The retinal directional effect: a model based on the gaussian distribution of cone orientations

Parametric representation of Stiles-Crawford functions: normal variation of peak location and directionality

Evidence suggests that the psychophysically determined Stiles-Crawford effect of the first kind (SCE) reflects waveguide properties of human photoreceptors. The peak of the SCE data set is assumed to reflect the principal alignment tendencies, and the spread (e.g., rho value, the curvature or width at half-height) is assumed to reflect the directionality (i.e., interreceptor differences in alignment) of the population of photoreceptors being tested. As such, disruption of the normal SCE can be used and/or has been used (1) to document early natural history of retinal pathology involving the photoreceptors, (2) to provide a firm rationale for therapeutic intervention, and (3) to provide a method for monitoring therapies designed to alter the natural course of retinal-disease processes. We report large-sample norms for foveal SCE peak location and spread (horizontal peak location, nasal 0.51 +/- 0.72, horizontal rho value 0.047 +/- 0.013, vertical peak location, superior 0.20 +/- 0.64, vertical rho value 0.053 +/- 0.012), compare these norms with values determined in other laboratories, and discuss the various mathematical forms used for the empirical description of SCE data sets.

The Stiles-Crawford effect of the second kind (SCII): a review

The background which led Stiles to the discovery that the color of a monochromatic ray of light varied with its angle of incidence on the retina, and the developments in the subject since 1937 when this discovery was reported are summarized. Stiles's original measurements of the 'hue shift' did not successfully quantify SCII in every part of the spectrum, since it provided only two degrees of freedom while the color changes sometimes require three. Nevertheless, they were the paradigm for most subsequent work for the next quarter of a century. Full quantification of the effect was first obtained by trichromatic matching on Stiles's NPL trichromator almost 25 years after the initial discovery. The phenomena were then also fully described quantitatively with an elaboration of Stiles's original theory ('self-screening' theory), on the assumption that the ordinary laws of additivity are valid for color matches of three primaries striking the retina at one angle of obliquity to a test incident at a different angle. More recent experiments suggest that this initial assumption may not be generally true and that 'self-screening' theory may not generally provide a satisfactory description of the color changes throughout the visible spectrum, even for measurements of the effect obtained under conditions in which the additivity assumption seems to be valid. However, the available data strongly imply that absorptions of photons obliquely incident on foveal cones depend upon spectra clearly different from those upon which absorptions of normally incident photons depend.

The directional sensitivities of the Stiles' colour mechanisms

Field sensitivities of the three IIj (j = 3, 4, 5) mechanisms of Stiles were measured for monochromatic backgrounds of different wave numbers (mu)-1 traversing the eye through different points (r) displaced along a horizontal chord through the centre of the entrance pupil. Each mechanism shows an insensitivity to the direction of retinal incidence of short-wave backgrounds not previously described. The spectral densities of the centre-most part of the lens and of the macular pigment were measured on this eye. With reasonable assumptions the former allowed for correction at the receptor level of the directional sensitivity; together with the latter it allowed correction for the spectral sensitivity as well. No correction for the attenuation of the high spatial frequencies of the background as it traversed the pupil at different r was needed. The anomalies of section 2 (above) disappear after correction for losses in the eye media. After these corrections, for every mu and r, the results are well described by the parabola 'tentatively' suggested by Stiles (1939) for each mechanism, allowing only a small amount of variance attributable to experimental imprecision alone. Each mechanism is most sensitive to backgrounds going through essentially the same point of the pupil, independent of background. This result is inconsistent with a qualitative explanation of the 'hue shift' suggested by Safir, Hyams & Philpot (1971). The field sensitivity spectra for backgrounds traversing the pupil at this most effective point and at the 3.5 mm margin, are the data needed to predict this observer's brightness and colour matches of monochromatic lights passing through the entrance pupil at these two points according to a unified theory of the two Stiles-Crawford effects. In the following paper these predictions are quantified and confronted with results of the matching experiments (Alpern, Kitahara & Tamaki, 1982).

