J Neurophysiol 113: 3312–3322, 2015.
First published March 11, 2015; doi:10.1152/jn.00771.2014.
The effect of saccade metrics on the corollary discharge contribution to
perceived eye location
Sonia Bansal,1 Laurence C. Jayet Bray,2 Matthew S. Peterson,1,3 and Wilsaan M. Joiner1,2
1
Department of Neuroscience, George Mason University, Fairfax, Virginia; 2Department of Bioengineering, George Mason
University, Fairfax, Virginia; 3Department of Psychology, George Mason University, Fairfax, Virginia
Submitted 2 October 2014; accepted in final form 10 March 2015
corollary discharge; saccade; visual error; visual perception; movement variability
that accompanies rapid eye
movements (saccades) creates a complex problem for the
visual system. Despite the shifts of the retinal image with each
saccade, the visual scene is still perceived as stable and
continuous, revealing that the brain actively and accurately
integrates visual and motor information over multiple eye
movements (for review, see Wurtz 2008). The neural mechanisms that underlie perceptual stability are assumed to require
knowledge about the upcoming saccade movement vector and
update of a map in retinotopic coordinates (Duhamel et al.
1992; Melcher and Colby 2008; Nakamura and Colby 2002;
Sommer and Wurtz 2006; Wurtz 2008). Supported by neural
and behavioral studies in nonhuman primates (Joiner et al.
THE DISRUPTION TO VISUAL INPUT
Address for reprint requests and other correspondence: W. Joiner, Dept. of
Bioengineering, George Mason Univ., Nguyen Engineering Bldg., 1G5, 4400
Univ. Dr., Rm. 3800, Fairfax, VA 22030 (e-mail: [email protected]).
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2013; Sommer and Wurtz 2002, 2004a, 2004b) and humans
(Bellebaum et al. 2005, 2006; Bridgeman et al. 1975; Duhamel
et al. 1992; Joiner et al. 2010, 2013; Ostendorf et al. 2010), this
remapping is hypothesized to be mediated by a corollary
discharge (CD) signal. This internal signal does not generate
the movement but is a copy of the efferent motor command
sent to the muscles to produce movement (Sperry 1950; von
Holst and Mittelstaedt 1950). The CD internally conveys the
information of the impending saccade vector (movement amplitude and direction) to the required neural sensory areas to
compensate for the impending changes in the retina position
attributable to the upcoming eye movement (Duhamel et al.
1992; Gottlieb et al. 1998; Hall and Colby 2011; Nakamura
and Colby 2002; Sommer and Wurtz 2006).
The CD of saccadic eye movements has been studied in the
laboratory using behavioral tasks that examine motor behavior
and perception across saccades. In a paradigm of the saccadic
suppression of displacement developed by Bridgeman et al.
(1975), subjects are required to make a saccade to a peripheral
target following a central fixation period. During the movement, the target is extinguished and, in one variant of the task,
immediately reappears at a displaced location. In a second task
condition, the target reappears after a blank period following
the saccade onset (e.g., 250 ms). After the target reappearance,
subjects are required to report the direction of target displacement, and, on the basis of this two-alternative forced-choice
decision, the resulting psychometric function provides an estimate of the perceptual threshold (the smallest displacement
that is detected at greater than chance level) and bias (the
displacement amount at which the probability of either directional report is at chance level, the perceived target location).
It has been proposed that the accurate detection of target
displacement in this task relies on the CD accompanying each
saccade, allowing a comparison of the target location before
and after the movement. This comparison has been shown to be
affected by saccadic suppression; the threshold for detecting
small target displacements is higher when the target immediately reappears at a shifted location than when a blank period
precedes the target reappearance (Deubel et al. 1996, 2002).
