VARIABILITY ANDDEVELOPMENT OF A NORMATIVE

DATA BASE FOR SACCADIC EYEMOVEMENTS

A. TERRY BAHILL,ALLAN BROCKENBROUGH

andB. TODDTROOST

From the Department of Electrical Engineering,Carnegie-Mellon University and the Department

of Neurology, University of PittsburghMedical School, Pittsburgh, Pa.

Reprinted from

INVESTIGATIVE OPHTHALMOLOGY& VISUAL SCIENCE

St. Louis

Vol. 21, No. 1, Part 1, pp. 116-125, July, 1981(Copyright © 1981 by The Association forResearch in Vision and Ophthalmology)

(Printed in the U. S. A.)

Variability and development of a normativedata base for saccadic eye movements

A, Terry Bahill, Allan Brockenbrough, and B, Todd Troost

The duration, peak velocity, and acceleration of the saccadic eye movements of 13 normalsubjects are plotted as functions of saccadic magnitude. The apparent peak velocity of asaccadic eye movement is sensitive to the algorithms used to calculate the velocity. The velocitychannel filter should have zero phase shift and a cutoff frequency between 60 and 100 Hz inorder to limit noise but pass all the signal information. Some subjects fatigue rapidly; theirparameters fall outside the normal range of values.

Key words: saccadic eye movements, main sequence, duration, velocity,acceleration, filtering, differentiation, power spectra, fatigue, bandwith, linearity

C/accadic peak veloeity-magnitude-dura-tion parameters, called the main sequenceparameters,1'2 have been used to define sac-cades. Eye movements were called saccadesif their peak velocity-magnitude-durationparameters matched normative data. Thistechnique has been used for regular sac-cades,3"6 closely spaced saccades,7 overlap-ping saccades,8 non—Hering's law saccades,9fast phases of nystagmus,10"12 voluntary nys-tagmus,13 dynamic overshoots,14 and frac-tionated saccades in internuclear ophthal-moplegia.15 Many of these studies used dif-ferent normative data bases. In this paper wetry to explain possible reasons for the vari-ability in these data bases.

From the Department of Electrical Engineering, Car-negie-Mellon University and the Department of Neu-rology, University of Pittsburgh Medical School,Pittsburgh, Pa.

Supported in part by grants from the National Institutesof Health (R23EY02382), the National Science Foun-dation (ENG 7722418) and the United States Naval AirSystems Command.

Submitted for publication July 24, 1980.Reprint requests: A. Terry Bahill, Biomedical Engineer-

ing Program, Department of Electrical Engineering,Carnegie-Mellon University, Pittsburgh, Pa. 15213.

The great utility of these peak velocity-magnitude-duration parameters has prompt-ed questions of how much they are affectedby fatigue, intersubject and intrasubject vari-ability, instrumental noise, low-pass filteringof the data, and by the algorithms used tocompute the parameter values. We answeredthese questions in defining the quantitativeaspects of a normal data base.

Developing a consistent set of valid nor-mative saccadic eye movement data thatcould be used for intralaboratory compari-sons was difficult. First, many normal sub-jects in a homogeneous age group had to berecorded. Second, the eye movements offatigued subjects had to be rejected. This re-quired a visual examination of the velocityprofile of each individual saccade. Third,peak velocities and durations had to be plot-ted as functions of saccadic magnitudes, notof target displacements. Fourth, the velocitywaveform, not the position waveform, had tobe used to define the beginning and end ofeach saccade. Fifth, zero-phase digital filtersand algorithms had to be used to calculatevelocity. Sixth, Bode diagrams of the filtershad to be measured and plotted, particularlyfor the velocity channel. Seventh, it had to be

116 0146-0404/81/070116+10$01.00/0 © 1981 Assoc. for Res. in Vis. and Ophthal., Inc.

