THRESHOLD INTENSITY OF ILLUMINATION AND FLICKER FREQUENCY FOR THE EYE OF THE SUN-FISH

The sun-fish Lepomis responds to a moving system of stripes by a motion of its body. By changing the velocity of motion of the stripe system different flicker frequencies can be produced and thus the relation of flicker frequency to critical intensity of illumination can be studied. Threshold illumination varies with flicker frequency in such a way that with increasing flicker frequency the intensity of illumination must be increased to produce a threshold response in the fish. The curve of critical illumination as a function of frequency is made up of two distinct parts. For an intensity range below 0.04 millilambert and flicker frequencies below 10 per second, the rods are in function. For higher intensities and flicker frequencies above 10, the cones come into play. The maximum frequency of flicker which can be perceived by the fish''s eye is slightly above 50 per second. The flicker curve for the eye of Lepomis can easily be compared with that for the human eye. The extent of the curve for the fish is greater at low illuminations, the fish being capable of distinguishing flicker at illuminations lower than can the human eye. The transition of rod vision to cone vision occurs for the fish and for the human eye at the same intensity and flicker frequency. The maximum frequency of flicker which can be perceived is for both about the same.     

ON CRITICAL FREQUENCY AND CRITICAL ILLUMINATION FOR RESPONSE TO FLICKERED LIGHT

The curve of mean critical flicker frequency as a function of illumination has been determined for the reaction of the sunfish Lepomis to flicker. It exhibits expected quantitative disagreements with the curve of mean critical illumination as a function of flicker frequency in the same organism. The form of the dependence of the variation of critical frequency of flicker upon illumination can be predicted from a knowledge of the way in which variation of critical illumination depends upon flicker frequency. It is pointed out that these findings have an important bearing upon the interpretation of the data of intensity discrimination.     

THE VISUAL ACUITY AND INTENSITY DISCRIMINATION OF DROSOPHILA

Drosophila possesses an inherited reflex response to a moving visual pattern which can be used to measure its capacity for intensity discrimination and its visual acuity at different illuminations. It is found that these two properties of vision run approximately parallel courses as functions of the prevailing intensity. Visual acuity varies with the logarithm of the intensity in much the same sigmoid way as in man, the bee, and the fiddler crab. The resolving power is very poor at low illuminations and increases at high illuminations. The maximum visual acuity is 0.0018, which is 1/1000 of the maximum of the human eye and 1/10 that of the bee. The intensity discrimination of Drosophila is also extremely poor, even at its best. At low illuminations for two intensities to be recognized as different, the higher must be nearly 100 times the lower. This ratio decreases as the intensity increases, and reaches a minimum of 2.5 which is maintained at the highest intensities. The minimum value of ΔI/I for Drosophila is 1.5, which is to be compared with 0.25 for the bee and 0.006 for man. An explanation of the variation of visual acuity with illumination is given in terms of the variation in number of elements functional in the retinal mosaic at different intensities, this being dependent on the general statistical distribution of thresholds in the ommatidial population. Visual acuity is thus determined by the integral form of this distribution and corresponds to the total number of elements functional. The idea that intensity discrimination is determined by the differential form of this distribution—that is, that it depends on the rate of entrance of functional elements with intensity—is shown to be untenable in the light of the correspondence of the two visual functions. It is suggested that, like visual acuity, intensity discrimination may also have to be considered as a function of the total number of elements active at a given intensity.     

THE VISUAL ACUITY OF THE HONEY BEE

1. Bees respond by a characteristic reflex to a movement in their visual field. By confining the field to a series of parallel dark and luminous bars it is possible to determine the size of bar to which the bees respond under different conditions and in this way to measure the resolving power or visual acuity of the eye. The maximum visual acuity of the bee is lower than the lowest human visual acuity. Under similar, maximal conditions the fineness of resolution of the human eye is about 100 times that of the bee. 2. The eye of the bee is a mosaic composed of hexagonal pyramids of variable apical angle. The size of this angle determines the angular separation between adjacent ommatidia and therefore sets the structural limits to the resolving power of the eye. It is found that the visual angle corresponding to the maximum visual acuity as found experimentally is identical with the structural angular separation of adjacent ommatidia in the region of maximum density of ommatidia population. When this region of maximum ommatidia population is rendered non-functional by being covered with an opaque paint, the maximum visual acuity then corresponds to the angular separation of those remaining ommatidia which now constitute the maximum density of population. 3. The angular separation of adjacent ommatidia is much smaller in the vertical (dorso-ventral) axis than in the horizontal (anterio-posterior) axis. The experimentally found visual acuity varies correspondingly. From this and other experiments as well as from the shape of the eye itself, it is shown that the bee''s eye is essentially an instrument for uni-directional visual resolution, functional along the dorso-ventral axis. The resolution of the visual pattern is therefore determined by the vertical angular separation of those ocular elements situated in the region of maximum density of ommatidia population. 4. The visual acuity of the bee varies with the illumination in much the same way that it does for the human eye. It is low at low illuminations; as the intensity of illumination increases it increases at first slowly and then rapidly; and finally at high intensities it becomes constant. The resolving power of a structure like the bee''s eye depends on the distance which separates the discrete receiving elements. The data then mean that at low illuminations the distance between receiving elements is large and that this distance decreases as the illumination increases. Since such a moving system cannot be true anatomically it must be interpreted functionally. It is therefore proposed that the threshold of the various ommatidia are not the same but that they vary as any other characteristic of a population. The visual acuity will then depend on the distance apart of those elements whose thresholds are such that they are functional at the particular illumination under investigation. Taking due consideration of the angular separation of ommatidia it is possible to derive a distribution curve for the thresholds of the ommatidia which resembles the usual probability curves, and which describes the data with complete fidelity.     