Additionally, it has been shown that the threshold for shift
discrimination improves with exposure; there is a decrease in
the perceptual threshold with an increase in the initial viewing
period of the target (Zimmermann et al. 2013). As demonstrated by various studies, normal subjects report accurate
estimates of target location and displacement (small bias and
threshold measures) for a range of saccade amplitudes (Bridgeman et al. 1975; Collins et al. 2009; Deubel et al. 1996, 2002;
Joiner et al. 2013; Ostendorf et al. 2010; Wexler and Collins
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Bansal S, Jayet Bray LC, Peterson MS, Joiner WM. The effect
of saccade metrics on the corollary discharge contribution to perceived eye location. J Neurophysiol 113: 3312–3322, 2015. First
published March 11, 2015; doi:10.1152/jn.00771.2014.—Corollary
discharge (CD) is hypothesized to provide the movement information
(direction and amplitude) required to compensate for the saccadeinduced disruptions to visual input. Here, we investigated to what
extent these conveyed metrics influence perceptual stability in human
subjects with a target-displacement detection task. Subjects made
saccades to targets located at different amplitudes (4°, 6°, or 8°) and
directions (horizontal or vertical). During the saccade, the target
disappeared and then reappeared at a shifted location either in the
same direction or opposite to the movement vector. Subjects reported
the target displacement direction, and from these reports we determined the perceptual threshold for shift detection and estimate of
target location. Our results indicate that the thresholds for all amplitudes and directions generally scaled with saccade amplitude. Additionally, subjects on average produced hypometric saccades with an
estimated CD gain ⬍1. Finally, we examined the contribution of
different error signals to perceptual performance, the saccade error
(movement-to-movement variability in saccade amplitude) and visual
error (distance between the fovea and the shifted target location).
Perceptual judgment was not influenced by the fluctuations in movement amplitude, and performance was largely the same across movement directions for different magnitudes of visual error. Importantly,
subjects reported the correct direction of target displacement above
chance level for very small visual errors (⬍0.75°), even when these
errors were opposite the target-shift direction. Collectively, these
results suggest that the CD-based compensatory mechanisms for
visual disruptions are highly accurate and comparable for saccades
with different metrics.
THE EFFECT OF SACCADE METRICS ON PERCEIVED EYE LOCATION
experiment to examine the CD-based detection of transsaccadic target displacements for saccades to targets at different
amplitudes (4°, 6°, and 8°) and directions (horizontal and
vertical). We specifically investigated the systematic changes
in perceptual threshold and bias for these different saccade
vectors and the influence of movement-by-movement saccade
variability and the resulting visual error on the detection of
these transsaccadic target shifts.
MATERIALS AND METHODS
We recorded the eye movements of 10 healthy human subjects
between the ages of 18 and 24 yr. Subjects had normal vision and
were naive as to the aim of the study, which consisted of making
perceptual judgments about the location of presented visual stimuli.
Experimental protocols were approved by the Institutional Review
Board of George Mason University, and informed consent was obtained from each participant. Subjects completed the experiments in
multiple test sessions over 3 days and did not receive any training in
the tasks before obtaining the experimental data.
Apparatus and measurement. Eye movements were recorded using
the Eyelink II eye tracker (head-mounted binocular eye tracker,
500-Hz temporal resolution, 0.2° spatial resolution; SR Research,
Mississauga, Ontario, Canada). Stimuli were presented on a 19-in
CRT-monitor (screen resolution 1,024 ⫻ 768 pixels; refresh rate 120
Hz) at a viewing distance of 62.5 cm. Subjects were seated in a dimly
lit room in a stationary chair with their head stabilized by a chinrest.
Stimulus presentation, eye movement, and manual keyboard response
data acquisition were achieved using real-time experimental control
software (Experiment Builder, SR Research). At the start of each
experiment session, a nine-point gaze calibration was performed
followed by a nine-point validation. Calibration and/or validation
were repeated until the error was smaller than 1° on average, as
previously done in studies conducted under these standard calibration
settings (Peterson and Wong 2008; Wong and Peterson 2011).
