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.     

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 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.     

Brightness as a function of retinal locus

Brightness functions were determined for the dark-adapted fovea and periphery. In one series of experiments, observers matched numbers to the brightness of a 1° white target at various intensities, presented half the time to the fovea, the other half to one of five peripheral loci: 5°, 12°, 20°, 35°, and 60°. In a second series, observers matched the brightness of a 1° white target in the fovea of one eye to the brightness of an identical target in the periphery of the other eye at various intensities. Thresholds were also determined for the fovea and for the five peripheral loci by a staircase procedure. The magnitude estimations and the interocular matches concur in showing that a stimulus of fixed luminance appears brighter in the periphery than in the fovea. The brightness was found to be maximal at 20°. Brightness grows as a similar power function of luminance at all six retinal positions.     

Brightness as a function of retinal locus

Brightness functions were determined for the dark-adapted fovea and periphery. In one series of experiments, observers matched numbers to the brightness of a 1° white target at various intensities, presented half the time to the fovea, the other half to one of five peripheral loci: 5°, 12°, 20°, 35°, and 60°. In a second series, observers matched the brightness of a 1° white target in the fovea of one eye to the brightness of an identical target in the periphery of the other eye at various intensities. Thresholds were also determined for the fovea and for the five peripheral loci by a staircase procedure. The magnitude estimations and the interocular matches concur in showing that a stimulus of fixed luminance appears brighter in the periphery than in the fovea. The brightness was found to be maximal at 20°. Brightness grows as a similar power function of luminance at all six retinal positions.     

Cross-modality matching functions generated by magnitude estimation

It is possible to generate cross-modality matching functions by having subjects make magnitude estimates of sets of stimuli appropriate to different modalities. The sets are interspersed among each other in the same test session and judged on a common absolute scale of sensory magnitude. An appropriate statistical device locates stimulus levels that appear, on the average, to match. The method is fast, efficient, circumvents the need for continuous stimulus adjustment, and holds promise for the study of the individual as well as the average psychophysical function. To illustrate its potential uses, advantages, and limitations, we used the method to generate cross-modality matching functions relating loudness and brightness. Compared to the scales of loudness and brightness generated by the magnitude estimations of the same stimuli, the matching functions (1) conform better to power functions, (2) may show less variation in slope (exponent), and (3) show far less variation in absolute magnitude (position).     

Cross-modality matching of brightness to loudness by 5-year-olds

The purpose was to determine whether 5-year-old children could match the brightness of a light to the loudness of a sound, and whether the resulting cross-modality function resembled the power function produced by adults. Each of five children adjusted the voltage on a 15D-W lamp to make the apparent brightness appear equal to the loudness of a 500-Hz tone, which the E set to eight different levels. The results resembled those of five adults who performed the same task.     

Synesthetic perception and poetic metaphor

To explore the role of cross-modal perception in the apprehension of synesthetic metaphors, subjects read 15 short lines from poetry, each of which contained a metaphor relating visual and auditory qualities; the subjects' task was to set the loudness of a 1000-Hz tone and the brightness of a white light to match the levels implied by each metaphor. The sound settings and light settings suggest that a cross-modal equivalence between loudness and brightness largely underlay the responses to the metaphors. This general cross-modal equivalence was characterized by some notable intersubject differences and was modified, in part, by certain metaphors that resisted complete equivalence. Even so, the metaphorically induced settings of loudness and brightness are mainly governed by a cross-modality matching function that is qualitatively like the relation found in people with visual-auditory synesthesia, and that is quantitatively like the function obtained in more traditional psychophysical studies.     

Duration,luminance, and the brightness exponent

The relation of brightness to duration and luminance has been studied by matching one brightness to another and also by matching numbers to brightnesses (magnitude estimation). The two methods concur in confirming certain well-known visual functions: Bloch’s law, the Broca-Sulzer effect, and the shift of the Broca-Sulzer enhancement to shorter durations when luminance increases. It is shown that the shift with luminance requires the exponent of the power function for short-flash brightness to be larger than the exponent for stimuli of longer duration. An attempt is made to analyze some of the reasons why the procedure advocated by Graham may not give comparable results.     

