Temporal Resolution and Temporal Summation

In the spatial domain, detection of two lights in space requires the appropriate detector array (Fig. 1). For us to discriminate the two lines, a response given by detector array C to F is required. All of these detector arrays provide a Yes-No-Yes response and thus allow the discrimination of the two lines.

Figure 1

Detector array C and beyond allows the detection of the two lines.

In the temporal domain, the same principle applies, except now the stimulus is separated in time (Fig. 2). The separation between the two lines is in the temporal domain (two flashes are delivered) after a time interval t. The detector array now has different temporal integration times. For example, detector A integrates over time = t, whereas detector array B has an integration time of time = 0.5t, array C, time = 0.33t, and so on. Because of the shorter integration time for detector array C and beyond, such an array will be able to discriminate the two flashes that are separated by an interval of t.

Figure 2

Speed of integration allows the detection of intermittent stimuli. Detector arrangement C and beyond allows discrimination of the stimuli over time.

To detect a flash of light one after the other, an appropriate integration time is required (Fig. 3). The period of integration is up to 0.1 seconds or 100 ms (for rods) and 10 to 15 ms for cones. The advantage of long integration time is that under limited light level conditions, a threshold will be reached, whereas when light levels are not limiting (cone or photopic vision), a short integration time is preferable to improve temporal resolution.

Figure 3

Flashes of light are presented to the eye. (a) With a short integration time, the flashes are detected. (b) No flashes are perceived (that is, the stimulus appeared as one bright flash) with a long integration time.

Temporal integration time is related to temporal summation. Temporal summation refers to the eye's ability to sum the effects of individual quanta of light over time. However, temporal summation only occurs within a certain period of time, called the critical duration or critical period. According to Bloch's law of vision, within this critical duration, the threshold is reached when the total luminous energy is reached. Bloch's law of temporal summation is analogous to Ricco's law of spatial summation. Bloch's law states that total luminous energy is a constant value (k), thus threshold is reached when the product of luminance (L) and stimulus duration (t) equals this constant. In other words, when luminance is halved, a doubling in stimulus duration is required to reach threshold. When luminance is doubled, the threshold can be reached in half the duration. Bloch's law is expressed as:

L · t
                        n
                     = k
                

where L is the luminance of the stimulus, t is the duration of the stimulus, k is a constant value, and n describes whether temporal summation is complete (n = 1) or partial (0 < n < 1). No temporal summation occurs when n = 0 (Fig. 4).

Figure 4

Temporal summation data plotted as logL versus logt, showing where Bloch's law applies.

Critical duration is shorter for stimulus of high luminance as threshold is reached faster and slower for stimulus of low luminance as a longer period of time is required to sum the quanta to reach threshold. Temporal summation ceases beyond the temporal integration time. Above this value, threshold is dependent only on luminance rather than the product of luminance and duration.

Temporal summation is also affected by other test variables, such as background luminance and the size of the stimulus. Critical duration is longer for brighter background and smaller test stimuli. When temporal summation data areplotted as logL t versus logt rather than logL versus logt (as in Fig. 4), the slope of zero identifies Bloch's law (Fig. 5).

Figure 5

Luminance-duration versus time curves. Bloch's law holds when the gradient of the line is zero. Integration time (critical duration) can be determined from above. Beyond critical duration, Bloch's law breaks down (when the gradient is greater than zero). (more...)

The above plots show that temporal summation is longer for low light levels, indicating the larger temporal summation characteristics for scotopic vision. As light intensity is increased, e.g., 25,000 trolands, the critical duration is of the order of 20–30 msec. The interrelationship between temporal integration and spatial summation is shown on the right panel, where Bloch's law is measured for different sizes of test stimuli. Decreasing test size results in increased temporal summation, and hence poorer temporal discrimination. We will investigate this phenomenon further when we review flicker discrimination for different sized stimuli in the next section.

Broca-Sulzer Effect

In addition to basic discrimination characteristics of temporal resolution, there are several interesting perceptual phenomena. One of these phenomena is the Broca-Sulzer effect, which describes the apparent transient increase in brightness of a flash of short duration. Subjective flash brightness occurs with flash durations of 50 to 100 milliseconds. This phenomenon is associated with temporal summation and explains the leveling off of brightness to a plateau. When the light is turned on, time is required for temporal summation to reach threshold for light of low luminance. Light of high luminance reaches this threshold very quickly. As flash duration increases, brightness levels off to a plateau as temporal summation begins to breakdown, according to Bloch's law, after the critical duration. The apparent transient peak in brightness is probably attributable to an underlying neural mechanism (Fig. 6).

Figure 6

Apparent brightness of flashes with various luminances, as a function of flash duration. Broca and Sulzer data from Hart (8).

