuity.

METHODS

Three healthy volunteers served as subjects. CTView was used to generate optically aberrated logMAR charts. Accommodation was paralyzed and pupils dilated. The foveal achromatic axis of the eye was aligned to a 3-mm pupil and the eye was optimally refracted. Aberrated acuity charts were read until five letters were missed. Data were normalized for each subject to the acuity obtained by reading unaberrated charts and plotted as letters lost as a function of Zernike mode.

RESULTS

Defocus (Z2(0)) decreased letter acuity more than astigmatism (Z2(2), Z2(-2)). Coma (Z3(1), Z3(-1)) decreased acuity more than trefoil (Z3(3), Z3(-3)). Spherical aberration (Z4(0)) and secondary astigmatism (Z2(2), Z4(-2)) decreased acuity much more than quadrafoil (Z4(4), Z4(-4)).

CONCLUSIONS

1. For an equal amount of RMS error not all coefficients of the Zernike polynomial induce equivalent losses in high and low contrast logMAR acuity. 2. Wavefront error concentrated near the center of the pyramid adversely affects visual acuity more than modes near the edge of the pyramid. 3. Large changes in chart appearance are not reflected in equally large decreases in visual performance (ie, subjects could correctly identify highly aberrated letters). 4. Interactions between modes complicate weighting each Zernike mode for visual impact.

Effects of longitudinal chromatic aberration on accommodation and emmetropization

PURPOSE

Less accommodation was found when human subjects read in blue (peak at about 440 nm) than when they read in red light (above 600 nm; [Kroger & Binder, British Journal of Ophthalmology 84 (2000) 890]). On the other hand, emmetropization in chickens did not appear to compensate for the chromatic defocus (385 nm versus 665 nm; [Rohrer, Schaeffel & Zrenner, Journal of Physiology 449 (1992) 363]). The apparently contradictory result was studied in more detail in humans and chickens.

METHODS

Accommodation was measured with an eccentric infrared photorefractor, the PowerRefractor, in human subjects reading under quasi-monochromatic illumination conditions. Chickens were refracted in quasi-monochromatic ambient illumination but with no particular fixation target. In a second experiment, they were also raised in monochromatic light for two days and subsequently refracted both in complete darkness, in monochromatic light, and in white light, both without and with cycloplegia.

RESULTS

Consistent with the initial report by Kroger and Binder [British Journal of Ophthalmology 84 (2000) 890], accommodation in human subjects was found to shift in accordance with the chromatic aberration function. An immediate shift in accommodation tonus was also found in the chickens when they were refracted under red and in blue ambient illumination (average difference between refractions in both conditions: 1.26+/-0.54 D, p<0.001 paired t-test). This value is close to the chromatic focus difference between the two wavelengths (1.5 D [Mandelman & Sivak, Vision Research 23 (1983) 1555]). When chickens were raised in blue or red light for two days, and their refractions were subsequently measured in complete darkness, they showed also a difference in refractions (1.41+/-1.00 D; ANOVA: p<0.0012, post hoc t-test: at least p<0.05 among different groups). This difference was no longer significant when they were refracted in white light but became again significant when they were cyclopleged (0.57+/-0.58 D, p=0.039, unpaired t-test). The latter observation makes it unlikely that the difference resulted just from a shift in the resting tonus of accommodation.

CONCLUSIONS

(1) Imposed chromatic defocus produces a shift in accommodation tonus in both humans and chickens which is, in the case of the chicken, followed by a shift in cycloplegic refractive state into the same direction, (2) the difference to the previous study by Rohrer, Schaeffel and Zrenner [Journal of Physiology 449 (1992) 363] can be explained from the fact that shorter wavelengths were used than in the present study, at which emmetropization was no longer functional and, (3) the small amplitude and the variability of the shifts in refraction do not allow clear statements about the role of the "lag of accommodation" in refractive development but they show that several cone types contribute to emmetropization.