ON THE RELATION BETWEEN MEASUREMENTS OF INTENSITY DISCRIMINATION AND OF VISUAL ACUITY IN THE HONEY BEE

1. Bees respond by a characteristic reflex to a movement of their visual field. By confining the field to a series of parallel stripes of two alternating different brightnesses it is possible to determine for any width of stripe, at any brightness of one of the two sets of stripes, the brightness of the second at which the bee will first respond to a displacement of the field. Thus the relations between visual acuity and intensity discrimination can be studied. 2. For each width of stripe and visual angle subtended by the stripe the discrimination power of the bee''s eye for different brightnesses was studied. For each visual acuity the intensity discrimination varies with illumination in a characteristic, consistent manner. The discrimination is poor at low illuminations; as the intensity of illumination increases the discrimination increases, and reaches a constant level at high illuminations. 3. From the intensity discrimination curves obtained at different visual acuities, visual acuity curves can be reconstructed for different values of ΔI/I. The curves thus obtained are identical in form with the curve found previously by direct test for the relation between visual acuity and illumination.     

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 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.     

A THEORY OF VISUAL INTENSITY DISCRIMINATION

1. A theory of visual intensity discrimination is proposed in terms of the photochemical events which take place at the moment when a photosensory system already adapted to the intensity I is exposed to the just perceptibly higher intensity I+ΔI. Unlike previous formulations this theory predicts that the fraction ΔI/I, after rapidly decreasing as I increases, does not increase again at high intensities, but reaches a constant value which is maintained even at the highest intensities. 2. The theory describes quantitatively the intensity discrimination data of Drosophila, of the bee, and of Mya. 3. With some carefully considered exceptions the intensity discrimination data of the human eye fall into two classes: those with small test areas or with red light, which form a single continuous curve describing the function of the retinal cones alone, and those with larger areas, and with white, orange, and yellow light, which form a double curve showing a clear inflection point, and represent the separate function of the rods at intensities below the inflection point and of the cones at intensities above it. 4. The theory describes all these data quantitatively by treating the rods and cones as two independently functioning photosensory systems in accordance with the well established duplicity idea. 5. In terms of the theory the data of intensity discrimination give critical information about the order of both the photochemical and dark reactions in each photosensory system. The reactions turn out to be variously monomolecular and bimolecular for the different animals.     

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 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.     

Melanopsin-based brightness discrimination in mice and humans

Photoreception in the mammalian retina is not restricted to rods and cones but extends to a small number of intrinsically photoreceptive retinal ganglion cells (ipRGCs), expressing the photopigment melanopsin. ipRGCs are known to support various accessory visual functions including circadian photoentrainment and pupillary reflexes. However, despite anatomical and physiological evidence that they contribute to the thalamocortical visual projection, no aspect of visual discrimination has been shown to rely upon ipRGCs. Based on their currently known roles, we hypothesized that ipRGCs may contribute to distinguishing brightness. This percept is related to an object's luminance-a photometric measure of light intensity relevant for cone photoreceptors. However, the perceived brightness of different sources is not always predicted by their respective luminance. Here, we used parallel behavioral and electrophysiological experiments to first show that melanopsin contributes to brightness discrimination in both retinally degenerate and fully sighted mice. We continued to use comparable paradigms in psychophysical experiments to provide evidence for a similar role in healthy human subjects. These data represent the first direct evidence that an aspect of visual discrimination in normally sighted subjects can be supported by inner retinal photoreceptors.     

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.     

