Vergence — where it appears
Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.
The depth a pair calls zero
Two eyes verged on a point agree — the same coordinate in both pictures — not on a plane at the fixation distance but on a circle through both eyes and that point. Found by bisection along 121 azimuths and fitted rather than assumed, it is a circle to 0.0000 cm; at 26° off centre it lies 23 cm nearer than a flat wall does.
Both coordinates agree on a circle and a line
Two eyes fixating a point straight ahead see their horizontal image coordinates agree on a whole vertical cylinder over the Vieth–Müller circle, the same radius at every height to the last bit. Their vertical coordinates agree on almost none of it — 7.35 px apart at 26° aside and 30 cm up, 29.26 px when the fixation is brought to 60 cm. The points where both agree are the circle and one vertical line, and the line is the axis of the motion that carries one eye onto the other.
Raise the gaze, and the line is gone
Turn two eyes 20° aside in the plane they share and the horopter keeps its vertical line — but the line stays in the median plane, 1.277 m ahead, not at the point being looked at. Raise the gaze as well and the rule by which each eye rolls decides the rest: Helmholtz's rule keeps a line; Listing's law and Fick's rule make the eyes' relative motion slide 3.93 mm and 7.09 mm along its axis, no point stays put, and the horopter becomes one curve.
Vergence moves the shells and does not respace them
Turn two eyes inward and the depths a whole-pixel reading can report stop being planes and become a family of near-circles through both eyes — the twenty-pixel shell standing at 0.74 m forty degrees aside where a parallel pair puts it at 3.82. The spacing between consecutive shells is the same to 0.07 per cent across the whole field, so vergence relabels the rays and does not sharpen them, and the resolution argument for turning the eyes in does not exist.
A stereo picture is drawn for a level head
Every stereo pair is drawn for two eyes level with each other — a point's two images share a row and differ only across it. Tilt the head 10° in front of a television and that difference turns partly vertical, 14.46 arcminutes for anything drawn at infinity, and the two sightlines to a point stop meeting. At a desk monitor the same fifteen-arcminute limit arrives at 2.58°.
Named alongside it
The objects these essays reach for when they reach for this one.
Binocular disparityDisparityHoropterStereo pairBaselineViewing positionTriangulationConicDegeneracyDemonstrationDepth from disparityDepth uncertainty