INTENSITY DISCRIMINATION IN THE HUMAN EYE : II. THE RELATION BETWEENΔI/IAND INTENSITY FOR DIFFERENT PARTS OF THE SPECTRUM

1. A new apparatus is described for measuring visual intensity discrimination over a large range of intensities, with white light and with selected portions of the spectrum. With it measurements were made of the intensity ΔI which is just perceptible when it is added for a short time to a portion of a field of intensity I to which the eye has been adapted. 2. For white and for all colors the fraction ΔI/I decreases as I increases and reaches an asymptotic minimum value at high values of I. In addition, with white light the relation between ΔI/I and I shows two sections, one at low intensities and the other at high intensities, the two being separated by an abrupt transition. These findings are contrary to the generally accepted measurements of Koenig and Brodhun; however, they confirm the recent work of Steinhardt, as well as the older work of Blanchard and of Aubert. The abrupt transition is in keeping with the Duplicity theory which attributes the two sections to the functions of the rods and cones respectively. 3. Measurements with five parts of the spectrum amplify these relationships in terms of the different spectral sensibilities of the rods and cones. With extreme red light the relation of ΔI/I to I shows only a high intensity section corresponding to cone function, while with other colors the low intensity rod section appears and increases in extent as the light used moves toward the violet end of the spectrum. 4. Like most of the previously published data from various sources, the present numerical data are all described with precision by the theory which supposes that intensity discrimination is determined by the initial photochemical and chemical events in the rods and cones.     

INTENSITY DISCRIMINATION IN THE HUMAN EYE : I. THE RELATION OFΔI/ITO INTENSITY

New measurements of the brightness difference sensibility of the eye corroborate the data of previous workers which show that ΔI/I decreases as I increases. Contrary to previous report, ΔI/I does not normally increase again at high intensities, but instead decreases steadily, approaching a finite limiting value, which depends on the area of the test-field and on the brightness of the surrounding field. On a logarithmic plot, the data of ΔI/I against I for test-fields below 2° are continuous, whereas those for test-fields above 2° show a sharp discontinuity in the region of intensity in which ΔI/I decreases rapidly. This discontinuity is shown to divide the data into predominantly rod function at low intensities, and predominantly cone function at high intensities. Fields below 2° give higher values of ΔI/I at all intensities, when compared with larger fields. Fields greater than one or two degrees differ from one another principally on the low intensity side of the break. Changes in area above this limit are therefore mainly effective by changing the number of rods concerned. This is confirmed by experiments controlling the relative numbers of rods and cones with lights of different wavelength and with different retinal locations. At high intensities ΔI/I is extremely sensitive to changes in brightness of surrounding visual fields, except for large test-fields which effectually furnish their own surrounds. This sensitivity is especially marked for fields of less than half a degree in diameter. Although the effect is most conspicuous for high intensities, the surround brightness seems to affect the relation between variables as a whole, except in very small fields where absence of a surround of adequate brightness results in the distortion of the theoretical relation otherwise found. The theoretical relationship for intensity discrimination derived by Hecht is shown to fit practically all of the data. Changes in experimental variables such as retinal image area, wavelength, fixation, and criterion may be described as affecting the numerical quantities of this relationship.     

THE VISUAL DISCRIMINATION OF INTENSITY AND THE WEBER-FECHNER LAW

1. A study of the historical development of the Weber-Fechner law shows that it fails to describe intensity perception; first, because it is based on observations which do not record intensity discrimination accurately, and second, because it omits the essentially discontinuous nature of the recognition of intensity differences. 2. There is presented a series of data, assembled from various sources, which proves that in the visual discrimination of intensity the threshold difference ΔI bears no constant relation to the intensity I. The evidence shows unequivocally that as the intensity rises, the ratio See PDF for Equation first decreases and then increases. 3. The data are then subjected to analysis in terms of a photochemical system already proposed for the visual activity of the rods and cones. It is found that for the retinal elements to discriminate between one intensity and the next perceptible one, the transition from one to the other must involve the decomposition of a constant amount of photosensitive material. 4. The magnitude of this unitary increment in the quantity of photochemical action is greater for the rods than for the cones. Therefore, below a certain critical illumination—the cone threshold—intensity discrimination is controlled by the rods alone, but above this point it is determined by the cones alone. 5. The unitary increments in retinal photochemical action may be interpreted as being recorded by each rod and cone; or as conditioning the variability of the retinal cells so that each increment involves a constant increase in the number of active elements; or as a combination of the two interpretations. 6. Comparison with critical data of such diverse nature as dark adaptation, absolute thresholds, and visual acuity shows that the analysis is consistent with well established facts of vision.     

