Fig 1.
The left-hand column shows data for observer V from De Lange [14] and the right-hand column, data for observer DHK from Kelly [15] both measured using sinusoidally flickering stimuli.
The data are shown twice: The upper panels show the logarithm of the reciprocal of the just-detectable contrast (the contrast sensitivity) as a function of frequency (Hz) plotted on a logarithmic scale. The lower panels show the same data replotted as the logarithm of the reciprocal of the just-detectable amplitude (the amplitude sensitivity) also as a function of frequency (logarithmic scale). Different symbols and colors denote different mean retinal illuminances (log10 photopic trolands) as indicated in the key. The black curves are arbitrary smooth functions fitted to each dataset to facilitate comparison. Data are from Figure 5 in De Lange [14], who used a 2° diameter, centrally fixated, white flickering test field in a steady 60° diameter surround of same luminance and chromaticity, and from data tabulated in Table 1 in Kelly [15], who used a centrally-fixated, 50° diameter white target vignetted gradually from 50 to 68°.
Fig 2.
Log10 amplitude sensitivities for observers V (left panel) and L (right panel) measured at the eight (V) or seven (L) mean retinal illuminances (log10 photopic trolands) noted in the key.
The sensitivities are plotted as a function of frequency (Hz), which in this figure and Figs 3–6 is shown on a linear frequency scale. Data replotted from Figures 5 and 6 in De Lange [14]. De Lange used a 2° diameter, centrally fixated, white flickering test field in a steady 60° diameter surround of same luminance and chromaticity. The solid red lines are best least-squares linear fits to the high-frequency region of each curve. The solid black and dashed yellow lines show fits of our light adaptation model. The dashed yellow lines indicate those (mesopic) levels for which the flicker detection is likely to be mediated by rods and cones, while the black lines indicate those (photopic) levels for which the detection is likely to be mediated solely by cones. (The levels thought to be photopic are also highlighted in yellow in the key).
Fig 3.
Same as Fig 2, but amplitude sensitivities for observer DHK from Table 1 in Kelly [15].
Kelly used a 50° diameter white target vignetted from 50 to 68°.
Fig 4.
Same as Fig 2, but amplitudes sensitivities for observers HJM (left panel) and RK (right panel) from Figure 3 in Roufs [17].
Roufs used centrally fixated, 1° diameter “practically” white target with no surround.
Fig 5.
Same as Fig 2, but amplitude sensitivities for protanopic observers ML (left panel) and MM (right panel) provided by AS, originally shown in Figures 3 and 4 in Stockman et al. [13].
Stockman et al. used a centrally-fixated, 4° diameter, 610-nm target superimposed on 9° diameter 540-nm background. The ratio of the target and background radiances was fixed to produce a maximum M-cone contrast of 13%. The error bars are ±1 standard error of the mean. This combination of background and target radiances helped to eliminate rod intrusion at low retinal illuminances (as confirmed in their bleaching control experiments).
Fig 6.
Same as Fig 2 for data from three sources.
First, observer AR replotted from Figure 2 of Rovamo et al. [18] measured using a white 1.66° diameter flickering target inside a 3.32° diameter equiluminant white surround. Second, observers WS and TU replotted from Figure 2 in Swanson et al. [19] measured using a 2° diameter flickering target illuminated by a mixture of red and green LEDs (light-emitting-diodes) that appeared metameric with a 600-nm light. Third, observers VMC and TEW replotted from Figure 2 in von Wiegand et al. [20] measured using a flickering LED target with a dominant wavelength of 625-nm that extended to 1° diameter and then fell with a cosine intensity profile to zero intensity by 2° centred within a larger 18° diameter annular surround of the same mean luminance and chromaticity. Both were superimposed on an 18° diameter 565-nm background intended to suppress rods.
Table 1.
Values in degrees are the diameters of the circular targets or backgrounds. Illuminance ranges are in units of log10 trolands.
Fig 7.
The reciprocal of the slopes of the red lines in Figs 2–6 (Hz per log10 unit sensitivity) plotted as a function of the mean intensity in log10 photopic trolands.
The lines were fitted to the higher frequency amplitude-sensitivity data for each observer for each mean light level. The error bars are ±1 standard error of the fitted slope (see Table A). The solid blue line is the linear regression (Pearson correlation coefficient = 0.801, p<0.0001) and the dashed red lines are the 95% confidence intervals.
Fig 8.
The direct cascade used to model flicker sensitivity is shown along the vertical black line labelled MODEL and has six low-pass stages (1–6) and two inhibitory stages (A and B).
