Model for cone directionality reflectometric measurements based on scattering

Visual Axis and Stiles-Crawford Effect Peak Show a Positional Correlation in Normal Eyes: A Cohort Study

Purpose

The purpose of this study was to locate the visual axis and evaluate its correlation with the Stiles-Crawford effect (SCE) peak.

Methods

Ten young, healthy individuals (20 eyes) were enrolled. An optical system was developed to locate the visual axis and measure SCE. To locate the visual axis, 2 small laser spots at 450 nm and 680 nm were co-aligned and delivered to the retina. The participants were asked to move a translatable pinhole until these spots were perceived to overlap each other. The same system assessed SCE at 680 nm using a bipartite, 2-channel (reference and test) Maxwellian-view optical system. The peak positions were estimated using a two-dimensional Gaussian fitting function and correlated with the visual axis positions.

Results

Both the visual axis (x = 0.24 ± 0.35 mm, y = -0.16 ± 0.34 mm) and the SCE peak (x = 0.27 ± 0.35 mm, y = -0.15 ± 0.31 mm) showed intersubject variability among the cohort. The SCE peak positions were highly correlated in both the horizontal and vertical meridians to the visual axes (R2 = 0.98 and 0.96 for the x and y coordinates, respectively). Nine of the 10 participants demonstrated mirror symmetry for the coordinates of the visual axis and the SCE peak between the eyes (R2 = 0.71 for the visual axis and 0.76 for the SCE peak).

Conclusions

The visual axis and SCE peak locations varied among the participants; however, they were highly correlated with each other for each individual. These findings suggest a potential mechanism underlying the foveal cone photoreceptor alignment.

Patches of Dysflective Cones in Eyes With No Known Disease

Purpose

To characterize the structure and function of patches of dysflective cones in the foveal region of subjects with normal vision and no known pathology. Dysflective cones are cones that have little or no reflective properties in optical coherence tomography (OCT) or adaptive optics scanning laser ophthalmoscope (AOSLO) images yet exhibit measurable function.

Methods

AOSLO images were surveyed for the presence of hyporeflective cone patches, and subjects were brought back for imaging to determine the changes in the hyporeflective region. Adaptive optics microperimetry (AOMP) was used to assess the function of hyporeflective patches in four subjects to determine that they did, in fact, contain dysflective cones. AOMP utilized a stimulus size of less than 1 arcmin to measure thresholds inside and outside the hyporeflective region.

Results

Nineteen out of 47 individuals retrospectively reviewed had one or more regions with hyporeflective cone patches in one or both eyes. Ten subjects with hyporeflective cone patches were brought back for imaging. Seven of the 10 had resolved at follow up, and in three subjects new hyporeflective patches appeared in a different location. All AOMP-measured subjects had measurable function in the dysflective cone region. Three out of four subjects showed no difference in light sensitivity in the dysflective region compared to adjacent areas, and one subject showed a 3× reduction in sensitivity in the area.

Conclusions

Patches of dysflective cone have been identified in subjects with normal vision and no known pathology, and we have observed instances where dysflective cones in these subjects regain normal reflective properties.

Simultaneous directional full-field OCT using path-length and carrier multiplexing

Full-field swept-source optical coherence tomography (FF-SS-OCT) is an emerging technology with potential applications in ophthalmic imaging, microscopy, metrology, and other domains. Here we demonstrate a novel method of multiplexing FF-SS-OCT signals using carrier modulation (CM). The principle of CM could be used to inspect various properties of the scattered light, e.g. its spectrum, polarization, Doppler shift, or distribution in the pupil. The last of these will be explored in this work, where CM was used to acquire images passing through two different optical pupils. The two pupils contained semicircular optical windows with perpendicular orientations, with each window permitting measurement of scattering anisotropy in one dimension by inducing an optical delay between the images formed by the two halves of the pupil. Together, the two forms of multiplexing permit measurement of differential scattering anisotropy in the x and y dimensions simultaneously. To demonstrate the feasibility of this technique our carrier multiplexed directional FF-OCT (CM-D-FF-OCT) system was used to acquire images of a microlens array, human hair, onion skin and in vivo human retina. The results of these studies are presented and briefly discussed in the context of future development and application of this technique.

