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NEUROSCIENCE |
1 The Physiological Laboratory, University of Cambridge, Downing Street, Cambridge CB2 3EG, UK
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Abstract |
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(Received 15 January 2006;
accepted after revision 11 April 2006;
first published online 13 April 2006)
Corresponding author R. H. S. Carpenter: The Physiological Laboratory, University of Cambridge, Downing Street, Cambridge CB2 3EG, UK. Email: rhsc1{at}cam.ac.uk
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Introduction |
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, that is attributable to stimulus detection by the term c.
There have been many studies examining the relationship between average measures of c and either the luminance or contrast, C, of the stimulus (Liang & Pieron, 1945; Bartlett & MacLeod, 1954; Hildreth, 1973; Jaskowski, 1984; Burkhardt et al. 1987; Doma & Hallett, 1988; Plainis & Murray, 2000; McKeefry et al. 2003; Carpenter, 2004; Ludwig et al. 2004). While such work has addressed the reaction time for detecting the sudden appearance of a stimulus, the relationship between latency and changes in the contrast of a pre-existing stimulus has rarely been investigated. Previous studies have examined contrast discrimination and reaction time incidentally as a way of investigating another phenomenon (Westendorf & Blake, 1988), or have not attempted to model the relationship between the two (Steinman & Veniar, 1944), or have examined very small increments in contrast, where discrimination performance is predominantly probabilistic (Tiippana et al. 2001). More recently, Palmer et al. (2005) have investigated contrast discrimination from a single suprathreshold level, although they fitted their data separately from those for contrast detection. Overall, the quantitative relationship between contrast discrimination and reaction time is not well known.
We can speculate as to what the relationship might be, however. Given an appropriate definition of contrast, and measuring thresholds over a sufficiently wide range, discrimination thresholds are well described by a Weber law in contrast (Whittle, 1986; Kingdom & Whittle, 1996). Such a result is consistent with a transducer function that is a logarithmic transform of the contrast (Fechner, 1860), and suggests that reaction times should increase in an arithmetic ratio as stimulus contrast increases in a geometric ratio (Henmon, 1906). At very low contrasts, however, it may be expected that the ability of the transducer to respond is limited by internal noise. Therefore, if reaction times to step changes in contrast involve a linear rise-to-threshold unit of threshold K, whose rate of rise is proportional to step changes in the logarithm of target contrast plus internal noise, the following equation results:
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| (1) |
In this study, we measured reaction times to step changes in luminous contrast, to see whether eqn (1) could successfully predict reaction time in the more general case. We determined both saccadic and manual reaction times to see if they could be modelled using identical parameters for the contrast processor, as might be expected if a common target detection stage precedes each type of reaction.
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Methods |
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Four healthy subjects, A, B, C and D, with ages in the range 23–59 years, participated, having given informed consent. Three of them (A, B and C) were highly experienced observers. Stimuli were viewed binocularly through natural pupils, using spectacles if required, and head movements minimized through the use of a chin rest. The study conformed to the Declaration of Helsinki, and the recording technique and general procedures were approved by our institutional Ethical Committee.
Stimuli and task
We presented stimuli on a calibrated video monitor system (ViSaGe graphics card: Cambridge Research Systems Ltd, Rochester, UK, and GDM-F520 monitor, frame rate 100 Hz; Sony, Tokyo, Japan) in a dimly illuminated room. The background luminance was 20 cd m–2 (CIE 1931; x = 0.278, y = 0.290) and subtended 22 deg by 17 deg (HxV) at the 1 m viewing distance.
The fixation target was a grey (C = –0.2) 0.2 deg dot in the centre of the screen, and remained present throughout testing. A trial commenced with the abrupt onset of two 0.5 deg spots, centred 4 deg either side of fixation, at the initial contrast (Ci). After a random delay one of the spots abruptly changed to the final contrast (Cf), this being the signal for the subject to perform either a saccade to the peripheral stimulus (saccadic reaction time task) or to maintain fixation but push one of two buttons corresponding to the location of the stimulus (manual reaction time task). Upon the detection of a response, the two spots were extinguished abruptly, and the subject returned fixation to the fixation dot if required. There was 570 ms between the extinguishing of the spots and beginning of the next trial.
