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Fixation disparity: binocular vergence accuracy for a visual display at different positions relative to the eyes.


Binocular vision requires that the vergence angle between the two visual axes be adjusted for proper fusion of the two retinal images so that the point of regard is projected onto the fovea of each eye (i.e., the center region of the retina with the best spatial resolution). The vergence angle depends on the actual viewing distance: When a person looks at infinity, his or her visual axes are parallel; the closer the target, the stronger the force that the extraocular muscles have to exert in order to turn the visual axes toward each other. In an open-loop condition (i.e., without a fixation stimulus), the eyes assume a vergence resting position, also referred to as tonic vergence or dark vergence (when measured in a dark visual field). The resting position varies among individuals with an average of about 3.6[degrees], corresponding to a distance of 1 m (Jaschinski-Kruza, 1991; Rosenfield, 1997; Tyrrell & Leibowitz, 1990).

A muscular system can be evaluated by measuring how accurately it is able to operate. In optimal binocular vision, a fixated target is imaged onto the center of the fovea in each eye so that the principal visual directions of both eyes intersect at the fixation point (Figure 1a). Slight deviations from this optimal state may occur in people with normal binocular vision (indicated by good stereoscopic acuity), depending on individual disposition or the current viewing conditions. These small errors in vergence typically amount to a few minutes of arc; they are smaller than the Panum area, the region of sensory fusion where vergence errors do not lead to double vision (Howard & Rogers, 1995). These fixation disparities are called exo or eso when the eyes converge slightly behind or in front of the fixation point, respectively, as illustrated in Figures 1b and 1c. People with more exo fixation disparity at 40 cm tend to experience asthenopic complaints and visual fatigue when doing visual near work (Evans, 1997 ; Pickwell, Kaye, & Jenkins, 1991; Scheiman & Wick, 1994; Sheedy & Saladin, 1983).

However, the traditional condition of measuring fixation disparity at the typical reading distance of 40 cm does not apply to computer workstations, where the viewing distance is typically longer and the vertical gaze direction is also different compared with that for books or papers on the desk. The following two parameters of screen position can have an effect on fixation disparity. First, when the viewing distance is shortened from 100 to 30 cm, fixation disparity changes into the exo direction; this was tested at horizontal gaze (Jaschinski, 1997, 200 la, 200 ib). An exo fixation disparity at a close target means that the vergence near response (relative to the more distant resting position) lags behind the near stimulus. Second, depending on screen height relative to eye level, the eyes and/or the head will incline to adjust the required vertical gaze inclination, defined in the present study as the angle between horizontal and the line from eye to screen.

When gaze direction is lowered from +150 above horizontal to -45[degrees] below, fixation disparity changes into the eso direction (Jaschinski, Koitcheva, & Heuer, 1998). This effect was found at a fixed viewing distance of 40 cm while either the head was inclined (with eye position unchanged relative to the head) or the eyes were inclined (keeping the head upright); the latter procedure induced larger and more reliable effects on fixation disparity. These eso changes in fixation disparity were correlated with corresponding near shifts in the resting position of vergence when the gaze is lowered (Heuer & Owens, 1989), presumably because these measures of vergence are correlated (Jaschinski-Kruza, 1994). Mon-Williams, Plooy, Burgess-Limerick, and Wann (1998) and Mon-Williams, Burgess-Limerick, Plooy, and Wann (1999) reported similar effects of eye inclination in measurements of heterophoria. This measure of vergence does not describe the mechanism of fusion; rather, it reflects resting vergence but includes t he influence of accommodation on vergence (Owens & Tyrrell, 1992; Jaschinski, 2001a).

In order to extend our previous fixation disparity studies (cited earlier), which used laboratory settings with headrests, dim room lighting, and polarizing filter foils on the black background screen surface, our aim in the present study was to investigate fixation disparity at a visual display in conditions that resemble viewing conditions in the office with respect to natural head and body posture and normal office environment. This experiment is a prerequisite in order to deduce ergonomics design principles for the workplace. Therefore we used viewing distances (100 to 40 cm) and vertical gaze inclinations (horizontal and -25[degrees] downward) that are typical for computer workstations (Jaschinski, Heuer, & Kylian, 1998, 1999). Our participants were free to assume a comfortable posture with natural combinations of eye and head inclinations. The reliability of results and individual differences were investigated by including a retest one week later.



