The experiments were designed to determine the relative contribution of visual angle, distance and gain in the visual-manual control of isometric force. The findings are clear in showing that visual angle organizes the amount and structure of the variability of isometric force. Visual angle is a variable that is geometrically derived from the combination of the gain (force/pixel ratio) of the visual display and the distance that the performer’s eye is from the visual information on the computer screen (see ). Visual angle has been shown to be a powerful mediator of the perception of object properties and distances (Levin and Haber 1993
; Gogel and Eby 1997
), and manipulation of visual angle alters neural firing properties in visual cortex (Rosenbluth and Allman 2002
). Gibbs (1962)
hypothesized that visual angle may mediate visual-manual control but emphasis has been given to the role of gain in visual displays of tracking behavior (cf. Jagacinski and Flach 2003
; Wickens 1984
The findings of Experiment 1 showed that increments of gain (with distance held constant) reduced the amount of isometric force variability (Stephens and Taylor 1974
; Newell and McDonald 1994
; Vaillancourt et al. 2002
). Experiment 2 showed that increments of visual distance (with gain held constant) increased the amount of variability of force output, suggesting that visual angle may play a critical role in isometric manual control. The independent manipulation of visual distance and gain in Experiment 3 a3orded a stronger test of the relative contribution of visual angle, visual distance and visual gain to the force output. This experiment included different combinations of visual distance and gain that produced the same visual angle in force control. The findings revealed that isometric force variability is mediated over a wide parameter range largely by the visual angle independent of the respective visual distance or the gain.
This interpretation of the relative importance of visual angle to gain and distance was confirmed by the results of the multiple regression analysis on the data of all three experiments. This outcome is consistent with the expectations that arise from a consideration of the geometry of the visual information of the force output to the eye of the performer (see ). Nevertheless, future experiments could examine more precisely the possible asymmetry of the contribution of gain and distance to visual angle effects in force control.
The pattern of findings obtained on the amount of variability as a function of visual angle, distance and gain were complemented by those on the structure of the force variability. That is, increments in visual angle led to higher levels of irregularity and lower levels in the amount of force variability. Here we used ApEn (Pincus 1991
) as a robust indicator of the irregularity of the force output. This inverse relation between the amount and structure of variability is consistent with findings on force variability from several previous experiments on isometric force control (Newell and Slifkin 1998
; Vaillancourt and Newell 2003
These findings regarding distance, gain, and visual angle raise the question as to why visual angle was a better predictor of performance variability than gain or distance. A potential answer to this question may be found in a consideration of the specific aspect of each variable. For instance, there is a difference in the dimensionality between distance and visual angle. Distance is a perceptual variable in one dimension, whereas in contrast, visual angle takes into account the distance from the video display and the height of the force fluctuations, thereby providing a perceptual variable combining two dimensions. Gain on the other hand incorporates one dimension (height on screen) in the perceptual domain and maps this to the motor coordinates (Newtons). Thus, visual angle may be a more powerful predictor than distance and gain in visual-motor control because of the extra dimension included in the variable (Levin and Haber 1993
Previous studies have revealed a quazi U- or J-shaped function for the amount of force variability as a function of visual gain in both isometric force (Newell and McDonald 1994
) and tracking (Gibbs 1962
; Hess 1973
) tasks. Namely, increments of visual information gain up to some level facilitate performance beyond which there is a performance decrement. The current study did not find an increase in force variability when visual angle was increased past a critical value, although a broad range of visual angles was examined spanning from 0.05° to 6°. However, we would anticipate that further increases in the visual angle could potentially cause force variability to increase. Such a finding would be consistent with a U or J shaped functions shown in tracking tasks when display gain is manipulated (Gibbs 1962
; Hess 1973
), rather than the nonlinear function observed here ().
It has been hypothesized that the cross over of effort and instability of the output determines the optimal level of gain in tracking tasks (Wickens 1984
) and the relevance of these constructs to gain and visual angle effects in isometric force control needs to be examined. High gain or visual angle conditions can lead to over corrections, oscillations and instability as realized in the enhanced amount and structure of the variability. This is because in a high visual angle condition a small change of output on the screen can lead to a larger than required modulation of the isometric output, thus increasing rather than decreasing variability. This perspective is consistent with the idea that there is some minimal variation in motor output that cannot be reduced due to the neuromuscular and mechanical constraints as reflected in tremor (Elble and Koller 1990
; Vaillancourt and Newell 2000
). Thus, behaviorally in tasks such as isometric control there is an error deadzone in which error correction is not invoked until a critical value is reached resulting in a spatial range where errors in performance cannot be reduced any further (Wolpert et al. 1992
The change in force variability as a function of visual angle occurred predominantly in the range of less than 1°. In visual angle conditions larger than 1° force variability changed at a much slower rate and tended to plateau (). The same pattern of findings was observed for ApEn. The approximately 1° error deadzone is larger than that traditionally attributed to an oculo-motor deadzone (Wyman and Steinman 1973
) and thus the effects here are much more readily interpreted in terms of sensori-motor processes (Wolpert et al. 1992
These spatially mediated findings of visual angle parallel previous findings in the temporal domain. For instance, when visual feedback is presented intermittently from 0.2 to 25 Hz during an isometric force task, force variability declines hyperbolically toward an asymptote (Slifkin et al. 2000
). Most of the changes in force variability occur from 0 to 6.4 Hz, and the changes in force variability after 6.4 Hz are minimal. Thus, it is evident that both spatial and temporal visual feedback modulates force variability, and that after a critical value force variability changes at a much slower rate in both dimensions. An fMRI study has shown that visuomotor related signals occur in the parietal and premotor cortex at both infrequent (0.4 Hz) and frequent (25 Hz) visual feedback, but only frequent visual feedback recruited the lateral cerebellum to process visuomotor signals (Vaillancourt et al. 2006
We speculate that a similar mechanism could be operating in the cerebellum for the spatial domain, in that low visual angles may not elicit visuomotor activation in the lateral cerebellum thereby limiting the participant’s ability to reduce force variability. In contrast, with high visual angles we hypothesize that the cerebellum processes additional visuomotor signals thereby allowing the participant to reduce force variability. One interesting possibility that needs to be explored further is that a common mechanism for both spatial and temporal properties of visual feedback could be operating at the level of the cerebellum to modulate force variability. The alternative possibility is that the different regions of the cerebellum process visuomotor signals related to spatial and temporal feedback.
Finally, it should be noted that while the findings show that visual angle is the organizing visual variable in regulating force output this does not in practice rule out the important experimental role of visual distance or gain as independent variables in driving the variability of isometric force output. In most manual control experiments visual gain is varied with the viewing distance held constant, and moreover the distance of the eye of the observer to the computer screen is usually not reported. These manipulations of gain and distance alter the visual angle and have a direct impact on the measured force variability. In addition, we also note that while visual angle was isolated as an important control variable in this isometric task, this finding may not apply in other contexts such as movement tasks where other informational variables are more relevant. In conclusion, the findings from our experiments show that the standard visual gain effect in visual-motor force control is more generally and fundamentally a visual angle effect (Gibbs 1962