Task and procedure. In this experiment, each trial began with a
central fixation cross (0.3° in extent). Subjects were required to
maintain fixation on this cross for a variable period (random duration
between 1,200 and 1,800 ms, Fig. 1A). After the fixation period, an
initial target was presented at one of three amplitudes (4°, 6°, or 8°)
and four directions (upward, downward, leftward, or rightward) from
the fixation cross, 12 possible combinations (Fig. 1B). Subjects were
required to make a saccade to the initial target. Once the eye position
exceeded a virtual square window (3.2° in extent) around the fixation
point, the target was extinguished and followed by a 250-ms blank
period (Deubel et al. 1996). (We should note that previous studies,
including our own, have compared perceptual performance with and
without this gap period; Joiner et al. 2013; Ostendorf et al. 2010;
Wexler and Collins 2014). We chose to concentrate on the condition
with the blank because of our interest in the properties of the saccade
CD rather than the effect of saccadic suppression on perception. In
addition, previous results suggest that differences in perception attributable to CD are observable during this condition (Ostendorf et al.
2010). Therefore, all results presented here are from experiments
conducted with a 250-ms blank period. The initial target then reappeared at a shifted randomized position in line with the movement
(⫾0.5° collinear increments) between ⫾2.5°. The target shift was
randomly drawn from a Gaussian distribution centered at 0°, with the
smaller, less prominent shifts being sampled more than the larger,
more detectable shifts (Fig. 1B). Following the reappearance of the
target, the subject made a manual response using keyboard arrow keys
(upward, rightward, downward, or leftward) to indicate the direction
in which the target shifted. Subjects had to make this manual response
within 3,000 ms. No instructions were given on reaction time, and all
subjects were able to respond within the 3,000-ms time window. No
feedback was given to subjects to indicate correct or incorrect re-
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2014). Similar to end point variability, these perceptual thresholds have been shown to increase with movement amplitude
for horizontal saccades (Bridgeman et al. 1975; Li and Matin
1990, 1997; Niemeier et al. 2003, 2007), suggesting that the
brain optimally integrates premovement expectations of the
visual scene with noisy sensory and motor information (Bays
and Husain 2007; Niemeier et al. 2003, 2007; van Opstal and
van Gisbergen 1989).
CD has also been studied with the “double-step task” developed by Hallett and Lightstone (1976). In this task, two targets
are flashed successively and extinguished before the subject
can perform the required eye movements. The task is conducted in the dark so that no visual feedback is possible, and
the targets are arranged to ensure that correct performance
requires internal information of the first saccade vector. If a
subject were to make a saccade to the second target based
solely on where that target fell on the retina instead of the
CD-based updated eye location from the first movement, then
the second saccade would not compensate for errors (overshoots and undershoots) in the first saccade. Several studies
have demonstrated that both human subjects and monkeys are
able to make trial-by-trial adjustments in the second saccade to
adjust for errors on the first movement (Bellebaum et al. 2005;
Joiner et al. 2010; Munuera et al. 2009; Quaia et al. 2010;
Sommer and Wurtz 2002). It is unlikely that proprioception
from the eye muscles plays a significant role in this process, as
it has been shown that performance is not affected when these
signals are eliminated and likely to be too slow to be effectively utilized (Guthrie et al. 1983; Lewis et al. 2001; Poletti et
al. 2013; Wang et al. 2007). Thus the second saccade provides
an assessment of the accuracy of the CD representation of the
first eye movement. In our previous study that utilized this task,
we showed that the CD of the first saccade conveyed accurate
amplitude and direction movement information (Joiner et al.
2010). However, the trial-by-trial adjustment in the second
saccade was significantly more accurate for primary horizontal
saccades than for vertical, suggesting differences in the precision of the CD movement vector information.
As described above, the CD representation of movement
amplitude and direction has been examined for perceptual
behavior and motor performance. Specifically, the results of Li
and Matin (1990, 1997) demonstrated that the accuracy of this
representation for perception scales with horizontal movement
amplitude. In our previous work, we showed that the accuracy
of this representation for motor sequences is influenced by the
direction of the initial eye movement (Joiner et al. 2010). This
performance difference may be due to the neural origin of the
respective motor commands; the motor signals and the associated CD for horizontal and vertical saccades are generated by
distinct neural areas, which may result in divergent CD properties and behaviors when based on these respective signals
(Leigh and Zee 2006).
