Directional vision

In the classical science of vision, directional vision describes that when a point of the retina is stimulated by light, this not only leads to a light sensation (image), but also a directional sensation that is recorded by the brain in one combined image of both eyes, as a direction in which the observer is central (egocentric direction).

Alhazen (Ibn al-Haytham), an Arab scholar from the 11th century, was the first to propose that vision is possible because light reflects off objects and then enters the eye ^[1] after which perceptions arise in the brain that are partly the result of activities of the observer, such as directing the eyes.^[2] In the 19th century, this idea was elaborated by Ewald Hering. He assumed that each eye saw direction (visual direction) and introduced the idea of ​​a “cyclopean eye” for egocentric direction, as if we saw the world from a single central point between both eyes. Combined with the results of research on the horopter this can explain single and double images. The explanation of sensory fusion, in which two double images merge into one new image with a new direction, was only possible when nerve cells were found in the brain that become active when a specific direction is stimulated simultaneously in the left and right eyes. The perception of depth based on differences in the directions between both eyes (disparity) is discussed in a separate article, Stereopis. The following describes the main line of this, mainly classical, development and discusses concepts that help in reading the source documents.

Each eye has a small area, the fovea (f), with which it can see most sharply. When seeing, this area is automatically focused on the point that has the attention, the fixation point. The direction in which the eye then looks is called the principal oculocentric direction. According to Herings' law this direction is perceaved as straight ahead.^{[citation needed]}

If a point on the retina is stimulated by light, this not only gives a light sensation, but also a directional sensation. This direction is called visual direction and is expressed in the angle with the principal direction.^{[citation needed]}

If two eyes simultaneously see a point P in space, the brain receives information about two visual directions that, due to the positioning of the eyes in the horizontal plane, lie next to each other. The brain interprets this as seeing two objects next to each other. These are called double images.^{[citation needed]}

In case the visual directions in teh two eyes are equal, the double images seem to coincide with each other. This is called a single image.^{[citation needed]}

Because both eyes look at space from different positions, the visual directions in the two eyes are unequal for most points in space. If you pay attention, you can see these two different directions. Normally double images are invisible because we are not aware of them, unless there is a deviation such as diplopia.^{[citation needed]}

Hering described in 1861 that we seem to perceive the world from a point, midway between both eyes, instead of from each eye separately.^[3] He called this point a cyclopean eye, after the cyplopes in Greek mythology.^[4] Hering also described a method to show how the two retinal images in this cyclopean eye are apparently merged into a combined image. He called this method cyclopean projection. He illustrated this method with a pencil held so that it points away from the observer, see the figure. The method basically involves rotating the images of the two eyes around the fixation point towards each other until they coincide in the cyclopean eye. Geometrically this does not change the direction, but it does give a concise description of how we seem to see directions. This is also called Hering's law of common binocular direction.^[5]

Hering's law states that the directions derived from the two eyes’ images will be perceived as if the observer is viewing the scene from a single vantage point between the two eyes. This point is called the cyclopean eye.^{[citation needed]}

Hering's Cyclopean projection is intended as a description of what he observed and not as an explanation of how the egocentric image is formed in the brain. How the images from the two eyes are merged has been extensively investigated using a theoretical model, the geometric horopter. The geometric horopter is a circle through the fixation point and both eyes. Points on this circle have been shown to project (approximately) onto corresponding points in both eyes. These are points that look in the same visual direction in both eyes.^[6] In empirical research it has been established that it is possible to measure and compare the visual directions in both eyes and thus determine the observed horopter (empirical horopter). It turns out that this horopter is not a line but a vertical (frontoparallel) plane through the fixation point and that the shape of this plane differs per person. At short fixation distances the plane as seen from the observer is concave (hollow), at slightly greater distances flatter and at greater distances flat or convex. Furthermore, the plane curves towards the observer at the top and away from the observer at the bottom. It is generally assumed that these are adaptations to the environment, including how the eyes move in the recesses in the skull.^[7][8]

In early theories, the geometric horopter is presented as a screen on which the visual world is depicted. Points that are closer (C) or further away (P) hit the screen at two different points.^{[citation needed]}

Although the above-mentioned screen does not actually exist, it does provide a correct description of how double images are seen. In the case where the directions of both eyes cross before the horopter (point C), the left double image comes from the right eye and vice versa. This situation is known as "crossed disparity". At a point that is further away than the horopter (P), the image of the left eye is seen to the left of the image of the right eye. Researchers call this "parallel disparity". And at a point on the horopter, the two directions coincide and so only 1 image is seen.^{[citation needed]}

Disparate points are retinal points with a different directional characteristic in both eyes, which therefore look in different visual directions. The size of the difference is expressed as an angle difference, or in a distance on the retina or on the horopter. The angle difference of the two visual directions is called disparity. Disparity is a measure of the distance between two double images and is also a measure of depth (stereopsis).^{[citation needed]}

Hering located the cyclopean eye on the horopter.

The procedure for drawing the egocentric directions is as follows: draw the principal direction of the cyclopean eye by drawing a line from the cyclopean eye to the fixation point. Then place the left eye on the cyclopean eye and rotate it so that the principal direction of the left eye coincides with the principal direction of the cyclopean eye. Repeat this for the right eye.^{[citation needed]}

Points on (the distance of) the horopter now end in two coincident egocentric directions and all other points in two different directions. Hering's cyclopean projection thus provides an explanation for the occurrence of single vision versus double vision.^{[citation needed]}

Observational research shows that points with unequal visual directions in both eyes are sometimes not seen double, but single, in a direction that lies between the two visual directions. This phenomenon is called sensory fusion. With a strong dominant eye, the perceived direction of the fused image is closer to the direction seen by the dominant eye.^[10]

The occurrence of fusion is due to Panum^[11][12] and measured by Ogle^[9] by moving a vertical rod in space and determining when the rod is perceived as single or double. The result is not a line, like the geometric horopter, but an area extending on either side of the geometric horopter. This area is called Panum's fusion area. Ogle also found that double images with a large disparity are seen on the horopter and double images with smaller disparities are seen (slightly) further away or closer than the horopter; the depth sensation is less vivid and less great than with fused images.^[9]

Hering described an experiment to test Panum's theory. In the experiment, a thin rod is held straight ahead in the direction of view in the midsagittal plane.^[3] If the center of the rod is fixed, then the center of the rod should appear single and the ends double and receding in depth, as in the figure. Hering did not find this and thus rejected the theory.^{[citation needed]}

Hering's experiment is a special case of the midsagittal-strip illusion. This illusion explains that and why the fused image is seen transversely to the direction of view and not as Hering assumed.^{[citation needed]}

As soon as a point that has the attention threatens to move outside Panum's fusion area, an automatic eye movement (vergence movement) ensures that the point comes to lie in the middle of Panum's fusion area again. In research on this reflex, the vergence horopter is defined as the set of points within Panum's fusion range that do not elicit a reflex. The measured horopter falls centrally within Panum's fusion range. In the vertical plane, the vergence horopter is less inclined than the corresponding fusion range.^[13]

The existence of fusion is not explained by classical theory. Theories that make use of the fact that neurons have been found in the visual cortex that look in a specific visual direction via each eye seem to be able to explain this phenomenon better.^[14]