Factors Affecting CFF

The Ferry-Porter law states that CFF is proportional to the logarithm of the luminance of flickering stimulus (L). It can be expressed as:

CFF = a logL + b
                

where a and b are constants. With foveal observation, this relationship holds over a wide range (0.5 to 10,000 trolands) (Fig. 7). The above equation implies that when CFF is plotted as a function of logL, a straight line will identify the region where the Ferry-Porter law holds. As the intensity of the test stimulus is increased, our perception of flicker also increases. From a practical point of view, if a stimulus is flickering, such as computer monitor, decreasing the intensity level will eliminate the flicker.

Figure 7

CFF at the fovea over a range of retinal illuminance (photon = troland) of the test field, showing conformity of the Ferry-Porter law over four logarithmic units. Hecht and Verrijp's data from Hart (8).

Spectral Composition

Under photopic levels, lights of different wavelengths, when adjusted to match them for brightness, conforms to the Ferry-Porter law and follows the logarithmic function as brightness increases. However, under scotopic levels (rods functioning), the wavelengths fan out (Fig. 8). This is attributable to the different spectral sensitivities of the scotopic system to the photopic system. If plotted as scotopic photons, the bottom part of the curve would collapse into one and appear like the 19° curve in Fig. 10. Note that the temporal resolution to short wavelength test stimuli is different. However, in general terms, the plot below is correct, although the units chosen for the scotopic component (lower branches) give the misconception that temporal resolution is different for the rod system.

Figure 8

CFF of 19° test field over a range of retinal illuminance (photon = troland) for different monochromatic lights of different wavelengths. Hecht and Shlaer's data from Hart (8).

An important aspect of cone vision is that when the short-wavelength pathway is isolated (1), the temporal resolution is lower, close to 10–15 Hz, rather than the closer to 60 Hz for the longer wavelength pathways. This general phenomenon is characteristic of the short-wavelength pathway that is known to have larger spatial summation approximately 15' at about one degree eccentricity (the location of high S-cone density), whereas the longer wavelength pathways have a spatial summation of 4' (2). In the temporal domain, at high light levels, the S-cone pathways has a temporal summation time of approximately 100 ms, whereas the longer-wavelength cone pathway has a temporal integration of approximately 50 msec (3).

Retinal Position

Because the CFF is different for rod and cones, the CFF for the test field will depend on the proportion of rods and cones being stimulated. Because the proportion of rod and cones changes with eccentricity, a foveal test stimulus will follow the Ferry-Porter law and show no kink (one branch only) in the curve because only cones are present at the fovea. An extrafoveal test stimulus will show a kink (two branches) in the CFF function because the rods determine the CFF at low retinal illuminances and the cones determining CFF at higher retinal illuminance. Note that the Ferry-Porter law applies over a decreasing range as the eccentricity increases, and that temporal resolution is poorer for eccentric locations (Fig. 9).

Figure 9

CFF of a 2° white test field over a range of retinal illuminances (photon = troland) measured at the fovea, 5° above the fovea, and 15° above the fovea. Hecht and Verrijp's data from Hart (8).

The Ferry-Porter law has been further examined for a single cone type, using conditions that eliminate detection of the flickering stimulus by rods. Under these conditions, the law has been found to hold, despite changes in stimulus size or modulation amplitude (4). However, the slope of the Ferry-Porter law changes with eccentricity, becoming steeper with eccentrically presented targets. This latter finding is consistent with previous work, suggesting that there is an increase in the speed of photopic retinal responses in the periphery, once stimuli have been appropriately scaled (5). This increase in speed has been hypothesized to relate to the change in cone photoreceptor outer-segment length that occurs in the periphery (5). Such scaling has not been performed to the classic data sets presented here.

Size of Test Field

Because of the different populations of rods and cones in the retina and different spatial summation properties, CFF will be dependent on the area of the retina being stimulated. Instead of varying retinal eccentricity as above, the size of the centrally fixated test field is varied (Fig. 10). As the test field increases, two branches begin to appear. The lower branch represents rod function. The maximum CFF, and hence maximum temporal resolution, is achieved by large test targets that have the shortest integration time noted earlier.

Figure 10

CFF over a range of retinal illuminance (photon = troland) for a centrally fixated test stimulus of different sizes. Hecht and Smith's data from Brown (9).

The Talbot-Plateau law describes the brightness of an intermittent light source that has a frequency above the CFF. This law states that above CFF, subjectively fused intermittent light and objectively steady light (of equal color and brightness) will have exactly the same luminance. In another words, brightness sensation from the intermittent light source is the same as if the light perceived during the various periods of stimulation had been uniformly distributed over the whole time. The Talbot-Plateau law applies only above the CFF.

The Brücke-Bartley (brightness enhancement) effect is a phenomenon related to the Broca-Sulzer effect. When the frequency is gradually lowered below the CFF, the effective brightness of the test field begins to rise. Not only does the brightness reach a value equal to that of the uninterrupted light, but the brightness even transcends it, reaching a maximum when the flash rate is about 8 to 10 Hz.