Lags and leads of accommodation in humans: Fact or fiction?

The focusing response of the human eye — accommodation — exhibits errors known as lags and leads. Lags occur when the stimulus is near and the eye appears to focus farther than the stimulus. Leads occur with far stimuli where the eye appears to focus nearer than the stimulus. We used objective and subjective measures simultaneously to determine where the eye is best focused. The objective measures were made with a wavefront sensor and an autorefractor, both of which analyze light reflected from the retina. These measures exhibited typical accommodative errors, mostly lags. The subjective measure was visual acuity, which of course depends not only on the eye's optics but also on photoreception and neural processing of the retinal image. The subjective measure revealed much smaller errors. Acuity was maximized at or very close to the distance of the accommodative stimulus. Thus, accommodation is accurate in terms of maximizing visual performance.

Speckle reduction in double-pass retinal images

The double pass (DP) technique quantifies the optical quality of the eye by measuring its point spread function. The low reflectivity of the retina requires the use of a high-brightness, point-like illumination source, and thus, DP systems use laser diodes (LDs). However, LDs light produces speckle, and a low-cost solution to reduce speckle is to include a vibrating mirror in the beam path. With the goal of finding an all-optical solution, here we perform a comparative study of the amount of speckle produced by three semiconductor light sources: an LD, a light emitting diode (LED), and a superluminescent diode (SLED). We also compare the results with the speckle reduction that is obtained with a vibrating mirror. We find that the SLED is a good alternative to LD illumination, as the amount of speckle in the image is almost as low as that obtained with an LD and a vibrating mirror in the beam path.

Adaptive optics imaging of the human retina

Adaptive Optics (AO) retinal imaging has provided revolutionary tools to scientists and clinicians for studying retinal structure and function in the living eye. From animal models to clinical patients, AO imaging is changing the way scientists are approaching the study of the retina. By providing cellular and subcellular details without the need for histology, it is now possible to perform large scale studies as well as to understand how an individual retina changes over time. Because AO retinal imaging is non-invasive and when performed with near-IR wavelengths both safe and easily tolerated by patients, it holds promise for being incorporated into clinical trials providing cell specific approaches to monitoring diseases and therapeutic interventions. AO is being used to enhance the ability of OCT, fluorescence imaging, and reflectance imaging. By incorporating imaging that is sensitive to differences in the scattering properties of retinal tissue, it is especially sensitive to disease, which can drastically impact retinal tissue properties. This review examines human AO retinal imaging with a concentration on the use of the Adaptive Optics Scanning Laser Ophthalmoscope (AOSLO). It first covers the background and the overall approaches to human AO retinal imaging, and the technology involved, and then concentrates on using AO retinal imaging to study the structure and function of the retina.

Differential detection of retinal directionality

An adaptive optics fundus camera has been developed that uses simultaneous capture of multiple images via adjacent pupil sectors to provide directional sensitivity. In the chosen realization, a shallow refractive pyramid prism is used to subdivide backscattered light from the retina into four solid angles. Parafoveal fundus images have been captured for the eyes of three healthy subjects and directional scattering has been determined using horizontal and vertical differentials. The results for the photoreceptor cones, blood vessels, and the optic disc are discussed. In the case of cones, the observations are compared with numerical simulations based on a simplistic light-scattering model. Ultimately, the method may have diagnostic potential for diseases that perturb the microscopic structure of the retina.

Response for light scattered in the ocular fundus from double-pass and Hartmann-Shack estimations

Double-pass (DP) and Hartmann-Shack (HS) are complementary techniques based on reflections of light in the ocular fundus that may be used to estimate the optical properties of the human eye. Under conventional data processing, both of these assessment modes provide information on aberrations. In addition, DP data contain the effects of scattering. In the ocular fundus, this phenomenon may arise from the interaction of light with not only the retina, but also deeper layers up to which certain wavelengths may penetrate. In this work, we estimate the response of the ocular fundus to incident light by fitting the deviations between DP and HS estimations using an exponential model. In measurements with negligible intraocular scattering, such differences may be related to the lateral spreading of light that occurs in the ocular fundus due to the diffusive properties of the media at the working wavelength. The proposed model was applied in young healthy eyes to evaluate the performance of scattering in such a population. Besides giving a parameter with information on the ocular fundus, the model contributes to the understanding of the differences between DP and HS estimations.

