Brightness exponent as a function of retinal eccentricity in the peripheral visual field: Effects of dark and light adaptation

Using a method of direct magnitude estimation, the exponent of the brightness power function was determined under dark and light adaptation at luminance levels well above threshold. The exponent was estimated for functions describing the brightness of stimuli presented at the fovea and the following peripheral retinal loci: 10, 20, 30, 40, and 50 deg nasally eccentric to the fovea along the horizontal meridian of the right eye. The exponent for a 1-sec flash was found to be approximately .33 at the fovea and increased slightly with increasing retinal eccentricity.The effect of adaptation on the brightness exponent was not so large when the target luminance was set well above threshold.     

Dark-adaptation of the human rod system: A new hypothesis

Following a long, full bleach, rod dark-adaptation curves from two normal trichromats were obtained with test fields of various size, exposure time and retinal eccentricity. The results show that there is a substantial region of threshold recovery with an approximately constant, linear slope of about 0.27 log per minute of dark-adaptation, which is independent of the test variables. It is suggested that the increase in sensitivity during this constant, linear slope is completely determined by changes in the concentration of bleached rhodopsin. The relationship between change of relative threshold (T) and fraction of bleached rhodopsin ( B ) is given by T=B ^3,7. This exponential law is well described by the displacement of the equilibrium between the active and inactive states of an allosteric enzyme built as a tetrarner.     

COLOR THRESHOLD MEASUREMENTS IN SCOTOPIC VISION

The absolute and the color threshold in scotopic vision generally coincide during dark adaptation, indicating that color-threshold intensity is a measure of the concentration of rhodopsin, and that different modes of rhodopsin regeneration are reflected in the measurements of the color threshold.     

RODS AS COLOR RECEPTORS IN PHOTOPIC VISION

Comparing a foveal and an extra-foveal field during dark adaptation, transition from chromatic to achromatic vision at intensity levels above the cone plateau started around the break of the dark adaptation curve. Pre-stimulating the two fields in a dark-adapted state with deep red, and test-stimulating when returning sensitivity had reached absolute threshold of the dark-adapted eye, with green filters at intensities above the specific threshold, the fields matched as to hue and saturation. It appears that rod and cone activities are integrated and function as a synchronized unit during the initial recovery phase of dark adaptation.     

Interpersonal and intrapersonal variance of exponent of power function observed in grip strength task.

For grip strength there is a power function with an exponent of 1.7 between the subjective magnitude and the actual force exerted by a subject, but large variabilities among and within individuals were found. We focused on these variabilities and investigated the relationship between them by conducting a ratio production procedure requiring trials of maximum effort and half of maximum effort. For 30 adults we conducted four measurement trials, two on the same day, and the remaining two trials on a day or two later. The mean value of the exponent, the standard deviation, and the coefficient of variation of the four trials for each subject were calculated. The mean value of the exponent of the power function for all subjects was 1.6. This value approximated the value of 1.7 reported by Stevens and Mack. The values ranged from .50 to 5.39. The correlation between subjects' mean exponent value and standard deviation was .90, and the correlation between the mean value of the exponent and the coefficient of variation was .50. There was a close relationship between interpersonal and intrapersonal variance.     

Light and dark adaptation of visually perceived eye level controlled by visual pitch

The pitch of a visual field systematically influences the elevation at which a monocularly viewing subject sets a target so as to appear at visually perceived eye level (VPEL). The deviation of the setting from true eye level averages approximately 0.6 times the angle of pitch while viewing a fully illuminated complexly structured visual field and is only slightly less with one or two pitched-from-vertical lines in a dark field (Matin & Li, 1994a). The deviation of VPEL from baseline following 20 min of dark adaptation reaches its full value less than 1 min after the onset of illumination of the pitched visual field and decays exponentially in darkness following 5 min of exposure to visual pitch, either 30° topbackward or 20° topforward. The magnitude of the VPEL deviation measured with the dark-adapted right eye following left-eye exposure to pitch was 85% of the deviation that followed pitch exposure of the right eye itself. Time constants for VPEL decay to the dark baseline were the same for same-eye and cross-adaptation conditions and averaged about 4 min. The time constants for decay during dark adaptation were somewhat smaller, and the change during dark adaptation extended over a 16% smaller range following the viewing of the dim two-line pitched-from-vertical stimulus than following the viewing of the complex field. The temporal course of light and dark adaptation of VPEL is virtually identical to the course of light and dark adaptation of the scotopic luminance threshold following exposure to the same luminance. We suggest that, following rod stimulation along particular retinal orientations by portions of the pitched visual field, the storage of the adaptation process resides in the retinogeniculate system and is manifested in the focal system as a change in luminance threshold and in the ambient system as a change in VPEL. The linear model previously developed to account for VPEL, which was based on the interaction of influences from the pitched visual field and extraretinal influences from the body-referenced mechanism, was employed to incorporate the effects of adaptation. Connections between VPEL adaptation and other cases of perceptual adaptation of visual direction are described.     

