Disparity, Convergence, and Depth (Visual Depth Perception 10)

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows binocular disparity together with the convergence angle required for the eyes to fix on F. The angles and together determine the depth of objects on the axis.

Contributed by: Keith Stroyan (March 2011)
Open content licensed under CC BY-NC-SA



Binocular disparity has been studied since Euclid, but was popularized by Wheatstone about 150 years ago with the invention of the stereoscope. A stereoscope shows two slightly different images to the separate eyes and gives the scene the appearance of depth. However, disparity alone does not determine depth, as shown in the Demonstration "Binocular Disparity versus Depth (Visual Depth Perception 9)" (see Related Links). To simplify derivations for this Demonstration we take no aim offset and set the nodePercent equal to zero, that is, nodes are (unrealistically) at the center of the eye.

The exact formula for depth when the fixate and distraction are on the axis (including sign) from (in radians) for a given fixate distance is given by the following formula with interocular distance :


Binocular disparity does not determine depth since it requires the absolute fixate distance . The value of could come from a convergence cue since the convergence angle of the eyes is related to fixate distance by


so (after simplification) depth from static cues is


For more information about stereoscopic vision, see the Wikipedia page.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.