When figure-ground segmentation modulates brightness: the case of phantom illumination

In the phantom illumination illusion, luminance ramps ranging from black to white induce a brightness enhancement on an otherwise homogeneous dark background. The strength of the illusion was tested with regard to the extension of the brightness inducing perimeter, surrounding the target area by manipulating the number of inducers (exp. 1) and the size of the inducers (exp. 2). Participants' task was to rate the difference in brightness between the target area and the background. Results show that the illusion occurs only when the target area is not completely segregated from the background by luminance ramps; vice versa, when the target area is delimited by a continuous gradient, it appears darker than the background. These findings suggest a major role of figure-ground organization in the appearance of the illusion. This hypothesis was tested in a rating task experiment with three types of target area shapes circumscribed by four types of edges: luminance contours, illusory contours, no contours, and ambiguous contours. Illusory contours, just as luminance contours, hinder the illusion and produce a darkening of the target area. A control experiment measured the brightness of the previous stimuli without luminance ramps: all configurations resulted in a darkening of the target area. Results from all experiments suggest that figure-ground segmentation plays a major role in the determination of both illumination and lightness in stimuli with luminance gradients.     

Target size and luminance in apparent brightness of the peripheral visual field.

Four target sizes between 15 and 120 min. of arc with six luminance levels covering the range between 398.1 and 1.26 cd/m2 in steps of .5 log units were presented to 0, 20, 40, 60, and 80 degrees nasal retinal loci. In both peripheral and foveal viewing, magnitude estimates to apparent brightness judged by 12 Ss changed as a function of target size and luminance. The exponent of the power function was not dependent on retinal loci but on target size. However, when target size increased, the apparent brightness was slightly greater with peripheral viewing than with foveal viewing.     

Brighter noise: Sensory enhancement of perceived loudness by concurrent visual stimulation

Two experiments investigated the effect of concurrently presented light on the perceived loudness of a low-level burst of white noise. The results suggest two points. First, white noise presented with light tends to be rated as louder than noise presented alone. Second, the enhancement in loudness judgments is resistant to two experimental manipulations: varying the probability that light accompanies sound and shifting from a rating method to a forced choice comparison. Both manipulations were previously shown to eliminate a complementary noise-induced enhancement in ratings of brightness. Whereas noise-induced enhancement of brightness seems to reflect a late-stage decisional process, such as a response bias, the present results suggest that light-induced enhancement of loudness may reflect an early-stage sensory interaction.     

Consistency of individual exponents in cross-modal matching

An important question about individual differences in the exponent of the psychophysical power law is how they should be interpreted. The differences may reflect permanent characteristics of individuals, and it has been argued that, if this is so, the range of these differences is so great as to identify the class of data as exceptional among the physical and biological sciences. Cited as evidence of such permanence has been the correlation between individual exponents obtained on two separate occasions. In a previous paper, we showed that increasing the time interval between occasions reduced the correlation to a nonsignificant level; we argued, therefore, that obtained individual differences in exponents, even though large, depended upon the operation of factors only incidentally associated with the particular observer. In a series of new studies of session-to-session correlation between individual exponents, we provide evidence that: (1) our original finding for magnitude estimates of visual size is repeatable, with the correlation dropping to nearly zero after 1 week; (2) when judged line length is matched to brightness, a delay of I week is sufficient to produce a nonsignificant correlation; (3) in contrast, magnitude estimates of loudness yield significant correlations after a week’s delay; (4) but, when moduli are arbitrarily changed between sessions by the experimenter, these correlations for magnitude estimates of loudness drop to a nonsignificant level, even for a zero-delay condition. We conclude that, whereas in some scaling tasks the passage of time alone between sessions is sufficient to disrupt what appears to be the mnemonic basis for session-to-session correlation, in other (less familiar) tasks, more positive interference (in the form of a modulus change) is needed to achieve the same end. The evidence is consistent with the belief that enduring characteristics of the observer contribute only a small portion of the variability in individual power law exponents.     

Nonmonotone backward masking functions and brightness reversals

Increasing the target-field luminance aids detection for a simultaneously presented black target disc and a black masking annulus. At an intermediate interval separating the onset of the target from the mask, increasing the target-field luminance reduces target detection. This decrease in performance occurs with both temporal and spatial forced choice tasks. With a spatial forced choice, an observer's performance can fall below chance. We associate below-chance performance with a brightness reversal of the black target disc, such that the target disc appears brighter than its surround. The occurrence of brightness reversals follows from our model of the Broca-Sulzer effect, and nonmonotone masking functions result from a generalization of luminance summation.     