Direct quantitative judgments of sums and a two-stage model for psychophysical judgments

Judged magnitudes of differences between stimuli have previously been shown to support a two-stage interpretation of magnitude estimation, in which input transformations and output transformations are each describable as power functions. In an effort to provide support for the model independent of the difference estimation procedure. the present investigation employed two additional judgment tasks. We obtained magnitude judgments and category judgments of the combined magnitudes (sums) of paired weights from two groups of Ss. Values of the inferred input exponent k calculated from the two sets of data were very similar and were also remarkably similar to the exponent previously calculated from magnitude estimations of differences between weights. The output exponent calculated from magnitude judgments of sums described a concave upward function; however. the similar function describing category judgments was essentially linear. These results show that the inferred input exponent is not the result of the difference estimation task, and in addition provides support for the contention that the interval scale may be a less biased sensory measure than the magnitude scale. The introduction of an additive constant to the model improved its fit to the data but the rule by which it was introduced made very little difference.     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equals k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equa Is k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

TRANSITION FROM ROD TO CONE VISION: II. Successive contrast

S tabell , B. & S tabell , U. Transition from rod to cone vision. II. Successive contrast. Scad J. Psychol., 1969, 10 137–139—Transition from chromatic rod to chromatic cone activity during dark adaptation is interpreted as a kind of color mixing.     

SCALES FOR SUBJECTIVE DISTANCE

By means of the method of ratio estimation, scale values were obtained for subjective distance. In three experiments different stimulus ranges of the objective distances were used. It was found: ( 1 ) Subjective distance is a power function of the objective distance. ( 2 ) The exponent of the function varies with the stimulus range. With increasing stimulus range the exponent has a tendency to decrease. It is conceivable that the change of the exponent may be explained by an adaptation of the subjective range to the stimulus range.     

Undermatching on concurrent variable-interval schedules and the power law.

The phenomenon of undermatching on concurrent variable-interval schedules is shown to be derivable by transforming the individual interreinforcement intervals of each variable-interval schedule and averaging the transformed values to produce an "estimate" of the rate of reinforcement the schedules deliver. If the transformation is based on a power function with a fractional exponent, such as is found in many studies of temporal control in animals, matching response rations to the ratios of these estimated rates of reinforcement yields undermatching. If the concurrent variable-interval schedules are arranged such that the individual intervals in each schedule have a constant proportionality (a procedure found in many commonly used variable-interval schedules) the slope of the line relating logarithms of response ratios and of programmed reinforcement ratios is identical to the exponent of the power transformation applied to the individual time intervals in the variable-interval schedules. In other cases this simple relation does not hold but the degree of undermatching is greater the lower the value of the exponent of the power function. This account of undermatching predicts values similar to those typically observed.     

NIGHT VISION AS CHROMATIC VISION

Assuming that night vision is an exclusive function of the rods, and that it is colorless, the duplicity theory states that rod vision is achromatic vision. Studies relevant to color in night vision are reviewed. It is concluded that color may be observed well below the breakpoint of the dark adaptation curve, and that the duplicity theory therefore needs revision.     

Rod involvement in peripheral color processing

Abstract.— It has previously been suggested that rods act as blue receptors in peripheral color vision. Two experiments examining this issue were conducted. Experiment 1 investigated the perceived hue of a test light presented at a luminance level above chromatic threshold. At 8° in the periphery, the 500 nm test light was perceived as more blue under conditions of dark adaptation than after light adaptation. Similar differences were not found for foveal presentation. The increased blue in the periphery after dark adaptation was attributed to a rod contribution. In Experiment 2 an attempt was made to mix a rod contribution obtained with a 470 nm light below chromatic threshold, with a cone color obtained from a 670 nm light presented above chromatic threshold. No evidence was obtained to support the idea that a blue produced by rods stimulated below chromatic threshold could mix with a red produced by cones stimulated above chromatic threshold. The results are discussed in terms of a rod contribution to hue which is dependent on the luminance level of short wavelength stimulation.     

