Stereoscopic acuity
Encyclopedia
Stereoscopic acuity, also stereoacuity, is the smallest detectable depth difference that can be seen in binocular vision.
, i.e., the difference in their binocular parallax
.
Conversion to the angle of disparity dγ is performed by inserting the position difference dz in the formula
dγ = c a dz/z2
where a is the interocular separation of the observer and z the distance of the fixed peg from the eye. To transfer dγ into the usual unit of minutes of arc, a multiplicative constant c is inserted whose value is 3437. In the calculation a, dz and z must be in the same units, say, feet, inches, cm or meters. 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 8cm. As targets come closer, this interval gets smaller by the inverse square of the distance, so that an equivalent detectable depth interval at ¼ meter is 0.01 cm or the depth of impression of the head on a coin. These vary small values of normal stereoacuity, expressed in differences of either object distances, or angle of disparity, makes it a hyperacuity.
in which separate panels are shown to each eye by superimposing them in a stereoscope using prisms or goggles with color or polarizing filters or alternating occlusion (for a review see http://rspb.royalsocietypublishing.org/content/early/2011/04/09/rspb.2010.2777.long). A good procedure is a chart, analogous to the familiar Snellen visual acuity chart, in which one letter in each row differs in depth (front or behind) sequentially increasing in difficulty. For children the fly test is ideal: the image of a fly is transilluminated by polarized light; wearing polarizing glasses the wing appears at a different depth and allows stereopsis to be demonstrated by trying to pull on it.
The distinction between screening for the presence of stereopsis and a measurement of stereoacuity is valuable. To ascertain that depth can be seen in a binocular views, a test must be easily administered and not subject to deception. The random-dot stereogram is used widely for this purpose and has the advantage that for the uninitiated the object shape is unknown. It is made of random small pattern elements; depth can be created only in multiples of elements and therefore may not reach the small threshold disparity which is the purpose of stereoacuity measurements.
A population study revealed a surprisingly high incidence of good stereoacuity: . Out of 188 biology students, 97.3% could perform at 2.3 minutes of arc or better.
Specification and Measurement
Stereoacuity is most simply explained by considering one of its earliest test: 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 this difference in the two positions, converted into an angle of binocular disparityBinocular disparity
Binocular disparity refers to the difference in image location of an object seen by the left and right eyes, resulting from the eyes' horizontal separation. The brain uses binocular disparity to extract depth information from the two-dimensional retinal images in stereopsis...
, i.e., the difference in their binocular parallax
Parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. The term is derived from the Greek παράλλαξις , meaning "alteration"...
.
Conversion to the angle of disparity dγ is performed by inserting the position difference dz in the formula
dγ = c a dz/z2
where a is the interocular separation of the observer and z the distance of the fixed peg from the eye. To transfer dγ into the usual unit of minutes of arc, a multiplicative constant c is inserted whose value is 3437. In the calculation a, dz and z must be in the same units, say, feet, inches, cm or meters. 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 8cm. As targets come closer, this interval gets smaller by the inverse square of the distance, so that an equivalent detectable depth interval at ¼ meter is 0.01 cm or the depth of impression of the head on a coin. These vary small values of normal stereoacuity, expressed in differences of either object distances, or angle of disparity, makes it a hyperacuity.
Tests of Stereoacuity
Since the two-peg device, named Howard-Dolman after its inventors , is cumbersome, stereoacuity is usually measured using a stereogramStereogram
A stereogram is pair of two-dimensional panels depicting the view of a scene or an object from the vantage points of the right and left eyes. Observing the panels superimposed in a stereoscope results in the experience of three-dimensionality by virtue of the fact that object depth is encoded as...
in which separate panels are shown to each eye by superimposing them in a stereoscope using prisms or goggles with color or polarizing filters or alternating occlusion (for a review see http://rspb.royalsocietypublishing.org/content/early/2011/04/09/rspb.2010.2777.long). A good procedure is a chart, analogous to the familiar Snellen visual acuity chart, in which one letter in each row differs in depth (front or behind) sequentially increasing in difficulty. For children the fly test is ideal: the image of a fly is transilluminated by polarized light; wearing polarizing glasses the wing appears at a different depth and allows stereopsis to be demonstrated by trying to pull on it.
Expected Performance
There is no equivalent in stereoacuity of the normal 20/20 visual acuity standard and in any case, the numerical score, even if expressed in disparity angle, depends to some extent on the test being used. Superior observers under ideal conditions can achieve 0.1 arc min or even better.The distinction between screening for the presence of stereopsis and a measurement of stereoacuity is valuable. To ascertain that depth can be seen in a binocular views, a test must be easily administered and not subject to deception. The random-dot stereogram is used widely for this purpose and has the advantage that for the uninitiated the object shape is unknown. It is made of random small pattern elements; depth can be created only in multiples of elements and therefore may not reach the small threshold disparity which is the purpose of stereoacuity measurements.
A population study revealed a surprisingly high incidence of good stereoacuity: . Out of 188 biology students, 97.3% could perform at 2.3 minutes of arc or better.
Factors Influencing Stereoacuity
Optimum stereoacuity requires that the following mitigating factors be avoided:- Low contrast
- Short duration exposures (less than 500 milliseconds) [5]
- Fuzzy or closely spaced pattern elements .
- Uncorrected or unequally corrected refractive errors (monovision)