THE SIMPLEX FLICKER THRESHOLD CONTOUR FOR THE ZEBRA FINCH

The flicker response contour has been determined, with equality of light-dark time ratio, for the diurnal bird the Australian zebra finch. This bird has only cones in the retina. The curve of log critical intensity as a function of flash frequency is simplex, a normal probability integral. In this respect it is like that for other vertebrates not exhibiting visual duplexity. The parameters of the curve most closely approach those for the turtle Pseudemys (extrapolated to about the same temperature); it is not improbable that the approximation of these two curves would be less close for other values of the light-time fraction. Some points of interpretive visual theory are discussed in relation to the present measurements.     

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.     

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.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : V. FLASH DURATION AND CRITICAL INTENSITY FOR RESPONSE TO FLICKER

The relation between flash duration and mean critical intensity (white light) for threshold recognition of visual flicker, as a function of flash frequency, was investigated by means of measurements at five values of the light-time fraction: 0.10, 0.25, 0.50, 0.75, 0.90, with flash frequencies of the interrupted beam ranging from 2 to 60 per second. A square area, 6.1 x 6.1°, centrally fixated) was viewed monocularly; the discriminometer used provides automatically an artificial pupil 1.8 mm. in diameter. Except for the slight day-to-day fluctuation in the magnitudes of the parameters, the data for the observer used are shown to form an essentially homogeneous group. As for other animals tested, the F - log I_m curve is enlarged and moved toward lower flash intensities as the light-time fraction is decreased. The high intensity segments of the duplex curves are fitted by normal probability integrals for which F _max. and the abscissa of inflection are rectilinear functions of t_L(t_L + t_D), with opposite slopes. The third parameter, (σ''_{log I}, is invariant. The low intensity segments are composites, their shapes determined by the summation of the lower part of the high intensity curve with an overlapping low intensity population of effects. Both the rising and the declining branches of this latter assemblage suffer competitive partial suppression by the effects in the high intensity population. The detailed analysis shows that these results are consistent with the theory of the central, rather than peripheral, location of the dynamically recognizable elements in the determination of flicker.     

CRITICAL ILLUMINATION AND CRITICAL FREQUENCY FOR RESPONSE TO FLICKERED LIGHT,IN DRAGONFLY LARVAE

Curves relating flicker frequency (F) to mean critical illumination (I_m) for threshold response to flickered light, with equal durations of light and no light intervals, and relating illumination (I) to mean critical flicker frequency (F_m) for the same response, have been obtained from homogeneous data based upon the reactions of dragonfly larvae (Anax junius). These curves exhibit the properties already described in the case of the fish Lepomis. The curve for F_m lies above the curve of I_m by an amount which, as a function of I, can be predicted from a knowledge either of the variation of I_m or of F_m. The law of the observable connection between F and I is properly expressed as a band, not as a simple curve. The variation of I_m (and of F_m) is not due to "experimental error," but is an expression of the variable character of the organism''s capacity to exhibit the reaction which is the basis of the measurements. As in other series of measurements, P.E. _I is a rectilinear function of I_m; P.E. _F passes through a maximum as F (or I) increases. The form of P.E. _F as a function of I can be predicted from the measurements of P.E. _I. It is pointed out that the equations which have been proposed for the interpretation of curves of critical flicker frequency as a function of intensity, based upon the balance of light adaptation and dark adaptation, have in fact the character of "population curves;" and that their contained constants do not have the properties requisite for the consistent application of the view that the shape of the F - I curve is governed by the steady state condition of adaptation. These curves can, however, be understood as resulting from the achievement of a certain level of difference between the average effect of a light flash and its average after effect during the dark interval.     