Computational model of the effect of light scattering from cataracts in the human eye

A model of the human eye has been developed, including scattering from cataracts inside the nucleus of the lens. The cataracts are modeled as spherical particles with refractive index different from that of the surrounding lens medium. Scattering from the retina is also included in the simulations. Variations of scattering particle diameter, number of particles, and wavelength of the illuminating light are investigated. It is shown that particle size is the most important parameter affecting the scattered light, and that the scattering from the retina can mask the effect of the scattering particles, for some range of the parameters.

Unbiased estimation of refractive state of aberrated eyes

We seek unbiased methods for estimating the target vergence required to maximize visual acuity based on wavefront aberration measurements. Experiments were designed to minimize the impact of confounding factors that have hampered previous research. Objective wavefront refractions and subjective acuity refractions were obtained for the same monochromatic wavelength. Accommodation and pupil fluctuations were eliminated by cycloplegia. Unbiased subjective refractions that maximize visual acuity for high contrast letters were performed with a computer controlled forced choice staircase procedure, using 0.125 diopter steps of defocus. All experiments were performed for two pupil diameters (3mm and 6mm). As reported in the literature, subjective refractive error does not change appreciably when the pupil dilates. For 3mm pupils most metrics yielded objective refractions that were about 0.1D more hyperopic than subjective acuity refractions. When pupil diameter increased to 6mm, this bias changed in the myopic direction and the variability between metrics also increased. These inaccuracies were small compared to the precision of the measurements, which implies that most metrics provided unbiased estimates of refractive state for medium and large pupils. Thus a variety of image quality metrics may be used to determine ocular refractive state for monochromatic (635nm) light, thereby achieving accurate results without the need for empirical correction factors.

Simulating human photoreceptor optics using a liquid-filled photonic crystal fiber

We introduce a liquid-filled photonic crystal fiber to simulate a retinal cone photoreceptor mosaic and the directionality selective mechanism broadly known as the Stiles-Crawford effect. Experimental measurements are realized across the visible spectrum to study waveguide coupling and directionality at different managed waveguide parameters. The crystal fiber method is a hybrid tool between theory and a real biological sample and a valuable addition as a retina model for real eye simulations.

Directional model analysis of the spectral reflection from the fovea and para-fovea

Directional and nondirectional spectral reflection data from 0, 1, 2, 4, and 8 deg eccentricity, and the optic disk, were analyzed from 400 to 950 nm with an existing optical reflection model. The optical model, developed for the fovea, appeared to be also suitable for more eccentric locations. The optical densities of melanin and of the macular pigments zeaxanthin and lutein peaked in the fovea, in correspondence with literature data. The amplitude of the directional component, originating in the cone photoreceptors, had its maximum at 1 deg. The maximum of the directionality (peakedness) occurred at a slightly higher eccentricity.

Measuring directionality of the retinal reflection with a Shack-Hartmann wavefront sensor

The directional sensitivity of the retina, known as the Stiles-Crawford effect (SCE), originates from the waveguide property of photoreceptors. This effect has been extensively studied in normal and pathologic eyes using highly customized optical instrumentation. Here we investigate a new approach based on a Shack-Hartmann wavefront sensor (SHWS), a technology that has been traditionally employed for measuring wave aberrations (phase) of the eye and is available in clinics. Using a modified research-grade SHWS, we demonstrate in five healthy subjects and at four retinal eccentricities that intensity information can be readily extracted from the SHWS measurement and the spatial distribution of which is consistent with that produced by the optical SCE. The technique is found sufficiently sensitive even at near-infrared wavelengths where the optical SCE is faint. We demonstrate that the optical SCE signal is confined to the core of the SHWS spots with the tails being diffuse and non-directional, suggesting cones fail to recapture light that is multiply scattered in the retina. The high sensitivity of the SHWS to the optical SCE raises concern as to how this effect, intrinsic to the retina, may impact the SHWS measurement of ocular aberrations.

