# User:Eugene M. Izhikevich/Proposed/Flicker fusion

Flicker fusion is the visual phenomenon in which a repetitively presented stimulus (the flickering stimulus) appears as a single continuous stimulus.

## Significance of flicker fusion

Every day, billions of people worldwide operate under flickering artificial lighting conditions, or observe flickering computer/TV displays and/or cinematic pictures. Although the flickering stimuli in these conditions are visible for only a fraction of the viewing time, they appear as continuous and stable because we perceptually integrate successive flashes in a process called flicker fusion. Flicker fusion is critical to stable perception under flickering light conditions, and is the basis for cinematic and computerized movies and animation.

## Background

In 1824, Peter Mark Roget (who also wrote the famous Thesaurus) first presented the concept of “persistence of vision” to the Royal Society of London, as the ability of the retina to retain an image of an object for 1/20 to 1/5 second after its removal from the field of vision (Roget, 1825). A second principle - the "phi phenomenon" or stroboscopic effect (the basis for the famous Gestalt School of Psychology) - is closely related to flicker fusion. It was first studied by Max Wertheimer (the founder of Gestalt Psychology) and Hugo Munsterberg between 1912-16 (Munsterberg, 1916; Wertheimer, 1925). Wertheimer and Munsterberg found that subjects can perceptually bridge the temporal gap between two consecutive displays, so that a series of static images appear as continuous movement. The discovery of flicker fusion became the perceptual basis for moving pictures, television, and all media based on stroboscopic presentation of stimuli.

## Key concepts related to flicker fusion

Temporal integration (or temporal summation) is the phenomenon in which a stimulus becomes more detectable, or obtains higher contrast, as a result of increasing its duration.

Bloch’s law states that for durations below the critical duration ($$\mathit{\boldsymbol{t_c}}$$), perceived contrast ($$\mathit{\boldsymbol{\Psi}}$$) is linearly determined by stimulus contrast or intensity (I) as a function of stimulus duration (t) (Bloch, 1885). $\boldsymbol{\mathit{\Psi = I \cdot t(t \le t_c)}}$

The critical duration is the stimulus duration at which increased duration will not increase the probability of detection of a stimulus, or increase its perceived contrast.

The Brücke-Bartley effect is the phenomenon in which a flickering stimulus appears brighter than the same stimulus presented unflickering. There is a peak perceived flicker brightness at about 8 to 10 Hz (Bartley, 1939; Brücke, 1864).

The minimal frequency at which flickering stimuli appear continuous is called the critical flicker frequency.

The Talbot-Plateau law describes the perceived contrast of a fused flickering stimulus (a flickering stimulus with a frequency above the critical flicker frequency) as equivalent to the perceived contrast of a non-flickering stimulus with the same average luminance (Plateau, 1835). Average luminance of the flickering stimulus is measured over a period of one or more whole cycles of flicker.

## Perceptual factors affecting the critical flicker fusion threshold

This critical flicker fusion threshold depends on the stimulus’ luminance (the Ferry-Porter law), size (the Granit-Harper law), color, retinal eccentricity, background luminance, and other factors.

The Ferry-Porter law states that critical flicker frequency will increase proportionally as a function of the logarithm of the stimulus luminance (L) (Ferry, 1892; Porter, 1902):

$\boldsymbol{CFF = a\log{L} + b}$

Where a and b are constants ( Figure 1).

Figure 1: Critical flicker frequency as a function of stimulus luminance (Hecht and Verrijp, 1933b).

The Ferry-Porter law also applies to purely chromatic stimuli at photopic light levels. Due to the different spectral sensitivity of rod photoreceptors versus cone photoreceptors, however, the slope of the curve under scotopic light levels varies as a function of wavelength ( Figure 2).

Figure 2: Critical flicker frequency of a 19° test field as a function of retinal illuminance and monochromatic wavelength (Hecht and Shlaer, 1936).

The Granit-Harper law states that the critical flicker frequency increases linearly with the logarithm of the stimulus area ( Figure 3).

Figure 3: Critical flicker frequency as a function of retinal illuminance and stimulus size (Hecht and Smith, 1936).

It follows from the Granit-Harper law that retinal eccentricity will affect the critical flicker frequency as a function of stimulus luminance because of the different ratios of cone photoreceptors and rod photoreceptors at different eccentricities ( Figure 4).

Figure 4: Critical flicker frequency as a function of retinal illuminance and retinal position (Hecht and Verrijp, 1933a).

## The neural correlates of flicker fusion

Figure 5: Multi-unit recording from upper layers of area V1 in a rhesus monkey. The response to the second stimulus recovers as the inter-stimulus interval (ISI; the interval between the end of the first stimulus and the beginning of the second stimulus), increases beyond 30 milliseconds. Modified from (Macknik, 2006) with kind permission from Elsevier.

Physiological evidence in humans and monkeys shows that flicker rates above the perceptual critical flicker frequency threshold can nevertheless generate cortical and subcortical visual responses (Martinez-Conde et al., 2002). Thus the temporal integration underlying flicker fusion does not occur at the level of the retina, but must take place later in the visual hierarchy.

Single-unit recordings in the primary visual cortex of primates suggests that, for two brief-duration targets presented in close succession, the after-discharge to the first target interferes with the onset-response to the second target (Macknik, 2006) (see Figure 5). The onset-response to the second flash is absent for inter-stimuli intervals of 30 msec or shorter (equivalent to 17 Hz periodic). If the flashes are separated by more than 30 ms, the after-discharge to the first flash and the onset-response to the second flash begin to recover (i.e. equivalent to <17 Hz flicker). These intervals roughly coincide with the critical flicker fusion threshold in humans for 100% contrast stimuli in the fovea (Di Lollo and Bischof, 1995; Fukuda, 1979; Gorea, Wardak et al., 2000; Lennie, Pokorny et al., 1993).

This suggests that perceptual flicker fusion may be due to the lack of robust transient responses to the flickering stimulus.

## References

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