The directional sensitivities of the Stiles' colour mechanisms

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.

Estimating middle-wavelength and long-wavelength cone sensitivity with large, long-duration targets and small, brief targets

Incremental threshold versus field-intensity curves (tvi) and spectral sensitivity functions were measured for 500 nm and 667 nm test flashes, either under the standard two-colour threshold conditions of Stiles (target: 1.0 deg, 200 ms)--which are known to favour detection by the chromatically-opponent pathways--or with a smaller (0.1 deg), shorter-duration (10 ms) target--chosen to favour detection by the non-opponent (achromatic) pathway. The data reveal differences between the two conditions: for the small, brief target, the tvi curves were shallower and less dependent upon wavelength, and the spectral sensitivity functions were narrower than for the standard target.

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 pi mechanisms of W S Stiles: an historical review

The origins, development, and status of the pi mechanism theory are reviewed. The paper is divided into four sections. In the first section Stiles's general ideas about 'color mechanisms' are examined, and it is concluded that foremost amongst these is a mathematical theory that specifies certain formal rules or laws that should govern a certain class of observations. In the case of pi mechanisms, the class of observations is that of two-color thresholds, and the defining laws are the two well-known displacement laws. Five other laws that two-color increment-threshold observations should obey, if the latter are governed by ideal pi mechanisms, are abstracted from Stiles's writings. In the second section literature pertinent to the testing of the seven Stilesian laws is reviewed, and it is asked whether or not the seven pi mechanisms of Stiles do in fact obey the laws. In the third section the relation of the pi mechanism concept to physiological concepts is examined, and its relation to the 'cone fundamental' is discussed; the evidence pertinent to the question: "Are any of the pi mechanisms of the single-fundamental type?" is then reviewed. The last section is devoted to the evolution of Stiles's ideas in the period after 1959 when Stiles's own investigations and those of others propelled him to reject the initial (1953) pi mechanism theory as an adequate characterization of the data of the two-color threshold.

Electroretinograms evoked by sinusoidal excitation of human cones

The amplitude and phase of the fundamental Fourier component of the human electroretinogram (e.r.g.) were recorded with a synchronous detection method under conditions in which each of the three species of cones can be assumed most sensitive in turn. Weber-Fechner behaviour is well established at, or more distal in the retina than, the source of these voltages. Results over the frequency range 7-50 Hz exclude a diffusion model of human flicker perception. The e.r.g. phase vs. frequency plot found with a 'red' test differs from that obtained with a 'green'. The shapes of the e.r.g. field sensitivity action spectra agree with those of the subject's IIj(mu) (j = 3, 4 and 5) mechanisms of Stiles and with in situ measurements of the absorbance spectra of human cone pigments. Threshold phase with each test was independent of background wave-length but, consistent with the results in 3, the phase of the response to the 'red' test (25 Hz) differed significantly from that to the 'green'. If these differences resulted from the absorption of test photons of different colours at different points along the outer segment (independent of cone spectral sensitivity), they would be as clear on dichromats as on trichromats. Results on a protanope are inconsistent with this prediction. We infer that differences in phase are due to the different kinetics of different cone mechanisms and that the e.r.g.s studied here are evoked by exciting only the most sensitive cone mechanism, even though dark-adaptation studies prove that at e.r.g. threshold the test is well above psychophysical threshold for all three cone species. If the inference in 5 is correct, studies of sensitivity across the retina suggest that the spatial distribution of long-, middle- and short-wave-sensitive cones in the human retina differ remarkably.

Factors influencing threshold of the fundamental electrical response to sinusoidal excitation of human photoreceptors

The amplitude and phase of the fundamental Fourier component of the electroretinogram (e.r.g.) in response to sinusoidally modulated light were studied in the range 7-50 Hz. Sensitivity was best at the lowest frequency. The threshold-frequency relationship divided into two parts. A weak steady background depressed sensitivity of the low, but increased sensitivity of the high, frequency component. At 8 Hz a small test spot was 0.7 log10 units more effective on the most sensitive part of the retina than on the optic disk. On the fovea, it was 0.1-0.2 log10 units less effective than on the disk. The fovea was 0.7 log10 units more sensitive to 25 Hz than the blind spot. Psychophysical and e.r.g. dark-adaptation curves were similar, but the former was 10(4) times more sensitive than the latter. Four sets of experiments examined the possibility that the Fourier component of the e.r.g. response at the modulation frequency of 8 Hz during the 'rod' phase of the e.r.g. dark-adaptation curve arose from excitation of rods alone. The only hint of a possible cone contribution was a very small but systematic increase in phase delay with increase in background wave number found while measuring the field sensitivity action spectrum. No suggestion was found that the fundamental Fourier component of threshold e.r.g. responses at the modulation frequency of 25 Hz was influenced by photons absorbed in rods.

The directional sensitivity of retinal rods

Rod field sensitivity, 10-S(r) (i.e. the reciprocal of the radiance of a background required for 10-fold elevation of rod threshold) was measured for monochromatic backgrounds traversing the pupil at various points (r) on three subjects. The wave-length dependency of the directional sensitivities of the three foveal cone mechanisms of the principal subject have been reported previously (Alpern & Kitahara, 1983). Rods, as cones, are less sensitive to obliquely incident, than to normally incident backgrounds. At the pupil margin (4 mm) the effect is between 0.368 and 0.976 log10 units smaller for rods. After correction for losses by corneal reflexion and by absorption in the lens, S(r) for rods is reasonably described by the parabolic equation used by Stiles (1937) to quantify the directional sensitivity of cones. The small effect for rods precludes a description as consistently precise as this equation provides for cones. The steepness of the parabolic curve best fitting the directional sensitivity data of the rods of the principal subject was independent of background wave number. For a second subject, whose rods are supposed to be smaller, it was directly proportional to the square of that wave number. The latter is the expectation if the directional sensitivity of this subject's rods were determined by principles outlined in the diffraction theory of Simon (1970).

The dependence of the colour and brightness of a monochromatic light upon its angle of incidence on the retina

The changes in brightness and colour of a monochromatic test light as its angle of incidence on the retina was changed from normal (pupil centre traverse) to oblique (3.5 mm temporal pupil traverse), was measured by matching it with three normally incident primaries. Results on two normal trichromats were generally in accord with published data on the Stiles-Crawford intensity and colour effects. One observer was also the subject of the preceding paper (Alpern & Kitahara, 1983) in which the field sensitivities of his foveal IIj(mu) (j = 3, 4, 5) mechanisms for normally, and obliquely, incident backgrounds were reported. For normal incidence, the colour matching functions are in rough accord with expectation if the action spectra of the three cone mechanisms, which provide the photoreceptor basis for his trichromacy, were the same IIj mechanisms for normal incidence. A unified theory is developed for both Stiles-Crawford intensity and colour effects, assuming that the same visual pigments in the same set of univariantly signalling cones absorbs both the normal incident primaries and the obliquely incident test. Given no free parameters for curve fitting, the Stiles-Crawford intensity effect data are in reasonable agreement with the theory if the photoreceptor basis of these matches were the normally and obliquely incident IIj(mu) mechanisms. The Stiles-Crawford colour effect data contradict the expectations of the unified theory applied with these same IIj(mu) mechanisms. Either II3(mu) is not a valid operational definition of the action spectrum of his short-wave sensitive photoreceptors or at least one assumption of the unified theory is false.

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.