Psychophysically measuring the efficiency of rods

Abstract

Recent studies suggest that the efficiency of cones to detect photons can be evaluated by measuring the equivalent input noise (EIN; derived from contrast thresholds measured in the presence and absence of visual noise) under specific conditions in which the contrast threshold is limited by the variability in the number of photons detected by photoreceptors (i.e., photon noise). These conditions can be identified based on the known properties of photon noise: spatially and temporally white and inversely proportional to the luminance intensity. The present study aims to adapt this psychophysical paradigm to evaluate the efficiency of rods to detect photons. A motion direction discrimination task was used to evaluate the EIN over a wide range of luminance intensities for various spatial and temporal frequencies when the display was blue or red (to which rods have little sensitivity). The target was either a Gabor patch presented at 20 degrees of eccentricity (first experiment) or a rotating sine-wave annulus with a radius of 10 degrees of eccentricity (second experiment). In both experiments, the EIN was found to be inversely proportional to luminance intensity over a limited range of luminance intensities for both display colors. At these luminance intensities, the EIN was roughly independent of the spatial and temporal frequencies, matching the properties of photon noise. Furthermore, under these conditions, contrast thresholds were lower (i.e., better) when the display was blue rather than red, which suggests that vision was mediated by rods when the display was blue. We conclude that the efficiency of rods to detect photons can be evaluated by measuring contrast thresholds in the presence and absence of visual noise over a limited range of luminance intensities with a blue display.

Figure 1.

Stimuli examples presented on the blue display without external noise (top) and the red display with external noise (bottom) during the first experiment. The target was a sine-wave grating, and the participant was asked to gaze at the white fixation point presented at 20° to the left or right of the target, depending on whether the participant viewed the target with his left or right eye, respectively.

Figure 2.

Normalized spectral energy distribution of the blue and red color gun emitted by the display.

Figure 3.

Contrast thresholds in the absence of noise as a function of photopic luminance intensity for each participant (different graphs) for different temporal frequencies (different symbols) when the display was red or blue (red and blue lines, respectively).

Figure 4.

Geometric mean contrast thresholds in noise measured when the display was red or blue (respective lines) as a function of temporal frequency. The error bars represent the standard error of the mean computed in log units.

Figure 5.

EIN (derived from the data presented in Figures 3 and 4) as a function of photopic luminance intensity for each participant (different graphs). The thick lines illustrate the de Vries–Rose law (i.e., log–log slopes of –1), representing the impact of photon noise (see Equation 4) when the display was red or blue (respective colors) for each participant.

Figure 6.

Geometric mean photon noise measures when the display was red or blue (respective lines) as a function of temporal frequency. The error bars represent the standard error of the mean computed in log units.

Figure 7.

Stimuli examples presented on a red display without visual noise (left) and on a blue display with noise (right) during the second experiment. The black dot in the middle of the annulus was the fixation point, and the larger black annulus helped maintain central fixation when the central fixation point was not visible under scotopic conditions.

Figure 8.

Contrast thresholds in the absence of noise as a function of photopic luminance intensity for each participant (different graphs) for different combinations of spatial and temporal frequencies (different symbols) tested over red and blue displays (red and blue lines, respectively).

Figure 9.

Contrast thresholds in noise measured when the display was red or blue (respective lines) as a function of temporal frequency. The contrast thresholds in noise measured at 8 and 16 cpc are represent by the solid lines and dotted lines, respectively. The error bars represent the standard error of the mean computed in log units.

Figure 10.

EIN (derived from the data presented in Figures 8 and 9) as a function of photopic luminance intensity for each participant (different graphs). The de Vries–Rose law is represented by a slope of –1 over the red and blue data (red-fit slope and blue-fit slope, respectively) for each participant.

Figure 11.

Geometric mean of the photon noise evaluated when the display was red or blue for the two spatial frequencies as a function of temporal frequency. The error bars represent the standard error of the mean calculated in log units.

Figure 12.

Geometric mean of the EIN evaluated at the highest luminance intensity when the display was red or blue for the two spatial frequencies as a function of temporal frequency. The error bars represent the standard error of the mean calculated in log units.

Figure 13.

Contrast thresholds (geometric mean over five measurements) in the presence and absence of noise as a function of photopic luminance intensity for each participant (different graphs) tested over red and blue displays (red and blue lines, respectively). Note that participant P4 was not sensitive enough to perceive the stimulus at the maximum contrast at the lowest luminance intensity over the red display (both with and without noise), which is marked as 1.