Volume 21Number 1, Part 1 Variability and validity of saccadic parameters 117

Fig, 1, Target and eye positions at the start of a typical recording session. The sinusoidaltracking is included to ensure linearity. Candidate saccades are pointed to by the arrows. Theoperator has rejected the eye blink (boxes with X) that occurred just before saccadic trackingbegan. The target jumps were 20 deg. Rightward movements are represented by upwarddeflections in all our figures. This figure shows a soft saturation, a nonlinearity, in the left eyechannel, as illustrated by the attenuation of the two microsaccades of left eye on extreme rightgaze.

demonstrated that the recording system waslinear for the entire range of measurement. Adata base such as this has not been previouslypublished. Some authors1 published data foronly one subject; they measured16 but did notpublish their velocity channel bandwidth.Some authors12' 17 published mixed electro-oculogram (EOG) and photocell data and didnot explicitly state the bandwidth of the eyevelocity records. Some authors18 did notmeasure their bandwidths, and others19 usedEOG and mixed the results of measurementsof one eye alone and the movement of thetwo eyes averaged together.

There are two purposes of this article; toprovide a valid normative data base for humansaccadic eye movements and to explain differ-ences in previously published data.

Methods

Saccadic refixations in response to discretetarget movements were measured. The targetwaveforms were generated either with an analogfunction generator or with a computer. The targetwas a small red laser dot (3 mm diameter) pro-jected on a white screen 57 cm from the subject.

The target voltage drove a galvanometer that hada small mirror attached. The movement of themirror deflected the laser beam to produce thehorizontally moving dot on the screen. Subjectsviewed the target binocularly in a dimly illumi-nated room. Informed consent was obtained afterthe equipment and the experiment were ex-plained to the subjects,

The movement of each eye was measured withstandard photoelectric techniques.14 The linearrange for the measurement of horizontal eyemovements extended ±10 deg from primary po-sition. The system was linear for 20 deg of eyerotation. This limit on linearity was prescribed bythe size of the iris and the covering of the iris bythe eyelids. It is difficult, but not impossible, toobtain valid data for saccadic eye movementslarger than 20 deg with this technique.8 Instru-ment noise was less than 1 mv and was, therefore,smaller than signals produced by eye movementsof 1 min arc, which were on the order of 30 mv.Saccades as small as 3 min arc have been recordedon this equipment.20 The target movement andthe movements of the eyes were amplified (0 to 300Hz bandwidth), passed through an analog to digi-tal converter sampling at 1000 Hz, and stored on adisk in the computer.

It took 2 to 15 min to adjust the photocells and

118 Bahill et alInvest. Ophthalmol. Vis. Sci,

July 1981

q!000

100

10

q 100

10

q100000

10000

0 1SACCADIC MAGNITUDE

101000

100

Fig, 2. Main sequence diagrams showing peakvelocity, duration, and the first peak accelerationas functions of saccadic magnitude for the saccadiceye movements of 13 normal subjects. The mag-nitudes were computed from records with abandwidth extending from 0 to 300 Hz; peak ve-locities and durations were derived from recordswith an 80 Hz bandwidth; accelerations were de-rived from 60 Hz bandwidth records. The unitsare degrees for magnitude, degrees per second forpeak velocity, milliseconds for duration, and de-grees per second squared for acceleration.

obtain linear recordings over the central range.The subject was allowed to rest for a few minutesand was then asked to track a random amplitudesquare wave target movement for 3 min. A 3 minrest period was allowed, and then the calibrationand the 3 min test were repeated. Finally, thecalibration test was repeated and the session wasover.

The peak velocity-magnitude-duration param-eters are changed primarily by fatigue.8 Fatigue isused here in a broad sense to include musclefatigue, tiredness, and inattention. We haveavoided these effects by keeping our recordingsessions short, about 3 min each, and by ensuring

mental alertness through verbal admonishmentssuch as, "Track very carefully now." We believethat a continuous interactive process is extremelyimportant in obtaining consistent, valid data. In-trasubject and intersubject variability is sig-nificantly reduced by such attention to detail. Wetherefore monitored the analog records as the datawere being taken. If the data were noisy or non-linear they were discarded and the equipment wasreadjusted. These techniques have been successfulin minimizing aberrant effects.