THE RELATION BETWEEN VISUAL ACUITY AND ILLUMINATION

1. An apparatus for measuring the visual acuity of the eye at different illuminations is described. The test object is continuously variable in size and is presented at a fixed distance from the eye in the center of a 30° field. Observation of the field is through an artificial pupil. The maximum intensity obtainable is more than enough to cover the complete physiological range for the eye with white light though only 110 watts are consumed by the source. Means for varying the intensity over a range of 1:10¹⁰ in small steps are provided. 2. The relation of visual acuity and illumination for two trained observers was measured, using two different types of test object, a broken circle and a grating. The measurements with both test objects show a break at a visual acuity of 0.16, all values below that being mediated by the rods and those above by the cones. The grating gives higher visual acuities at intensities less than about 30 photons and lower visual acuities above that. The maximum visual acuity attainable with the grating under the same conditions is about 30 per cent lower than that with the C. It is shown that the limiting factor in the resolution of the eye for the grating is the diameter of the pupil when it is less than 2.3 mm. and the size of the central cones when the pupil is larger than that. The value of the diameter of the cone derived on that basis from the visual acuity data agrees with that derived from direct cone count in a unit of area. 3. The data for the cones made with both test objects are adequately described by one and the same form of the stationary state equation derived by Hecht for the photoreceptor system. This fact, together with certain considerations about the difference in the nature of the two test objects with regard to the resolvable area, leads to the conclusion that detail perception is a function of a distance rather than an area. All the data for the rods can likewise be described by another variety of the same equation, although the data are too fragmentary to make the choice of the form as certain as might be desired.     

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.     

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 INFLUENCE OF LIGHT ADAPTATION ON SUBSEQUENT DARK ADAPTATION OF THE EYE

The course of dark adaptation of the human eye varies with the intensity used for the light adaptation which precedes it. Preadaptation to intensities below 200 photons is followed only by rod adaptation, while preadaptation to intensities above 4000 photons is followed first by cone adaptation and then by rod adaptation. With increasing intensities of preadaptation, cone dark adaptation remains essentially the same in form, but covers an increasing range of threshold intensities. At the highest preadaptation the range of the subsequent cone dark adaptation covers more than 3 log units. Rod dark adaptation appears in two types—a rapid and a delayed. The rapid rod dark adaptation is evident after preadaptations to low intensities corresponding to those usually associated with rod function. The delayed rod dark adaptation shows up only after preadaptation to intensities which are hundreds of times higher than those which produce the maximal function of the rods in flicker, intensity discrimination, and visual acuity. The delayed form remains essentially constant in shape following different intensities of preadaptation. However, its time of appearance increases with the preadaptation intensity; after the highest preadaptation, it appears only after 12 or 13 minutes in the dark. These two modes of rod dark adaptation are probably the expression of two methods of formation of visual purple in the rods after its bleaching by the preadaptation lights.     

Human wavelength discrimination of monochromatic light explained by optimal wavelength decoding of light of unknown intensity

We show that human ability to discriminate the wavelength of monochromatic light can be understood as maximum likelihood decoding of the cone absorptions, with a signal processing efficiency that is independent of the wavelength. This work is built on the framework of ideal observer analysis of visual discrimination used in many previous works. A distinctive aspect of our work is that we highlight a perceptual confound that observers should confuse a change in input light wavelength with a change in input intensity. Hence a simple ideal observer model which assumes that an observer has a full knowledge of input intensity should over-estimate human ability in discriminating wavelengths of two inputs of unequal intensity. This confound also makes it difficult to consistently measure human ability in wavelength discrimination by asking observers to distinguish two input colors while matching their brightness. We argue that the best experimental method for reliable measurement of discrimination thresholds is the one of Pokorny and Smith, in which observers only need to distinguish two inputs, regardless of whether they differ in hue or brightness. We mathematically formulate wavelength discrimination under this wavelength-intensity confound and show a good agreement between our theoretical prediction and the behavioral data. Our analysis explains why the discrimination threshold varies with the input wavelength, and shows how sensitively the threshold depends on the relative densities of the three types of cones in the retina (and in particular predict discriminations in dichromats). Our mathematical formulation and solution can be applied to general problems of sensory discrimination when there is a perceptual confound from other sensory feature dimensions.     

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.     

