Human Factors: Perception of depth (stereopsis)

Perception of depth (stereopsis): selecting Leopard tank gunners (1972)

The Leopard 1A1 tank is equipped with a stereoscopic range finder with its system of lenses positioned 1.70 metres apart. The range finder also has a graticule (grid) that is virtually projected in the gunners’ view. Each position of the graticule corresponds to a certain (known) distance. When the graticule and a target are viewed at the same perceived distance, the target’s distance is known. The tank gunner therefore has to ‘place’ the graticule as close as possible near the target. The gunner has to be very precise when determining the distance. Apparently very small visual deviations are associated with large physical distance differences. The precision with which the gunner can adjust the barrel/gun settings is firstly determined by his visual depth discernment. The selection of potential tank gunners must therefore take a close look at the visual depth discernment of the candidates.

Leopard 1 (source:


A Leopard tank during shooting trials
A Leopard tank during shooting trials



In 1972, the Human Factors Institute TNO was approached by the Royal Netherlands Army. What is the best way to select tank gunners for the Leopard 1 tank? Can TNO develop a new test for determining the visual depth discernment of candidates?
A solution was found. To understand that, first some background on visual depth discernment.

Visual depth discernment

The image formed on the retina of a single eye contains no information about the distance of objects. After all, a retina image is a two-dimensional projection of the outside world. Nevertheless, even with the use of one eye, conclusions can be made about distance based upon perspective: the angle at which objects of known size are observed and the partial masking of distant objects by objects that are closer to us. The fact that our spatial awareness hardly changes when we use only one eye is the best proof of the effectiveness of this capability.

However, to determine very small relative distance differences, people are dependent on the use of information derived from two eyes. Stereopsis, also known as stereoscopic depth perception or binocular parallax, is the ability of both eyes to see the same object as one image and to create a perception of depth. This parallax is a direct consequence of the fact that our eyes perceive the world from slightly different positions. Objects that are at different distances from us are projected differently in terms of the horizontal position on the left and right retinas. That effect will be larger, and the depth vision will therefore be more sensitive, the farther apart the eyes are. That is also the reason why the lenses of the Leopard range finder are placed so far apart. 

Visual depth discernment through parallax projection

Wheatstone developed the stereogram in which the binocular parallax acts as a stimulus for depth perception. A stereogram consists of two almost identical (half)images of a spatial representation. Presented separately to the left and right eyes, they provide a spatial awareness of the images. With increasing depth difference, the parallax will increase.

That phenomenon is used by increasing the distance between the two points in a single half image. The range finder virtually projects the graticule at different distances in the environment in a similar way. An attempt is made to minimise the perceived distance difference between the target and the graticule in order to measure the distance. The measurement accuracy is the smallest angle difference (parallax) that can still be observed by a candidate tank gunner.

Stereogram – the binocular image at the right

Gunner selection

The value of the threshold parallax is important for the tank gunner’s selection. But to you measure the threshold parallax? Various tests were in use in the early 1970s; the outcomes correlated poorly. A new test had to be developed. Two different principles were available:

  1. tests in which depth discrimination relates to real objects in one’s view,
  2. tests in which the perceived image is only generated as a subjective perception by means of a stereogram.

The depth vision test developed by TNO was unique. The test used a noise pattern stereogram: each of the two half-images consists exclusively of a pattern of elements distributed according to chance, e.g. squares, dots, scratches and the like. In one of the half-images, a certain configuration of elements, for example a square, has undergone a shift relative to an identical configuration in the other half-image. This creates an artificial parallax between the configuration and the remainder of the noise pattern. The relevant configuration cannot be recognised separately in every half-frame: a perfect camouflage.

However, as soon as the stereogram is seen binocularly, the configuration will be seen in depth and reveal its shape. The figure hidden in the stereogram is only visible to someone who has the ability to see binocular depth, at least when the introduced parallax is greater than the threshold parallax of that person.
Good test results are obtained if the hidden figure in the stereogram is executed as a disk that lacks a sector of 60°. This image can be offered in four easily recognisable positions (left, top, right, bottom). This appraoch is analogous to the well-known Landolt ring. For statistical reasons, it has been decided to offer the hidden figure four times.

To see the hidden figures, one must view the stereogram with a test device (“stereoscope”). Twelve stereograms were made for the test device with ascending parallax values of 5 to 400 arc seconds. The constructed test device contains a rotating drum with internal illumination. The stereograms are mounted on the drum that can be turned with a knob.

A first prototype of the test device


Final test device for measuring visual depth discernment

Advantages of the new test

  1. The gunner candidate only needs to report whether or not a certain figure is visible. That is a lot easier than assessing a depth difference in the existing tests. This saved an enormous amount of time to test candidates.
  2. Monocular information is completely excluded by the test design. Only the binocular stereopsis is measured.

The device was subjected to tests with a number of test persons in order to define the reliability and validity This included determining the waste percentage, the sum of false positives and false negatives divided by the total number of candidates tested (see: source).

The museum has two working devices for measuring visual depth discernment: one early prototype and the final test device.


Report ‘Het testen op dieptezien voor de selectie van schutters voor de Leopardtank’, drs. J. Walraven en J. Boogaard Instituut voor Zintuigfysiologie RVO-TNO, Soesterberg. pdf [In Dutch]