An important aspect of the calibration routinewas the tracking of a slow (0.2 Hz) sinusoid. Asinusoid of this frequency is very easy to track andmost humans can track it with very few saccades.These records were inspected to ensure that therecording system was linear. With a linear systemthe eye movements looked sinusoidal, and mi-crosaccades could be seen in each channel at bothextremes of gaze. It is not sufficient to have thesubject look at a few selected targets to check forlinearity, since soft saturation at the end pointsand discontinuities will be missed. At least onecycle of this sinusoidal tracking was included inevery disk file of data to ensure linear recordings(Fig. 1). Visual inspection of this sinusoid by theexperimenter is a necessary and sufficient test todetect common instrumentation nonlinearities.

Saccadic data analysis was performed on a PDF11/34 computer with interactive graphics pro-grams. The eye movement data were displayed ona graphics terminal where the operator specifiedwhich sections of the data were to be averagedtogether to define the voltages corresponding toeach of the fixation points. This produced the degper volt calibration factors. Typically 5 to 10 sec ofdata were averaged to obtain each of these factors.The velocity as a function of time was calculatedfor each eye and was stored in a file called thevelocity channel. The acceleration as a function oftime was calculated from the velocity data withsimilar algorithms and filters. Saccadelike events,where the velocity exceeded 20 deg/sec, weremarked while in the interactive graphics mode.The operator either accepted the event if it ap-peared to be a saccade or discarded the event if itappeared to be a blink or an artifact.

The magnitude, duration, peak velocity, andsize of the first peak acceleration were computedfor each saccade. A two point central differencealgorithm and a 80 Hz, zero-phase, low-pass filterwere used to compute the velocity as a function oftime. The beginning and end of each saccade wasdefined by this velocity trace. Since the peak ve-locity of a saccade occurs just about in the middle

Volume 21Number 1, Part 1 Variability and validity qfsaccadic parameters 119

of the saccade, the time of peak velocity was de-termined. Then the points before and after thecenter of the saccade where the velocity was 5deg/sec were located, When the velocity droppedinto the ±5 deg/sec noise band, we said the eyehad reached zero velocity. These points weredefined to be the beginning and the end of thesaccade and were used to determine the mag-nitude and duration of the saccade. Defining thesaccadic size by means of the zero-velocity pointsrather than the presaccadic and postsaccadic posi-tions eliminated the effects of glissades and thusgreatly reduced the scatter in the data.

We used a 80 Hz (3 dB point) filter in the veloc-ity channel. It was a rectangular window in thefrequency domain corresponding to 5 lobes of asine function in the time domain, ±17 datapoints.21 Its frequency response is shown in Fig. 4.The maximum attenuation in the passband was 1.2dB, and the maximum gain in the passband was0.3 dB. This filter had 6% overshoot when excitedwith a step input. Since normal eye movements donot look like step responses, this presented nolimitations. The same filter was used for the accel-eration channel, but the 3 dB point was reduced to60 Hz. When higher cutoff frequencies were tried,the computed peak accelerations changed, and theacceleration records became noisier. We did notbelieve that the peak accelerations computed withthe higher bandwidths were more accurate. The60 Hz cutoff frequency was the best compromisebetween noise and high-frequency information.

There were two reasons why we sampled at arate as high as 1000 Hz: it allowed saccadic dura-tion to be estimated within 1 msec, and it alloweda velocity channel bandwidth of over 100 Hz, A1000 Hz sampling rate yields a 500 Hz Nyquistfrequency. Therefore all signal and noise compo-nents above 500 Hz had to be removed withanalog filters before sampling. We used 300 Hzanalog filters (20 dB/decade roll off). To calculatevelocity we used a two point central differencealgorithm, 2hy(i) = y(i + 1) - y(i - 1), where h,the sampling interval, is 1 msec. This algorithmacts as a low-pass filter that is shown 4 dB at 250Hz. It has no phase shift. For an analog-to-digitalconverter operating at 200 samples per second,this velocity algorithm would remove all frequen-cies above 50 Hz. Furthermore, for this algorithmthere is an optimal sampling rate that givesthe most accurate velocity estimates; this rate de-pends on the accuracy in evaluating the originalfunction. The 1000 Hz sampling rate is optimal forthe accuracy with which we can evaluate eye po-sition.