The 25 participants (11 men, 14 women) had a mean age of 24 years (SD - [+ or -]5 years; range = 17-36 years) and normal or corrected-to-normal vision with a visual acuity of 1.0 or better (decimal units). Heterophoria was tested with the Pola-test method (Zeiss, Oberkochen, Germany; Lie & Opheim, 1990), which determines the power of prisms in front of the eyes in order to compensate a vergence error when peripheral fusion stimuli are presented. This heterophoria (mean [+ or -] SD), in prism diopter ([DELTA]), was 1.45[DELTA] [+ or -] 2.68[DELTA] at 5 m and 1.25[DELTA] [+ or -] 3.32[DELTA] at 40 cm; positive or negative values indicate an eso or exo condition, respectively.

Visual Tests

For measuring fixation disparity we determined the physical horizontal offset of dichoptic nonius lines when the participant perceived them as collinear (see Figure 2). Fixation disparity was calculated relative to physical coincidence of the nonius lines. In a control condition we presented both nonius lines to the right and to the left eye; the resulting measure (called nonius bias) does not describe vergence but, rather, the ability of the person to judge small amounts of nonius offset (Jaschinski, Brode, & Griefahn, 1999).

A single test run comprised a continuous series of 60 short-term presentations of the nonius lines (100 ms duration at 2 s intervals), with Trials 1 through 30 for the nonius bias and Trials 31 through 60 for fixation disparity. The fusion stimulus remained stationary on the screen. Liquid crystal (LC) shutter spectacles were operated in synchrony with the appropriate images on the cathode ray tube (CRT) screen. In order to determine the point of subjective coincidence, the amount of nonius offset was varied in small steps of 0.66 mm arc using adaptive psychometric procedures.

After each presentation, the participant indicated, by pressing a computer mouse key, whether the upper nonius line was perceived to the right or to the left of the lower nonius line. These responses were analyzed as follows: Whenever the response reversed within the series of trials, either from right to left or from left to right, the mean between the two corresponding amounts of nonius offset was taken as an estimate of the actual subjective coincidence. In cases of two reversals within three trials, only the first reversal was taken to have independent estimates. Because these estimates may not be normally distributed, median values were calculated to describe the nonius bias and fixation disparity of a run. For methodological details see Jaschinski (1998).

Dark characters were presented on a monochrome CRT screen of 30 cd/[m.sup.2] luminance with a bright background. The test area on the screen (7 x 13 cm) was surrounded by white cardboard illuminated by the 180 1x room lighting to 5 cd/[m.sup.2]. All luminances were measured through the activated shutter spectacles. The fusion stimulus, a string of letters (XOXOXOX), subtended 27.5 x 200 min arc and was visible to both eyes. Two nonius lines (each 27.5 mm arc high with a vertical separation of 35 mm arc) were presented above and below the central character, O. The stimulus dimensions were identical in terms of visual angle at all viewing distances; the stroke width was 5 mm arc. The nonius offset was produced by shifting the two nonius lines symmetrically in opposite directions so that they appeared centered about the fixation target.


Participants were seated at a computer workstation with separate desks for keyboard and screen. The height of the chair and of the keyboard desk were adjusted for each individual. After participants had assumed a comfortable sitting posture, the shutter spectacles, fixed at a freely adjustable swivel, were placed in front of the eyes and the screen was moved to the appropriate position relative to the eyes. Before each run the participant's head posture was measured by observing the head in side view through a protractor with a pendulum. The actual head inclination was defined as the angle between horizontal and the ear-eye line (from the external auditory meatus to the outer canthus, also called Reid's line).

Sessions and Conditions

A session included six runs: We used viewing distances of 40, 60, and 100 cm with a horizontal gaze direction and a declined gaze direction of -25[degrees] (i.e., the screen was located 18.6, 28.0, and 46.6 cm below eye level at these three viewing distances). All measures refer to the fixation target on the screen. In order to test for reliability, all measurements were repeated in a second session approximately seven days later.

Statistical Analyses

BMDP Statistical Software (Dixon, 1992) was used for analyses of variance (ANOVAs) with repeated measures (Programs 2V and 8V, with Greenhouse-Geisser adjusted error probabilities).


The gaze inclination from 0[degrees] to -25[degrees] was made partly by inclining the head and partly by inclining the eyes within the head. The head was significantly more declined at the lower screens, by 5.74[degrees] on average, F(1, 24) = 44.41, p < .00 1. Accordingly, 25.0[degrees] - 5.74[degrees] = 19.26[degrees] was the mean change in eye inclination between the two conditions of gaze inclination. These measures were independent of viewing distance.