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 FLICKER RESPONSE CONTOUR FOR PHRYNOSOMA (HORNED LIZARD; CONE RETINA)

The lizard Phrynosoma, with purely cone retina, provides a simplex flicker response contour (log critical flash intensity as a function of flash frequency). It is well described as a normal probability integral (F - log I). The Phrynosoma curve differs markedly, in higher slope and in higher median intensity level, from that obtained under the same conditions for the turtle Pseudemys, also with entirely cone retina. Other comparisons having a bearing on the duplexity doctrine are discussed.     

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

The curve connecting mean critical illumination (I_m) and flicker frequency (F) for response of the sunfish Lepomis (Enneacanthus gloriosus) to flicker is systematically displaced toward lower intensities by raising the temperature. The rod and cone portions of the curve are affected in a similar way, so that (until maximum F is approached) the shift is a nearly constant fraction of I_m for a given change of temperature. These relationships are precisely similar to those found in the larvae of the dragonfly Anax. The modifications of the variability functions are also completely analogous. The effects found are consistent with the view that response to flicker is basically a matter of discrimination between effect of flashes of light and their after effects,—a form of intensity discrimination. They are not consistent with the stationary state formulation of the shape of the flicker curve. An examination of the relationships between the cone portion and the rod portion of the curves for the sunfish suggests a basis for their separation, and provides an explanation for certain "anomalous" features of human flicker curves. It is pointed out how tests of this matter will be made.     

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.     

CRITICAL FREQUENCY OF FLICKER AS A FUNCTION OF INTENSITY OF ILLUMINATION FOR THE EYE OF THE BEE

The bee''s characteristic response to a movement of its visual field is used for the study of the relation between critical frequency of flicker and illumination. The critical flicker frequency varies with illumination in such a way that with increasing flicker frequency the intensity of illumination must be increased to produce a threshold response in the bee. The illuminations required to give a response in a bee at different flicker frequencies closely correspond to the intensities for threshold response in visual acuity tests. This is due to the different thresholds of excitability of the elements of the ommatidial mosaic. An analysis of the variation of the values for threshold intensities at the several flicker frequencies shows that the variation depends upon flicker frequency and upon the number of elements functioning at different intensities.     

Response entrainment of movement fibers in the optic tract of crayfish

The response properties of jittery movement fibers (JMF) in the crayfish optic tract reacting to a non-moving temporally patterned light were analyzed. The JMFs usually show no response during the regular flickering of stationary light with a flash duration of less than 50 msec when the stimulus frequency is between 4 and 20 per second; however they do respond when the flickering stops if a certain number of flashes have been given. The response appears about 50 msec after the first missing flash, i.e., the latency of the response after the last flash of the train changed from 100 to 300 msec. Thus, the “off” response at the end of the flicker is entrained to the stimulus repetition interval and locked onto the time of the first missing flash. The response of a sustaining fiber to an identical stimulus has quite different features as illustrated in Fig. 2. Some of the fibers show responses to the beginning part of the flicker but not necessarily to each flash, and habituate after several flashes. When a single flash longer than 250 msec is given, the fiber shows an “off” response with about 50 msec latency, as it does to sustained light. Some fibers show a double burst of “off” discharge to single flashes; the first at 50 msec is followed after 120 msec by the second one. However, when the flash duration is between 250 and 50 msec, a single flash elicits little or no response. The latency of the “off” response is as much as 300 msec for short single flashes less than 50 msec. An “on” response to flashes of light is observed when the inter-stimulus interval is more than 5 sec. The responses to the beginning part of flicker train are not simply locked to the just preceding flash except the “on” response to the very first one, but they can be the long latency responses to the flash before that. This response is modified in latency by the succeeding flashes in flicker trains and becomes entrained to the missing flash. Four types of entrainment are classified on the basis of the change in latency from the missing flash with regard to the number of flashes in a train. In most cases, 10 flashes are sufficient to entrain the response to the first missing flash. Non-resposiveness, i.e., habituation, during a regular flicker, may be due to an active inhibitory process, initiated by each succeeding light pulse. The response to the missing flash, therefore results from a disinhibited modified response to the last flash. Some JMFs continue to respond to the flicker even after a considerable number of flashes but only when the repetition interval is about 120 msec corresponding well to the interval of the double burst “off” discharge, thus the JMF has a resonant frequency of about 8 Hz. The JMFs appear to be acting as an irregularity detector in temporal sequence.     