1000

800

600

400

200

0

100

75

50

25

0

100000

80000

60000

40000

20000

00 5 10 15

SACCADIC MAGNITUDE

20 25

Fig, 3, Same saccadic data of Fig. 2 plotted withlinear coordinates.

Table I

Saccadic magnitude(deg)

Peak velocityand S.D.(deg/sec)

Durationand S.D.

(msec)

5 261 ±42 42 ± 810 410 ±67 51 ± 815 499 ± 43 54 ± 720 657 ± 78 64 ± 6

Results

Our normative data base contains over 900saccadic eye movements from 13 normal sub-jects ranging from 20 to 35 years of age. Figs.2 and 3 show the peak acceleration, the peakvelocity, and the duration all as functions ofsaccadic magnitude. The peak velocity andthe duration were computed from the veloc-ity data, which had a bandwidth of 80 Hz; themagnitude was derived from 300 Hz band-width eye position data by timing data de-rived from the velocity channel; and acceler-ation was derived from 60 Hz bandwidth

120 Bahill et alInvest. Ophthalmol. Vis. Sci.

July 1981

ao 40 30 60 70 80 90 100 125 150 200

Frequency (Hz)

Fig. 4, Apparent peak velocity of two typical saccacles as a function of the low-pass filter cutofffrequency, and the response of our digital velocity channel filter. The optimal velocity channelfilter should have a cutoff value above 60 Hz so that the apparent peak velocity is not at-tenuated, but below 100 Hz where computational noise increases the apparent peak velocity.

data. The solid lines are the means and onestandard deviation on each side of the mean.Table I provides numerical values for a fewsaccadic sizes.

An equation that fits the data is;

The parameter values shown in Figs. 2 and3 are very sensitive to the bandwidths of theinstrumentation. Low-pass filtering at vari-ous frequencies can effect the apparent peakvelocity and the apparent duration. The ap-parent magnitude can also be affected, de-pending on the algorithm used. Fig. 4 showsthe apparent peak velocity of two saccades asa function of the cutoff frequency of our ve-locity channel filter.

When the cutoff frequency of our velocitychannel filter was varied, the apparent peakvelocity of most saccades behaved as shownin Fig. 4. It increased as the filter cutoff fre-quency increased from 15 to 50 Hz and re-mained relatively constant as this frequencyincreased from 50 to 100 Hz. We were sur-prised to see that varying the cutoff fre-

quency of the velocity channel filter in therange from 40 to 60 Hz would have an affecton the apparent peak velocity, since when wecalculated the power spectrum of a saccadewe found little energy above 40 Hz (Fig. 5).But then we realized that it was not thepower spectrum of the position channel thatwe should be studying, but rather the powerspectrum of the velocity channel. Fig, 5shows these two power spectra for a typical10 deg saccade. The power spectrum of thevelocity channel is broader than the spec-trum of the position channel. The velocityspectrum of the left eye is not down 40 dBuntil 74 Hz. Therefore the velocity channelfilter may decrease the apparent peak veloc-ity of a saccade unless its cutoff is 74 Hz ormore. The gradual rise in the apparent peakvelocity curve of Fig. 4 above 100 Hz is aconsequence of the differentiation algorithmand quantization noise. A velocity channelfilter with a cutoff between 60 and 100 Hzseems to be optimal. The shape of the appar-ent maximum acceleration plot was similar tothe apparent peak velocity plot.