Fixation disparity was significantly affected by viewing distance, F(2, 48) = 29.87, p < .001, and gaze inclination F(1, 24) 15.75, p < .001. The interaction was not significant, suggesting that the effects of viewing distance and gaze inclination were independent. The two sessions did not reveal significantly different results, F(1, 24) = 1.01, p = .325. Thus for illustration and further analysis, the data were averaged across the two sessions. Figure 3 illustrates the mean results; viewing distance is plotted linearly in the unit [m.sup.-1], which is proportional to the actual vergence angle in degree. Thus viewing distances of 40, 60, and 100 cm correspond to 2.5, 1.66, and 1.0 [m.sup.-1], respectively. In this way, fixation disparity typically has a linear slope.

Mean fixation disparity changed from +2.2 mm arc (eso) at 100 cm to -0.3 mm arc (exo) at 40 cm. Such lines are referred to as proximity-fixation-disparity curves. Lowering gaze direction by -25[degrees] induced a mean eso change in fixation disparity of 0.6 mm arc. The nonius bias, the control variable, was not affected by viewing distance, gaze inclination, or time. The mean nonius bias of 0.38 mm arc is included in Figure 3. A nonzero nonius bias means that physically collinear nonius lines (vertically separated by 35 mm arc in the present test) are not perceived in line.

Possible individual differences in fixation disparity effects were analyzed with a second ANOVA, with participants (subjects) as an explicit random factor (BMDP Program 8V). The Subjects x Viewing Distance interaction was significant, F(48, 48) = 3.59, p < .00 1, whereas the Subjects x Gaze Inclination interaction was not, F(24, 48) = 1.03, p = .449; thus the participants differed reliably in their change in fixation disparity as a function of viewing distance but not as a function of gaze inclination.

In order to evaluate the reliability of proximity-fixation-disparity curves on the individual level, for each participant we calculated the linear regression of fixation disparity as a function of proximity ([m.sup.-1]). These slopes were significantly correlated between Session 1 and Session 2 at horizontal and declined gaze, respectively (r = .57 and r = .59, p < .002; see Figure 4). The test-retest correlations of the individual differences between the fixation disparity at 0[degrees] and -25[degrees] gaze inclination, however, were not significant.


Our participants were able to assume a normal working posture, the room had a normal illumination level, and LC shutter spectacles were used to present nonius lines separately to the two eyes on a bright-background CRT screen. Further, viewing distances and screen heights were within the usual range of those at computer workstations. In these conditions, which resemble typical viewing conditions for work in the office, effects of viewing distance on fixation disparity were of more practical relevance than were effects of gaze inclination.

First, mean fixation disparity was 2.5 mm arc more exo at 40 cm than at 100 cm, but it was only 0.6 mm arc more eso at a declined gaze (-25[degrees]) relative to horizontal. Second, the subject factor in the ANOVA and the test-retest correlations suggest that participants had reliably different individual effects as a function of viewing distance but not as a function of gaze inclination. However, the small gaze inclination effects agree quantitatively with previous observations with much larger variation, from +15[degrees] to -45[degrees] in Jaschinski, Koitcheva, et al. (1998). The mean amount of 19.3[degrees] for eye inclination and 5.7[degrees] for head inclination in the present study would have produced corresponding eso shifts of about 0.7 mm arc and 0.1 mm arc, respectively, in Jaschinski, Koitcheva, et al. (1998), in which these two ways of inclining gaze were investigated separately.

It has been shown (Jaschinski, 2001a) that the resting state of vergence determines the viewing distance at which fixation disparity agrees with the nonius bias. This point was reached at 55 cm for horizontal gaze in the present mean data but at 140 cm (or 0.70[m.sup.-1]) in Jaschinski (2001a) with a sample of participants having a mean vergence resting position of 0.70[m.sup.-1]. That sample had a mean heterophoria of -0.05[DELTA] at 5 m and of -1.20[DELTA] at 40 cm, measured with the same test as described in the Method section. In the present study, the corresponding heterophoria measures were more positive (eso) - that is, closer (1.45[DELTA] at 5 m and 1.25[DELTA] at 40 cm). Taking into account the correlation between resting position and heterophoria (Owens & Tyrrell, 1992), we assume that the present sample had a closer resting vergence (which had not been measured); this may explain the rather close intercept of the fixation disparity curve with the nonius bias level.

