We assessed the usefulness of stereopsis across the visual field by quantifying how retinal eccentricity and distance from the horopter affect humans' relative dependence on monocular and binocular cues about 3D orientation. The reliabilities of monocular and binocular cues both decline with eccentricity, but the reliability of binocular information decreases more rapidly. Binocular cue reliability also declines with increasing distance from the horopter, whereas the reliability of monocular cues is virtually unaffected. We measured how subjects integrated these cues to orient their hands when grasping oriented discs at different eccentricities and distances from the horopter. Subjects relied increasingly less on binocular disparity as targets' retinal eccentricity and distance from the horopter increased. The measured cue influences were consistent with what would be predicted from the relative cue reliabilities at the various target locations. Our results showed that relative reliability affects how cues influence motor control and that stereopsis is of limited use in the periphery and away from the horopter because monocular cues are more reliable in these regions.

*D*

_{ij}) on trial

*i*at eccentricity

*j*that the comparison stimulus was more slanted than the standard stimulus or vice versa. We characterized the discrimination process using a cumulative Gaussian function parameterized by the difference in slant (Δ

*S*

_{ij}) between the standard and comparison targets, the point of subjective equality between the standard and comparison (

*μ*

_{j}) at that eccentricity, and the 84% threshold (

*σ*

_{j}). The final term in the first likelihood function assumed that the comparison stimulus was chosen at random after an attentional lapse.

*μ*

_{j}and

*σ*

_{j}at each eccentricity and the two parameters related to attentional lapse for each viewing condition (a total of eight parameters per viewing condition) that maximized the likelihood of the data. We excluded three subjects from the results because their high attentional lapse rates (>20–30%) resulted in poor threshold estimates. The estimated attentional lapse rates for the seven included subjects were 1.3 ± 1.0% (mean ±

*SEM*) for the monocular conditions and 7.1 ± 3.3% for the binocular conditions.

*SEM*s of the individual data; this prevented individual thresholds with very high uncertainties from dominating the overall results. A repeated-measures ANOVA revealed a significant effect of eccentricity (

*F*(2,12) = 6.04,

*p*= .049). Standard

*t*-tests would have underestimated significance levels due to high standard deviations in the differences between conditions, so, to compare the effects of eccentricity on our weighted mean data, we used the weighted group means to estimate the differences between conditions and Z scores to compare whether these differences significantly differed from zero. For the monocular viewing condition, there was no significant difference between thresholds for targets at 0° and 7.5° of retinal eccentricity (Z = 0.58,

*p*= .56), which were both around 3°. These thresholds were significantly lower than the 6.5° mean monocular threshold measured at 15° of retinal eccentricity (0°/15°: Z = 5.04,

*p*< .001; 7.5°/15°: Z = 4.79,

*p*< .001). The binocular thresholds at 0° and 7.5° were close to 4° and were also not significantly different (Z = 1.12,

*p*= .26), but the 10.7° mean binocular threshold at 15° of retinal eccentricity was significantly higher than at the other two positions (0°/15°: Z = 2.84,

*p*< .01; 7.5°/15°: Z = 3.15,

*p*< .01). Particularly at fixation, these thresholds were much higher than what we predicted from the previously published data. One reason is that Fendick and Westheimer's (1983) subjects had extensive practice, and another is that stimulus properties such as spatial frequency affect the rate at which disparity thresholds increase with eccentricity (Siderov & Harwerth, 1995).

*μ*m layer of silver; Schlegel Electronic Materials, Inc., Rochester, NY) over the rubber thimbles, and wires sewn to the conductive fabric were connected to the Optotrak Data Acquisition Unit II, which recorded voltages across both the starting cube and metal disc at 120 Hz to identify when the thumb or index finger was in contact with either object.