Volume 21"Number 1, Part 1 Variability and validity of saccadic parameters 121

-20

-40

-601 10

Position Power Spectrum, Right Eye

Position Power Spectrum, Left Eye

30 90

Velocity Power Spectrum, Right Eye

1 '10 20 30 40 50 50 70

Velocity Power Spectrum , Left Eye

Fig. 5, Power spectral density functions for a typical saccade. The velocity spectrum for the lefteye has significant power out to 74 Hz, Such large differences between the spectra of the rightand left eyes are not uncommon. Power is in decibels (dB) and frequency is in hertz (Hz).

How many significant digits are there inour calculated values of magnitude and peakvelocity? The biggest source of noise, and theonly step involving a qualitative decision by ahuman, is setting the calibration levels to getthe degrees per volt calibration factors. Wehad two experimenters do this 16 times on 3separate days. The largest difference was1.3%, with a 0.2% S.D., so that we can saywith 95% confidence that our data are repro-ducible to ±0.4%. This means that the mag-nitude of a 10 deg saccade may vary from runto run in the second digit after the decimalpoint, but the first digit after the decimalpoint will not vary. For magnitude we list thefirst digit after the decimal point. Theanalog-to-digital converter has 12-bit resolu-tion; this fact also implies that the first digitafter the decimal place is significant but thatthe third digit cannot be fully resolved. Forpeak velocity the digit in the units place is sub-ject to variation on repeated trials. For exam-ple, a velocity of 411 deg/sec may actuallybe 410 or 412 deg/sec. (The theoretical max-imum error of our numerical algorithm is also1 deg/sec.) This implies that the 67 deg/secS.D. of our data was due to human eye move-ment variability and not our data analysis pro-grams. Because we sampled every millisec-ond, our average error in duration was 1 msec.

In order to understand the large variabilityin saccadic parameters reported by others, on

2 separate days we recorded the slowest sub-ject used by Schmidt et al,18 We included hisnormometric22 saccades (e.g., saccade 6 inFig. 6) in our data base.

Initially an automatic processing routinewas used. It showed that half of the eyemovements were more than 1 S.D. below themean; many were apparently 3 and 4 S.D.below the mean. When such a quick look atthe data reveals abnormalities, a detailedexamination of the velocity profiles of the in-dividual eye movements is called for.

This inspection of the velocity tracesshowed that eye movements in the first 30sec of the session were normometric saccadeswithin 1 S.D. of the mean; after this, none ofthe movements was normometric.

Fig. 6 shows eye movements recorded 6,49, and 61 sec after the start of one session. Itis easy to see that if movement 49 weretreated as a 19 deg saccade (because thetarget jump was 19 deg) a great deal of varia-bility would be added to the data. The peakvelocity of movement 49 (460 deg/sec) wouldbe much too slow for a 19 deg saccade, and itsduration of 109 msec would be much too longfor a 19 deg saccade. However, if this eyemovement were treated as a 10 deg, 55 msec,460 deg/sec saccade followed by a 9 deg, 54msec, 333 deg/sec saccade, then little vari-ability would be introduced into the data.The large glissade appended to the dynamic

122 Bahitt et al. Invest. Ophthalmol. Vis. Sci.July 1981

velocity

Fig, 6. Saccadic eye movements of a subject enter-ing a state of fatigue. The records are from sixth,forty-ninth, and sixty-first seconds of the recordingsession. The saccade of record 6 is a normometricsaccade that is within 1 S.D. of the mean shown inFigs. 2 and 3. The eye movement of record 49 iscomposed of two closely spaced saccades. The eyemovement of record 61 has a dynamic saccade of15 deg and a glissade of 4 deg. If the peak velocityof such a movement were said to be the peak ve-locity of a 19 deg saccade, a great deal of variabilitywould be added to the data. The calibration barsrepresent 10 deg, 500 deg/sec, 30,000 deg/sec2,and 100 msec. Bandwidths were 0 to 300 Hz forposition, 0 to 80 Hz for velocity, and 0 to 60 Hz foracceleration. The photocells were adjusted quicklyand consequently the data are noisy.

saccade in record 61 offers a more subtleexample of how the variability of saccadicparameters will be increased if the velocitytraces are not used to monitor for fatigue.