INTERMITTENT STIMULATION BY LIGHT : III. THE RELATION BETWEEN INTENSITY AND CRITICAL FUSION FREQUENCY FOR DIFFERENT RETINAL LOCATIONS

When measurements of the critical fusion frequency for white light over a large range of intensities are made with the rod-free area of the fovea, the relation between critical frequency and log I is given by a single sigmoid curve, the middle portion of which approximates a straight line whose slope is 11.0. This single relation must be a function of the foveal cones. When the measurements are made with a retinal area placed 5° from the fovea, and therefore containing both rods and cones, the relation between critical frequency and log I shows two clearly separated sections. At the lower intensities the relation is sigmoid and reaches an upper level at about 10 cycles per second, which is maintained for 1.25 log units, and is followed by another sigmoid relationship at the higher intensities similar to the one given by the rod-free area alone. These two parts of the data are obviously separate functions of the rods at low intensities and of the cones at high intensities. This is further borne out by similar measurements made with retinal areas 15° and 20° from the fovea where the ratio of rods to cones is anatomically greater than at 5°. The two sections of the data come out farther apart on the intensity scale, the rod portion being at lower intensities and the cone portion at higher intensities than at 5°. The general form of the relation between critical frequency and intensity is therefore determined by the relative predominance of the cones and the rods in the retinal area used for the measurements.     

THE FLICKER RESPONSE CONTOUR FOR THE GECKO (ROD RETINA)

The flicker response contour for the gecko Sphaerodactylus (retina with only rods) agrees in all essential respects (intensity range, shape) with that for the turtle Pseudemys (cone retina), as determined under equivalent conditions with the same apparatus. With experimentally determined correction for the expansion of the iris at the very lowest intensities, the F - log I contour for the gecko is a simple probability integral. Its maximum F is lower than that for other animals; this means simply a smaller number of available sensory elements. The quantitative parallelism in the magnitudes of the intensities at the inflection of F - log I and the shape constants for rod and cone animals show that assumptions from comparative histological evidence concerning the properties of rods and cones in relation to visual performance may be quite misleading.     

THE SPECTRAL SENSIBILITY OF THE SUN-FISH AS EVIDENCE FOR A DOUBLE VISUAL SYSTEM

1. An extension of a previously described method makes possible the measurement of the visibility function of Lepomis at high intensities of spectral illumination. This is accomplished by determining the relative energies of various spectral beams which will just produce a visual orienting response by the animal to the movement of a pattern composed of fine lines. 2. The function so determined is different from that obtained with a pattern composed of wide bars and spaces at a lower intensity level. 3. This difference furnishes direct and quantitative proof that the eye of Lepomis is a physiologically duplex visual system and parallels the known anatomical distinctions between the rods and cones. 4. A comparison of the visibility curves of the two systems indicates that both functions are similar in shape but that the cone curve is shifted to the red. 5. It is suggested that this relation between the two systems, which is also found in the human and the fowl, indicates that the photosensory substance is the same in each case for the rods and cones. According to this hypothesis, the shift of the cone curve is due to a common physical cause which depends on differences in the properties of the solvent media in the cones and in the rods.     

ANOXIA AND BRIGHTNESS DISCRIMINATION

1. Brightness discrimination has been studied with individuals breathing oxygen concentrations corresponding to 7 altitudes between sea level and 17,000 feet. The brightnesses were 0.1, 0.01, and 0.001 millilambert involving only daylight (cone) vision. 2. At these light intensities, brightness discrimination begins to deteriorate at fairly low altitudes. The deterioration is obvious at 8,000 feet, and becomes marked at 15,000 feet, where at low brightness, the contrast must be increased 100 per cent over the sea level value before it can be recognized. 3. The impairment of brightness discrimination with increase in altitude is greater at higher altitudes than at lower. The impairment starts slowly and becomes increasingly rapid the higher the altitude. 4. Impairment of brightness discrimination varies inversely with the light intensity. It is most evident under the lowest light intensities studied, but shows in all of them. However, it decreases in such a way that the deterioration is negligible in full daylight and sunlight. 5. The thresholds of night (rod) vision and day (cone) vision are equally affected by anoxia. 6. The quantitative form of the relation between brightness discrimination ΔI/I and the prevailing brightness I remains the same at all oxygen concentrations. The curve merely shifts along the log I axis, and the extent of the shift indicates the visual deterioration. 7. The data are described in terms of retinal chemistry. Since anoxia causes only a shift in log I it is shown that the photochemical receptor system cannot be affected. Instead the conversion of photochemical change into visual function is impaired in such a way that the conversion factor varies as the fourth power of the arterial oxygen saturation.     

