Listing's law

Donders' lawListing's planetorsion
Listing's law, named after German mathematician Johann Benedict Listing (1808–1882), describes the three-dimensional orientation of the eye and its axes of rotation.wikipedia
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Johann Benedict Listing

Johann ListingListingJ. B. Listing
Listing's law, named after German mathematician Johann Benedict Listing (1808–1882), describes the three-dimensional orientation of the eye and its axes of rotation.
In ophthalmology, Listing's law describes an essential element of extraocular eye muscle coordination.

Saccade

saccadessaccadicsaccadic eye movements
Listing's law has been shown to hold when the head is stationary and upright and gaze is directed toward far targets, i.e., when the eyes are either fixating, making saccades, or pursuing moving visual targets.
(Torsion is clockwise or counterclockwise rotation around the line of sight when the eye is at its central primary position; defined this way, Listing's law says that, when the head is motionless, torsion is kept at zero.)

Extraocular muscles

extraocular muscleeye muscleseye muscle
The eye muscles may also contribute to Listing's law by having position-dependent pulling directions during motion, i.e., this might be the mechanism that implements the 'half angle' rule described above.
The extraocular muscle pulley system is fundamental to the movement of the eye muscles, in particular also to ensure conformity to Listing's law.

Eye tracking on the ISS

Eye Tracking DeviceEye Tracking Device (ETD)Eye tracking experiment
Alternatively, it can be measured using eye tracking (see also Eye tracking on the ISS for an example).
In the first set of experiments, conducted by Prof. Clarke’s team in cooperation with the Moscow Institute for Biomedical Problems, the Eye Tracking Device was used for the measurement of Listing's plane – a coordinate framework, which is used to define the movement of the eyes in the head.

Cyclodisparity

cyclodisparities
Disorders of the eye muscles (such as strabismus) often cause torsional offsets in eye position that are particularly troublesome when they differ between the two eyes, as the resulting cyclodisparity may lead to cyclodisplopia (double vision due to relative torsion) and may prevent binocular fusion.
The resulting cyclovergence at near gaze is smaller than the cyclovergence predicted by Listing's law.

Mathematician

mathematiciansapplied mathematicianMathematics
Listing's law, named after German mathematician Johann Benedict Listing (1808–1882), describes the three-dimensional orientation of the eye and its axes of rotation.

Three-dimensional space

three-dimensional3Dthree dimensions
Listing's law, named after German mathematician Johann Benedict Listing (1808–1882), describes the three-dimensional orientation of the eye and its axes of rotation.

Human eye

eyeeyeseyeball
Listing's law, named after German mathematician Johann Benedict Listing (1808–1882), describes the three-dimensional orientation of the eye and its axes of rotation.

Rotation

rotatingrotatespin
Listing's law, named after German mathematician Johann Benedict Listing (1808–1882), describes the three-dimensional orientation of the eye and its axes of rotation.

Vergence

convergenceconvergedivergence
Listing's law (often abbreviated L1) has been generalized to yield the binocular extension of Listing's law (often abbreviated L2) which also covers vergence.

Coordinate-free

component-freeCoordinate-free treatmentcoordinate-independent
(Note that this is not the same description of ocular torsion as rotation around the line of sight: whereas movements that start or end at the primary position can indeed be performed without any rotation about the line of sight, this is not the case for arbitrary movements.) Listing's law can also be formulated in a coordinate-free form using geometric algebra.

Geometric algebra

geometric productgeometric algebra formulationgrade projection
(Note that this is not the same description of ocular torsion as rotation around the line of sight: whereas movements that start or end at the primary position can indeed be performed without any rotation about the line of sight, this is not the case for arbitrary movements.) Listing's law can also be formulated in a coordinate-free form using geometric algebra.

Commutative property

commutativecommutativitycommute
(This complication is one of the most difficult aspects of Listing's law to understand, but it follows directly from the non-commutative laws of physical rotation, which specify that one rotation followed by a second rotation does not yield the same result as these same rotations performed in the inverse order.)

Vestibulo–ocular reflex

vestibulo-ocular reflexoculocephalic reflexoculovestibular reflex
Listing's law is not obeyed when the eyes counter-rotate during head rotation to maintain gaze stability, either due to the Vestibulo-ocular reflex (VOR) or the optokinetic reflex.

Optokinetic response

optokinetic reflexoptokinetic nystagmusoptokinetic
Listing's law is not obeyed when the eyes counter-rotate during head rotation to maintain gaze stability, either due to the Vestibulo-ocular reflex (VOR) or the optokinetic reflex.

Stereopsis

stereoscopic visionstereo visionStereovision
Torsion is not good for binocular vision because it complicates the already difficult problem of matching images from the two eyes for stereopsis (depth vision).

Strabismus

squintcross-eyedheterotropia
Disorders of the eye muscles (such as strabismus) often cause torsional offsets in eye position that are particularly troublesome when they differ between the two eyes, as the resulting cyclodisparity may lead to cyclodisplopia (double vision due to relative torsion) and may prevent binocular fusion.

Strabismus surgery

surgeryalignment surgerycorrective operations to her eye muscles
The influence of strabismus surgery on the Listing's planes of the two eyes is not fully understood.

Eye tracking

eye trackereye-trackingeye trackers
Alternatively, it can be measured using eye tracking (see also Eye tracking on the ISS for an example).

Hermann von Helmholtz

HelmholtzHermann HelmholtzHermann Ludwig Ferdinand von Helmholtz
(It is not clear how Listing derived this idea.) Listing's law was first confirmed experimentally by the 19th century polymath Hermann von Helmholtz, who compared visual afterimages at various eye positions to predictions derived from Listing's law and found that they matched.

Afterimage

afterimagesafter imagepositive afterimage
(It is not clear how Listing derived this idea.) Listing's law was first confirmed experimentally by the 19th century polymath Hermann von Helmholtz, who compared visual afterimages at various eye positions to predictions derived from Listing's law and found that they matched.

Scleral lens

scleralScleral contact lensscleral contact lenses
The orientation of Listing's plane (equivalently, the location of the primary position) of an individual can be measured using scleral coils.

Cyclovergence

They mainly occur due to Listing's law, which, under normal circumstances, constrains the cyclorotation in dependence on the vertical and horizontal movements of the eye.

Marius Tscherning

M. H. E. TscherningMarius Hans Erik TscherningTscherning
He conducted research of entoptic phenomenon, Purkinje images, the etiology of myopia, and Listing's law of ocular movement.