The saccadic deterioration was similar inboth recording sessions. Once fatigued, thissubject's fixations became unstable andsmooth pursuit tracking was mostly saccadic.

Humans make thousands of saccades a day.However, they are not repetitive in timingand amplitude, and they are seldom largerthan 15 deg in amplitude.23 A long recordingsession containing large saccades can fatiguehumans. However, none of the other 27 pa-tients and normals we have recorded this pastyear has fatigued as rapidly as the subjectwhose data are shown in Fig, 6.

Discussion

The particular computer algorithm usedcan affect the saccadic parameters. On oneoccasion the velocity records of a typical sac-cade were derived (1) with a finite-impulseresponse, noncausal, zero-phase, rectangu-lar-window digital filter, with a cutoff fre-quency of 55 Hz and a spread of ±50 points(msec), and (2) with a fifth-order, recursive,linear-phase, digital, Butterworth filter witha cutoff of 55 Hz.21 The peak velocities anddurations derived with use of the two filterswere almost the same; these measurementswere not affected by the phase shift. How-ever, the magnitudes calculated with thelinear-phase filter were in error. The begin-ning and ending times of the saccade weredetermined on the velocity record and werethen transferred to the position trace in orderto calculate saccadic magnitude. A phase shiftbetween these records produced errors. Forthe linear-phase filter, the calculated startingpoint was always too late, thus making thesaccade seem too small. The calculated end-ing point was also too late; however, thismade the saccade appear either too large ortoo small depending on whether or not theeye movement had overshoot. Hence the er-rors in magnitude were stochastic. Use of alinear-phase filter would have increased thestandard deviation of the data. The resultsobtained with the zero-phase filter were

Volume 21Number 1, Part 1 Variability and validity of saccadic parameters 123

more accurate, and the standard deviations ofthe data were smaller.

We recommend the following overallbandwidths for saccadic eye movement data: 0to 300 Hz for position, 0 to 80 Hz for velocity,and 0 to 60 Hz for acceleration. Larger band-widths produce larger standard deviations be-cause of biological, instrumental, and compu-tational noise. Smaller bandwidths producevariability between data bases. Zero-phasedigital filters are best. If analog filters must beused, then Butterworth filters with the abovebandwidths could be used. However, timinginformation could not be transferred betweenthe position and velocity channels.

It is very important that the bandwidths begiven when quantitative parameters for sac-cades are reported. However, it is notsufficient to give only the bandwidth of therecording system. The differentiators havedynamics, and interlaboratory comparisonscan not be made unless the frequency charac-teristics of these differentiators are known. Itwould be best if this velocity channel band-width were measured by putting sinusoids inand measuring the sinusoids coming out. Be-cause this bandwidth depends upon systembandwidth, sampling rate, the velocity al-gorithm, and the velocity channel filters,theoretical calculation of this bandwidthwould be difficult.

The analog and digital filters of Balohet al.19 matched each other very well. Theyused 35 Hz analog filters on their data. Theytried higher frequency filters and saw no effecton the apparent peak velocity. One of thereasons was that they used a 50 Hz digital filterand their velocity algorithm acted as an 89 Hzfilter. Neither was flat in the pass band. Thecascade of these two digital operations had a 3dB point at 35 Hz. If they had increased theirsampling rate, then the digital operationswould have had higher frequency cutoff val-ues and there would have been some differ-ence in apparent peak velocity as the cutofffrequency of the analog filter was increased.

The differentiation algorithm acts as a low-pass filter. To evaluate the velocity at point iwe used the data at points 1 msec before andafter point i. For a 1000 Hz sampling rate, this

yields a bandwidth of 223 Hz. We couldchange the algorithm to use points 4 msecbefore and after the point i. This algorithmwould have a bandwidth of 56 Hz. Thiswould have reduced the accuracy of the ve-locity computation and increased the highfrequency noise, but it would have saved thetime and expense of the extra velocity channelfilter. We did not do this originally because wewanted to see and understand each operationseparately.

