Increment Threshold Functions Research Articles

Mechanisms contributing to increment threshold and decrement threshold spectral sensitivities

The shape of the human spectral sensitivity function depends on how it is measured. In the increment threshold (IT) technique, sensitivity is typically measured as the inverse of threshold for detection of increments of monochromatic light presented for relatively long durations on achromatic pedestals. Spectral sensitivity functions derived from IT techniques have long been used to reveal contribution from opponent color channels. Although IT functions have been studied extensively, little attention has been given to functions derived from decrement thresholds (DT), partly due to technical challenges of producing appropriate stimuli. Comparison of IT and DT spectral sensitivities may be of interest because there are known asymmetries in the visual system between on- and off-pathways and between increment and decrement responses within these pathways. Consequently, spectral sensitivity functions obtained using DT measures may reveal a different complement of contributing mechanisms than those that produce IT functions. We report here that IT and DT derived spectral sensitivities were essentially identical over much of the visible spectrum. However, decrement sensitivity was slightly greater than increment sensitivity in the shorter wavelengths at modest light levels. This difference was not present at higher light levels, implicating rod pathways as a possible source of the difference. In sum, it appears that under conditions shown to reveal strong contribution from opponent mechanisms, decrement functions are either 1) determined by a similar complement of spectrally opponent mechanisms as those that define increment spectral sensitivities or 2) that the present conditions are insensitive to underlying asymmetries.

QUEST+: A general multidimensional Bayesian adaptive psychometric method.

QUEST+ is a Bayesian adaptive psychometric testing method that allows an arbitrary number of stimulus dimensions, psychometric function parameters, and trial outcomes. It is a generalization and extension of the original QUEST procedure and incorporates many subsequent developments in the area of parametric adaptive testing. With a single procedure, it is possible to implement a wide variety of experimental designs, including conventional threshold measurement; measurement of psychometric function parameters, such as slope and lapse; estimation of the contrast sensitivity function; measurement of increment threshold functions; measurement of noise-masking functions; Thurstone scale estimation using pair comparisons; and categorical ratings on linear and circular stimulus dimensions. QUEST+ provides a general method to accelerate data collection in many areas of cognitive and perceptual science.

Increment Threshold Functions in Retinopathy of Prematurity.

PurposeTo assess scotopic background adaptation in subjects with a history of preterm birth and retinopathy of prematurity (ROP). Retinopathy of prematurity is known to have long-term effects on rod photoreceptor and rod mediated postreceptor retinal function.MethodsRod-mediated thresholds for detection of 3° diameter, 50 ms stimuli presented 20° from fixation were measured using a spatial forced choice method in 36 subjects (aged 9–17 years) with a history of preterm birth and 11 age similar term-born subjects. Thresholds were measured first in the dark-adapted condition and then in the presence of 6 steady background lights (−2.8 to +2.0 log scot td). A model of the increment threshold function was fit to each subject's thresholds to estimate the dark-adapted threshold (TDA) and the Eigengrau (A0, the background that elevates threshold 0.3 log unit above TDA).ResultsIn subjects with a history of severe ROP, both TDA and A0 were significantly elevated relative to those in former preterms who never had ROP and term-born control subjects. Subjects who had mild ROP had normal TDA but elevated A0. Neither TDA nor A0 differed significantly between former preterms who never had ROP and term-born controls.ConclusionsThe results suggest that in severe ROP, threshold is affected at a preadaptation site, possibly the rod outer segment. In mild ROP, changes in the Eigengrau may reflect increased intrinsic noise in the photoreceptor or postreceptor circuitry or both.

The binocular neural mechanism: disparity coding schemes and population coding

Stereoacuity thresholds measured on disparity pedestals are generally found to increase exponentially as the pedestals move away from horopters. However, Farell, Li, and McKee recently found that for sinusoidal stimuli this threshold function had a dip—a pedestal effect. This paper examines the underlying neural mechanism. We suggest a general disparity coding scheme with two position parameters, which are necessary to account for the phenomenon that the response of the energy model depends on the absolute phase of the stimulus. This scheme was implemented to simulate the responses, calculated from an energy model, of the neurons of a full V1 cortical column. To explain the stereo pedestal effect, we propose a decoding mechanism, which is first processed along the phase dimension and then along the orientation dimension. The final step of the decoding mechanism, probability summation over the outputs of spatial frequency channels, yields the dip, producing a disparity increment threshold function similar to the psychophysical result.