Frequency dependent flicker response enhancement in the lamina ganglionaris ofDrosophila

Summary At low light intensity and within the narrow frequency range of 55 to 66 s^–1, the eye ofDrosophila will follow a flashing light source by enhancing it's flicker response to every other flash. By contrast, at lower and higher frequencies the eye will follow every cycle of a respective flash frequency upto a fusion point around 200 s^–1.While the receptor cells involved are retinula cells R1–6, the flicker response enhancement is established to originate postsynaptically in the Large Monopolar Cells of the lamina with which the peripheral retinula cells synapse, and which respond with the cornealpositive on-transient component of the ERG. Not only is a prescribed frequency required for the enhancement, but also continuity of cue — since brief periods of light flashes within the required frequency range are resolved at every cycle.The flicker response behaviour provides further credence to the existence of fine tuning mechanisms together with amplification within the lamina neuropile.We are grateful to the late Dr. Richard Wright for his comments, and to Professor Aubrey Manning for the hospitality his Department gave to N.L.     

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.     

INTERMITTENT STIMULATION BY LIGHT : V. THE RELATION BETWEEN INTENSITY AND CRITICAL FREQUENCY FOR DIFFERENT PARTS OF THE SPECTRUM

1. An optical system is described which furnishes large flickering fields whose brightness, even when reduced with monochromatic filters, is capable of covering the complete range of the relation between critical frequency and intensity. 2. For a centrally located test field of 19° diameter, with light from different parts of the spectrum, the data divide into a low intensity section identified with rod function, and a high intensity section identified with cone function. The transition between the two sections is marked by an inflection point which is sharp, except for 450 and 490 mµ where, though clearly present, it is somewhat rounded. 3. The intensity range covered by the flicker function is smallest in the red, and increases steadily as the wave-length decreases. The increase is due entirely to the extent of the low intensity, rod section which is smallest (non-existent for S. S.) in the red and largest in the violet. The high intensity cone portion for all colors is in the same position on the intensity axis, and the only effect of decreasing wave-length is to shift the rod section to lower intensities without changing its shape. 4. The measurements are faithfully described by two similar equations, one for the rods and one for the cones, both equations being derived from the general stationary state equation already used for various visual functions.     

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.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : VI. WAVE-LENGTH AND FLASH DURATION IN FLICKER

For spectral regions associated with violet, blue, green, and red the relation between mean critical flash intensity I_m for visual flicker and the flash frequency F is modified as already found with white light when the light time fraction t_L in the flash cycle is changed. For a square image 6.13° on a side, foveally fixated, the "rod" and "cone" contributions to the duplex contour are analyzed in the way already used for white. It is pointed out that several customary qualitative criteria for cone functioning do not necessarily give concordant results. The analysis shows that the three parameters of the probability summations giving the "rod" and "cone" curves are changed independently as a function of wave-length composition of the light, and of the light time fraction. The correlation of these changes, and of those found in the associated variability functions, can be understood in terms of differences in (1) the numbers of neural units potentially excitable and (2) in the numbers of elements of neural effect obtained from them. In a multivariate situation of this kind it is necessary to compare intensities of luminous flux required to activate half the total population of potentially available elements when this total size is held constant for the different conditions. The results of this comparison, for the filtered lights used, are discussed in relation to certain aspects of excitation vs. wave-length. The problem is a general one, arising where the effects produced as a function of a particular variable are concerned. In the distinction between (1) units excited and (2) the actions they produce may be found the clue for the curious fact that with certain wave-lengths the critical intensities are lower than for white. The extension of the observations to other parts of the retina may be expected to further this analysis.