REACTIONS OF LIMULUS TO ILLUMINATED FIELDS OF DIFFERENT AREA AND FLICKER FREQUENCY

In phototropic tests with young Limulus, the phototropic reactions to flickering fields were studied. If the two fields are equal in area and brightness but different in flicker frequency, the number of animals going to the two fields is proportional to their flicker frequencies. Equal stimulating effects of two fields differing in flicker frequency are obtained by reduction of the area of the faster flickering field. The areas for equal effect must be inversely proportional to their flicker frequencies. It seems that equal effects are dependent upon equality of the number of active excitation elements per unit of time.     

THE FLICKER RESPONSE CONTOUR FOR THE CRAYFISH. I

The F - log I curve for threshold response to visual flicker has been determined for the crayfish Cambarus bartoni. As predicted on the basis of the higher curvature of the optic surface, the flicker response contour is more asymmetrical than for bee and dragonfly nymph under comparable conditions of temperature and light time fraction of flash cycle. The mechanical origin of this asymmetry is thus confirmed, and is further supported by the similar forms of the F - log I curves in bee, dragonfly larva, and crayfish in the lower portion of the curves (up to F = 70 per cent F_max.). The slope of the fundamental curve for crayfish, deduced by analysis of the data, is lower than for bee, dragonfly nymph, or Asellus. This signifies a wider spread of the effective distribution of elemental log I thresholds involvable in the response to flicker, and may be traced either to the greater curvature of the eye-surfaces or to their position upon movable pedicles. The results are therefore consistent with the statistical conception of the nature of effects recognizable as due to the activity of excitable elements.     

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.     

THE VISUAL INTENSITY DISCRIMINATION OF THE HONEY BEE

1. Bees respond by a characteristic reflex to a movement in their visual field. By confining the field to a series of parallel stripes of different brightness it is possible to determine at any brightness of one of the two stripe systems the brightness of the second at which the bee will first respond to a displacement of the field. Thus intensity discrimination can be determined. 2. The discriminating power of the bee''s eye varies with illumination in much the same way that it does for the human eye. The discrimination is poor at low illumination; as the intensity of illumination increases the discrimination increases and seems to reach a constant level at high illuminations. 3. The probable error of See PDF for Equation decreases with increasing I exactly in the same way as does See PDF for Equation itself. The logarithm of the probable error of ΔI is a rectilinear function of log I for all but the very lowest intensities. Such relationships show that the measurements exhibit an internal self-consistency which is beyond accident. 4. A comparison of the efficiency of the bee''s eye with that of the human eye shows that the range over which the human eye can perceive and discriminate different brightnesses is very much greater than for the bee''s eye. When the discrimination power of the human eye has reached almost a constant maximal level the bee''s discrimination is still very poor, and at an illumination where as well the discrimination power of the human eye and the bee''s eye are at their best, the intensity discrimination of the bee is twenty times worse than in the human eye.     

How Long Depends on How Fast—Perceived Flicker Dilates Subjective Duration

How do humans perceive the passage of time and the duration of events without a dedicated sensory system for timing? Previous studies have demonstrated that when a stimulus changes over time, its duration is subjectively dilated, indicating that duration judgments are based on the number of changes within an interval. In this study, we tested predictions derived from three different accounts describing the relation between a changing stimulus and its subjective duration as either based on (1) the objective rate of changes of the stimulus, (2) the perceived saliency of the changes, or (3) the neural energy expended in processing the stimulus. We used visual stimuli flickering at different frequencies (4–166 Hz) to study how the number of changes affects subjective duration. To this end, we assessed the subjective duration of these stimuli and measured participants'' behavioral flicker fusion threshold (the highest frequency perceived as flicker), as well as their threshold for a frequency-specific neural response to the flicker using EEG. We found that only consciously perceived flicker dilated perceived duration, such that a 2 s long stimulus flickering at 4 Hz was perceived as lasting as long as a 2.7 s steady stimulus. This effect was most pronounced at the slowest flicker frequencies, at which participants reported the most consistent flicker perception. Flicker frequencies higher than the flicker fusion threshold did not affect perceived duration at all, even if they evoked a significant frequency-specific neural response. In sum, our findings indicate that time perception in the peri-second range is driven by the subjective saliency of the stimulus'' temporal features rather than the objective rate of stimulus changes or the neural response to the changes.     

