Visual Plane
every picture states the point it is correct from
Concept

Horopter — where it appears

The set of points two eyes see at the same place in both pictures, for one fixation. In the plane of the eyes it is the circle through both eyes and the fixated point; in space it is that circle and one line, or a single curve when the eyes' rolls differ, and disparity is measured from it.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

in units of the 1.20 m fixation distance0.0000 cm over 121 azimuths

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.

depth · Horopter fixatedthe lineHelmholtz · straight aheadpitch 0: a circle and a line

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.

depth · Horopter fixatedListing's law · 20° right and 20° uppitch 3.93 mm: one curve

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.

depth · Horopter where the eyes are aimedin plan, framed to the shells drawnzero at 0.92 m, 40° aside

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.

depth · Disparity

Named alongside it

The objects these essays reach for when they reach for this one.

Binocular disparityVergenceBaselineDisparityStereo pairViewing positionTriangulationConicDegeneracyDemonstrationDepth from disparityDepth uncertainty

All concepts