Continuous measurement of visible persistence

In the synchrony judgment paradigm, observers judge whether a click precedes or follows the onset of a light flash and, on other trials, whether or not a click precedes light termination. The interclick interval defines the duration of visible persistence. An elaboration of this method consists of two phases: In Phase 1, the luminance of a reference stimulus is psychophysically matched to the peak brightness of the test flash. Five luminance values between .1 and 1.0 of the reference stimulus are used subsequently. In Phase 2, a random one of the five reference stimuli, a test flash, and a click are presented; the observer judges whether the click occurred before or after the brightness of test flash reached the reference value (on onset trials) or decayed below it (on termination trials). This method was validated on 3 subjects with test stimuli whose luminance rises and decays slowly in time, and then was used to trace out the precise subjective rise and decay (temporal brightness response function) of brief flashes.     

Brightness perception in the visual field

Summary Apparent brightness was measured at different positions in the visual field for scotopic, mesopic, and photopic adaptation levels by means of a magnitude estimation technique. Apparent brightness of targets with a given luminance remained rather constant throughout the visual field for the mesopic and photopic adaptation level; for the scotopic adaptation level targets in the foveal and perifoveal area had to be more intense in order to appear as bright as targets in the far periphery (beyond 20° eccentricity). For the photopic range, two brightness power functions with different exponents were obtained for the luminance range from 1 to 100 mL at each eccentricity. The exponent for the range from 1 to 10 mL is considerably greater than the exponent beyond 10 mL, and appears to increase with increasing eccentricity.The experiments described in this paper were partly supported by Deutsche Forschungsgemeinschaft and SFB 50-C 6.     

Brightness function: Binocular versus monocular stimulation

A dozen observers matched numbers to the apparent brightness of a target viewed by one eye or by both eyes. Brightness grew as a power function of luminance, and the functions were practically identical for the two modes of viewing. Throughout its course, the obtained binocular function tended to fall about a decibel above the monocular function. This small degree of binocular summation, of the order of a jnd, mayor may not be significant.     

Some new luminance-gradient effects

Three compelling luminance-gradient effects are described. The first effect concerns a brightness enhancement and a luminous mist spreading out from a central area having the same luminance as the white background and surrounded by four rectangular inducers shaded with a linear luminance gradient. The second effect is perceived with a photographically reversed configuration, and concerns what may be considered a brightness reduction or the enhancement of a darkness quality of a target area of the visual scene. The third effect concerns the perception of a self-luminous disk inside a somewhat foggy medium. The effects are worthy of further examination because they challenge current theories of luminosity perception and brightness perception in general.     

The phantom illumination illusion

A novel brightness illusion in planar patterns is reported. The illusion occurs, for example, when surfaces with a luminance ramp shaded from black to white are positioned on a black homogeneous background, so that each white end of the surfaces faces a single point of the plane of the pattern. The illusion consists of the enhancement of the brightness of the background in a relatively wide area around the white ends of the surfaces. A parametric study was conducted in which participants were asked to rate the difference in brightness between the parts of the background inside and outside a virtual circle formed by disks with different luminance ramps. The results show that mean ratings of brightness depended on the luminance of the background, the luminance range of ramps, and the kind of ramp. Discussion of these results with reference to other brightness illusions (assimilation, neon color spreading, anomalous surfaces, visual phantoms, grating induction, and the glare effect) shows that t hephantom illumination illusion derives from processes producing the perception of ambient illumination.     

Perceived vibration and the loudness of low-frequency tones

Vibration and low-frequency tones were scaled for loudness by two numerical estimation procedures and by cross-modality matching. The same ranges of frequencies, from 30 to 250 Hz, were delivered to the ear and to the fingertip. For vibratory loudness, two sets of power functions were obtained, of which the low-frequency set was somewhat steeper. Tonal loudness gave a family of power functions of approximately the same slope at all the frequencies tested. For frequencies above 100 Hz, the growth of loudness is about the same for both modalities. Below this frequency, vibratory loudness grows more rapidly than tonal loudness.