Increment threshold functions for radial frequency motion trajectories exhibit a dipper function above threshold

Increment threshold functions for radial frequency motion trajectories exhibit a dipper function above threshold

The lingering effects of artificial scotomata

Prolonged fixation produces artificial scotomata in dynamic random noise: peripheral, zero-contrast regions disappear. When the noise's contrast is suddently zeroed, dynamic afterimages are seen where the scotomata had been (Ramachandran & Gregory, Nature, 1991). We measured contrast increment thresholds for dynamic noise coextensive with these afterimages, using various pedestal and adapting contrasts. When the adapting contrast was zero, increment thresholds formed a dipper-shaped function of pedestal contrast. When the adapting contrast was high, the dip disappeared, but there was no change to the left or right side of the function. Inverting popular theories for dipper-shaped increment-threshold functions, we infer linear transduction and/or intrinsic certainty from the lack of dipper. However, changes in transduction or certainty should also be reflected in absolute threshold. To explain adaptation's lack of effect on detection without a pedestal, we are forced to believe in a lingering effect of the sensitivity loss responsible for the artificial scotomata (Morgan & Solomon, ECVP, 2003), one that perfectly balances the effect of linear transduction and/or uncertainty reduction on absolute threshold.

Disparity increment thresholds for gratings.

The classic increment disparity threshold function rises steeply, usually exponentially, with disparity pedestal. Thus a smaller difference in stereoscopic depth can be resolved the nearer it is to the fixation plane. This result has been obtained with relatively broad-bandwidth stimuli. We show here that the increment threshold function for narrow-bandwidth stimuli differs subtly from the classic function: Thresholds vary only modestly over a +/- quarter-cycle pedestal range, by a factor of about 2, and frequently show a dip, yielding best stereo acuity not at the fixation plane but at moderate disparities (20 degrees-30 degrees in phase) on either side of it. Though the dip has not been noted previously, it is consistent with models of disparity processing in which filter sensitivity or selectivity is greatest at a disparity of zero. Moreover, the relatively flat increment threshold function observed at any one scale is compatible with a steeply rising function for broad-bandwidth stimuli.

Background adaptation in a rat model of retinopathy of prematurity.

Low dark-adapted, scotopic retinal and visual sensitivity in retinopathy of prematurity (ROP) could be due to disease of the inner retina, or the recently described rod photoreceptor abnormalities. Receptoral disease decreases catch of quanta from both test flashes and steady background lights; increment threshold functions are shifted up and right. In diseases with normal receptors but low retinal sensitivity due to abnormal post receptoral processing, the increment threshold functions are shifted up with no horizontal translation. Herein we test the hypothesis that the rod photoreceptors are the site of ROP disease which causes low dark adapted b-wave sensitivity. The effect of steady background light on the ERG b-wave in a rat model of ROP is studied. ERG stimulus/response functions were obtained using full-field stimuli in the dark-adapted state, and in the presence of a steady background light. In each adaptation condition, log sigma, the test flash intensity that produced a half-maximum b-wave amplitude, was calculated. In pilot experiments, the background light selected had raised log sigma about a log unit in controls. In dark-adapted ROP rats log sigma was significantly higher, 0.35 log unit, than in controls. In the presence of the background light, log sigma in ROP and control rats did not differ significantly indicating a relative shift, up and right, of the increment sensitivity function for the less sensitive ROP rats. The effect of the background light is consistent with receptoral disease causing low dark adapted b-wave sensitivity in ROP rats.

Constant dark-rearing effects on visual adaptation of the zebrafish ERG

Anatomical and electrophysiological studies have shown that zebrafish retinal neurons develop in a sequential manner. Several studies have examined the impact of restricted rearing environments on zebrafish visual development, but the results have been mixed. The purpose of this study was to examine the development of light adaptation properties of the zebrafish electroretinogram (ERG), and examine the effects of constant dark rearing on retinal development. Subjects were zebrafish, Danio rerio, reared under normal lighting conditions and zebrafish reared in constant dark from fertilization to 6 days postfertilization (dpf). Increment threshold functions were obtained from a- and b-wave ERG responses from normally reared subjects at different ages and from animals exposed to early constant dark rearing. Dark-reared subjects were tested immediately following constant dark exposure (6–9 dpf) and after exposure to normal cyclic lighting (11–13 dpf). Adult zebrafish were significantly more sensitive at lower background illuminations than were larvae zebrafish. Also, constant dark rearing had a differential effect on the a- and b-wave response measures. Constant dark rearing raised b-wave threshold uniformly across background illuminations, while only producing higher a-wave thresholds at low levels of illumination. These results are consistent with findings in studies on zebrafish retinal development, and may help explain some of the discrepancies across studies examining the effects of restricted rearing.