The probability density function for the random delay was distributed as a decaying exponential with a half-life of 500 ms, to counteract the influence of foreperiod on reaction time (Luce, 1986), truncated to a maximum of 3000 ms. We also interleaved false positive trials, in which Cf = Ci; for these trials, the two spots automatically extinguished abruptly 500 ms after the ‘appearance’ of Cf. We performed runs of 200 sequential trials of either exclusively manual or saccadic reaction times, using a single value for the initial contrast Ci and five values for Cf, randomly interleaved. The probability of a false positive stimulus was 0.05.
We measured the subject's eye position using a binocular infra-red oculometer (Ober Consulting, Poznan, Poland) (Ober et al. 2003) mounted on the bridge of the nose. The oculometer compares the reflectance from the medial sclera and pupil of each eye using dual differential phase-locked infra-red detectors; the bandwidth is 250 Hz, and it is linear to 7% within +30 deg, with a noise level equivalent to 10 min arc. Its output was sampled at 100 Hz, in synchrony with the frame rate of the display. A computer system (SPIC; Carpenter, 1994) controlled the presentation of stimuli and the recording of eye movements, using a criterion based on velocity and acceleration to detect saccades automatically in real time, although an observer reviewed all records after each run and deleted any misclassifications caused by blinking, rapid head movements or other artefacts.
Median reaction times
For a given task, the distribution of reaction times typically has a positive skew; however, when the same data are plotted as a function of the reciprocal of reaction time (promptness) in general the distributions become Gaussian (Carpenter, 1981). We estimated median reaction times and its standard deviation using a normal distribution fitted to the promptness data by minimizing the Kolmogorov-Smirnov statistic, after excluding any reaction times 
50 or 
800 ms.
For a given initial contrast Ci, the probability that the final contrast Cf was detected was calculated from the number of correct responses (i.e. a saccade or button press corresponding to the location of the stimulus) divided by the total number of correct responses and non-responses within the > 50 to < 800 ms window. Reaction times 800 ms were counted as non-responses. We present data for a given combination of Ci and Cf only if the subject detected Cf with a probability of at least 0.8. We calculated response errors for each stimulus condition as the number of responses in the wrong direction divided by the number of wrong and right responses, again within a > 50 to < 800 ms window. For observers A, B and C, response errors never exceeded 2% for any stimulus condition; for observer D, response errors were typically somewhat higher but did not exceed 8%.
Contrast thresholds
We measured contrast thresholds with a two-alternative forced choice (2-AFC) procedure, using the arrangement of the fixation point and stimuli as described earlier. A trial began with the abrupt onset of both spots displayed at the initial contrast Ci, with one altering to the final contrast Cf after a random delay distributed uniformly between 500 and 1500 ms. After a further 500 ms, both spots reduced linearly to zero contrast over 200 ms to discourage responding to the offset of a stimulus. Subjects responded by means of a button press, and received auditory feedback on whether or not their choice was correct. There was a 500 ms delay in between trials. We used two interleaved 30-presentation ZEST (King-Smith et al. 1994) procedures to estimate thresholds, performing this determination twice and taking the geometric mean.
