The mean resting position of vergence (referred to as dark vergence when measured in a dark visual field to exclude any fixation stimulus) is about 1 m, with an inter-individual range of 50 cm to infinity. For fixation targets closer than dark vergence the static vergence response shows a negative error (defined as response minus stimulus), i.e. an under-convergence, also referred to as exo-fixation disparity. Conversely, for targets more distant than dark vergence, an over-convergence or eso-fixation disparity occurs. These observations were made with peripheral fusion stimuli that lead to large fixation disparities of up to 10 deg (Francis and Owens, 1983, Vision Res., 23: 13-19).

The aim of the present experiment was to investigate the role of dark vergence in the presence of strong fusion stimuli (a string of text characters) in foveal vision similar to those that are usually present in normal vision and clinical optometric tests. The resulting fixation disparities amount to only a few minutes of arc. Fixation disparity was measured psychophysically (with dichoptically presented vernier lines) at viewing distances of 460, 100, 60, 40, and 30 cm in 40 young adult subjects with normal binocular vision. The resulting distance-dependent fixation disparity curves were compared with dark vergence, which was measured with flashed vernier targets in a dark surround without any fixation target.

We found a significant linear effect of viewing distance (expressed in vergence angle): mean fixation disparity was 1.9 minarc (eso) at 460 cm and - 3.2 minarc (exo) at 30 cm. When the vergence response was expressed as gain, i.e. as percentage of the stimulus distance (relative to dark vergence) no significant effect of distance was observed (for stimuli closer than dark vergence). Thus, the linear slope of the distance-dependent fixation disparity curve reflects a convergence gain of less than 100%, which does not vary with viewing distance. The individual neutral points between eso- and exo-fixation disparity were significantly correlated with the individual dark vergence (r = 0.7). Thus, the fixation disparity of a subject tends to be zero close to the individual dark vergence.

These results suggest that two factors may contribute to an exo-fixation disparity at short viewing distances: the first factor is the gain of the convergence mechanism: the lower the gain, the steeper the fixation disparity curve. The second factor is dark vergence: the more distant the dark vergence, the larger the exo-fixation disparity. Slope and dark vergence were not correlated with each other. A multiple regression analysis showed that the individual fixation disparity at 40 cm can be predicted (r = 0.6) from the individual measures of slope, dark vergence and vernier bias; the latter is the offset required to align the vernier lines without dichoptical separation (Jaschinski et al., 1998, Vision Res., 39: 669-677).