Temporal-contrast discrimination and its neural correlates.

Reported differences in neuronal contrast processing between the parallel magnocellular (M) and parvocellular (P) visual pathways invite the hypothesis that contrast discrimination in the human visual system is more sensitive at low contrasts and less sensitive at high contrasts, for stimuli modulated at high compared with low temporal frequencies. In the present study, an edgeless temporally modulated uniform field was selected as the stimulus for psychophysical contrast discrimination, and contrast-increment thresholds for pedestal contrasts ranging from 5.5% to 78.2% were determined with a temporal two-alternative forced-choice staircase procedure. The increment thresholds for five normal subjects were adequately fit by power functions with exponents that shifted continuously from about 0.5 (square-root-law behavior) to about 1.0 (Weber's-law behavior) as stimulus temporal frequency increased from 1 to 30 Hz. A neural simulation, with the use of published contrast-response functions of magnocellular and parvocellular neurons, adjusted with an estimate of response variance, produced two distinct 'neural increment-threshold functions' that were similar to the psychophysical results obtained at the highest and the lowest temporal frequencies, respectively. A shift from a relatively more noise-limited neural mechanism to one whose response is predominantly determined by gain is suggested to account for the change of the contrast-increment-threshold function with increasing temporal frequency.

Dark-light: model for nightblindness from the human rhodopsin Gly-90-->Asp mutation.

A human rhodopsin mutation, Gly-90-->Asp (Gly90Asp), cosegregated with an unusual trait of congenital nightblindness in 22 at-risk members of a large autosomal dominant kindred. Although rhodopsin mutations typically are associated with retinal degeneration, Gly90Asp-affected subjects up to age 33 did not show clinical retinal changes. Absolute threshold for visual perception was elevated nearly 3 logarithmic units in 7 individuals tested (ages 11-64), indicating greatly compromised rod threshold signaling. However, in vivo rhodopsin density was normal. Although the 38-year-old proband could not perceive dim lights, his rod increment threshold function was normal on brighter backgrounds. The impaired rod vision for dim but not bright backgrounds is consistent with a mechanism of increased basal "dark-light" from thermal isomerization equivalent to an increase of > 10(4) over that of wild-type rhodopsin. The Gly90Asp mutation on the second transmembrane helix places an extra negative charge in the opsin pocket; this could contribute to partial deprotonation of the retinal Schiff base and thereby increase photoreceptor noise. In vitro evidence had suggested that transducin is activated by the Gly90Asp mutation in the absence of both the retinal chromophore and light, termed "constitutive activity." The apparent preservation of functioning rods despite extensive and lifelong night-blindness in this kindred is inconsistent with one current hypothesis that chronic rod activation from constitutively active mutant rhodopsin necessarily contributes significantly to photoreceptor demise in human retinal dystrophies.

Depletion of retinal dopamine does not affect the ERG b-wave increment threshold function in goldfish in vivo.

Increment threshold functions of the electroretinogram (ERG) b-wave were obtained from goldfish using an in vivo preparation to study intraretinal mechanisms underlying the increase in perceived brightness induced by depletion of retinal dopamine by 6-hydroxydopamine (6-OHDA). Goldfish received unilateral intraocular injections of 6-OHDA plus pargyline on successive days. Depletion of retinal dopamine was confirmed by the absence of tyrosine-hydroxylase immunoreactivity at 2 to 3 weeks postinjection as compared to sham-injected eyes from the same fish. There was no difference among normal, sham-injected or 6-OHDA-injected eyes with regard to ERG waveform, intensity-response functions or increment threshold functions. Dopamine-depleted eyes showed a Purkinje shift, that is, a transition from rod-to-cone dominated vision with increasing levels of adaptation. We conclude (1) dopamine-depleted eyes are capable of photopic vision; and (2) the ERG b-wave is not diagnostic for luminosity coding at photopic backgrounds. We also predict that (1) dopamine is not required for the transition from scotopic to photopic vision in goldfish; (2) the ERG b-wave in goldfish is influenced by chromatic interactions; (3) horizontal cell spinules, though correlated with photopic mechanisms in the fish retina, are not necessary for the transition from scotopic to photopic vision; and (4) the OFF pathway, not the ON pathway, is involved in the action of dopamine on luminosity coding in the retina.

