A transient Stiles-Crawford effect

Directional sensitivity of the retina: A layered scattering model of outer-segment photoreceptor pigments

Photoreceptor outer segments have been modeled as stacked arrays of discs or membrane infoldings containing visual pigments with light-induced dipole moments. Waveguiding has been excluded so fields diffract beyond the physical boundaries of each photoreceptor cell. Optical reciprocity is used to argue for identical radiative and light gathering properties of pigments to model vision. Two models have been introduced: one a macroscopic model that assumes a uniform pigment density across each layer and another microscopic model that includes the spatial location of each pigment molecule within each layer. Both models result in highly similar directionality at the pupil plane which proves to be insensitive to the exact details of the outer-segment packing being predominantly determined by the first and last contributing layers as set by the fraction of bleaching. The versatility of the microscopic model is demonstrated with an array of examples that includes the Stiles-Crawford effect, visibility of a focused beam of light and the role of defocus.

Retinal light distributions, the Stiles-Crawford effect and apodization

Analysis of retinal image formation for beams of coherent and incoherent radiation emphasizes the role of the Poynting vector's inclination with respect to the retinal image plane. Coherent beams interfere and give rise to a single Poynting vector that highlights the unique direction of incidence of energy flow, whereas multiple incoherent beams, especially incoherent extended sources in the pupil, generate electro-magnetic disturbances in the image plane each characterized by Poynting vectors of their own. As a result, the Stiles-Crawford diminution of luminant efficiency adds differently depending on the coherence of the entering light. Two practical considerations follow: first, in performing diffraction calculations for the retinal image from known wavefronts in the pupil plane, apodization terms should not be factored in, and, second, in principle, for perfect imaging in standard target viewing, Stiles-Crawford integration with increasing pupil diameter is not expected.

Directional sensitivity of the retina: 75 years of Stiles-Crawford effect

The reduction of the brightness when a light beam's entry into the eye is shifted from the centre to the edge of the pupil has from the outset been shown to be due to a change in luminous efficiency of radiation when it is incident obliquely on the retina. The phenomenon is most prominent in photopic vision and this has concentrated attention on the properties of retinal cones, where responsibility has yet to be assigned to factors such as differences in shape, fine structure and configuration, and membrane anchoring of photopigment molecules. Geometrical optics and waveguide formulations have been applied to the question of how light is guided in receptors, but details of their geometry and optical parameters even if they become available will make calculations complex and of only moderate generality. In practice, the diminution of oblique light helps visual performance by reducing deleterious influence of ocular aberrations and of glare caused by light scattering when the pupil is wide. Receptor orientation can come into play in ocular conditions due to mechanical disturbance and has been shown to have potentiality as a tool for clinical diagnosis. Currently, open questions include microanatomical and molecular differences between rods and cones, the coupling of the optical image of the eye with the transducing apparatus in the photoreceptors, possible phototropism and more convincing methods of estimating the actual spatial distribution of photon events as it affects visual resolution.

Photoreceptor waveguides and effective retinal image quality

Individual photoreceptor waveguiding suggests that the entire retina can be considered as a composite fiber-optic element relating a retinal image to a corresponding waveguided image. In such a scheme, a visual sensation is produced only when the latter interacts with the pigments of the outer photoreceptor segments. Here the possible consequences of photoreceptor waveguiding on vision are studied with important implications for the pupil-apodization method commonly used to incorporate directional effects of the retina. In the absence of aberrations, it is found that the two approaches give identical predictions for an effective retinal image only when the pupil apodization is chosen twice as narrow as suggested by the traditional Stiles-Crawford effect. In addition, phase variations in the retinal field due to ocular aberrations can delicately alter a waveguided image, and this may provide plausible justification for an improved visual sensation as compared with what should be expected on the grounds of a retinal image only.

Specifying and controlling the optical image on the human retina

A review covering the trends that led to the current state of knowledge in the areas of: (a) schematic models of the eye, and the definition of the retinal image in terms of first-order optics; (b) the description of the actual image on the retina and methods for accessing and characterizing it; (c) available procedures for controlling the quality of the retinal image in defined situations; and (d) intra-receptoral optical effects that cause differences between the light distribution on the retinal surface and at the level of interaction with photopigment molecules.

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.