Fitting procedure
We weighted fits by the observed variability (i.e. minimizing 
) for the regression analyses, and calculated 95% confidence intervals using a Monte Carlo technique (Motulsky & Christopoulos, 2004). We used the same weighted sum-of-squares (SSQ) to calculate values for the coefficient of determination:
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Results |
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The fitted values for the noise term C0 obtained in Figs 3 and 4 should allow us to estimate how contrast discrimination thresholds change as the initial contrast Ci changes. Figure 5 shows psychophysical thresholds as a function of the initial contrast, expressed as both a final contrast Cf (circles) and a contrast increment threshold Cf
–
Ci (squares), using a stimulus configuration identical to that for measuring manual reaction times. The fitted functions are derived from eqn (1), and are of the form:
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| (2) |
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Discussion |
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) for both saccadic and manual reaction times was well described by eqn (1), consistent with previous work showing the utility of using common models for these two response modalities (Ludwig et al. 2004; Palmer et al. 2005). Furthermore, the results of three of our four observers suggested that the contrast processor preceding both manual and saccadic responses had identical parameters, suggesting that a common detection stage may underlie different reaction time tasks. General features of reaction time models
The data here may be considered in the context of previous data relating reaction times to the detection of targets. A number of models have been proposed to describe the relationship between c and target luminance L or contrast C for a target appearance task. Bartlett & Macleod (1954) found c was inversely proportional to log(
L/Lo), where Lo was a constant. Carpenter (2004) similarly found a logarithmic transform using stimulus contrast, although with noise incorporated additively in both the numerator and denominator, i.e. log ([C + C0]/Co); this formulation is identical to our eqn (1) when the initial contrast Ci is zero. Other studies have described the relationship between luminance and c as a power law, Pieron's Law (Liang & Pieron, 1945):
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| (3) |
Inherent in all of these formulations is the idea that c may be explained by a linear rise-to-threshold mechanism of threshold K, whose rate-of-rise is inversely proportional to some transformation of the stimulus whose output may be termed 
. Therefore:
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| (4) |
should be. Table 2 summarizes some of the formulations that have been proposed previously. Based on our finding with reaction times to suprathreshold changes in contrast, we suggest a more general form of eqn (4), such that:
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| (5) |
gives the change in the output of the transducer that is transforming the input stimulus. If such an equation is accepted, this places constraints on what forms can take. In particular, when a detection task is performed,
=
–
0, meaning that 0, the output of the transducer when no stimulus is present, must be a calculable value. A number of the formulations listed in Table 2 do not allow this value to be calculated as they do not incorporate additive noise in the transducer.
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given in eqn (1), this does not mean that other models may not show equal, or even greater, success in fitting our data. It is not the primary purpose of this paper to attempt a systematic comparison of this kind, but rather to assess the utility of a simple model, based on well established observations of contrast processing, in predicting reaction times to step changes in contrast. The values of R2 given in the legends for Figs 2 and 3 indicate that our model explains a high proportion of the variation in our data in most cases. The task employed here involved processing of the near periphery for detection of change in contrast in one of two spots; this may have added an additional cognitive component which might tend to increase overall reaction times compared to a task involving a single central target – however, unpublished observations from our lab indicate that the model presented here also has utility in such tasks. It is well established that contrast processing changes as a function of the spatio-temporal characteristics of the stimulus (Legge, 1978; Plainis & Murray, 2000; Murray & Plainis, 2003; Ludwig et al. 2004), presumably due to the existence of parallel pathways within the visual system. Given the differing contrast gains of the magnocellular and parvocellular pathways (Kaplan & Shapley, 1986) one might anticipate that small contrast increments would be detected by the magnocellular subsystem and larger contrast increments by the parvocellular subsystem, thereby making it difficult to model the relationship between reaction time and contrast discrimination as a unitary process. In our particular experiment, the use of a contrast pedestal that is present for much of the time should tend to bias detection to the magnocellular system over a greater contrast range, however (Pokorny & Smith, 1997). This bias should be further enhanced by the use of stimuli with abrupt onsets, as are typically used in reaction-time experiments.
Comparison of different formulations for
In Table 2, there is a general divide between those authors favouring a logarithmic transformation of their data, and those preferring a power function. It would be useful therefore to see how a theoretical data set, generated using a logarithmic transform for , appears when the analysis erroneously assumes a power-function transform.