The effect of viewing distance on fixation disparity has been confirmed to be a reliable individual parameter of the vergence system in young adults with normal binocular vision (Jaschinski, 1997). The slope of fixation disparity curves as a function of vergence stimulus (i.e., viewing distance in the present case) reflects the gain factor of the fusional vergence mechanism, as shown in vergence control studies (Hung, 1992; Jaschinski, 2001a, 2001b; Schor, 1983): A person with a low vergence gain has a steep fixation disparity curve (i.e., a more exo fixation disparity at near). The present study suggests that the slope, and thus vergence gain, appear to be independent of gaze inclination. Given that fixation disparity is correlated with the resting position of vergence (Jaschinski-Kruza, 1994), we conclude that changes in fixation disparity with gaze inclination are induced by inclination effects in the resting position. These observations correspond to findings of Heuer and Owens (1989); Jaschinski, Koitche va, et al. (1998); and Mon-Williams et al. (1998), and to a result of Mon-Williams et al. (1999). Heterophoria showed a near shift at lower eye inclination but was not significantly different at viewing distances of 33, 50, and 100 cm.

These optometric findings have the following implications for the ergonomics of computer workstations. Previous laboratory studies (Jaschinski, 1998) suggest that people with a steep slope of fixation disparity as a function of viewing distance (30-100 cm) -- that is, those who have a weak vergence system because of a smaller vergence gain -- tend to prefer viewing distances longer than about 50 cm in order to avoid visual fatigue induced by near screens. This aspect of fixation disparity may contribute to observations in field studies that not all young adults accept a screen around 50 cm but, rather, prefer longer viewing distances. Within the large interindividual range of 50 to 100 cm, participants adjusted the screen to an individual (closer or more distant) position (Jaschinski, Heuer, et al., 1998, 1999).

Thus measurement of the proximity-fixation-disparity curve may be an optometric tool to determine whether a weak vergence system may be the origin of a person's visual fatigue at near computer screens. Although such a diagnostic optometric procedure might be justified in single cases, when a person suffers from otherwise unexplained visual fatigue, it is certainly not necessary for each user. It has been shown (Jaschinski, Heuer, et al., 1999) that experimental participants are able to find out whether the proximity of the screen may cause visual fatigue when they apply the following ergonomics procedure: The person may work at the screen first at a long viewing distance and then at a short one (for about 30 mm each) and then may try to adjust the screen to a preferred viewing distance within the available range. After this procedure, the person will probably have experienced whether or not proximity is the origin of visual symptoms. Both this trial procedure and the method for measuring fixation disparity wi th consumer computer technology is described at

Participants at computer workstations prefer a slightly declined gaze angle in the range between horizontal and about -25[degrees] downward (with a mean of about -10[degrees] as summarized in Sommerich, Joines, and Psihogios (2001). Moreover, within this interindividual range, participants tend to prefer a certain individual screen height (Jaschinski, Heuer, et al., 1998, 1999). However, these findings may not be related to the vergence system, given that the present study found only small group mean effects that were not reliable on the individual level. Lowering the screen reduces the ocular surface area and, thus, the risk of dry eyes; however, it also increases musculoskeletal strain in the neck to maintain the head position. Further, the eyes assume a certain individual vertical declination at rest. Consequently, the most comfortable screen height may be a compromise among several factors (Abe et al., 1995; Burgess-Limerick, Mon-Williams, & Coppard, 2000; Menozzi, von Buol, Krueger, & Miege, 1994; Sommer ich, et al., 2001).




The authors thank C. R. Cavonius for his comments on the manuscript, Matthias Bonacker and Ewald Alshuth for technical support, and Frank Siewert for optometric testing of heterophoria.

Date received: July 17, 2001

Date accepted: January 21, 2002


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Stephanie Jainta received her master's degree in psychology in 2002 at the University of Munster, Germany, and is a scientific assistant at the Institut fur Arbeitsphysiologie, Dortmund, Germany.

Wolfgang Jaschinski received his Ph.D. in ergonomics in 1988 at Technical University of Darmstadt, Germany, and is head of the Individual Visual Performance research group at the Institut fur Arbeitsphysiologie, Dortmund, Germany.

Address correspondence to Wolfgang Jaschinski, Institut fur Arbeitsphysiologie, Ardeystrasse 67, D-44139, Dortmund, Germany;
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Author:Jainta, Stephanie; Jaschinski, Wolfgang
Publication:Human Factors
Geographic Code:4EUGE
Date:Sep 22, 2002
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