THE RELATION BETWEEN VISUAL ACUITY AND ILLUMINATION

1. Visual acuity varies in a definite manner with the illumination. At low intensities visual acuity increases slowly in proportion to log I; at higher intensities it increases nearly ten times more rapidly in relation to log I; at the highest illuminations it remains constant regardless of the changes in log I. 2. These variations in visual acuity measure the variations in the resolving power of the retina. The retina is a surface composed of discrete rods and cones. Therefore its resolving power depends on the number of elements present in a unit area. The changes in visual acuity then presuppose that the number of elements in the retina is variable. This cannot be true anatomically; therefore it must be assumed functionally. 3. To explain on such a basis the variations of visual acuity, it is postulated that the thresholds of the cones and of the rods are distributed in relation to the illumination in a statistical manner similar to that of other populations. In addition the rods as a whole have thresholds lower than the cones. Then at low intensities the increase in visual acuity depends on the augmentation of the functional rod population which accompanies intensity increase; and at higher intensities the increase in visual acuity depends on the augmentation of the functional cone population. The number of cones per unit foveal area is much greater than the number of rods per unit peripheral area, which accounts for the relative rates of increase of rod and cone visual acuity with intensity. At the highest illuminations all the cones are functional and no increase in visual acuity is possible. 4. If this division into rod visual acuity and cone visual acuity is correct, a completely color-blind person should have only rod visual acuity. It is shown by a study of the data of two such individuals that this is true. 5. The rod and cone threshold distribution has been presented as a purely statistical assumption. It can be shown, however, that it is really a necessary consequence of a photochemical system which has already been used to describe other properties of vision. This system consists of a photosensitive material in reversible relation with its precursors which are its products of decomposition as well. 6. On the basis of these and other data it is shown that a minimal retinal area in the fovea, which can mediate all the steps in such functions as visual acuity, intensity discrimination, and color vision, contains about 540 cones. Certain suggestions with regard to a quantitative mechanism for color vision are then correlated with these findings, and are shown to be in harmony with accurately known phenomena in related fields of physiology.     

ON THE VARIABILITY OF CRITICAL ILLUMINATION FOR FLICKER FUSION AND INTENSITY DISCRIMINATION

From the data of experiments with bees in which threshold response is employed as a means of recognizing visual discrimination between stripes of equal width alternately illuminated by intensities I ₁ and I ₂, it is shown that the detectable increment of intensity ΔI, where ΔI = I ₂ - I ₁, is directly proportional to σ_I2 (I ₁ being fixed). From tests of visual acuity, where I ₁ = 0 and the width of the stripes is varied, σ_I2 = kI ₂ + const.; here I ₂ = ΔI, and ΔI/I ₂ = 1. When the visual excitability of the bee is changed by dark adaptation, λI ≡ kΔI (= k'' σ_ΔI) = k'''' I + const. For the measurements of critical illumination at threshold response to flicker, σ_I2 (= σ_ΔI) = k I ₂ = k'' ΔI + const. The data for critical illumination producing threshold response to flicker in the sun-fish Lepomis show for the rods σ_I2 = K I ₂ for the cones σ_I2 = K''(I ₂ + const.). The data thus indicate that in all these experiments essentially the same visual function is being examined, and that the recognition of the production of a difference in effect by alternately illuminated stripes takes place in such a way that d (ΔI)/d (σ_I2) = const., and that ΔI is directly proportional to I (or "I ₂," depending on the nature of the experiment). It is pointed out that the curve for each of the cases considered can be gotten equally well if mean I or σ_I is plotted as a function of the independent variable involved in the experiment. Certain consequences of these and related facts are important for the treatment of the general problem of intensity discrimination.     

The contribution of single and double cones to spectral sensitivity in budgerigars during changing light conditions

Bird colour vision is mediated by single cones, while double cones and rods mediate luminance vision in bright and dim light, respectively. In daylight conditions, birds use colour vision to discriminate large objects such as fruit and plumage patches, and luminance vision to detect fine spatial detail and motion. However, decreasing light intensity favours achromatic mechanisms and eventually, in dim light, luminance vision outperforms colour vision in all visual tasks. We have used behavioural tests in budgerigars (Melopsittacus undulatus) to investigate how single cones, double cones and rods contribute to spectral sensitivity for large (3.4°) static monochromatic stimuli at light intensities ranging from 0.08 to 63.5 cd/m². We found no influences of rods at any intensity level. Single cones dominate the spectral sensitivity function at intensities above 1.1 cd/m², as predicted by a receptor noise-limited colour discrimination model. Below 1.1 cd/m², spectral sensitivity is lower than expected at all wavelengths except 575 nm, which corresponds to double cone function. We suggest that luminance vision mediated by double cones restores visual sensitivity when single cone sensitivity quickly decreases at light intensities close to the absolute threshold of colour vision.     