The saturation of monochromatic lights obliquely incident on the retina

Foveal dark-adaptation undertaken to test the hypothesis that the excitation of rods causes the desaturation of 'yellow' lights in a 1 degree field traversing the margin of the pupil, fails to exclude that possibility. The desaturation is largest for a 1 degree outside diameter annular test, is still measurable with a 0.5 degree circular disk, but disappears for a 0.29 degree disk. The supersaturation of obliquely incident 501.2 nm test light follows the opposite pattern; it disappears with an annulus and is largest for a 0.29 degree circular field. It is unlikely that rods replace short-wave sensitive cones in the trichromatic match of an obliquely incident test with normally incident primaries. If rods as well as all three cones species are involved, the matches might not be trichromatic in the strong sense. Grassmann's law of scalar multiplication was tested and shown not to hold for the match of an obliquely incident test with normally incident primaries, though it remains valid whenever, both primaries and test strike the retina at the same angle of incidence (independent of that angle). The result in section 3 (above) cannot be due to rod intrusion. It persists (and becomes more conspicuous) on backgrounds (4.0 log scotopic td) which saturate rods. Moreover obliquely incident 'yellow' lights remain desaturated in intervals in the dark after a full bleach, whilst the test field is below rod threshold. The amount of desaturation does not differ appreciably from that normally found. The assumption of the unified theory of Alpern, Kitahara & Tamaki (1983) that the outer segments of only a single set of three cone species (with acceptance angles wide enough to include the entire exit pupil) contain the visual pigments absorbing both the normally incident primaries and the obliquely incident test is disproved by these results. Failure of Grassmann's law is most conspicuous under the conditions for which the changes in saturation upon changing from normal to oblique incidence are greatest and least when the saturation changes are the smallest. Either all unified theories of the Stiles-Crawford effects are wrong or all the effects of oblique incidence operate at a stage in the visual process at which the effects of radiation of different wave-lengths are no longer compounded by the simple linear laws.

The Stiles--Crawford function of an albino observer

Stiles--Crawford functions (SCF's) were measured for both eyes of an albino observer with a marked pendular nystagmus using an eye position monitoring system. Both eyes demonstrated directional sensitivity as revealed by their SCF's. The directional sensitivity of both eyes was less than that of either the foveal or parafoveal region of normal observers. In addition, there was a significant difference between the SCF's for the albino observer's two eyes. Our results suggest that the psychophysical SCF is predominantly the result of the orientational distribution of groups of receptors on the retina.

A study of the Stiles-Crawford (S-C) function at 35 degrees in the temporal field and the stability of the foveal S-C function peak over time

Directional sensitivity of the retina (the Stiles-Crawford function of the first kind) was measured at a point 35 degrees from fixation and at the point of fixation. Three normal observers were used. The peripheral test point intercepted the retina between the optic nerve head and the ora serrata. At both test points, photopic and scotopic (one subject) Stiles-Crawford function peaks were contained within the pupillary bound and approximated the center of the pupil. Directionality at the two points was rather similar. These findings add strength to the argument that retinal receptors align approximately with the center of the exit pupil of the eye. Evidence for stability in Stiles-Crawford peak location in time is also presented.

Light path and photon capture in turtle photoreceptors

1. The directional selectivity of individual cones was examined by intracellular recording in the eye of the turtle. Sensitivites were determined from linear responses to dim flashes of monochromatic light incident on a cell over a range of angles to its long axis. 2. With light near the optimum wave-length, some red- and green-sensitive cones showed a high sensitivity for light entering axially and lower sensitivities for light entering obliquely. In contrast, other cells had lower peak sensitivities and less pronounced directional selectivities. The highest axial sensitivities observed in red receptors were about 320 muV photon(-1) mu2; in these cells, the sensitivity declined to half for rays 6-9 degrees off the axis as measured in the retina. Green receptors had lower axial sensitivities and broader angular profiles. 3. On the assumption that rays at all angles contribute independently to the over-all sensitivity, the sensitivity of a cell to large cones of rays was successfully predicted from the angular selectivity determined with a narrow pencil of rays. The shape of small responses to dim stimuli delivered on and off the axis of the cell was invariant, implying that a cone signals the number of photons absorbed but not their angle of incidence. 4. Short wave-lengths have previously been shown to be filtered out by the oil droplets present in turtle cones. At short wave-lengths, the angular profiles showed a depression in axial sensitivity consistent with this filtering action. 5. Diameters of inner segments, oil droplets, and outer segments were measured in red-, green-, and blue-sensitive cones, since these dimensions are expected to influence the cones' angular acceptances and ability to collect light. The diameters of the structure were in approximately the same proportions for each type of receptor, but the absolute values of the diameters were found to be scaled in relation to the wave-length of maximum sensitivity. 6. Optical determinations of the efficiency with which axial rays are concentrated by red receptors gave a mean value of 55%. 7. Receptors in histological sections of the whole eye were found to be oriented with their long axes directed approximately toward the pupil. 8. The observed directional selectivities and collecting efficiencies agree well with the behaviour of a model retinal cone developed by Winston & Enoch (1971) on a geometrical optical treatment. 9. Effective collecting areas are derived for red-, green- and blue-sensitive cones; these permit conversion of observed flash sensitivities into the mean peak hyperpolarization produced by isomerization of a visual pigment molecule. The figure obtained is about 25 muV for red-sensitive cones and 21muV for green-sensitive cones.