A model of visible persistence based on linear systems.

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Visual stimuli appear to persist beyond the offset of the physical stimulus. Coltheart (1980) suggested the need to distinguish among several types of persistence. I confine my attention to one of those types, visible persistence. According to Coltheart, term 'visible' denotes the sine qua non of this form of persistence, namely, that it can be 'seen'. Visible persistence is the form of persistence that makes fluorescent lights and computer monitors possible.Several paradigms have been used to measure visible persistence, including: synchrony judgements, two - pulse thresholds, and integration tasks. Several counter - intuitive relationships are obtained in measuring the duration of visible persistence using those paradigms. Visible - persistence duration is inversely related to the duration of the physical stimulus. If there are two stimuli, as in a two - pulse experiment, the inverse relationship is obtained for both the first and the second pulse. Persistence duration is also inversely related to stimulus intensity, although the relationship is weaker for intensity than for duration.We recently discovered another counter - intuitive finding. Monocular presentation is superior to binocular presentation in a persistence task based on integration (i.e., Di Lollo, 1980). In almost every other visual task, binocular presentation is superior to monocular (Blake & Fox, 1973). This superiority makes sense in the context of articles showing that binocular viewing improves flicker detection (e.g., Sherrington, 1904). Flicker is the opposite of persistence. If we assume that the goal of the visual system is to detect change, then the various counter - intuitive findings become less counter - intuitive. Factors that improve vision will improve the likelihood of detecting change. Bright lights, long lights, and binocular viewing make it is easier to detect change. Because persistence is the failure to detect change, these same conditions lead to shorter persistence estimates. A similar idea has been expressed by Dixon and Di Lollo (1992).Linear Systems. Models based on linear filters have done an excellent job of accounting for low - level visual phenomena (Loftus, Duncan & Gehrig, 1992; Sperling, 1964; Watson, 1986). With a linear filters approach, a stimulus is conceptualized as consisting of a series of impulses. If the system's response to an impulse is known, then the system's response to any arbitrary stimulus can be computed. An impulse is a burst of stimulation that is infinitely thin, infinitely tall, and has unit area. The response of the visual system to an impulse is known as the impulse response function. The Gamma function is a good candidate for the impulse response function (Equation 1). Once we choose a shape for the impulse response function, we can compute the system response to an entire stimulus, a(t), by convolving the gamma distribution with the distribution of the physical stimulus, Equations 2 and 3.Impulse response function,Equation not transcribed (1)Distribution function for gamma, (2)Equation not transcribed (3)where k = contrast and d = durationPersistence Model for Synchrony Judgements. The model for synchrony judgements assumes that subjects judge a light as having gone off when its intensity falls some criterion amount from maximum. Because of the form of the a(t) function, the time at which the function reaches its maximum and begins to decline, tSymbol not transcribed, depends on the duration of the stimulus:Equation not transcribed (4)Thus, in general, the model predicts an inverse duration effect. …