John Z. Levinson

Flicker Fusion Phenomena Rapid flicker is attenuated many times over by repeated temporal summation before it is "seen."

The high-frequency temporal behavior of the human visual system has been shown to have some of the properties of a linear low-pass filter. For such a system it is appropriate to consider a repetitive stimulus as having separable Fourier harmonic components. The direct-current component or average luminance is important in that it sets the adaptation level. It is therefore convenient to keep it constant when varying other stimulus parameters, such as frequency or wave form. Of the alternating-current components, only the fundamental is important at high frequencies, the higher harmonics being relatively more attenuated. Any linear low-pass filter system responds in a predictable way to sinusoidal stimulation, whether continuous or of short duration. In the case of the visual system, predictable behavior is found at high frequencies, and it leads to discovery of hitherto unobserved pseudoflash and real flash phenomena. Measurement of a new characteristic time is suggested. At low frequencies the use of half and whole-sinusoidal flashes leads to the discovery of some interesting relations with flicker thresholds, but these remain for future discussion.

Studies with artificial neurons. III. Mechanisms of flicker-fusion.

Summary1.A simple model is described which establishes a relationship between physiological and psychophysical flicker-fusion data. The three components of the model are a transducer, a filter and a flicker-detector. The model is consistent with the view that fusion is purely retinal.2.An electronic analog is used to realize the model. Its essential elements are a source of generator pot1ential, a low-pass filter, and a simulated ganglion cell.3.The model was originally designed to reproduce the psychophysical results obtained by de Lange. Special importance is attached to the envelope of his curves; the model reproduces this envelope. His low-intensity results are duplicated accurately, while the high-intensity, high-frequency data are derived somewhat less accurately. The high-intensity low-frequency data are attributed to a mechanism not included in the model.4.In the simulation of physiological data obtained by Enroth, close resemblance to the firing characteristics of retinal ganglia in cat is shown by the model. Firing occurs for bursts lasting for at most half the period of the alternating stimulus, the number of spikes per burst diminishing to unity as “fusion” is approached.5.The phase lags and latencies of responses in the model satisfy neurophysiological evidence. Both off-latency and inhibition-latency are satisfactorily reproduced.6.The model has been used to simulate two-component flicker data. The “flicker-detector” employed leads to results very similar to those obtained psychophysically. The phase characteristics of the assumed filter agree less well.

Fusion of Complex Flicker

Brown and Forsyth have recently performed a flicker-fusion experiment showing clearly that there is more to flicker than meets the eye. This report presents an analysis of their results which indicates the likelihood that at fusion threshold all but one of the Fourier components of their presentation are imperceptible.

Fusion of complex flicker II.

Flicker waveform has been found to have a slight but specific effect upon fusion threshold. A depression of threshold amplitude of about 30 percent occurs if a second harmonic of near-threshold amplitude is added to the fundamental. The magnitude of the depression depends critically on the relative phase of the two components of the waveform.

One-Stage Model for Visual Temporal Integration

Many characteristics of visual temporal integration, found in both psychophysics and physiology, have been thought of as arising from a number of cascaded integrations, or exponential delays. As an alternative, a single process is proposed which has a temporal response identical with that of the many-stage model. This process is readily visualized as taking place within a single receptor cell. It consists of a number of subprocesses, the number being proportional to the number of photons absorbed. Each subprocess consists of three steps: (1) initiation by photon absorption, (2) counting of a series of random events, and (3) emission of a signal when the count reaches a specific number. Response is taken to be the summation of all the signals produced by the subprocesses. Temporal delay and spread of the response is entirely attributed to the time required to accumulate the independent random events of step (2). Possible physiological correlates of the three steps are touched on, but only speculatively.

Studies with Artificial Neurons, IV: Binaural Temporal Resolution of Clicks

A psychophysical experiment performed by Guttman, van Bergeijk, and David in 1960 showed that binaural auditory resolution of repetitively presented, closely spaced clicks improves as repetition rate is increased. We propose a model in which the action of a single neuron can account for the phenomenon; it depends on a self‐inhibition function that serves to vary temporal resolution with stimulus rate. Single‐spike (click) stimuli elicit output bursts of variable duration; burst lengths are controlled by an output‐derived feedback whose level depends on stimulus repetition rate. An electronic model of a neuron, simulating a cochlear‐nucleus unit, accurately replicates the essential features of the psychophysical data. Two time constants, estimated by extrapolation, are postulated for single units in the human auditory system.

Model for Monaural‐Pulse Interval Discrimination

A model is proposed to account for some auditory click‐fusion results obtained by Guttman, van Bergeijk, and David several years ago. These results showed that the critical time interval between the members of a click pair at which each member could just be separately perceived (as measured by binaural fusion) was a function of the repetition frequency with which the pairs were presented. As repetition frequency went up, the critical interval decreased. The model postulates that each click is represented in the nervous system by a short burst of spikes. A low‐pass neural filter (or integrator) is assumed not to resolve the individual spikes in a burst, but rather to “see” the burst as a single event. With an interburst interval longer than the interspike interval within a burst, the filter would see two events. The shorter the bursts, the closer the events can be spaced. A single‐neuron model is proposed that generates bursts in response to single input spikes; the length of these bursts decreases with increasing input frequencies. The model has two critical parameters: one is the time constant of the excitatory input, which is short, and the other is the time constant of an output‐derived inhibitory feedback, which is long.