Macular pigment density assessed by directional fundus reflectance

Light radiated from foveal photoreceptors was analyzed in the eye's pupil at 470 nm and 532 nm. The reflectance of the inner limiting membrane was then measured at 6 deg from the fovea for the same wavelengths, allowing us to determine the macular pigment (MP) density D(dir) using the directional reflectance technique. In addition we measured the MP density D(nd) using the nondirectional reflectance technique (26 subjects). The mean values of D(dir) and D(nd) were 0.419+/-0.097 and 0.195+/-0.042 D.U., respectively (sample field of 2 deg). They were highly correlated (p<0.0001). Comparison of D(dir) and D(nd) implies that 57+/-12% of the light reflected from the fovea comes from layers anterior to MP at 470 nm. The mean directionality factors rho that we have measured at 470 nm and 532 nm were equal to 0.239+/-0.028 and 0.210+/-0.028 mm(-2), respectively. They were correlated (p<0.0001) and followed the spectral dependence suggested by Marcos.

Alignment parameters of foveal cones

In the fovea we measured the orientation and directional characteristics of photoreceptors with an optical technique in a group of 29 subjects. At 6 deg eccentricity, we determined the direction of the normal to the inner limiting membrane (ILM) by analyzing light reflected specularly by the ILM. We found a strong correlation between the orientation of photoreceptor axes and the direction of the normal to the ILM. Therefore, we cannot answer the question of the mechanism of photoreceptor alignment without taking into account the direction of the normal to the underlying retinal pigment epithelium, in addition to phototropic and apodization processes. For a wavelength of 532 nm, the mean value of the directionality factor rho was 0.212 mm(-2) (SD: 0.026 mm(-2)) when measured at the fovea (2 deg sample field). We look for reasons likely to explain the discrepancy between rho values given by different optical methods.

Directional and nondirectional spectral reflection from the human fovea

A model of the directional and nondirectional reflection spectrum of the human fovea is developed, incorporating reflectors, absorbers, and a wavelength-dependent optical Stiles-Crawford effect (OSCE). Data from 102 healthy subjects between 18 and 75 years obtained with the fundus reflection analyzer (FRA), an imaging spectrograph that measures the directional reflection profile of the human fovea in the pupil plane from 400 to 950 nm, were analyzed. Subgroups of young (<40 years) and old (>50 years) observers were defined. Mean results of the young group defined a template for directionality versus wavelength. For the whole group, mean reflection at 550 nm from the cones was 2.12%, from the retinal pigment epithelium 0.56%, and from the choroid 7.92%. Lens density, cone disc reflection, and blood layer thickness showed significant trends versus age. The model for the first time simultaneously describes the spectra of the directional and nondirectional reflection of the human fovea. Rayleigh scatter losses of the media and in preretinal layers were assumed zero in the nondirectional pathway. Mean density of the macular pigment of a subgroup (53 subjects, 19 to 75 years) correlated significantly with independent data from reflectance and autoflourescence images obtained by scanning laser ophthalmoscope (SLO) and data from flicker photometry.

Designing a holographic modal wavefront sensor for the detection of static ocular aberrations

The extent to which holographic modal wavefront sensing can be applied to the detection of ocular aberrations was investigated. First, the idea of extending the dynamic range of the sensor by increasing the mask bias and the collection area of the pinhole detectors used in the sensor is reviewed. Errors in the detection of single-mode aberrations owing to reduced coherence from retinal scattering, photon, readout, and quantization noise are evaluated. A sensitivity-to-noise metric is introduced to evaluate sensor designs and is found to be maximized by using a pinhole detector radius of 8.6(flambda/NDelta) for every wave of mask bias (where f=transform lens focal length, lambda=wavelength, and N and Delta are the number and size of the hologram pixels, respectively). The problem of detecting ocular aberrations composed of multiple modes required a generalization of the sensitivity measure to include all incident aberration modes. A "detect and correct" ocular aberration detection scheme was implemented that reduced the effects of cross talk and showed a maximum sensitivity-to-noise ratio of 40, which varied inversely with the size of the ocular aberration being detected.

