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.     

CRITICAL INTENSITY AND FLASH DURATION FOR RESPONSE TO FLICKER: WITH ANAX LARVAE

Determinations of the flicker response curve (F – log I_m) with larvae of Anax junius (dragonfly) for various ratios t_L/t_D of light time to dark time in a flash cycle provide relations between t_L/t_D and the parameters of the probability integral fundamentally describing the F – log I function, including the variability of I. These relations are quantitatively of the same form as those found for this function in the sunfish, and are therefore non-specific. Their meaning for the theory of reaction to visual flicker is discussed. The asymmetry of the Anax curve, resulting from mechanical conditions affecting the reception of light by the arthropod eye, is (as predicted) reduced by relative lengthening of the fractional light time in a cycle.     

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.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : VII. THE FLICKER RESPONSE FUNCTION OUTSIDE THE FOVEA

The several parameters of the flicker response contour (F – log I) are considered as a function of wave-length composition (white, blue, and red) and light-time fraction, for an extra-foveal region (monocular, temporal retina). These data are compared with those secured for the same image area centrally fixated at the fovea. The systematic changes in the parameters are shown to be in rational relation to other relevant excitability data. Since for two retinal regions the primary contours are quite different, the systematic nature of the behavior of the parameters in the two cases is a real test of the power of the analysis proposed. Theoretical interpretation is required to deal with the properties of sets of performance contours under systematically varied conditions, and cannot rely simply on the comparison of (for example) two contours under the same arbitrary conditions at two retinal locations. In particular it is emphasized that a qualitative separation must be made of the two factors of (a) number of units and (b) the frequencies of their actions, before the wave-length problem can be dealt with effectively.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : XI. ON FLICKER WITH SUBDIVIDED FIELDS

In Vol. 27, No. 5, May 20, 1944, page 403, in the eighth line from the bottom of the page, the comma after "intensity" should be a semicolon. On page 413, in the second formula from the bottom of the page, for See PDF for Equation read See PDF for Equation On the same page, formula 2 should read See PDF for Equation On page 414, line 3, at the end of the line add "or" to read "of the level of I or of F." On page 422, in the first line below the figure legend, for "illuminate" read "illuminated." On page 430, line 22, for "lighteb dars" read "lighted bars."     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : VIII. THE FORM OF THE FLICKER CONTOUR

Flicker response curves (man) obtained with images formed entirely within the fovea are like those secured with lower animals having only one general class of retinal receptors. They are normal probability integrals (F vs. log I_m), and the properties of their parameters agree with those for visually simplex animals and for the "cone" portions of contours exhibiting visual duplexity. By several different procedures, involving experimental modifications of the "cone" curve, the "rod" part of the typical human duplex curve can be obtained free from overlapping by the extrapolated "cone" curve. It then has the probability integral form which the lower segment does not directly exhibit when combined with "cone" effects. These results are discussed with reference to the statistical nature of the fundamental form of the flicker contour and to the interpretation of duplex curves produced by the neural integration of two independently modifiable groups of sensory effects.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : X. MODIFICATIONS OF THE FLICKER RESPONSE CONTOUR,AND THE SIGNIFICANCE OF THE AVIAN PECTEN

1. When there is projected on the retina (man, monocularly) the shadow of a grid which forms a visual field in several distinct pieces (not including the fovea in the present tests), the ordinary properties of the flicker recognition contour (F vs. log I) as a function of the light-time cycle fraction (t_L) can be markedly disturbed. In the present experiments flicker was produced by the rotation of a cylinder with opaque vertical stripes. In the absence of such a grid shadow the "cone" segments of the contours form a set in which F_max. and the abscissa of inflection are opposite but rectilinear functions of t_L, while the third parameter of the probability integral (σ''_{log I}) remains constant. This is the case also with diverse other animals tested. In the data with the grid, however, analysis shows that even for low values of t_L (up to 0.50) there occurs an enhancement of the production of elements of neural effect, so that F_max. rises rather than falls as ordinarily with increase of t_L, although σ''_{log I} stays constant and hence the total number of acting units is presumed not to change. This constitutes valid evidence for neural integration of effects due to the illumination of separated retinal patches. Beginning at t_L = 0.75, and at 0.90, the slope of the "cone" curve is sharply increased, and the maximum F is far above its position in the absence of the grid. The decrease of σ''_{log I} (the slope constant) signifies, in terms of other information, an increase in the number of acting cone units. The abscissa of inflection is also much lowered, relatively, whereas without the grid it increases as t_L is made larger. These effects correspond subjectively to the fact that at the end-point flicker is most pronounced, on the "cone" curve, along the edges of the grid shadow where contrast is particularly evident with the longer light-times. The "rod" portion of the F - log I contour is not specifically affected by the presence of the grid shadow. Its form is obtainable at t_L = 0.90 free from the influence of summating "cone" contributions, because then almost no overlapping occurs. Analysis shows that when overlapping does occur a certain number of rod units are inhibited by concurrent cone excitation, and that the mean contribution of elements of neural action from each of the non-inhibited units is also reduced to an extent depending on the degree of overlap. The isolated "rod" curve at t_L = 0.90 is quite accurately in the form of a probability integral. The data thus give a new experimental proof of the occurrence of two distinct but interlocking populations of visual effects, and experimentally justify the analytical procedures which have been used to separate them. 2. The changing form of the F - log I contour as a function of t_L, produced in man when the illuminated field is divided into parts by a shadow pattern, is normally found with the bird Taeniopygia castenotis (Gould), the zebra finch. The retina has elements of one general structural type (cones), and the F - log I contour is a simplex symmetrical probability integral. The eye of this bird has a large, complex, and darkly pigmented pecten, which casts a foliated shadow on the retina. The change in form of the F - log I curve occurs with t_L above 0,50, and at t_L = 0.90 is quite extreme. It is more pronounced than the one that is secured in the human data with the particular grid we have used, but there is no doubt that it could be mimicked completely by the use of other grids. The increase of flicker acuity due to the pecten shadow is considerable, when the dark spaces are brief relative to the light. The evidence thus confirms the suggestion (Menner) drawn from comparative natural history that the visual significance of the avian pecten might be to increase the sensory effect of small moving images. It is theoretically important that (as in the human experiment) this may be brought about by an actual decrease of effective retinal area illuminated. It is also significant theoretically that despite the presence of shadows of pecten or of grid, and of the sensory influences thus introduced, the probability integral formulation remains effective.     

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 : 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.     

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.     

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.     

FLICKER RESPONSE CONTOURS FOR THE SPARROW,AND THE THEORY OF THE AVIAN PECTEN

The flicker contour for the house sparrow Passer domesticus is duplex, corresponding to the presence of both rods and cones in the retina. The presence of the pecten brings about changes in the "cone" part of the contour when the light-time in the flash cycle is varied. These changes are of the same sort as those we have already described for the visually simplex zebra finch, and for man provided with an artificial "pecten shadow." The changes are such as to greatly enhance flicker acuity for small dark-times (moving stripe technique). The form of the scotopic part of the duplex contour (also as in the case with man) gives no evidence that rod excitation is specifically influenced by the presence of the pecten. The changing integration of "rod" and "cone" effects as the light-time fraction is altered provides another means of testing the theory used for the analytical separation of the two components of the duplex flicker contour.     

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.     

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.     

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.     

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.     

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.