The upper panel of Fig. 6 gives a simulated set of data (open circles) for a contrast detection experiment when:
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–
c)) to values consistent with what would be expected from fitting true experimental data taken from our previous experiments (top panel, filled circles). We generated reaction times for contrasts increasing in 0.2 log unit steps from a just supra-threshold contrast. As expected, the data is perfectly fitted (R2
= 1.0) when plotted using a transform derived from the correct formulation for .
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=
C, equivalent to a power function with a unitary exponent (Plainis & Murray, 2000; McKeefry et al. 2003). Despite using an inappropriate transformation to plot the data, the results are still highly linear (R2
= 0.97), showing that – based on the linearity of the data over the range of reaction times expected in a typical experiment (see Figs 2 and 4) – the two models are difficult to distinguish. It is only at very low levels of contrast and, correspondingly, very large reaction times (not plotted), that the data in the lower panel would deviate markedly from linearity; unfortunately, this region that could potentially separate the two models is also the one where reaction times would be expected to be most variable (note for example the increasing variability with reaction time in Figs 1 and 2) and where the assumption of a linear rise-to-threshold mechanism is almost certainly violated (see below). Similar difficulties have been noted in trying to distinguish between logarithmic and power function models relating stimulus contrast to evoked potentials (Campbell & Kulikowski, 1972). Therefore, assessing the linearity of transformed data may not be a particularly sensitive method for deciding between competing models, and so it is not surprising that there are many competing formulations to relate stimulus contrast to reaction times.
There is, however, a distinct difference of over 20 ms between the two analyses in Fig. 5 when looking at the y-intercept, which estimates the contribution of the non-contrast dependent components to the reaction time. Therefore, rather than examining reaction times at very low levels of contrast, it may be that possible to distinguish between logarithmic and power-law functions for using careful studies designed to assess systematic deviations from linearity for high contrast stimuli.
Limitations in ‘rise-to-threshold’ integration models
The linear rise-to-threshold mechanism described in this paper (eqn (1)) predicts that reaction times continue to increase at a fixed rate as the magnitude of the change in the transducer () steadily decreases. This implies that the signal from the transducer is integrated completely, even when it is very small and reaction times are correspondingly very long. Clearly this is incorrect, as studies have shown that integration does not occur, or is incomplete, after a certain time window defined by the critical duration (Barlow, 1958; Roufs, 1972; Watson, 1979; Gorea & Tyler, 1986). Indeed, that the visual system operates as a perfect integrator for stimuli shorter than the critical duration is also untrue (Rashbass, 1970), although there are good theoretical reasons to expect behaviour consistent with that of a perfect integrator for sufficiently short stimuli (Watson, 1986). Unfortunately, our data do not extend to very long reaction times (Figs 1 and 2) and so we cannot say what might happen when reaction times exceed the critical duration. It is likely, however, that any analysis of long reaction times would be hampered by increasing measurement variability. Previous work that examined long reaction times to contrast increments visible with less than 100% accuracy failed to find a simple formulation to explain these data (Tiippana et al. 2001), although the study only investigated a metric based on the absolute magnitude of the change in contrast, rather than relative to the initial contrast.
