We explored the effects of luminance adaptation and S-cone adaptation on within-subject and between-subject variability of S-cone increment thresholds. Within-subject variability was evaluated in terms of both within-session variability (slope of the psychometric function) and test–retest variability (variation in thresholds between sessions). A small set of adaptation conditions was sufficient to show that within-subject (within-session) and between-subject (interobserver) variability were lower on more neutral backgrounds, and test–retest variability was lower for higher levels of S-cone adaptation. Both of these factors are relevant for SWAP, in which the high polarization associated with the adapting background is expected to increase within-session variability, and the low level of S-cone adaptation is expected to increase test–retest variability. In patients with glaucoma, there may be additional effects of rapid changes in adaptation condition on S-cone-mediated detection.
34
This study was not primarily designed to investigate the effects of aging. Nevertheless, a fairly wide range of ages was present among the observers. Log threshold was found to be associated with age in conditions A, E, and F and to some extent in condition D, with the average amount of threshold increase ranging from 0.116 to 0.210 dB/year
(Table 2) . This confirms published findings by Eisner et al.
35 for foveal conditions quite similar to our condition D (S-cone increments on a 580-nm, 3.0-log Td background), by Johnson et al.
36 for peripheral (central 30°) S-cone increments on low and high intensity broad-band yellow backgrounds, and by Remky et al.
37 for perifoveal (central 10°) S-cone increments on a 594-nm, 3.7-log Td background. We must conclude therefore that part of the interobserver variability in the present study is probably explained by age. In addition to the observed increase of log S-cone threshold with age, Johnson et al.
36 also reported an increase of interobserver variability in log S-cone threshold data for subjects aged more than 60 years. They attribute this to an increased interobserver variability in lens density.
31 We will point out in the discussion to follow, as has been argued before (e.g., Refs.
14 15 20 ), that the magnitude of the effects of interobserver variability in lens density, pupil diameter, and the sensitivity of the cone mechanisms on perimetric thresholds is strongly dependent on the adaptation state of the visual system.
Published data on point-wise normal perimetric variability under conventional, achromatic, adaptation conditions vary among studies, and reported data are on the order of 1 dB for within-session variability,
11 38 on the order of 2 dB for test–retest variability,
11 39 40 and approximately 2 to 5 dB for interobserver variability.
14 Variation in the results from different studies is presumably due in part to differences in methods of analysis. More pertinent to our findings, however, is the comparison of normal threshold variability between conventional perimetry and SWAP within single studies, which have shown a 1.6-fold lower within-session variability,
11 a 2.1-fold lower test–retest variability,
11 and a 1.9-fold lower interobserver variability
14 for conventional perimetry. These values correspond well with the current findings. The size of the effects observed (i.e., the change in variability across conditions) corresponded to a factor of 1.5 for within-session variability (from 4.0 to 5.8 dB, after converting the parameter β to the SD [in decibels] of a cumulative Gaussian function
41 ;
Fig. 3 , inset). Test–retest variability varied 2.6-fold (from 0.41–1.06 dB;
Fig. 4 ), and interobserver variability varied 1.8-fold (from 2.14 to 3.86 dB;
Fig. 5 ) across conditions.
Typically, psychophysical techniques show less variability when increment thresholds are measured (such as in conventional achromatic perimetry) than when absolute thresholds are measured (such as in dark-adapted perimetry
42 43 or in measurements of dark adaptation). Part of the explanation is that, if the visual system operates at an adaptation level at which Weber’s law holds, increment threshold is proportional to the intensity of the background. As a result, thresholds are only minimally affected by fluctuations in the observer’s pupil size or cone sensitivity or by variations in lens density across observers. Absolute thresholds, in contrast, are directly affected by all three factors.
The mean threshold data show a pattern similar to that found by Yeh et al.
24 When plotted as log S-cone increments as a function of log S-cone adaptation (as in
Fig. 2B ), thresholds obtained at a fixed luminance level follow Weber’s law for relatively high levels of S-cone adaptation (where the data points fall on a line of slope = 1), but not for lower S-cone adaptation levels (where the data level off to fall on a horizontal line). The curves in the
Figure 2B are S-cone tvi functions that show the transition from constant threshold behavior at lower S-cone adaptation levels to Weber-like behavior for higher S-cone adaptation levels. For different luminance levels, these S-cone tvi functions are shifted along a 45° angle, which Yeh et al. interpreted in terms of second-site adaptation.
The Yeh et al.
24 model was a modification of the chromatic discrimination model of Boynton and Kambe,
26 which included gain control mechanisms that allowed fitting color discrimination data from a wider range of retinal illuminance. The Boynton and Kambe model, in turn, built on a long tradition of describing color discrimination thresholds in terms of opponent processing,
21 22 44 45 that has been successful in capturing many aspects of classic color discrimination data. Our data are consistent with the data and the model of Yeh et al.,
24 and extend them to higher mean retinal illuminances.
SWAP test conditions are close to our condition D (assuming a pupil diameter between 3 and 5 mm;
Table 1 ,
Fig. 1 ) and must therefore be on the horizontal portion of an S-cone tvi function
(Fig. 2B) . For SWAP, this implies that the adaptation condition is such that the S-cones are near absolute threshold, and that Weber’s law does not hold for S-cone increment thresholds. This probably increases variability above the level that might be found in the region where Weber’s law holds.
The primary purpose of this study was to gain insight into the underlying causes of the relatively high variability in SWAP. The results indicate that lower S-cone threshold variability can be achieved in conditions with higher levels of S-cone adaptation. It is often implicitly assumed that minimizing the variability of a clinical measure is a desirable goal. Indeed, we believe that this is justified for many clinical uses of perimetry, such as early detection or longitudinal measurement of the progression of visual field defects. However, by using adaptation conditions that are in the Weber region, the test becomes less sensitive to any disease action that has equal effects on the stimulus and the adapting field. Only by testing near absolute threshold can such an effect of disease action be observed. On the one hand, for such tests that operate outside the Weber region, it is crucial to control properly for preretinal light absorption and pupil diameter. On the other hand, increasing S-cone adaptation to ensure Weber-like behavior results in a smaller amount of isolation of S-cone mechanisms from L- and M-cone mechanisms. In fact, requirements of isolation and of variability seem to counteract each other, and the choice of S-cone adaptation level should therefore reflect a tradeoff between the two. Currently, SWAP test conditions have been optimized to yield good isolation, thereby producing relatively high variability. This should be kept in mind and, wherever possible, compensated for by increasing the number of stimulus presentations or visual field measurements.
In conclusion, we showed systematic effects of S-cone adaptation and second-site polarization on different types of variability in S-cone increment thresholds. Further research is needed to explore the magnitude of these effects systematically and to extend these findings to perifoveal test conditions relevant for perimetry.