BRIGHTNESS DISCRIMINATION AS A FUNCTION OF THE DURATION OF THE INCREMENT IN INTENSITY

1. This investigation has been concerned with an analysis of brightness discrimination as it is influenced by the duration of ΔI. The durations used extend from 0.002 second to 0.5 second. 2. ΔI/I values at constant intensity are highest for the shortest duration and decrease with an increase in duration up to the limits of a critical exposure time. At durations longer than the critical duration the ratio ΔI/I remains constant. 3. The Bunsen-Roscoe law holds for the photolysis due to ΔI. This is shown by the fact that, within the limits of a critical duration, the product of ΔI and exposure time is constant for any value of prevailing intensity, I. 4. At durations greater than the critical duration the Bunsen-Roscoe law is superseded by the relation ΔI = Constant. This change of relation is considered in the light of Hartline''s discussion (1934). 5. The critical duration is a function of intensity. As intensity increases the critical duration decreases. 6. Hecht''s theory (1935) accounts for the data of this experiment if it be assumed that brightness discrimination is determined by a constant amount of photolysis.     

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°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.     

Frequency of seeing functions for intensity discrimination of various levels of adapting intensity

1. The percentage of times a human subject detects an increment (ΔI) in intensity was determined as a function of the magnitude of the increment and the magnitude of the stimulus (I) to which the increment is added. 2. Foveal stimulation was used, and five frequency of seeing curves were obtained at each of nine values of adapting intensity covering the range from –1.45 to 4.45 log photons. Each frequency of seeing curve shows the percentage of times an increment in intensity is detected as a function of the logarithm of the increment. 3. The slope of the frequency of seeing curve increases slightly with an increase in I and finally becomes independent of I at medium to high intensities. 4. The implications of the results for quantum theories of visual excitation are considered.     

CRITICAL ILLUMINATION AND FLICKER FREQUENCY IN RELATED FISHES

Flicker response curves have been obtained at 21.5°C. for three genera of fresh water teleosts: Enneacanthus (sunfish), Xiphophorus (swordtail), Platypoecilius (Platy), by the determination of mean critical intensities for response at fixed flicker frequencies, and for a certain homogeneous group of backcross hybrids of swordtail x Platy (Black Helleri). The curves exhibit marked differences in form and proportions. The same type of analysis is applicable to each, however. A low intensity rod-governed section has added to it a more extensive cone portion. Each part is accurately described by the equation F = F_max./(1 + e ^{-p log-p logI/I_i}), where F = flicker frequency, I = associated mean critical intensity, and I_i is the intensity at the inflection point of the sigmoid curve relating F to log I. There is no correlation between quantitative features of the rod and cone portions. Threshold intensities, p, I_i, and F_max. are separately and independently determined. The hybrid Black Helleri show quantitative agreement with the Xiphophorus parental stock in the values of p for rods and cones, and in the cone F_max.; the rod F_max. is very similar to that for the Platy stock; the general level of effective intensities is rather like that of the Platy form. This provides, among other things, a new kind of support for the duplicity doctrine. Various races of Platypoecilius maculatus, and P. variatus, give closely agreeing values of I_m at different flicker frequencies; and two species of sunfish also agree. The effect of cross-breeding is thus not a superficial thing. It indicates the possibility of further genetic investigation. The variability of the critical intensity for response to flicker follows the rules previously found to hold for other forms. The variation is the expression of a property of the tested organism. It is shown that, on the assumption of a frequency distribution of receptor element thresholds as a function of log I, with fluctuation in the excitabilities of the marginally excited elements, it is to be expected that the dispersion of critical flicker frequencies in repeated measurements will pass through a maximum as log I is increased, whereas the dispersion of critical intensities will be proportional to I_m; and that the proportionality factor in the case of different organisms bears no relation to the form or position of the respective curves relating mean critical intensity to flicker frequency. These deductions agree with the experimental findings.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : III. ΔI AS A FUNCTION OF AREA,INTENSITY, AND WAVE-LENGTH,FOR MONOCULAR AND BINOCULAR STIMULATION