Our model for relating contrast discrimination to latency requires only four free parameters; one to quantify the noise in the contrast transducer (C0), one to describe the threshold level in the rise-to-threshold mechanism (K), and two to account for delays in initiating saccades or manual button presses that are not due to contrast discrimination (given by the y-intercepts in Figs 3 and 4). Although this simple formulation accounts for the majority of the variability in reaction times with contrast (R2 values in Figs 3 and 4), it is unlikely that it can explain all aspects of contrast discrimination. It is well established that the presence of either a subthreshold or a just-suprathreshold contrast reduces the discrimination threshold to less than the detection threshold (Cornsweet & Pinsker, 1965; Whittle & Swanston, 1974; Whittle, 1986), an effect that is called facilitation. Facilitation has commonly been interpreted as indicating that the contrast transducer is accelerative at very low contrasts (Nachmias & Sansbury, 1974; Wilson, 1980; Foley & Legge, 1981; Switkes et al. 1988; Yang & Makous, 1995; Kontsevich & Tyler, 1999), as opposed to the logarithmic compression required to produce Weber's law at higher contrasts (Fechner, 1860). Our model cannot predict this kind of behaviour, and so fails to capture the small amount of facilitation seen in subjects A and B in their contrast discrimination functions (Fig. 5, squares, log Ci between –2 and –1). Despite this, our equation well predicts reaction times as contrast is increased from a value of Ci expected to cause facilitation (Figs 2 and 3, R2 values for Ci = 0.03), suggesting that variations in threshold behaviour due to facilitation may not be of much importance in determining reaction times to suprathreshold contrasts. The facilitation effect seen in Fig. 5 is weak in comparison to that found by other investigators, however. This may reflect the fact that the initial and final contrasts were presented asynchronously, preventing summation of the transient responses accompanying the abrupt onset of the contrast. Previous work has suggested that facilitation is lost when transient stimuli are presented upon static backgrounds (Georgeson & Georgeson, 1987; Anderson & Vingrys, 2000).
Based on our best-fitting values for the parameter K, given by the slopes of the lines in Figs 3 and 4, it should be possible to calculate psychophysical contrast discrimination thresholds to a stimulus of known duration. There are some problems that limit the usefulness of this calculation, however. Firstly, although the thresholds in Fig. 5 are nominally criterion-free measures, the reaction time data from which we derived K are not. Secondly, there is evidence that critical durations estimated from reaction times and from other measures of perceptual latency (Roufs, 1974; Williams & Lit, 1983; Ejima & Ohtani, 1987) differ at close-to-threshold contrasts, possibly due to separate criteria existing for detecting a target versus reacting to it (Ejima & Ohtani, 1987). Thirdly, and probably most importantly, the comparatively long duration of stimuli such as those used to measure contrast thresholds in our experiment is almost certainly outside the critical duration and so is longer than the time over which complete integration may be thought to occur (Barlow, 1958; Gorea & Tyler, 1986). This critical duration tcrit may be estimated from the values for R obtained in Fig. 5 using the equation:
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| (6) |
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References |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Barlow HB (1956). Retinal noise and absolute threshold. JOSA 46, 634–639.
Barlow
HB (1958). Temporal and spatial summation in human vision at different background intensities. J Physiol
141, 337–350.
Bartlett NR & MacLeod S (1954). Effect of flash and field luminance upon human reaction time. JOSA 44, 306–311.
Bloch AM (1885). Expériences sur la vision. Comptes Rendus la Société Biologie 3, 493–495.
Burkhardt DA, Keenan RM & Gottesman J (1987). Sensory latency and reaction time: dependence on contrast polarity and early linearity in human vision. JOSA A 4, 530–539.
Campbell
FW
&
Kulikowski
JJ (1972). The visual evoked potential as a function of contrast of a grating pattern. J Physiol
222, 345–356.
Carpenter RHS (1981). Oculomotor procrastination. In Eye Movements: Cognition and Visual Perception, ed. Fisher DF, Monty RA & Senders JW, pp. 237–246. Lawrence Erlbaum Associates, Hillsdale, NJ, USA.
Carpenter RHS (1994). SPIC: a PC-based system for rapid measurements of saccadic responses. J Physiol 480, page 4.
Carpenter RHS (2004). Contrast, probability and saccadic latency: evidence for independence of detection and decision. Current Biol 14, 1576–1580.[CrossRef][Medline]
Carpenter RHS & Williams MLL (1995). Neural computation of log likelihood in control of eye movements. Nature 377, 59–62.[CrossRef][Medline]
Cattell
JM (1886). The influence of the intensity of the stimulus on the length of the reaction time. Brain
8, 512–515.
Cornsweet
TN
&
Pinsker
HM (1965). Luminance discrimination of brief flashes under various conditions of adaptation. J Physiol
176, 294–310.