On the basis of the collective examples above, it is not clear
how the CD representation for both of these saccade metrics
(amplitude and direction) influences visual perception and
whether behavior remains consistent across these metrics.
Probing how subjects account for saccade-induced disruptions
to visual input for different movement metrics and relating this
behavior to movement generation may provide a better understanding of how visual stability is accomplished. To determine
the influence of saccade metrics, we designed a shift-detection
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THE EFFECT OF SACCADE METRICS ON PERCEIVED EYE LOCATION
Target Position
A
EXPERIMENTAL TASK
1200-1800
ms fixation
1
2
250 ms
blank
3
Forward
4
Backward
Saccade
Onset
Time
B
VISUAL STIMULI AND PROCEDURE
1
2
3
4
−2.5 −2 −1.5−1−0.5 0 0.5 1 1.5 2 2.5
Target Shift (°)
ESTIMATION OF PERCEPTION THRESHOLD AND BIAS
Threshold
1.0
Threshold (°)
100
75
0.5
0.0
−0.5
1.0
50
Bias (°)
Percentage Forward Responses
C
25
Bias
0
−2
−1
0
1
Target Shift (°)
2
0.5
0.0
−0.5
4
6
8
Fig. 1. Transsaccadic shift-detection task. A: task procedure. Each trial began with a
central fixation cross appearing for a variable period (1,200–1,800 ms), followed by
appearance of an initial target. Subjects were required to make a saccadic eye
movement toward this initial target, and the target was displaced during the saccade,
reappearing at a new location after a 250-ms blank. B: task conditions. The initial
target, T1, appeared randomly at 4°, 6°, or 8° horizontally or vertically from the central
fixation point. The displaced target, T2, appeared randomly at shifted positions
according the illustrated Gaussian distribution ranging from ⫺2.5° to 2.5° shifts. After
the appearance of the target at the shifted location, subjects were required to indicate the
direction of the displacement (backward or forward) using arrow keys on the keyboard
(upward, downward, leftward, and rightward). C: example psychometric curves. The
frequency of forward responses on the y-axis is plotted as a function of target
displacement on the x-axis. The manual response data were fitted to a cumulative
Gaussian distribution to determine the psychometric function. 3 sample psychometric
curves are shown with different slopes. 2 perceptual measures are derived, threshold
and bias. The threshold, as shown by the bar chart, top, right, is computed as the
difference in target displacement between the 50% and the 75% points of the
sample psychometric curves. The perceptual bias was taken as the displacement from 0 at the point where the forward and backward responses were equal
to 50%, as shown by the bar chart, bottom, right. In these example curves, the
different conditions for each curve result in varying thresholds and biases.
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Initial
Target
sponses. Each subject underwent three sessions of 312 trials each. The
amplitude and direction of the initial target was randomly and equally
distributed among all 12 possible combinations.
Saccade measures. Horizontal and vertical movements of at least
one of the two eyes were recorded, and the resulting data were
visualized, filtered, and analyzed offline using MATLAB v. 8.1.0
environment (Mathworks, Natick, MA). During the task, saccade
initiation was detected when the saccade left the 3.2° square fixation
window. For offline analyses, an eye movement was classified as a
saccade if both eye velocity and acceleration exceeded 50°/s and
2,000°/s2 respectively. Saccade onset and offset were determined
when the eye velocity and acceleration rose above and fell below
these criteria, respectively. Saccade end points were examined for
every amplitude and direction. Only trials where 1) the saccade was
initiated within the fixation window and its distance exceeded 1/3 of
the initial target amplitude and 2) the primary saccade end point was
within the average eye position ⫾ 2 SD were analyzed (on average
⬎76% trials). These remaining trials were included in the analyses of
both perceptual response and saccadic eye-movement data.