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 RELATION BETWEEN FOVEAL VISUAL ACUITY AND ILLUMINATION UNDER REDUCED OXYGEN TENSION

1. The foveal visual acuity of eleven subjects was studied in relation to illumination under normal atmospheric conditions and at simulated altitudes of 10,000 feet (14.3 per cent O₂) and 18,000 feet (10.3 per cent O₂). A mask was used to administer the desired mixtures of oxygen and nitrogen. At the end of each experiment, measurements were made while inhaling 100 per cent oxygen from a cylinder. A red filter (No. 70 Wratten) was used so as to study only the behavior of the cones of the retina. 2. The logarithm of illumination was plotted horizontally (abscissa) and the logarithm of visual acuity vertically (ordinate). The reduced oxygen tensions resulted in a shift of the curve to the right, along the intensity axis, the extent of the change being 0.24 of a log unit at 14.3 per cent O₂ and 0.47 of a log unit at 10.3 per cent O₂. These effects were completely counteracted within a few minutes by inhaling oxygen. 3. As a consequence of the shape of the curve, such a shift to the right resulted in a relatively large decrease of visual acuity at low illuminations. At increasing light intensities anoxia produced less and less change, until at very high illuminations the decrease was negligible. Thus with 10.34 per cent O₂ the visual acuity at 0.144 photons decreased an average of 0.344 of a log unit, to 45 per cent of its normal value. At 1320 photons, however, it decreased only 0.026 of a log unit, to 94 per cent of its normal value for that intensity.     

THE VISUAL ACUITY OF THE FIDDLER-CRAB,UCA PUGNAX

The visual acuity of the fiddler-crab can be measured at various illuminations by means of its response to a moving visual pattern. The method, although similar to that used by Hecht and Wolf for the bee and Hecht and Wald for Drosophila, must be modified to give consistent results. An explanation of the response to a visual pattern is given in terms of the structure of the eye. Visual acuity of the crab varies with log I as in man, the bee, and Drosophila. Hecht and Wolf''s explanation of the varying visual acuity with illumination in terms of the distribution of functional ommatidia in the eye is supported to that extent. In the fiddler-crab as in man, monocular and binocular visual acuity is similar with a maximum of 0.0042 for the fiddler-crab. This agrees fairly well with visual acuities of 0.0041, 0.0038, and 0.0032 as found in the field. In man and the bee, the minimum visual angle corresponds to the minimum angle of two adjacent receptors; in Drosophila and the fiddler-crab the minimum visual angle corresponds to approximately twice the minimum angle between two adjacent receptors.     

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.     

Selective Stimulation of Penumbral Cones Reveals Perception in the Shadow of Retinal Blood Vessels

In 1819, Johann Purkinje described how a moving light source that displaces the shadow of the retinal blood vessels to adjacent cones can produce the entopic percept of a branching tree. Here, we describe a novel method for producing a similar percept. We used a device that mixes 56 narrowband primaries under computer control, in conjunction with the method of silent substitution, to present observers with a spectral modulation that selectively targeted penumbral cones in the shadow of the retinal blood vessels. Such a modulation elicits a clear Purkinje-tree percept. We show that the percept is specific to penumbral L and M cone stimulation and is not produced by selective penumbral S cone stimulation. The Purkinje-tree percept was strongest at 16 Hz and fell off at lower (8 Hz) and higher (32 Hz) temporal frequencies. Selective stimulation of open-field cones that are not in shadow, with penumbral cones silenced, also produced the percept, but it was not seen when penumbral and open-field cones were modulated together. This indicates the need for spatial contrast between penumbral and open-field cones to create the Purkinje-tree percept. Our observation provides a new means for studying the response of retinally stabilized images and demonstrates that penumbral cones can support spatial vision. Further, the result illustrates a way in which silent substitution techniques can fail to be silent. We show that inadvertent penumbral cone stimulation can accompany melanopsin-directed modulations that are designed only to silence open-field cones. This in turn can result in visual responses that might be mistaken as melanopsin-driven.