Cone spacing and waveguide properties from cone directionality measurements

Abstract

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 waveguidescattering model [ Marcos et al. (1998) , J. Opt. Soc. Am A] predicts that the shape of this intensity distribution is determined by both the waveguide properties of the cone photoreceptors and by the topography of the cone mosaic (cone spacing). We have performed two types of cone directionality measurements. 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 (multipleentry 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 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.

Müller cells separate between wavelengths to improve day vision with minimal effect upon night vision

“…3d). We also applied our algorithm to cones and found it to match perfectly previous results for light propagation along these cells 23,[40][41][42] , which were obtained and examined by other methods such as coupled mode theory 22,[43][44][45] .…”

Measuring retinal contributions to the optical Stiles-Crawford effect with optical coherence tomography

“…1 (bottom). A retinal eccentricity of 2 degrees was chosen to facilitate comparison to optical and psychophysical SCE measurements in the literature [17,33]. B-scans were reconstructed following the protocol described in Zhang, et al [29] with careful attention to compensating dispersion by employing both hardware (water vial in reference channel) and software [25] techniques.…”

“…ρ also varies with the imaging wavelength and retinal eccentricity. As an additional complexity, there is increasing evidence that ρ is a function (a weighted sum) of two independent retinal components: waveguiding by cone photoreceptors (ρ wg ) and scatter by the optically rough retina (ρ scatter ) such as related to the topography of the cone mosaic [22,33,47,48]. The former, ρ wg , is wavelength independent, while the latter, ρ scatter , scales as 1/λ 2 , where λ is the wavelength of the light.…”

“…Meaningful comparison of our ρ oct measurements to that in the literature must therefore account for these differences. As examples, comparisons are made with measurements by Marcos and Burns [33] and Gorrand and Delori [17], which were chosen as they measured at 2 degree eccentricity, the same as used here. In order to compare the different directionality measurements, ρ Marcos and ρ Gorrand in the two published studies were converted to an equivalent ρ oct as described below and defined as ρ Marcos equiv and ρ Gorrand equiv (see Table 1).…”

“…To convert ρ Marcos to an equivalent ρ oct (i.e., ρ Marcos equiv ) requires determining ρ wg and ρ scatter , and then substituting into ρ oct = 2 ρ wg + ρ scatter (λ). In Marcos and Burns [33], ρ scatter (λ=543nm) = 0.089 at 2 degree eccentricity, obtained by taking the difference between directionality from single (0.189) and multiple (0.1) entry measurements. Single and multiple entry measurements are defined in the citation.…”