Effect of wavelength on in vivo images of the human cone mosaic

In images of the human fundus, the fraction of the total returning light that comes from the choroidal layers behind the retina increases with wavelength [Appl. Opt. 28, 1061 (1989); Vision Res. 36, 2229 (1996)]. There is also evidence that light originating behind the receptors is not coupled into the receptor waveguides en route to the pupil [S. A. Burns et al., Noninvasive Assessment of the Visual System, Vol. 11 of 1997 Trends in Optics and Photonics Series, D. Yager, ed. (Optical Society of America, 1997), p. al; Invest. Ophthalmol. Visual Sci. 38, 1657 (1997)]. These observations imply that the contrast of images of the cone mosaic should be greatly reduced with increasing wavelength. This hypothesis was tested by imaging the light distributions in both the planes of the photoreceptors and the pupil at three wavelengths, 550, 650, and 750 nm, with the Rochester adaptive optics ophthalmoscope. Surprisingly, the contrast of the retinal images varied only slightly with wavelength. Furthermore, the ratio of the receptorally guided component to the total reflected light measured in the pupil plane was found to be similar at each wavelength, suggesting that, throughout this wavelength range, the scattered light from the deeper layers in the retina is guided through the receptors on its return path to the pupil.

Directional light scanning laser ophthalmoscope

The cone photoreceptor mosaic of the living human eye has in a limited number of cases been imaged without the use of wavefront-correction techniques. To accomplish this, the directionality of the photoreceptors, as manifested by their waveguiding properties, may be used to advantage. In the present paper we provide a model of our recently proposed directional light scanning laser ophthalmoscope [Opt. Lett. 29, 968 (2004)] together with a detailed numerical analysis of the device. The outcome is compared with experimental results.

Guided light and diffraction model of human-eye photoreceptors

The photoreceptors of the living human eye are known to exhibit waveguide-characteristic features. This is evidenced by the Stiles-Crawford effect observed for light incident near the pupil rim, and by the directional component of light reflected off the retina in the related optical Stiles-Crawford effect. We describe a model for the coupling of light to/from photoreceptors on the basis of waveguide theory that includes diffraction between the eye pupil and the photoreceptor apertures, and we show that valuable insight can be gained from a Gaussian approximation to the mode field. We apply this knowledge to a detailed study of the relationship between the Stiles-Crawford effect and its optical counterpart.

Investigating the light absorption in a single pass through the photoreceptor layer by means of the lipofuscin fluorescence

Reflection densitometry has been widely used to measure the density difference of the bleachable cone photopigments in human eyes. Most such measurements make a series of assumptions concerning the amount of scattered light to derive an estimate of the true cone photopigment density from the density difference measurements. The current study made three types of measurements of the light returning from the eye before and after bleaching: the amount of light returning in the "directed" reflection, which is a double-pass estimate of the cone photopigment density; the amount of light in undirected or diffuse reflection; and the amount of fluorescence from lipofuscin in the RPE, which provides a single-pass measurement of optical density difference. For a 1 deg foveally fixated field, the density difference estimates for the three measurements were 0.68, 0.21, and 0.22 respectively. The lipofuscin fluorescence was found to be unguided. The background density difference was non-negligible and very close to the single pass estimate from fluorescence. These measurements each involve potentially different pathways of light through the retina, and therefore place different constraints on models of these pathways. A simple model comparing the directional and the fluorescence optical densities produced retinal coverage estimates around 70-75%. Estimates of the shape factor of the single pass optical Stiles-Crawford effect were evaluated from the dark-adapted and bleached fluorescence measurements. The values were closer to those obtained from psychophysical methods than to the double pass optical Stiles-Crawford shape factors obtained directly from retinal reflectometry.

