Editing Saccade (section)

==Timing and kinematics==
Saccades are one of the fastest movements produced by the human eye ([[blink]]s may reach even higher peak velocities). The peak [[angular speed]] of the eye during a saccade reaches up to 700°/s in humans for great saccades (25° of visual angle); in some monkeys, peak speed can reach 1000°/s.<ref>{{Cite journal|last=Fuchs|first=A. F.|date=1967-08-01|title=Saccadic and smooth pursuit eye movements in the monkey|journal=The Journal of Physiology|language=en|volume=191|issue=3|pages=609–631|doi=10.1113/jphysiol.1967.sp008271|pmid=4963872|issn=1469-7793|pmc=1365495}}</ref> Saccades to an unexpected stimulus normally take about 200 milliseconds (ms) to initiate, and then last from about 20–200 ms, depending on their amplitude (20–30 ms is typical in language reading). Under certain laboratory circumstances, the latency of, or reaction time to, saccade production can be cut nearly in half (express saccades). These saccades are generated by a neuronal mechanism that bypasses time-consuming circuits and activates the eye muscles more directly.<ref name="FischerBoch1983">{{cite journal |doi=10.1016/0006-8993(83)90760-6 |title=Saccadic eye movements after extremely short reaction times in the monkey |year=1983 |last1=Fischer |first1=B. |last2=Boch |first2=R. |journal=Brain Research |volume=260 |pages=21–6 |pmid=6402272 |issue=1|s2cid=7593382 }}</ref><ref name="FischerRamsperger1984">{{cite journal |doi=10.1007/BF00231145 |pmid=6519226 |title=Human express saccades: Extremely short reaction times of goal directed eye movements |year=1984 |last1=Fischer |first1=B. |last2=Ramsperger |first2=E. |journal=Experimental Brain Research |volume=57|issue=1 |pages=191–5 |s2cid=23189106 }}</ref>  Specific pre-target oscillatory ([[alpha rhythm]]s) and transient activities occurring in posterior-lateral [[parietal cortex]] and [[occipital cortex]] also characterize express saccades.<ref name="Hamm2010">{{cite journal |doi=10.1523/JNEUROSCI.0785-10.2010 |title=Preparatory Activations across a Distributed Cortical Network Determine Production of Express Saccades in Humans |year=2010 |last1=Hamm |first1=J. P. |last2=Dyckman |first2=K. A. |last3=Ethridge |first3=L. E. |last4=McDowell |first4=J. E. |last5=Clementz |first5=B. A. |journal=Journal of Neuroscience |volume=30 |issue=21 |pages=7350–7 |pmid=20505102 |pmc=3149561}}</ref>

To achieve such high speeds, there are specialized oculomotor burst neurons in the brainstem that wire into the ocular motor neuron. The burst neurons implement [[Bang–bang control|bang-bang control]]: they are either completely inhibited, or firing at its full rate of ~1000&nbsp;Hz.<ref>{{Citation |last=Enderle |first=John D |title=Neural control of saccades |date=2002-01-01 |journal=Progress in Brain Research |volume=140 |pages=21–49 |editor-last=Hyona |editor-first=J. |url=https://www.sciencedirect.com/science/article/pii/S0079612302400404 |access-date=2024-07-06 |series=The Brain's eye: Neurobiological and clinical aspects of oculomotor research |publisher=Elsevier |doi=10.1016/S0079-6123(02)40040-4 |pmid=12508580 |isbn=978-0-444-51097-6 |editor2-last=Munoz |editor2-first=D. P. |editor3-last=Heide |editor3-first=W. |editor4-last=Radach |editor4-first=R.}}</ref> Since the motion of the eye is essentially a linear system, bang-bang control minimizes travel time.<ref>{{Cite journal |last1=Enderle |first1=John D. |last2=Wolfe |first2=James W. |date=January 1987 |title=Time-Optimal Control of Saccadic Eye Movements |url=https://ieeexplore.ieee.org/document/4122432 |journal=IEEE Transactions on Biomedical Engineering |volume=BME-34 |issue=1 |pages=43–55 |doi=10.1109/TBME.1987.326014 |pmid=3557482 |issn=0018-9294}}</ref> After a saccade, a constant force is required to hold the position against elastic force, thus resulting in a pulse-step control.<ref>{{Cite journal |last1=Bahill |first1=A. Terry |last2=Stark |first2=Lawrence |date=1979 |title=The Trajectories of Saccadic Eye Movements |url=https://www.jstor.org/stable/24965071 |journal=Scientific American |volume=240 |issue=1 |pages=108–117 |doi=10.1038/scientificamerican0179-108 |jstor=24965071 |pmid=451521 |bibcode=1979SciAm.240a.108B |issn=0036-8733}}</ref>