*F*(2,14) = 14.06,

*p*< .01). On average, the corrected standard deviations for targets at both 0° and 7.5° of retinal eccentricity were just over 6°, and the mean standard deviation at 15° of eccentricity was 9.6°, which was significantly higher (0°/15°:

*t*(7) = 3.67,

*p*< .01; 7.5°/15°:

*t*(7) = 4.08,

*p*< .01) than at the other two positions according to paired one-tailed

*t*-tests with the significance level adjusted to .017 for multiple comparisons. The pattern of standard deviations across eccentricities was qualitatively similar to the pattern of uncertainties we measured in Experiment 1, but the standard deviations in the grasping task were slightly higher due to motor variability and measurement errors.

_{ grasp}was the grasp orientation when one of the fingers first contacted the target, and

*s*

_{ mono}and

*s*

_{ bin}were the slants suggested by the monocular and binocular cues.

*w*

_{ mono}and

*w*

_{ bin}were the relative weights (constrained to sum to 1) that quantified the contributions of the monocular and binocular cues to grasp orientation, and

*k*

_{1}and

*b*

_{1}were multiplicative and additive bias terms. Since some subjects showed small biases that grew over time, we included additive and multiplicative bias parameters (

*k*

_{2}and

*b*

_{2}) to account for effects that correlated with trial number (

*t*). The relative binocular cue weights are shown in Figure 10. As expected, the contribution of the binocular cue decreased with retinal eccentricity (

*F*(2,14) = 13.78,

*p*< .01). A one-tailed paired

*t*-test did not show a significant difference in relative binocular weights between targets at 0° and 7.5° of eccentricity (

*t*(7) = 1.83,

*p*= .055), but there was a strong trend in the expected direction. The binocular weight for stimuli presented at 15° in the periphery was significantly lower than the weights for targets at the other two positions (0°/15°:

*t*(7) = 4.77,

*p*< .01; 7.5°/15°:

*t*(7) = 3.82,

*p*< .01; Bonferroni-corrected significance level: .017).

*t*-tests (0°:

*t*(13) = 0.59,

*p*= .56; 7.5°:

*t*(13) = 0.36,

*p*= .73; 15°:

*t*(13) = 0.40,

*p*= .70). An ANOVA with eccentricity as a repeated measures factor and experiment (predicted versus actual) as a between-subjects factor showed the expected main effect of eccentricity (

*F*(2,26) = 21.29,

*p*< .001) but neither a significant effect of experiment (

*F*(1,13) = 0.25,

*p*= .63) nor a significant interaction between eccentricity and experiment (

*F*(2,26) = 0.09,

*p*= .89), indicating that subjects weighted the cues according to their relative uncertainties. While the predicted binocular cue weights appeared to be somewhat lower than the measured weights, the differences were small and consistent with what one would predict from confounding factors in the threshold measurements. For example, the conflicting monocular cues in the stimuli used to measure stereoscopic slant thresholds may have elevated the measured stereoscopic thresholds and thus led to underestimates of the predicted binocular cue weights.

*t*(7) = 1.36,

*p*= .22), a within-subjects repeated measures ANOVA showed a significant increase in this time with eccentricity (

*F*(2,14) = 8.14,

*p*< .01). It is possible that this reflected slower cue processing in the periphery, but, given that information was less reliable in the periphery, subjects may have used the additional milliseconds to reduce their uncertainty. Given the small size of the effect, it seems most likely that the difference in the reliability of information across the visual field was the primary factor driving the effect of retinal eccentricity on cue integration at the different target locations in this experiment.

*F*(2,16) = .28,

*p*= .67). This was generally reflected in the variability of each subject across different depths.

*F*(2,16) = 31.46,

*p*< .001). Post-hoc one-tailed paired

*t*-tests showed that the difference between relative binocular cue influences for targets on the horopter and at 0.5° of convergent disparity was marginally significant (

*t*(8) = 2.25,

*p*= .027) after adjusting the significance level to .017 to account for multiple comparisons, and the difference between 0.5° and 1° from the horopter was significant (

*t*(8) = 8.18,

*p*< .001). With the exception of Subject 8, binocular cue weights for targets 1° from the horopter were not significantly different from zero, indicating that subjects relied entirely on monocular information to estimate 3D orientation.