On the age dependency of the macular pigment optical density

Macular pigment may protect against age related macular degeneration (AMD), because of its capability to absorb blue light and scavenge free radicals. Since age is the major risk factor in AMD, a fundamental question to be answered is the possible age dependence of the macular pigment optical density (MPOD) in normal healthy subjects. In this study we used five methods to study a possible age effect: heterochromatic flickerphotometry, two setups for fundus reflectance spectroscopy, a Scanning Laser Ophthalmoscope (SLO) for obtaining reflectance, and the same SLO for autofluorescence maps. MPOD was determined from the reflected light by a full spectral analysis. We also used a new, directional analysis of the reflected light to estimate MPOD. The latter avoids the disturbing influence of stray-light. Digital subtraction at two wavelengths of log reflectance and digital subtraction of log autofluorescence obtained with the SLO provided MPOD maps. Together, all methods of measuring and of analysis provided seven MPOD estimates per subject. A total of 53 subjects, aged 19-76 years, completed all five measurements (and thus seven analyses). An additional 81 subjects, aged 18-70 years, were measured with one setup for fundus reflectance spectroscopy (and thus only two analyses). We could not find any association with age with all the objective techniques. Only MPOD values obtained with heterochromatic flickerphotometry showed a small, but significant decrease with age. This decrease was caused by an increase in the parafoveal data, suggesting that the central MPOD is unchanged with age. The bivariate correlation coefficients between all methods were significant (all p<0.001).

Absorption of the eye lens and macular pigment derived from the reflectance of cone photoreceptors

We measured the amplitude of the directional component of the bleached fundus reflectance, the so-called optical Stiles-Crawford effect, as a function of wavelength. The directional reflectance originates from within the outer segments of the photoreceptors. Thus only two anterior absorbers are of importance: macular pigment and the crystalline lens. Analysis of spectra obtained in pseudophakes established that the cone photoreceptors act as spectrally neutral reflectors. The reflectance spectra, expressed in density units, resembled the macular pigment density spectrum. Studying age effects in the lens of normal subjects resulted in a description of the optical density of the lens in terms of a "young" and an "aged" template. The young template represents the pigment O-beta-glucoside of 3-hydroxykynurenine, which dominates the light absorption in young eyes and decreases with age. The aged template represents the pigments accumulating in the lens with age. The total optical density increased with age, but it was lower in the wavelength region 500-650 nm than was previously assumed on the basis of psychophysical studies. Analysis of the spectra also provided precise individual estimates of the optical density of macular pigment. Finally, we observed a decrease in the photoreceptor reflectivity with age, possibly reflecting a degradation of the photoreceptors.

Measuring eye aberrations with Hartmann-Shack wave-front sensors: should the irradiance distribution across the eye pupil be taken into account?

A usual approximation in Hartmann-Shack aberrometry is that the centroid displacements are proportional to the spatial averages of the wave-front slopes at the sampling subapertures. However, these spatial averages are actually weighted by the local irradiance distribution across each microlens. The irradiance across the eye pupil is not uniform in usual reflectometric aberrometers, which is due to several factors including retinal scattering and cone waveguiding directionality. It is shown that neglecting this fact in usual least-squares reconstruction procedures gives rise to a biased estimation of the aberration coefficients. The magnitude of this bias depends on the actual irradiance distribution across the eye pupil, the mode being estimated, the detailed modal composition of the aberrated wave front, and the geometry of the wave-front sampling array. Order-of-magnitude calculations suggest that this bias may well be in the range 5%-10% for relatively smooth irradiance distributions. The systematic nature of this error makes it advisable to check for its presence and, if required, to compensate for it by an adequate choice of the least-squares reconstruction matrix.

Wavelength dependence of reflectometric cone photoreceptor directionality

We present evidence for the wavelength dependence of the directionality of light reflected from cone receptor cells (optical Stiles-Crawford effect): Blue light is more directional than red. According to the waveguide-scattering model of Marcos et al. [J. Opt. Soc. Am. A 15, 2012 (1998)], directionality is the sum of a waveguide component and a scattering component. The latter is proportional to 1 over wavelength squared, and it is related to the row-to-row spacing of the cone lattice. Our results allow a firm confirmation of Marcos et al.'s theory. For a 1.9-deg foveal area, group mean (n = 18) cone spacing was 3.42 microm, in good agreement with anatomical data. Group mean waveguide directionality was 0.077 mm(-2).

