On the Law for Minimal Discrimination of Intensities: II

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : I. A VISUAL DISCRIMINOMETER. II. THRESHOLD STIMULUS INTENSITY AND RETINAL POSITION

Monocular threshold stimulus intensities (ΔI_o, photons) were measured along the 0–180° meridian of human retinae for three observers. The test image was small (= 0.08°) and of short duration (= 0.20 second). ΔI_o was found to decrease as the angular distance from the fovea was increased. Actual counts of the number of retinal elements per mm.² along the 0–180° meridian (Østerberg) were compared with the obtained results. No direct correlation was found to exist between visual sensitivity and the number of retinal elements. Binocular threshold stimuli were also measured along the same meridian. The form of the function relating binocular visual sensitivity and retinal position was discovered to be essentially similar to that for monocular sensitivity, but is more symmetrical about the center of the fovea. The magnitude of the binocular measurement is in each case smaller than that of the monocular threshold stimulus intensity for the more sensitive eye. The ratio is statistically equal to 1.4 (a fact which suggests Piper's rule). These results are shown to be consistent with the hypothesis that the process critical for the eventuation of the threshold response is localized in the central nervous system. They are not consistent with the view that the quantitative properties of visual data are directly determined by properties of the peripheral retina.

CRITICAL ILLUMINATION AND FLICKER FREQUENCY, AS A FUNCTION OF FLASH DURATION: FOR THE SUNFISH

From the relations between critical illumination in a flash (I(m)) and the flash frequency (F) for response of the sunfish to visual flicker when the proportion of light time to dark time (t(L)/t(D)) in a flicker cycle is varied at one temperature (21.5 degrees ) the following results are obtained: At values of t(L)/t(D) between 1/9 and 9/1 the F - log I(m) curves are progressively shifted toward higher intensities and lower F(max.). F(max.) is a declining rectilinear function of the percentage of the flash cycle time occupied by light. The rod and the cone portions of the flicker curve are not shifted to the same extent. The cone portion and the rod region of the curve are each well described by a probability integral. In terms of F as 100 F/F(max.) the standard deviation of the underlying frequency distribution of elemental contributions, summed to produce the effect proportional to F, is independent of t(L)/t(D). The magnitude of log I(m) at the inflection point (r'), however, increases rectilinearly with the percentage light time in the cycle. The proportionality between I(m) and sigma(I(I1) ) is independent of t(L)/t(D). These effects are interpreted as consequences of the fact that the number of elements of excitation available for discrimination of flicker is increased by increasing the dark interval in a flash cycle. Decreasing the dark interval has therefore the same kind of effect as reducing the visual area, and not that produced by decreasing the temperature.

THE FLICKER RESPONSE CURVE FOR FUNDULUS

After Fundulus heteroclitus have been for some time in the laboratory, under conditions favorable for growth, and after habituation of the fishes to the simple routine manipulations of the observational procedure required, they are found to give reproducible values of the mean critical flash illumination (I(m)) resulting in response to visual flicker. The measurements were made with equality of light time and dark time in the flash cycle, at 21.5 degrees C. Log I(m) as a function of flash frequency F has the same general form as that obtained with other fishes tested, and for vertebrates typically: the curve is a drawn-out S, with a second inflection at the low I end. In details, however, the curve is somewhat extreme. Its composite form is readily resolved into the two usual parts. Each of these expresses a contribution in which log I, as a function of F, is accurately expressed by taking F as the summation (integral) of a probability distribution of d log I, as for the flicker response contour of other animals. As critical intensity I increases, the contribution of rod elements gradually fades out; this decay also adheres to a probability integral. The rod contribution seen in the curve for Fundulus is larger, absolutely and relatively to that from the cones, than that found with a number of other vertebrates. The additive overlapping of the rod and cone effects therefore produces a comparatively extreme distortion of the resulting F-log I curve. The F-log I(m) curve is shifted to lower intensities as result of previous exposure to supranormal temperatures. This effect is only very slowly reversible. The value of F(max.) for each of the components of the duplex curve remains unaffected. The rod and cone segments are shifted to the same extent. The persisting increase of excitability thus fails to reveal any chemical or other differentiation of the excitability mechanism in the two groups of elements. Certain bearings of the data upon the theory of the flicker response contour are discussed, with reference to the measurements of variation of critical intensity and to the form of the F-log I curve. The quantitative properties of the data accord with the theory derived from earlier observations on other forms.

THE FLICKER RESPONSE FUNCTION FOR THE TURTLE PSEUDEMYS

1. At constant temperature, with a fixed proportion of light time in a flash cycle (namely, t_L/t_D = 1), the mean critical intensity for motor response to visual flicker by the turtle Pseudemys scripta follows a probability integral (log I) as a function of flash frequency F. The fit is close and satisfactory; certain quite minor but consistent deviations are adequately explained by features of the experiments. 2. The variation (σ_I) of critical I is directly proportional to the mean critical intensity (I_m), over the entire explorable range. 3. These facts are consistent with the fact that the retina of this turtle is devoid of rods. It contains only cones, histologically, which, with their central representations, provide a single population of sensory effects. The properties of this population are compared with those of homologous populations deduced from corresponding measurements with other forms (various fishes; amphibian; man) which exhibit two such groups of sensory effects associated with the possession of retinal rods and cones. 4. Certain other formulations which have previously been applied to homologous data obtained with other organisms do not properly describe the Pseudemys measurements. 5. The use of a probability integral to describe the data of response to visual flicker for the dissection of the compound curves provided by animals possessing both rods and cones, is accordingly Justified. 6. Persisting differences among individuals of Pseudemys as regards the values of the critical flash intensity under various conditions of experimentation are of the same order of magnitude as are the transitory differences found in lots of other kinds of animals. 7. Determinations of mean critical flash frequency (F_m) at fixed levels of I lie slightly above determinations of I_m at fixed values of I, as with other forms. The variation of critical flash frequency goes through a maximum as log I is increased; its height is lower than with certain other forms, in correlation with the low general slope of the F - log I curve (more properly, band). 8. These facts are consistent with the view that the dispersions of the individual critical intensities (and flash frequencies) are determined by organic variation rather than by "experimental error." 9. When the temperature is altered the F - log I_m curve is shifted, with no change of F_max. or of shape; the curve moves to lower intensities as the temperature is raised. 10. The reciprocal of the mean critical intensity, at fixed flash frequency, is a measure of excitability. With increase of temperature (12.5° to 36°) 1/I_m for given F follows the Arrhenius equation, exhibiting a "break" at 29.5° (µ = 26,700, 12.5° to 29.5°; 12,400, 29.5° to 36°). This is explained by the necessary theory that, the number of elements of sensory effect required for the index response at fixed F being constant, the ease of their excitation is governed by temperature through its control of the velocity of an interrelated system of catalyzed processes common to all of the sensory elements concerned.