The cue for contour-curvature discrimination

Seven potential geometric cues for contour-curvature discrimination were tested: curvature, turningangle, arc-length, arc-length-divided-by-chord-length, maximum-deviation (sag), mean-deviation and area. Three experiments were performed, each requiring the discrimination of two simultaneously presented, 1-sec-duration, curved-line stimuli, whose chord-lengths ranged from 12 to 48 arcmin visual angle and whose curvatures ranged from 0 to 0.13 arcmin −1. Experiments 1 and 2 determined for each cue the smallest detectable increment (the increment threshold) as a function of cue value, for a set of spatial transformations of the stimulus (one- and two-dimensional scalings) equivalent to changes in viewing distance and direction. In accordance with statistical estimation theory, the “best” cue was defined as the most efficient one, that is, the one which best accounted for the variance in the data. As a control, Expt 3 compared increment-threshold functions for circular and elliptical arcs of constant chord-length and circular arcs of constant arc-length. Over all three experiments, only sag and its linear approximation, mean-deviation, accounted well for the variance in the data; sag provided the best predictor, and its increment-threshold function satisfied Weber's law over almost all of the stimulus range. Additionally, sag has a special theoretical property (shared only with mean-deviation and area): the relationship it defines (in proportional terms) between curved contours in an image of an object or a scene is constant and independent of viewing distance and direction.

Noise and the absolute thresholds of cone and rod vision

Literature data on light detection by cone and rod vision at absolute threshold are analysed in order (1) to decide whether the threshold performance of dark-adapted cone vision can, like that of rod vision, be consistently explained as limited by noise from a "dark light"; (2) to obtain comparable estimates of the dark noise and dark light of (foveal) cones and (peripheral) rods. The dark noise was estimated by a maximum-likelihood procedure from frequency-of-seeing data and compared with the dark light derived from increment-threshold functions. In both cone and rod vision, the estimated dark noise coincides with Poisson fluctuations of the estimated dark light if 17% (best estimate) of lambda max-quanta incident at the cornea produce excitations. At that fraction of quanta exciting, dark lights are equivalent to 112 isomerisations per sec in each foveal cone and 0.011 isomerisations per sec in each rod. It is concluded that (1) the threshold performance of dark-adapted cone as well as rod vision can be consistently described as noise-limited, but not by postulating a multi-quantum coincidence requirement for single receptors; (2) the underlying intrinsic activity in both the cone and the rod system is light-like as regards correspondence between noise effect and background adaptation effect. One possibility is that this activity is largely composed of events identical to the single-photon response, originating in the visual pigment, in cones as well as in rods.

Effects of interocular suppression on spectral sensitivity.

A stable form of interocular suppression, referred to as "permanent suppression," can be produced by presenting a contoured field to one eye and a spatially homogenous field to the fellow eye, a viewing condition analogous to the classic "hole-in-the-hand" illusion. We examined the relation between permanent suppression and binocular rivalry suppression by comparing the changes in the increment-threshold spectral sensitivity function produced by these two forms of suppression. Permanent suppression produced a reduction in spectral sensitivity; however, in contrast to binocular rivalry suppression, the sensitivity alterations associated with permanent suppression were independent of the test-probe wavelength. The different patterns of sensitivity loss observed during binocular rivalry and permanent suppression indicate that different neural mechanisms mediate these two forms of interocular suppression.

Developmental lead exposure selectively alters the scotopic ERG component of dark and light adaptation and increases rod calcium content

Electrophysiological studies have established that lead exposure produces selective rod deficits. The present electroretinographic (ERG) and correlated calcium experiments examined whether low-level or moderate-level developmental lead exposure (peak blood lead of 19 and 59μg/dl, respectively) altered dark adaptation and/or light adaptation. Developmental lead exposure produced long-term dose-response (1) decreases in the slope of the increment threshold function only at scotopic adapting backgrounds, (2) decreases only in the sensitivity of the rod phase of dark adaptation and (3) increases in the calcium content of rod outer segments which may partially mediate the ERG results. The relevance and applicability of these data to lead-exposed children have yet to be established.