We determined the percent gain of the mean saccade amplitude for
all target amplitudes and directions (Fig. 3D). This value was the ratio
(scaled by 100) between the mean saccade amplitude and the initial
target amplitude. A percentage ⬎100% signified that the mean saccade amplitude exceeded the target amplitude (overshoot); a percentage ⬍100% signified that the mean saccade amplitude fell short of the
target amplitude (undershoot). The saccade error (Fig. 4) was the
difference between the original target location and the primary saccade end point. Positive saccade errors represent hypometric movements (the target was in front of the saccade end point). The visual
error was the difference between the eye position at the time of target
reappearance and the shifted target location (Fig. 5).
Psychometric curves. Keyboard responses indicating the subject’s
perception of the target shift were plotted as a psychometric function
for each individual subject. As in our previous work (Joiner et al.
2013), the percentage of forward responses was plotted as a function
of target shift. The data were then fitted with a cumulative Gaussian
distribution as shown by the sample curves in Fig. 1C. From these
curves, the perceptual bias and threshold were derived. The perceptual
bias was taken as the displacement from 0 at the point where the
percentage of forward responses was equal to 50%. The bias is the
perceptual null location, the point where the forward and backward
judgments occur with equal frequency. We take this point as the
estimation of the postsaccadic judgment of the location of the presaccadic target. A positive bias indicated that the target location was
perceived to be ahead of the actual target position; a negative bias
indicated that the target location was perceived to be behind the actual
position. We quantified the difference between the perceptual estimate
(i.e., the bias) and the actual target location as a percent error of target
location, the bias divided by the initial target amplitude scaled by 100
(Fig. 3D). For example, a perceptual bias of 0.5° for a 4° target
location is a 12.5% error in target location (a 12.5% overestimation of
the target location). Thus a percentage above 0 signified that the
perceptual estimate exceeded the target amplitude (overestimation); a
negative percentage signified that the perceptual estimate was lower
than the target amplitude (underestimation).
The difference in shift size between the 50 and 75% points on
the psychometric curve represented the perceptual threshold. This
measure quantified the ability to perceive the target displacement;
larger thresholds or smaller slopes of the psychometric function
represented an increase in difficulty for accurately perceiving the
target shift (Fig. 1C).
Statistical analysis. The experimental data were not significantly
different from a normal distribution (Lilliefors test, P ⬎ 0.06 in all
cases). Statistical significance of multiple effects such as target eccentricity (4°, 6°, and 8°) and saccade direction (rightward, leftward,
upward, and downward) on perceptual threshold and bias was determined by an ANOVA test. For significance, two-tailed t-tests and
THE EFFECT OF SACCADE METRICS ON PERCEIVED EYE LOCATION
paired t-tests were used to compare results to set values or between
conditions, respectively. All statistical analyses were performed using
MATLAB and SPSS software (IBM SPSS Statistics, Version 20.0;
IBM, Armonk, NY). For all tests, the significance level was 0.05.
RESULTS
amplitude, in this case defining the threshold as a percentage of
the movement length. We observed that these normalized
thresholds were approximately constant across all movement
directions and amplitudes. The normalized threshold was not
significantly different across saccade amplitude or direction
(2-way ANOVA, P ⫽ 0.947 for the main effect of saccade
amplitude and P ⫽ 0.120 for saccade direction). Consistent
with previous studies of horizontal movements, the threshold
was ⬃10% of the movement amplitude for all directions and
amplitudes tested (Li and Matin 1990, 1997).
Similar to the threshold, the perceptual bias was significantly
different between saccade amplitudes, but the bias was not
significantly different between saccade directions (2-way
ANOVA, P ⬍ 0.01 for the main effect of saccade amplitude
and P ⫽ 0.88 for the main effect of saccade direction). This
was true even though there were significant differences in the
accuracy of the saccades; saccades to all targets generally fell
short of the target with an increase in end point error with
amplitude (1-way ANOVA, P ⫽ 0.03). The size of this error
was significantly larger for saccade targets in the vertical plane
than for the horizontal plane (paired t-test, P ⬍ 0.001). This is
demonstrated by the data from the sample subject presented in
Fig. 2. The mean saccade end points (colored squares) were
closer to the saccade targets (colored circles) for the horizontal
movements, especially at the larger amplitudes. However, the
bias for this subject was generally positive for all movement
directions and amplitudes. This was also true at the group level
(Fig. 3C); when the saccade targets were not shifted (shift of
0°), subjects generally perceived the target as moving backward against the direction of the saccade (reporting a forward
shift on ⬍50% of the trials). Targets shifted a small distance in
the direction of the saccade (generally ⬍0.5°) were perceived
as stationary (reporting a forward shift on ⬃50% of the trials).