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.     

INTERMITTENT STIMULATION BY LIGHT : II. THE MEASUREMENT OF CRITICAL FUSION FREQUENCY FOR THE HUMAN EYE

An apparatus and a procedure are described to measure the critical frequency of flicker using different portions of the eye. The observer, looking through a pupil of fixed dimensions, views a field of 2° whose illumination is periodically interrupted and which is surrounded by a field of 10° whose illumination is continuous but otherwise identical with the interrupted field. Various parts of the apparatus are concerned with controlling and recording the retinal position of the field, its intensity, its spectral composition, and the frequency of interruption of its illumination. The procedure is so simplified and regulated that a complete set of readings over the whole intensity range of vision can be made at one sitting without fatigue or strain.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : I. ANAX LARVAE

The curve of mean critical illumination (I_m) for response to flicker as a function of flicker frequency (F) for the larvae of the dragonfly Anax junius is progressively shifted toward higher intensities the lower the temperature. The maximum flicker frequency (one half the cycle time of light and no light) and the maximum intensity with which it is associated are very little if at all affected by change of temperature. These facts are in agreement with the requirements of the conception that recognition of critical illumination for reaction to flicker involves and depends upon a kind of intensity discrimination, namely between the effects of flashes and the after effects of these flashes during the intervals of no light. The shift of the F-I_m curve with change of temperature is quite inconsistent with the stationary state conception of the determination of the shape of the curve. The dispersion (P.E. _II1) of the measurements of I ₁ is directly proportional to I_m, but the factor of proportionality is less at high and at low temperature than at an intermediate temperature; the scatter of the values of P.E. _II1 is also a function of the temperature. These facts can also be shown to be concordant with the intensity discrimination basis for marginal recognition of flicker.     

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°) 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 σ_II1 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 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.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : III. SUNFISH

For the sunfish Enneacanthus the mean value of the critical illumination for response to visual flicker at constant flash frequency (with light time = dark time) is related to temperature by the Arrhenius equation. The temperature characteristic for 1/I_m is different above and below 20°C. In each range (12° to 20°; 20° to 30°) the temperature characteristic is the same for rod and cone segments of the duplex flicker response contour: 8,200 and 14,400. This makes it difficult, if not impossible, to consider that the two groups of elements are organized in a significantly different way chemically. For the presumptively rod-connected elements implicated in response to flicker, the curve is markedly discontinuous, so that the high and low temperature parts are dislocated; whereas for the cones they are not. This is entirely consistent with other (e.g., genetic) evidence pointing to their separate physical substrata. The uncommon exhibition of a higher µ over a higher range of temperature, previously found, however, in a few cases, together with the different relations of rod and cone effects to the critical temperature, explain aspects of these data which in earlier incomplete measurements were found to be puzzling.     

Flicker alternating potentials in the ERGs of insects in response to two different stimuli

Summary A special pattern of the flicker is studied in insects belonging to four Orders, i. e. the differential electrical synchronised response of the eye periodically stimulated by two slightly different alternating illuminations.After having checked that the flicker in response to a regular periodical stimulation at every frequency is made up of successive equal potentials, we use two slightly different alternate flickering flashes. It is established that the alternation of two periodical stimulations of a different duration, as well as the alternation of two periodical stimulations of a different intensity, results, over a certain frequency which depends on the insect studied, in the appearance of a flicker marked with the alternation of two potentials whose difference increases at the same time as the frequency of stimulation.The dependence of this phenomenon on modulation of the light flux is described. At a given frequency of stimulation, the alternation of a high and low potential is more obvious when the modulation is lower.A particular experiment allows us to admit that the differential threshold of electrical response to two different stimulations is under 0.25%, at the frequency 100 Hz, inCalliphora erythrocephala.All the phenomena observed can be explained by a mathematical theory which considers the characteristics of the amplitude of the response to sinusoidal stimulations of various frequencies, i. e. the characteristics of the transfer function of the frequencies.     

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.     

INTENSITY AND CRITICAL FREQUENCY FOR VISUAL FLICKER

Using the rotating striped cylinder device previously employed for determination of the flicker response function with lower animals, corresponding measurements have been made with human observers. The curves based upon the relation between critical flash frequency and critical intensity for the signalling of the recognition of flicker have the properties of human flicker fusion data as obtained by other methods. They also have the quantitative properties of the flicker curves provided by the motor responses of insects and fishes to the seen movement of flashes. This applies to the variation found in repeated measurements as well as to the nature of the analytical function describing the connection between flash frequency and intensity. The data for human visual flicker and those for the responses of lower animals are therefore essentially homologous.