Supplementary Material
Evidence against the facilitation of the vergence command
during saccade-vergence interactions
Tal Hendel and Moshe Gur
Faculty of Biomedical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Supplementary Figs. 1, 2
Supplementary Methods
Sum of eyes’ intra-saccadic vergence components (deg)
Target disparity (deg)
Supplementary Fig. 1 The figure is analogous to Figs. 3 and 4 in the text, but shows the data of two
more subjects (S7 and S8). The upper (lower) two panels are for convergent (divergent) movements.
For each subject the mean number of movements made to each target in each hemifield (± its
standard deviation) is as follows. Convergence: S7: left hemifield: 8.1±1.4, right hemifield: 8.6±1.1;
S8: 8.0±1.3, 8.1±1.3. Divergence: S7: 8.0±1.9, 7.5±1.6; S8: 9.1±1.1, 8.5±1.7.
Supplementary Fig 2 (a) A schematic diagram (top view) of the positioning of the camera relative
to the eye in our experiments. θ is the eye's rotation angle with respect to the fixation point, x is the
projection distance along the CCD plane of the pupil's center of mass, d is the distance of the
camera's nodal point from the eye, s is the lateral shift of the camera's nodal point (taken with respect
to the eye looking straight ahead), f is the camera's focal length, α is the rotation angle of the camera,
and R is the radius of the eye. (b) Taking realistic values for the parameters listed in (a) and for the
diameter of the pupil, and then using the expression given in the Supplementary Methods, we plotted
the theoretically calculated projected eye position vs. the real eye position. As can be seen, for the
range of eye positions used in our experiments (≤20° measured with respect to straight ahead), the
relationship between the two is linear (R2 = 0.999). (c) With the camera in a typical position, we took
a photograph of a cylindrical grid where the angular distance between the grid lines was known. The
circles show the measured projected positions of the grid lines vs. their known horizontal angular
positions. As the regression line demonstrates, the relationship between the two is indeed linear (R2
= 1.000).
Supplementary Methods
Although the linearity (and reliability) of video-oculography has been thoroughly demonstrated in
the past (Van der Geest and Frens 2002), we wanted to ensure that this was also the case in the
specific camera configuration used in our experiments. Supplementary Fig. 2a gives a schematic
diagram of the positioning of the camera relative to the eye in our experimental setup. Assuming that
the eye performs pure rotations (i.e., translation is negligible), it is easy to show using projective
geometry that an eye rotation of θ radians is projected at a distance of x cm along the CCD plane,
given by the following expression:
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where d is the distance of the camera's nodal point from the eye, s is the lateral shift of the camera's
nodal point with respect to the eye, f is the camera's focal length, α is the rotation angle of the
camera, and R is the radius of the eye. It is the distance x that is actually measured (note that
although in the expression above x is given in cm, it is extracted in pixels from the recorded movies).
By taking realistic values for these parameters (and for the diameter of the pupil) and plugging them
into the expression above, the relationship between the eye's rotation angle θ and the projection
distance x (i.e., the estimated position of the pupil's center of mass) is found to be virtually linear for
the range of angles used in our experiments (Supplementary Fig. 2b). We confirmed this theoretical
analysis by taking a photograph of a cylindrical grid with known angular distances between its lines
and measuring the distances between the lines in the projected grid. As can be seen in
Supplementary Fig. 2c, the relationship was found to be linear.
To ascertain that horizontal movements in the recorded movies corresponded with true horizontal
movements of the eye, a still photo of a horizontal grid was taken by each camera at the end of each
subject's experimental session. The torsion angle of the camera was extracted from this photo using an
image processing algorithm. The analysis was then resumed with the recorded movies counter-rotated by
the extracted torsion angle. The outcome of this procedure was further verified by checking that the
magnitude of any remaining vertical eye movement was negligible.
References
Van der Geest JN, Frens MA (2002) Recording eye movements with video-oculography and scleral
search coils: a direct comparison of two methods. J Neurosci Meth 114:185-195