This again indicates that overall the gain of the saccade CD
was ⬍1.
To examine the relationship between the perceptual bias and
saccade metrics, we compared the percent error in the target
location and the percent gain in the saccade amplitude. In Fig.
3D, we plot the percent error of the estimated target location
(⬎0 overestimation, ⬍0 underestimation) as a function of
percent gain in the mean saccade amplitude (⬎100% overshoot, ⬍100% undershoot) for all saccade amplitudes and
directions. The former is the perceptual bias as a percentage of
the target amplitude. The latter is the saccade amplitude as a
percentage of the required movement amplitude. The histograms to the right and above are the respective distributions of
the percent error and the percent gain, respectively. The mean
percent error of the estimated target location was significantly
⬍0 for all saccade directions and amplitudes (P ⬍ 0.001 for
each amplitude and direction, 12 comparisons, 2-tailed t-test),
but this percentage was not different between horizontal and
vertical saccades for each amplitude (P ⬎ 0.09 for all 3
comparisons, paired t-test). Thus we combined the horizontal
and vertical movements to specifically examine differences
across movement amplitude. As shown in the figure, the
majority of movements (100 out of 120 cases, 83%) undershot
the target location (mean percent gain of 94.6 ⫾ 3.8%, 88.7 ⫾
3.2%, and 85.4 ⫾ 3.1% for 4 o, 6°, and 8°, respectively).
However, despite regularly making movements less than the
required target amplitude, subjects largely (99 out of 120 cases,
82%) overestimated the target location (mean percent errors of
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Perceptual performance. We examined the perceptual detection of transsaccadic changes in target location as subjects
made eye movements to targets that required saccades of
various amplitudes (4°, 6°, and 8°) and directions (horizontal
and vertical). Unlike previous studies, we concentrated on this
detection when the target shift followed a blank period, rather
than a comparison of performance with and without the blank
period, and the accompanying saccadic suppression of target
displacement (see MATERIALS AND METHODS). The primary saccade end points during this target-displacement detection task
for a sample subject are presented in Fig. 2A. The colored small
circles are the end points for individual saccades, and the
ellipses represent 95% confidence intervals around these end
points for each amplitude and direction. The filled circles and
squares represent the target positions and mean saccade end
points, respectively. Consistent with previous reports, saccade
variability (Abrams et al. 1989; Leigh and Zee 2006; van Beers
2007) and undershoot (Collewijn et al. 1988; de Bie et al. 1987;
Leigh and Zee 2006) scaled with saccade amplitude; both the
size of the ellipses and the distance between the colored
squares and respective circles scale with movement amplitude.
The psychometric curves and corresponding threshold and
bias measurements for the same sample subject are shown in
Fig. 2B. The functions are derived from the percentage of
reported forward responses for the target-shift direction (see
MATERIALS AND METHODS). For all saccade directions, the slope
of the psychometric functions largely decreased with the increase in movement amplitude (3 of the 4 movement directions), corresponding to an increase in the perceptual thresholds (Fig. 2B). Thus the subject had increasing difficulty
distinguishing the direction of change in the target location, as
the change occurred further from the initial fixation. Additionally, the bias (the postsaccadic target shift that resulted in 50%
forward responses) was largely positive (11 out of the 12 cases,
91%) for all amplitudes and directions, indicating a mismatch
between the estimated post- and presaccadic target location.
Specifically, these positive bias estimates are compatible with
a CD signal whose gain was ⬍1 (subjects expected more
undershoot than they observed postsaccadically).