For noisy data, the 5 deg/sec criterion fordefining the beginning and end of the saccadedid not work well. In these cases we found thepoints where the velocity was 5% of the peakvelocity and then added 1 msec to the startand 3 msec to the end of the saccade. This newtime interval was then used to calculate themagnitude and the duration of the saccade.The values of 1 and 3 msec were chosen be-cause they predict the zero velocity points fornoise-free records of saccades between 1 and20 deg. For noisy data, the bandwidth of theposition channel was reduced from 300 to 125Hz, the bandwidth of the velocity channel wasreduced from 80 to 60 Hz, and the bandwidthof the acceleration channel was reduced from60 Hz to 45 Hz. The noisy data algorithm andfilters were not used to compile this normativedata base; they were sometimes used inanalyzing the data of clinical patients.

The peak velocity main sequence diagramhas been more useful than the duration dia-gram. Therefore, in this study, we tried toget accurate, consistent velocity data. If wehad focused on the duration data, we wouldhave used different algorithms. For example,our velocity channel filter in conjunction withdefining the beginning and the end of a sac-cade with the zero-velocity points increasedthe apparent duration of some saccades by asmuch as 20%. We did not correct for this.

There is an automatic processing feature inour program that does not require the inter-vention of an operator to make judgmentsabout whether the event is a saccade or anartifact. The automatic processing featureworks particularly well when a vertical EOGchannel is recorded and used as an eyeblinkdetector. These programs were suitable for

124 Bahill et al Invest. Ophthalmol Vis. Sci.July 1981

fast screening of patients but not for the for-mulation of a normative data base. The auto-matic processing feature was not used forthe peak velocity-magnitude-duration para-meters of this report.

The main sequence data have been plottedon both log-log coordinates and linear coor-dinates as Bahill16 did previously. Linearplots allocate most of the graph space to largesaccades, whereas log-log plots give spaceproportional to the frequency of occurrenceof the saccades. The frequency of occurrenceof natural saccades is a decaying exponential,with most saccades having an amplitude of 15deg or less.23 Thus linear plots emphasizethe physiologically unusual large saccades,whereas log-log plots give more weight tonormal sized saccades and make it possible toinclude small saccades. However, the linearplots of Fig. 3 are often more useful in clinicalsituations.

The data base we have described is usefulnot only for basic research but also for testingin the clinic, We plotted the eye movementparameters as functions of actual saccade sizerather than the size of the target jumps. Ourparadigm allowed us to accumulate largenumbers of saccades in less than 3 min.Rather than have subjects make multiplerefixations to a series of fixed targets, we ran-domly changed target size during the run.This helped to reduce fatigue and inatten-tion, which often occur in recording sessionslonger than 10 to 15 min. The technique istherefore well-suited for the study of pa-tients. It is important to note, however, thata subject with data out of our normal rangedoes not necessarily have a pathological con-dition. It suggests that the position and ve-locity waveforms of individual saccadesshould be studied in detail.

The standard deviations of our data aresmall because (1) we rejected data taken whenthe subjects became fatigued, as judged by acareful inspection of the eye position and eyevelocity records; (2) we plotted the parame-ters as functions of the size of the actual sac-cade, not as functions of the size of the targetmovement; (3) we only used data from the

linear range of our instrumentation; (4) thecomputer calculated the parameters from thevelocity trace, derived with a zero-phase digi-tal filter; and (5) we defined the size of thesaccade as the size of the initial, dynamic sac-cade. Either the eye movements with longglissades or drifts were discarded or else themagnitude of the dynamic saccade was care-fully calculated. For saccades with overshoot,the saccadic magnitude was defined to be thefoot-to-peak angle, i.e., the angle betweenzero velocity at the start of the saccade andzero velocity at the end of the saccade. Lessvariability was provided by this definition forthe size of the saccade than when the size ofthe saccade was defined as the angle betweenthe two steady state fixation points. Saccadeswith dynamic overshoot were treated as twosaccades: the main saccade and a small returnsaccade.

