The kinematics of far-near re-fixation saccades

On the role of ocular torsion in binocular visual matching

When an observer scans the visual surround, the images cast on the two retinae are slightly different due to the different viewpoints of the two eyes. Objects in the horizontal plane of regard can be seen single by aligning the lines of sight without changing the torsional stance of the eyes. Due to the peculiar ocular kinematics this is not possible for objects above or below the horizontal plane of regard. We provide evidence that binocular fusion can be achieved independently of viewing direction by adjusting the mutual torsional orientation of the eyes in the frontal plane. We characterize the fusion positions of the eyes across the oculomotor range by deriving simple trigonometric equations for the required torsion as a function of gaze direction and compute the iso-torsion contours yielding binocular fusion. Finally, we provide experimental evidence that eye positions in far-to-near re-fixation saccades indeed converge towards the predicted positions by adjusting the torsion of the eyes. This is the first report that describes the three-dimensional orientation of the eyes at binocular fusion positions based on the three-dimensional ocular kinematics. It closes a gap between the sensory and the motor side of binocular vision and stereoscopy.

Three-dimensional ocular kinematics underlying binocular single vision

We have analyzed the binocular coordination of the eyes during far-to-near refixation saccades based on the evaluation of distance ratios and angular directions of the projected target images relative to the eyes' rotation centers. By defining the geometric point of binocular single vision, called Helmholtz point, we found that disparities during fixations of targets at near distances were limited in the subject's three-dimensional visual field to the vertical and forward directions. These disparities collapsed to simple vertical disparities in the projective binocular image plane. Subjects were able to perfectly fuse the vertically disparate target images with respect to the projected Helmholtz point of single binocular vision, independent of the particular location relative to the horizontal plane of regard. Target image fusion was achieved by binocular torsion combined with corrective modulations of the differential half-vergence angles of the eyes in the horizontal plane. Our findings support the notion that oculomotor control combines vergence in the horizontal plane of regard with active torsion in the frontal plane to achieve fusion of the dichoptic binocular target images.