Sequential dependencies and regression in psychophysical judgments

A tendency for judgments of stimulus magnitude to be biased in the direction of the value of the immediately preceding stimulus is found in magnitude estimations of loudness. This produces a bias in the empirical psychophysical function that results in underestimation of the exponent of the unbiased function presumed to relate number and stimulus intensity, N = aSⁿ. The biased judgment can be represented as a power product of focal and preceding stimulus intensity, N_ij= aS ^m S_j ^b. A bias-free estimate of the correct exponent, n, can be obtained from the relation n = m + b.     

A test of a two-stage model of magnitude judgment

It has been suggested that the power law J = aⁿ, describing the relationship between numerical magnitude judgments and physical magnitudes, confounds a sensory or input function with an output function flawing to do with O’s use of numbers. Judged magnitudes of differences between stimuli offer some opportunity for separating these functions. We obtained magnitude judgments of differences between paired weights, as well as magnitude judgments of the weights making up the pairs. From the former we calculated simultaneously an input exponent and an output exponent, working upon Attneave’s assumption that both transformations are describable as power functions. The inferred input and output functions, in combination, closely predict the judgments of individual weights by the same Os. Although pooled data (geometric means of judgments) conform fairly well to a linear output function, individual data do not; i.e., individual Os deviate quite significantly fromlinearity and from one another in their use of numbers. Individual values of the inferred sensory exponent, k, show significantly better uniformity over Os than do values of the phenotypica! magnitude exponent previously found to describe interval judgments of weight.     

Changes in absolute detection threshold and in subjective intensity of suprathreshold stimuli during olfactory adaptation and recovery

Olfactory adaptation and recovery to methyl isobutyl ketone at a concentration 10 times the absolute detection threshold (I_{t o}) was intensively studied in two human Ss. A combined psychophysical procedure was used that allowed comparisons of changes in threshold (I_t) with changes in the subjective intensity of suprathreshold stimuli. Information was also obtained on the effect of the adapting stimulus on the psychophysical power function for this odorant. A threshold detection procedure was used to estimate changes in I_t; an unstructured magnitude-estimation procedure was used to monitor changes in the subjective intensity of suprathreshold stimuli and the psychophysical power function. The data provided additional information on the behavioral course of olfactory adaptation and recovery and suggested that this combined method can be used profitably for further investigations of this kind. Complementary to the work of Cain and Engen (1969), the results suggested an increase in the exponent of the power function with increasing adaptation.     

The standard model for perceived magnitude: a framework for (almost) everything known about it

The psychophysics of perceived magnitude entails three aspects of sensory systems: range of sensitivity (dynamic range [DR]), resolving power (the capacity to resolve small changes in stimulus intensity), and the form of the function relating perceived magnitude to signal strength throughout the DR. A simple model is proposed that integrates what is known about all three aspects into a single framework. According to the model, perceived magnitude is a power function of stimulus strength (S. S. Stevens, 1956), and both the exponent of that function and a measure of resolving power are inversely related to the log of DR (R. Teghtsoonian, 1971). The DR is thought to have a characteristic value for each sensory system and may be estimated directly by measurement of upper and lower limits, or indirectly by estimating the exponent of the power function under optimal conditions. A central feature of the model is that all DRs are assumed to be subjectively equal. It is also suggested that the impression of perceived magnitude may be mediated by a single mechanism, regardless of the sensory system that is activated. It remains to be seen whether brain science is able to identify a neural basis for such a mechanism.     

Tactile vibration: Change of exponent with frequency

When cross-modality matches were made between a 60-Hz vibration and such other continua as electric current through the finger, number, force of handgrip, and both binaural and monaural loudness, the exponent of the power function for vibration was found to be about 1.0 at 60 Hz. The dependence of the exponent on frequency has been studied in a series of intramodality matching experiments. The exponent appears to reach its largest value in the vicinity of 30 Hz and its lowest value in the vicinity of 250 Hz. The highest value is roughly twice the lowest value. Over the low-frequency range, there is a suggestive similarity between the power functions for vibration and those for auditory loudness. As a vibration sensor, the ear may behave much like the finger.     

SCALES OF UNPLEASANTNESS OF ELECTRICAL STIMULATION

The subjective unpleasantness elicited by an A.C. current of 50 c/sec. applied to two fingers was scaled by 14 subjects using the methods of magnitude and of category estimation. Nine current intensities, ranging between 2 and 10 times the individual sensation thresholds, were used as stimuli. A power function yielded a good fit to the magnitude-estimation data; the exponent was 1.81. The difference between this value and a considerably higher exponent reported by previous investigators was interpreted in terms of the wider stimulus range used in the present study. The relation between the category scale and the magnitude scale had the same general form as that found in several previous investigations.