[[File:Saccadic main sequence.svg|thumbnail|Saccadic main sequence, showing single saccades from a participant performing a visually-guided saccade task. It is called "main sequence" because it looks like the [[main sequence]] in astrophysics.]]
The amplitude of a saccade is the angular distance the eye travels during the movement. For amplitudes up to 15 or 20°, the velocity of a saccade linearly depends on the amplitude (the so-called ''saccadic main sequence'',<ref name=Bahill1975>{{cite journal|last1=Bahill|first1=A. Terry|last2=Clark|first2=Michael R.|last3=Stark|first3=Lawrence|title=The Main Sequence, A Tool for Studying Human Eye Movements|journal=Mathematical Biosciences|date=1975|volume=24|issue=3–4|page=191|doi=10.1016/0025-5564(75)90075-9 |citeseerx=10.1.1.212.416|s2cid=6937642 }}</ref> a term borrowed from [[main sequence|astrophysics]]; see Figure). For amplitudes larger than 20°, the peak velocity starts to plateau<ref name=Bahill1975/> (nonlinearly) toward the maximum velocity attainable by the eye at around 60°.  For instance, a 10° amplitude is associated with a velocity of 300°/s, and 30° is associated with 500°/s.<ref name="eb">"Sensory Reception: Human Vision: Structure and function of the Human Eye" vol. 27, p. 179  Encyclopædia Britannica,  1987</ref> Therefore, for larger amplitude ranges, the main sequence can best be modeled by an inverse [[power law]] function.<ref name=Baloh1975>{{cite journal|last1=Baloh|first1=Robert W.|last2=Sills|first2=Andrew W.|last3=Kumley|first3=Warren E.|last4=Honrubia|first4=Vicente|title=Quantitative measurement of saccade amplitude, duration, and velocity|journal=Neurology|date=1975|volume=25|issue=11|pages=1065–70|doi=10.1212/WNL.25.11.1065|pmid=1237825|s2cid=3261949}}</ref>

The high peak velocities and the main sequence relationship can also be used to distinguish [[microsaccade|micro-]]/saccades from other [[eye movements]] (like [[ocular tremor]], [[ocular drift]], and [[smooth pursuit]]). Velocity-based [[algorithm]]s are a common  approach for saccade detection in [[eye tracking]].<ref name="EngbertKliegl2002">{{cite journal |doi=10.1016/S0042-6989(03)00084-1 |doi-access=free |title=Microsaccades uncover the orientation of covert attention |year=2003 |last1=Engbert |first1=Ralf |last2=Kliegl |first2=Reinhold |journal=Vision Research |volume=43 |issue=9 |pages=1035–45 |pmid=12676246}}</ref><ref name=Marple1996>{{cite journal|last1=Marple-Horvat|first1=Dilwyn E.|last2=Gilbey|first2=Sean L.|last3=Hollands|first3=Mark Andrew|title=A method for automatic identification of saccades from eye movement recordings|journal=Journal of Neuroscience Methods|date=1996|volume=67|issue=2|pages=191–5|doi=10.1016/0165-0270(96)00049-0 |pmid=8872885|s2cid=36082798}}</ref><ref name=Ebisawa1988>{{cite journal|last1=Ebisawa|first1=Y.|last2=Minamitani|first2=H.|last3=Mori|first3=Y.|last4=Takase|first4=M.|title=New methods for removing saccades in analysis of smooth pursuit eye movement|journal=Biological Cybernetics|date=1988|volume=60|issue=2|pages=111–9|doi=10.1007/BF00202898|pmid=3228554|s2cid=44662137}}</ref> Although, depending on the demands on timing accuracy, acceleration-based methods are more precise.<ref name=Behrens2010>{{cite journal|last1=Behrens|first1=Frank|last2=MacKeben|first2=Manfred|last3=Schröder-Preikschat|first3=Wolfgang|title=An improved algorithm for automatic detection of saccades in eye movement data and for calculating saccade parameters|journal=Behavior Research Methods|date=2010|volume=42|issue=3|pages=701–8|doi=10.3758/BRM.42.3.701|doi-access=free|pmid=20805592}}</ref>

Saccades may rotate the eyes in any direction to relocate gaze direction (the direction of sight that corresponds to the fovea), but normally saccades do not rotate the eyes torsionally. (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.)

Head-fixed saccades can have amplitudes of up to 90° (from one edge of the oculomotor range to the other), but in normal conditions saccades are far smaller, and any shift of gaze larger than about 20° is accompanied by a head movement. During such gaze saccades, first, the eye produces a saccade to get gaze on target, whereas the head follows more slowly and the [[vestibulo-ocular reflex]] (VOR) causes the eyes to roll back in the head to keep gaze on the target. Since the VOR can actually rotate the eyes around the line of sight, combined eye and head movements do not always obey [[Listing's law]].<ref>{{cite journal |last1=Migliaccio |first1=Americo A. |last2=Schubert |first2=Michael C. |last3=Clendaniel |first3=Richard A. |last4=Carey |first4=John P. |last5=Della Santina |first5=Charles C. |last6=Minor |first6=Lloyd B. |last7=Zee |first7=David S. |title=Axis of Eye Rotation Changes with Head-Pitch Orientation during Head Impulses about Earth-Vertical |journal=Journal of the Association for Research in Otolaryngology |date=June 2006 |volume=7 |issue=2 |pages=140–150 |doi=10.1007/s10162-006-0029-8|pmid=16552499 |pmc=2504578 }}</ref>

The rotational inertia of the eye is negligible compared to the elastic and viscous force.