Measurements of ΔI as a function of retinal area illuminated have been obtained at various levels of standard intensity I ₁, using "white" light and light of three modal wave-lengths (λ465, 525, 680), for monocular stimulation and for simultaneous excitation of the two eyes ("binocular"), using several methods of varying (rectangular) area and retinal location, with control of exposure time. For data homogeneous with respect to method of presentation, log ΔI_m = -Z log A + C, where ΔI = Ĩ ₂ – I ₁, A is area illuminated, and C is a terminal constant (= log ΔI_m for A = 1 unit) depending on the units in which ΔI and A are expressed, and upon I ₁. The equation is readily deduced on dimensional grounds, without reference to specific theories of the nature of ΔI or of retinal area in terms of its excitable units. Z is independent of the units of I and A. Experimentally it is found to be the same for monocular and binocular excitations, as is to be expected. Also as is expected it is not independent of λ, and it is markedly influenced by the scheme according to which A is varied; it depends directly upon the rate at which potentially excitable elements are added when A is made to increase. For simultaneous excitation of the two eyes (when of very nearly equivalent excitability), ΔĪ_B is less than for stimulation of either eye alone, at all levels of I ₁, A, λ. The mean ratio (ΔĪ_L + ΔĪ_R)/2 to ΔI^B was 1.38. For white light, doubling A on one retina reduces ΔI_m in the ratio 1.21, or a little less than for binocular presentation under the same conditions. These facts are consistent with the view that the properties of ΔI are quantitatively determined by events central to the retina. The measure σ_1ΔI of organic variation in discrimination of intensities and ΔI_m are found to be in simple proportion, independent of I ₁, A, λ (and exposure time). Variability (σ_1ΔI) is not a function of the mode of presentation, save that it may be slightly higher when both retinas are excited, and its magnitude (for a given level of ΔI_m) is independent of the law according to which the adjustable intensity I ₂ is instrumentally controlled.     

THE VARIABILITY OF INTENSITY DISCRIMINATION BY THE HONEY BEE IN RELATION TO VISUAL ACUITY

Variation in the determined magnitudes of the difference in brightness between alternating members of a system of stripes requisite for the elicitation of a threshold response in bees shows that the intensity of excitation, as a function of width of stripe and of intensity of illumination, is determined by the intensity of illumination and by the frequency of occurrence of divisions between bright and less bright bars. The variation of ΔI is limited by the intensity of excitation, so that the curves relating P.E. (ΔI/I) have the same form in relation to I as do the curves for ΔI/I. The limiting rule according to which P.E. ΔI is a power function of I for stripes of maximum usable width is departed from more and more markedly, for lower intensities, as narrower stripes are employed.     

TIME AND INTENSITY IN PHOTOSENSORY STIMULATION

In its photosensory effect, the action of light depends on two variables,—intensity and time. If the intensity alone is varied, the photochemical effect is proportional to the logarithm of the intensity. If the time alone is varied, the effect is proportional to the time. Experiments here reported show that when both the intensity and the time are varied, the photochemical effect is equal to the product of their separate activities: E = kt log I. These results furnish the means of expressing directly the relation between the intensity of illumination and the reaction time of Mya.     

THE ORIENTATION OF ANIMALS BY OPPOSED BEAMS OF LIGHT

When orientation is attained under the influence of beams of parallel light opposed at 180° the deflection θ from a path at right angles to the beams is given by tan See PDF for Equation, where I ₁ and I ₂ are the photic intensities and H is the average angle between the photoreceptive surfaces. This expression is independent of the units in which I is measured, and holds whether the primary photosensory effect is proportional to I or to log I. When photokinetic side-to-side motions of the head occur, H decreases with increasing total acting light intensity, but increases if higher total light intensity restricts the amplitude of random movements; in each case, H is very nearly proportional to log I ₁ I ₂. For beams of light at 90°, See PDF for Equation. The application of these equations to some particular instances is discussed, and it is shown why certain simpler empirical formulæ previously found by others yield fair concordance with the experimental data. The result is thus in complete accord with the tropism theory, since the equations are based simply on the assumption that when orientation is attained photic excitation is the same on the two sides.     

Control of Retinal Sensitivity : I. Light and Dark Adaptation of Vertebrate Rods and Cones

Rods and cones in Necturus respond with graded hyperpolarization to test flashes spanning about 3.5 log units of intensity. Steady background levels hyperpolarize the rods, and the rod responses become progressively smaller as background level is increased. In cones, higher background levels reduce the effectiveness of test flashes, so higher ranges of test intensities are required to elicit the full range of graded responses. When backgrounds are terminated, cones return rapidly, but rods return slowly to the dark potential level. The effects of backgrounds on both rods and cones can be observed at intensities that cause negligible bleaching as determined by retinal densitometry. During dark adaptation, changes are observed in the rods and cones that are similar to those produced by backgrounds. Receptor sensitivities, derived from these results, show that rods saturate, cones obey Weber's law, and sensitization during dark adaptation follows a two-phase time-course.