Variations in photoreceptor directionally across the central retina

Cones show a differential sensitivity to light coming from different portions of the pupil, typically being most sensitive to light from the center of the pupil. We measured the directional properties of the cones across the central 6 deg of the retina, using an optical imaging technique. We find that the cones in the center of the fovea have the broadest tuning. The width of the angular tuning changes rapidly from 0 deg to 1 deg retinal eccentricity, with cones at 1 deg being much more narrowly tuned that the cones in the center of the fovea. Directional tuning of the cones remains relatively constant from 1 deg to 3 deg retinal eccentricity. Receptoral disarray contributes minimally to the measured directional properties of the foveal cones, and there is no evidence of asymmetry between horizontal and vertical retinal locations. There are only small differences among the five subjects in the change in angular tuning of the cones with retinal location. We find that at the foveal center the directional tuning of the cones is limited by the diameter of the cone apertures.

Light capture by human cones

1. The variation in visual efficiency of light with varying pupillary entry (the Stiles-Crawford effect) was measured to determine the proportion of light incident on the cones that escapes them without recovery by other cones. 2. The variation in detectability of interference fringes with varying pupillary entry of the interfering beams was measured to determine the proportion of incident light that was recaptured by cones in the dark stripes after escaping cones in the bright stripes of the fringes. 3. By exclusion, these observations determine the variation, with varying pupillary entry, in the proportion of incident light that was captured and absorbed by the first cones it entered. 4. Some 70-90% of the light absorbed by the cones when it passes through the centre of the pupil, is entirely lost to the visual system if it passes instead through the margin of the (dilated) pupil. 5. Over half the light that cones absorb when the light enters the margin of the pupil is light that has previously passed through other cones. 6. If the spread of recaptured light is assumed to be Gaussian, its standard deviation is at most one minute of visual angle. 7. Such recaptured light makes a previously unknown contribution to the various Stiles-Crawford effects.

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.

Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo

The directionality of the foveal receptors of four subjects is assessed with a technique based on light scattering, and a psychophysical technique. The width and orientation of the absorbance diagram (difference between the scattering diagram in a bleached and unbleached state of the visual pigment) are compared with the Stiles-Crawford function. Results show that the directionality in the scattering diagram points into approximately the same direction as the S-C function, but the width of the scattering diagram is slightly less. The alignment of foveal receptors is studied by partially bleaching the retina with oblique incidence from a nasal and temporal direction. Comparison of the absorbance diagrams with a diagram obtained with normal incident bleaching shows no significant shift in their orientations.

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.

Psychophysical studies of cone optical bandwidth in patients with retinitis pigmentosa

Estimates of variation in the alignment of cones with the pupil were obtained from the fovea and parafovea in normal subjects and in patients with retinitis pigmentosa known to have reduced directional sensitivity. The degree of cone disarray was inferred from differences in sensitivity between Stiles-Crawford functions obtained with a stimulus alone and with the stimulus superimposed on a background entering the pupil at a point corresponding to the peak of the Stiles-Crawford function. The magnitude of the selective effect of the background in normals was consistent with previous estimates of variations in photoreceptor alignment in the macula. In contrast, the selective adaptation effect was not present in patients with retinitis pigmentosa. These results exclude increased disarray among cones with normal optical bandwidths, but rather, suggest that morphological abnormalities increasing the optical bandwidths of individual cones underlie reduced directional sensitivity in these patients.

Adaptation to polarized light in humans

Recent investigators reported large adaptational effects in human vision dependent on the plane of linearly polarized light. In the present study, such adaptational effects were observed to be small or insignificant. Our observers adapted to intense homogenous, foveal fields of linearly polarized, orange-red light produced by a beam that entered the side of the pupil. Periodically the plane of polarization of the beam suddenly shifted 90 degrees without there being any change in the spectral distribution of the light or position of the beam in the pupil plane. The change of radiance of the beam could be adjusted to be as low as approx. 0.5%. Signal detection experiments revealed that observers typically could not detect a change of polarization of the field. Results obtained with the method of adjustment showed that the threshold of an increment flash presented on the intense field was not affected by changing the polarization of the field. Physiological implications of these results are discussed.

Stiles-Crawford effect and the bleaching of cone pigments

1. The efficiency of light entering the eye through various points in the pupil (Stiles-Crawford effect) was studied using two criteria: (a) visual brightness judged by flicker fusion and (b) the rate of cone pigment bleaching measured by reflexion densitometry.2. Both measurements were made in the same apparatus with the same geometry of presentation and both gave the same Stiles-Crawford effect.3. This suggests that the densitometer measures pigment deep in the outer segments of the cones where light is absorbed for vision.4. Foveal cones seem all to point in the same direction, since the fraction of pigment bleached by light entering the pupil at any one point is the same when measured by light entering anywhere.