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Concept
Stereoscopic acuity
Résumé
Stereoscopic acuity, also stereoacuity, is the smallest detectable depth difference that can be seen in binocular vision.
Stereoacuity is most simply explained by considering one of its earliest test, a two-peg device, named Howard-Dolman test after its inventors: The observer is shown a black peg at a distance of 6m (=20 feet). A second peg, below it, can be moved back and forth until it is just detectably nearer than the fixed one. Stereoacuity is defined as the minimum angle detectable, calculated as the difference between the angles subtended by both positions, A and B. Stereoacuity is possible due to binocular disparity, i.e., the difference in their binocular parallax.
Taking into account that a small angle expressed in radians can be approximated by its tangent, the formula to calculate stereoacuity dγ is this:
where a is the interocular separation of the observer, z the distance of the fixed peg from the eye and dz the position difference. To transfer dγ into the usual unit of minutes of arc, a multiplicative constant c is inserted whose value is 3437.75 (1 radian in arcminutes). In the calculation a, dz and z must be in the same units, say, feet, inches, cm or meters. Note: some authors have added another approximation to this formula, considering dz neglectable compared with z, i.e. dividing by instead of by (z-dz). This induces apreciable errors when calculating coarse stereoacuity at far distance.
For the average interocular distance of 6.5 cm, a target distance of 6m and a typical stereoacuity of 0.5 minute of arc, the just detectable depth interval is 8 cm. As targets come closer, this interval gets smaller by the inverse square of the distance, so that an equivalent detectable depth interval at 1⁄4 meter is 0.01 cm or the depth of impression of the head on a coin. These very small values of normal stereoacuity, expressed in differences of either object distances, or angle of disparity, makes it a hyperacuity.
Source officielle
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