The six variable speed LP-filters (1–4, and A, B) have the same corner frequency of 15 Hz in this example and the two fixed-speed LP-filters (5, 6) have a corner frequency of 30 Hz (see text). The effects on an impulsive input signal (top orange panel) at different stages of the model (denoted by the numbered red arrows) are shown as a function of time in the orange panels of right-hand column and, in the corresponding green panels, as the logarithm of amplitude of the response as a function of frequency. The amplitude spectrum of the input is flat with equal amplitude at all frequencies (top green panel). An early gain adjustment, g, controls the overall gain of the system. The second orange and green panels show the effects of the first LP-stage and the third orange and green panels, the effects of a cascade of three stages. Next, the fourth and fifth pair of panels show the additional effects of one and two feedforward stages, respectively. The two feedforward stages include a common scaler, k, after which the feedforward signal is subtracted from its input. They produce a triphasic temporal response (orange panels) and a bandpass frequency response (green panels). The sixth pair of panels show the effects of another LP-stage with a corner frequency of 15 Hz and the final pair the effects of two final stages with corner frequencies of 30 Hz. The Equivalent Model on the left is mathematically equivalent to the cascade but has lateral connections that are more consistent with other psychophysical and physiological data.
Fig 9.
The three panels show the model’s best fitting parameter values for each of the twelve observers.
The error bars are ±1 standard error of the fitted parameter. Panel [A] shows the best-fitting corner frequencies (fc) in Hz common to the six variable-speed LP-filters as a function of mean level (log10 photopic trolands). [Corner frequency (Hz) is inversely proportional to the time constant τ: fc is equal to 1/(2πτ) where τ is in seconds.] The solid blue line through the data is the descriptive standard or mean function defined by Eq (3). The dashed horizontal red line marks the constant corner frequency of the final two fixed-speed stages (30.9 Hz). The red and green crosses are the corner frequencies of a 3-stage LP filter fitted to primate L- and M-cone responses, respectively, measured by Baudin et al. [37] and shown in Fig 10. Panel [B] shows the logarithmic of the best-fitting overall gain, log10g, but with the data for each observer vertically shifted to align with the descriptive standard function shown by the solid blue line and defined by Eq (4). Panel [C] shows the best-fitting scaling factor, k, common to the two inhibitory feedforward stages and fixed across mean luminance levels. The horizontal solid blue line shows the mean value of k (0.80). Only the parameters for levels thought to be cone-mediated are shown.
Fig 10.
The panels in the left and right columns column show, respectively, the mean primate L-cone (red continuous lines) and M-cone (green continuous lines) responses measured by Baudin et al. [37] at mean levels of 1000, 5000, 10000 and 50000 photons absorbed per second (R*/s).
The dashed black lines show the best-fitting 3-stage LP filter responses with common corner frequencies, which vary with light level. For further details see text.
Fig 11.
The panels show the standard model predictions.
Panel [A] shows the predicted TCSFs as amplitude sensitivities at a range of light levels (0.5 to 5.5 log10 trolands in 0.5 log10 steps). The TCSFs end at the assumed CFF for each level. Panel [B] shows the predicted CFFs extrapolated from the individual TCSF fits (as coloured symbols) and the predictions of the standard model shown as the continuous blue line, the white circles are in 0.5 log10 unit intervals and correspond to the line endings in Panel [A]. The dashed white line is the best fitting Ferry-Porter slope to the standard model. Panel [C] shows predicted threshold-versus-intensity (TVI) curves for brief flashes. The red line is Stiles’ template for TVI curves. The colored symbols for individual observers have been vertically shifted to align with Stiles’ template removing individual differences in overall gain. Panel [D] shows the predicted flash thresholds as a function of flash duration (both on log scale) for a range of light levels from 0.5 to 5.5 log10 trolands in 0.5 log10 steps. We have added dashed straight lines to indicate complete temporal summation at short durations (with slopes of -1) and the long duration asymptote (with slopes of 0). The duration at which these lines intersect is the “critical duration” indicated by the yellow circles.
Fig 12.
The solid cream-colored lines show the logarithmic relative amplitude response of one LP-stage plotted as a function of frequency on a linear scale in Panel [A] and on a logarithmic scale in Panel [B].
The maximum response has been normalized to 1. The corner frequency, fc, is indicated by the vertical black lines, and frequency is marked off in multiples of fc. The red dashed lines show the asymptotic frequency response, which in panel [B] is a straight line with a slope of -1 consistent with there being just one stage. The red region highlights the range above 3.74 fc where the filter response is within 0.015 log10 unit of the asymptotic response. The black-dashed lines, indicating exponential loss of sensitivity with increasing frequency and which describe the measurements shown in Figs 2–6, are the best exponential fit to the single LP-filter (cream lines) between 0.33fc and 2.0fc. The green region highlights the range from 0.43 to 1.92 fc within which the filter is within ±0.015 log10 unit of the exponential response (which is a straight line in Panel [A]).
Fig 13.
Best-fitting slopes (Hz per log10 unit sensitivity) for the linear high-frequency sensitivity losses from table A as a function of the corresponding best-fitting corner frequencies (Hz) from table B for the amplitude-sensitivity data shown in Figs 2–6.
(Note that the slope is plotted to become more negative upwards.) The solid blue line is the linear regression line, which has a slope of -1.03±0.07, an intercept of -4.28±0.97 Hz per log10 unit, and an adjusted R2 of 0.81. The dashed red lines are the 95% confidence intervals for the regression. Only the parameters for levels thought to be cone-mediated are shown.