Effects of retinal scattering in the ocular double-pass process

The validity of double-pass wave-front measurements in the eye is reviewed analytically and computationally. A mathematical description of the scalar optical field in the exit pupil plane after an ocular double-pass process is presented. With the help of this description, the relationship between the phase information losses and the statistical properties of retinal scattering is demonstrated.

Wavelength dependence of the Stiles-Crawford effect explained by perception of backscattered light from the choroid

To explain the wavelength dependence of the directional sensitivity of human foveal cones (Stiles-Crawford I effect) we extended an existing fundus reflectance model for calculation of the total absorption by visual pigment. We took experimental data from literature for both the psychophysical and the optical Stiles-Crawford effect and optimized parameters to fit the experimental data. The wavelength dependence of the Stiles-Crawford effect could be well described with the geometrical optics model. Essential elements are self-screening and the inclusion of backscattered choroidal light for perception.

On the symmetry between eyes of wavefront aberration and cone directionality

There are two optical processes that control the retinal image sampled by the photoreceptor array: aberrations of the ocular optics and cone directionality (Stiles-Crawford effect). The shape of wavefront aberration and Stiles-Crawford functions are known to vary markedly across subjects. In this study we investigate in twelve subjects the symmetry between right and left eyes of wavefront aberration (measured using a spatially resolved refractometer) and cone directionality (measured using an imaging reflectometric technique). The pattern of aberrations is in general non-symmetric, suggesting that the development of aberrations follow independent paths in many right and left eye pairs. Cone directionality is in most cases mirror-symmetric (with one case of direct symmetry), suggesting some systematic process underlying cone orientation. Except in two subjects, symmetry in these two functions seems to be unrelated. Cone directionality apodization improves optical quality, but not optimally in all eyes, and it does not tend to increase symmetry in the optical performance of left and right eyes.

Comparison of cone directionality determined by psychophysical and reflectometric techniques

We measured the directionality of the cones with both a psychophysical (Stiles-Crawford I) technique and an optical technique. The two sets of measurements were made in the same subjects, with stimuli as similar as possible used. The two types of measurements gave similar estimates of the location in the pupil toward which the cones were optimally aligned. However, the two measurements gave quite dissimilar estimates of the width of the directional sensitivity. On average, optical measurements were half as broad as psychophysical measurements in the fovea, but there were substantial individual differences. At 2-deg retinal eccentricity the difference between techniques was even more marked.

Cone spacing and waveguide properties from cone directionality measurements

Reflectometric techniques estimate the directionality of the retinal cones by measuring the distribution of light at the pupil plane of light reflected off the bleached retina. The waveguide-scattering model of Marcos et al. [J. Opt. Soc. Am. A 15, 2012 (1998)] predicts that the shape of this intensity distribution is determined by both the waveguide properties of the cone photoreceptors and the topography of the cone mosaic (cone spacing). We have performed two types of cone directionality measurement. In the first type, cone directionality estimates are obtained by measuring the spatial distribution of light returning from the retina with a single-entry pupil position (single-entry measurements). In the second type, estimates are obtained by measuring the total amount of light guided back through the pupil as a function of entry pupil position (multiple-entry measurements). As predicted by the model, single-entry measurements provide narrower distributions than the multiple-entry measurements, since the former are affected by both waveguides and scattering and the latter are affected primarily by waveguides. Measurements at different retinal eccentricities and at two different wavelengths are consistent with the model. We show that the broader multiple-entry measurements are not accounted for by cone disarray. Results of multiple-entry measurements are closer to results from measurements of the psychophysical Stiles-Crawford effect (although still narrower), and the variation with retinal eccentricity and wavelength is similar. By combining single- and multiple-entry measurements, we can estimate cone spacing. The estimates at 0- and 2-deg retinal eccentricities are in good agreement with published anatomical data.