We thank Jeffrey S. Kallman for writing the digitalfilters, Jon E. Lieberman for writing the power spectraldensity programs, and Larry A. Abel for comments andsuggestions.

REFERENCES

1. Bahill AT, Clark MR, and Stark L: The main se-quence, a tool for studying human eye movements.Math. Biosciences 24:191, 1975.

2. Bahill AT and Stark L: The trajectories of saccadiceye movements. Sci Am 240:108, 1979.

3. Dodge R and Cline TS: The angle velocity of eyemovements. Psychol Rev 8:145, 1901.

4. Westheimer G: Mechanism of saccadic eye move-ments. Arch Ophthalmol 52:710, 1954.

5. Robinson DA: The mechanics of human saccadic eyemovement. J Physiol 174:245, 1964.

6. Becker W and Fuchs AF: Further properties of thehuman saccadic system: eye movements and cor-rectional saccades with and without visual fixationpoints. Vision Res 9:1247, 1969.

7. Bahill AT, Bahill KA, Clark MR, and Stark L:Closely spaced saccades. INVEST OPHTHALMOL 14:317, 1975.

8. Bahill AT and Stark L: Overlapping saccades andglissades are produced by fatigue in the saccadic eyemovement system. Exp Neurol 48:95, 1975.

9. Kenyon RV, Ciuffreda KJ, and Stark L: Dynamicvergence eye movements in strabismus and ambly-opia: symmetric vergence. INVEST OPHTHALMOL VisSci 19:60, 1980.

10. Komatsuzaki A, Alpert J, Harris H, and Cohen B:Effects of mesencephalie reticular formation lesionson optokinetic nystagmus. Exp Neurol 34:522, 1972.

Volume 21Number 1, Part 1 Variability and validity ofsaccadic parameters 125

11. Ron S, Robinson DA, and Skavenski AA: Saccadesand the quick phase of nystagmus. Vision Res12:2015, 1972.

12. Sharpe JA, Troost BT, Dell'Osso LF, and Daroff RB:Comparative velocities of different types of fast eyemovements in man. INVEST OPHTHALMOL 14:689,1975.

13. Shults WT, Stark L, Hoyt WF, and Ochs AL: Nor-mal saccadic structure of voluntary nystagmus. ArchOphthalmol 95:1399, 1977.

14. Bahill AT, Clark MR, and Stark L: Dynamic over-shoot in saccadic eye movements is caused byneurological control signal reversals. Exp Neurol48:107, 1975.

15. Feldon SE, Hoyt WF, and Stark L: Disordered in-hibition in internuclear ophthalmoplegia, analysis ofeye movement recordings with computer simula-tions. Brain 103:113, 1980.

16. Bahill AT: Neurological control and the hyperfinestructure ofsaccadic eye movements. University ofCalifornia Berkeley, Doctoral Dissertation for De-partment of Electrical Engineering and ComputerScience, 1975.

17. Boghen D, Troost BT, Daroff RB, Dell'Osso LF,and Birkett JE: Velocity characteristics of normalhuman saccades. INVEST OPHTHALMOL 13:619, 1974.

18. Schmidt D, Abel LA, Dell'Osso LF, and Daroff RB:Saccadic velocity characteristics: intrinsic variabilityand fatigue. Aviat Space Environ Med 50:393, 1979.

19. Baloh RWS Sills AW, Kumley WE, and Honrubia V:Quantitative measurement of saccade amplitude,duration, and velocity. Neurology 25:1065, 1975.

20. Bahill AT, Clark MR, and Stark L: Computer simu-lation of overshoot in saccadic eye movements.Comput Programs Biomed 4:230, 1975.

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