Doma H & Hallett PE (1988). Rod-cone dependence of saccadic eye-movement latency in a foveating task. Vision Res 28, 899–913.[CrossRef][Medline]
Ejima Y & Ohtani Y (1987). Simple reaction time to sinusoidal grating and perceptual integration time: contributions of perceptual and response processes. Vision Res 27, 269–276.[CrossRef][Medline]
Fechner GT (1860). Elemente der Psychophysik. In The Classical Psychologists, ed. Rand B, pp. 562–572. Houghton Mifflin, Boston.
Foley JM & Legge GE (1981). Contrast detection and near-threshold discrimination in human vision. Vision Res 21, 1041–1053.[CrossRef][Medline]
Georgeson MA & Georgeson JM (1987). Facilitation and masking of briefly presented gratings: time-course and contrast dependence. Vision Res 27, 369–379.[CrossRef][Medline]
Gorea A & Tyler CW (1986). New look at Bloch's law for contrast. JOSA A 3, 52–61.
Henmon VAC (1906). The time of perception as a measure of differences in sensations. Arch Archives of Philosophy, Psychology and Scientific Methods Philosophy Psychol Scientific Meth 8, 3–75.
Hildreth JD (1973). Bloch's law and a temporal integration model for simple reaction time to light. Perception Psychophysics 14, 421–432.
Jaskowski P (1984). Human reaction time to negative contrast stimuli. Acta Neurobiologiae Expis 44, 217–232.
Kaplan
E
&
Shapley
R (1986). The primate retina contains two types of ganglion cells, with high and low contrast sensitivity. Proc Natl Acad Sci U S A
83, 2755–2757.
Kingdom FA & Whittle P (1996). Contrast discrimination at high contrasts reveals the influence of local light adaptation on contrast processing. Vision Res 36, 817–829.[CrossRef][Medline]
King-Smith PE, Grigsby SS, Vingrys AJ, Benes SC & Supowit A (1994). Efficient and unbiased modifications of the QUEST threshold method: theory, simulations, experimental evaluation and practical implementation. Vision Res 34, 885–912.[CrossRef][Medline]
Kontsevich LL & Tyler CW (1999). Nonlinearities of near-threshold contrast transduction. Vision Res 39, 1869–1880.[CrossRef][Medline]
Laming D (1968). Information Theory of Choice Reaction Times. Academic, New York.
Legge G (1978). Sustained and transient mechanisms in human vision: temporal and spatial properties. Vision Res 18, 69–81.[CrossRef][Medline]
Liang T & Pieron H (1945). De l'influence specifique des eclairments monochromatiques sur le retard de la sensation visuelle. Comptes Rendus Hebdomadaire Academie Scientifique Paris 56, 221.
Luce DL (1986). Response Times. Oxford University Press, Oxford.
Ludwig CJH, Gilchrist ID & McSorley E (2004). The influence of spatial frequency and contrast on saccade latencies. Vision Res 44, 2597–2604.[CrossRef][Medline]
Mansfield RJW (1973). Latency functions in human vision. Vision Res 13, 2219–2234.[CrossRef][Medline]
McKeefry
DJ, Parry
NRA
&
Murray
IJ (2003). Simple reaction times in color space: the influence of chromaticity, contrast, and cone opponency. Invest Ophthalmol Visual Sci
44, 2267–2276.
Motulsky HJ & Christopoulos A (2004). Fitting Models to Biological Data Using Linear and Nonlinear Regression. Oxford University Press, New York.
Murray IJ & Plainis S (2003). Contrast coding and magno/parvo segregation revealed in reaction time studies. Vision Res 43, 2707–2719.[CrossRef][Medline]
Nachmias J & Sansbury RV (1974). Grating contrast: discrimination may be better than detection. Vision Res 14, 1039–1042.[CrossRef][Medline]
Ober JK, Przedpelska-Ober E, Gryncewicz W, Dylak J, Carpenter RHS & Ober JJ (2003). Hand-held system for ambulatory measurement of saccadic durations of neurological patients. In Modelling and Measurement in Medicin, ed. Gajda J, pp. 187–198. Komitet Biocybernityki i Inzyneierii Biomedycznej PAN, Warsaw.