Human VEP contrast modulation sensitivity: separation of magno- and parvocellular components

Human cortical visual evoked potentials (VEPs) were retrieved in real time (without averaging). The stimuli were sinusoidal gratings whose contrast was temporally modulated about some mean value. Electrophysiologically determined contrast modulation thresholds were measured at standing contrast over the range from 2.5% to 50%, defining an increment threshold function. Increment threshold functions were obtained under two different spatio-temporal stimulus conditions identified as “sustained” (4 c/deg grating modulated at 1.5 Hz) and “transient” (1 c/deg grating modulated at 20 Hz). Under each of these conditions, threshold responses were retrieved at both the fundamental and second harmonic of the contrast modulation frequency. Under “sustained” conditions log increment threshold responses at the fundamental of the contrast modulation frequency were a linear function of log mean contrast over the full range tested. Thresholds based upon responses at the second harmonic of the modulation frequency were similar to those at the fundamental except for a saturation effect (i.e., above a mean contrast of 25% there was little further reduction in modulation sensitivity). There was no contrast gain control under “transient” stimulus conditions. In other words, the same absolute amount of contrast change produced threshold responses for all mean levels up to 25%. This was true at both the fundamental and second harmonic of the modulation frequency. Stimulus differences produce striking differences in the electrophysiologically inferred increment threshold function for grating contrast, but fundamental and second harmonic evoked responses reflect processes with similar increment threshold behavior.

Effects of luminance level on the saturation function: Sensitivities based on saturation discrimination

AbstractThe saturation of a monochromatic light λ is defined as the reciprocal of the just noticeable colorimetric purity ΔP(λ) from a white, which is a conventional definition having been used previously often. The present study measures saturation functions of monochromatic lights at various luminance levels ranging from 10 to 1000 Td. The main result of this article is that the saturation function systematically changes in shape with the luminance level; as the luminance increases, the values of 1/ΔP(λ) relatively increase for shorter wavelengths. The chromatic sensitivity function C(λ) is defined by the reciprocal of the radiance of a monochromatic light λ added to the white field in order to detect a difference in chromaticity from the equal‐luminance reference white. The C(λ) functions at various luminance levels are shown to have three peaks at the short‐, middle‐, and long‐wavelength regions. These peaks are similar to those of the increment threshold functions, and the saturation function can be approximated by the ratio of the increment threshold spectral sensitivity to the relative luminous efficiency, except for the 570 nm data.

Effects of background illumination on cat horizontal cell responses

The process of light adaptation in cat horizontal cells was studied by means of intracellular recordings in the optically intact, in situ eye. Response vs intensity profiles were measured using increment- as well as decrement-flashes of “white light” on steady backgrounds. The effects of background illumination in the mesopic and photopic range on both purely rod-driven horizontal cells and mixed rod and cone input horizontal cells were investigated. Increasing the background illumination for mixed-input horizontal cells strongly reduced the contribution from the rod system. The rod aftereffect in the responses to high intensity flashes is totally suppressed at higher background levels. Light adaptation resulted in a sustained hyperpolarization without a substantial effect on the total response range of the response vs intensity curve. At higher background intensities more of the response range is made up of depolarizing responses to decrements of light. Increasing the background illumination also shifted the operating curve to higher intensities. Increment threshold functions, measured with a 3.9 deg diameter test spot on a large background (8.8 deg diameter) showed a linear relation between log threshold intensity and log background intensity with a slope of, on average, 0.64. The response vs intensity curve for the rod horizontal cell typically spanned a narrower intensity range and was displaced toward lower intensities as compared to that for the mixed input horizontal cells. Background illumination greatly reduced the total response range for rod horizontal cells. Increment threshold curves for rod horizontal cells clearly indicated loss in sensitivity due to response compression.

Rod increment thresholds in cone-rod dystrophy

Rod system increment threshold functions (ITFs) were studied in patients with cone-rod dystrophy (CRD). Rod thresholds (I(t)) for a 104-min, 500-nm test stimulus (TS), superimposed on an 11 degrees long wavelength background (luminance I(b)), were measured in eleven CRD patients and fourteen normal subjects. Thresholds in normals were also measured using a 7-min TS. A modified version of Weber's law [logI(t) = logK + log(I(n)(b) + c)] was fitted to the data from each subject and test condition to yield a description of the ITF in terms of the free parameters K, c, and n. Four of the CRD patients exhibited an abnormally high absolute threshold; of these, two showed abnormalities in K and c consistent with a reduced efficiency of quantum capture by the rods. Abnormalities in the ITFs of CRD patients did not resemble the effect of reducing the diameter of the TS from 104 to 7 min in normals. This suggests that threshold abnormalities in the CRD patients did not result from altered spatial summation. The results illustrate use of a parametric representation of the ITF to evaluate the loss of sensitivity in visual disorders.