Palmer J, Huk AC & Shadlen MN (2005). The effect of stimulus strength on the speed and accuracy of a perceptual decision. J Vision 5, 376–404.[CrossRef]
Plainis S & Murray IJ (2000). Neurophysiological interpretation of human visual reaction times: effect of contrast, spatial frequency and luminance. Neuropsychologia 38, 1555–1564.[CrossRef][Medline]
Pokorny J & Smith VC (1997). Psychophysical signatures associated with magnocellular and parvocellular pathway contrast gain. JOSA A 14, 2477–2486.[Medline]
Rashbass
C (1970). The visibility of transient changes of luminance. J Physiol
210, 165–186.
Ratcliff R (2001). Putting noise into neurophysiological models of simple decision making. Nature Neuroscience 4, 336–337.[CrossRef][Medline]
Roufs JAJ (1972). Dynamic properties of vision – I. Experimental relationships between flicker and flash thresholds. Vision Res 12, 261–278.[CrossRef][Medline]
Roufs JAJ (1974). Dyamic properties of vision – V. Perception lag and reaction time in relation to flicker and flash thresholds. Vision Res 14, 853–869.[CrossRef][Medline]
Rushton WAH (1961). Peripheral coding in the nervous system. In Sensory Communication, ed. Rosenblith WA, pp. 169–181. MIT Press, Cambridge, MA, USA.
Steinman A & Veniar S (1944). Simple reaction time to change as a substitute for the disjunctive reaction. J Exp Psychol 34, 152–158.[CrossRef]
Switkes E, Bradley A & DeValois KK (1988). Contrast dependence and mechanisms of masking interaction among chromatic and luminance gratings. JOSA A 15, 1149–1162.
Tiippana K, Paramei GV & Alshuth E (2001). Contrast discrimination and choice reaction times at near-threshold pedestals. Spatial Vision 15, 25–43.[CrossRef][Medline]
Vaughan HG Jr, Costa LD & Gilden L (1966). The functional relation of visual evoked response and reaction time to stimulus intensity. Vision Res 6, 645–656.[CrossRef][Medline]
Wald A (1944). On cumulative sums of random variables. Ann Mathemat Statistics 15, 283–296.
Watson AB (1979). Probability summation over time. Vision Res 19, 515–522.[CrossRef][Medline]
Watson AB (1986). Temporal sensitivity. In Handbook of Perception and Human Performance, ed. Boff K, Kaufman L & Thomas J, pp. 6.1–6.43. John Wiley and Sons, New York.
Westendorf D & Blake R (1988). Binocular reaction times to contrast increments. Vision Res 28, 355–359.[CrossRef][Medline]
Whittle P (1986). Increments and decrements: luminance discrimination. Vision Res 26, 1677–1691.[CrossRef][Medline]
Whittle P & Swanston MT (1974). Luminance discrimination of separated flashes: the effect of background luminance and the shapes of T.V.I. curves. Vision Res 14, 713–719.[CrossRef][Medline]
Williams JM & Lit A (1983). Luminance-dependant visual latency for the Hess effect, the Pulfrich effect, and simple reaction time. Vision Res 23, 171–179.[CrossRef][Medline]
Wilson HR (1980). A transducer function for threshold and suprathreshold human vision. Biol Cybernetics 38, 171–178.[CrossRef][Medline]
Yang J & Makous W (1995). Modeling pedestal experiments with amplitude instead of contrast. Vision Res 35, 1979–1989.[CrossRef][Medline]
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), 0.03 (
), 0.06 (
), 0.2 (•) and 0.9 (
). All other details are as given in 
, where Cthr is the psychophysical contrast threshold (estimated to be 0.005). The two panels plot the data using transforms based on the current formulation for 