The average perceptual threshold and bias measures across
all subjects are summarized in Fig. 3, A and C, respectively.
Note that all averages are above 0 and have low standard errors
(ⱕ0.22° in all cases), revealing that, despite the intersubject
variability, behavior was sufficiently similar across subjects.
Threshold measurements were significantly different between
saccade amplitudes, but the thresholds were not significantly
different between saccade directions (2-way ANOVA, P ⬍
0.01 for the main effect of saccade amplitude and P ⫽ 0.73 for
the main effect of saccade direction). Thus, similar to the
sample subject, the difficulty in shift detection increased with
saccade amplitude. To determine whether there was a systematic relationship between saccade amplitude and threshold, we
compared the normalized threshold (Fig. 3B). For each subject,
we scaled each threshold by that subject’s mean saccade
3315
THE EFFECT OF SACCADE METRICS ON PERCEIVED EYE LOCATION
A
PRIMARY SACCADE VARIABILITY
4 degree saccade
6 degree saccade
8 degree saccade
Mean Eye Position
Target Position
10
6
4
2
0
−2
−4
−6
−8
−10
−10
−8
−6
B
−4 −2
0
2
4
6
8
Primary Saccade Horizontal Position (°)
75
Bias (°)
0
75
-1
0
1
Target Shift (°)
1.0
100
0.5
2
100
0.5
0.0
-0.5
4 6 8
Amplitude (°)
Rightward
4 6 8
Amplitude (°)
1.0
0.5
0.0
-0.5
-2
-1
0
1
Target Shift (°)
Downward
75
50
2
1.0
0.5
0.0
-0.5
4 6 8
Amplitude (°)
1.0
0.5
0.0
Bias (°)
-0.5
1.0
25
0
-2
6.5 ⫾ 3.4%, 7.7 ⫾ 2.4%, and 7.3 ⫾ 2.3% for 4o, 6°, and 8°,
respectively). Note that the mean percent error of the estimated
target location is significantly ⬎0 for all amplitudes (P ⬍ 0.01
for all three cases, 2-tailed t-test), but the percent gain in the
mean saccade amplitude is significantly ⬍100% (P ⬍ 0.01 for
all 3 cases, 2-tailed t-test). As above, this again demonstrates
0.5
0
0.0
-0.5
2
1.0
50
25
1.0
Bias (°)
-1
0
1
Target Shift (°)
% of Forward
Responses
-2
0.0
75
0.0
-0.5
50
25
0
0.5
Bias (°)
Leftward
1.0
-0.5
50
25
Threshold (°)
100
Threshold (°)
Upward
100
Threshold (°)
% of Forward
Responses
PERCEPTUAL PERFORMANCE
-2
% of Forward
Responses
10
-1
0
1
Target Shift (°)
2
0.5
0.0
-0.5
4 6 8
Amplitude (°)
that overall subjects undershot the target amplitude with a CD
gain ⬍1.
In summary, our results for all four cardinal directions
were comparable to previous reports that examined horizontal saccades in human subjects (Collins et al. 2009; Deubel
et al. 1996; Ostendorf et al. 2010) and monkeys (Joiner et al.
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Fig. 2. Perceptual performance and primary
saccade eye positions for 1 subject. A: primary
saccade variability. The primary saccade horizontal and vertical positions, along with the
mean saccade amplitude (solid squares), are
displayed. Colored filled circles represent the
end points for individual saccades, and the ellipses
represent 95% confidence intervals for each
target amplitude (red: 4°, green: 6°, and blue:
8°) and direction (upward, downward, leftward, and rightward). B: perceptual performance measures. For each direction (upward,
downward, leftward, and rightward), 3 psychometric functions (red: 4°, green: 6°, and
blue: 8°) are shown with their respective perceptual threshold and bias measurements.
Primary Saccade Vertical Position (°)
8
Threshold (°)
3316
THE EFFECT OF SACCADE METRICS ON PERCEIVED EYE LOCATION
A
B
PERCEPTUAL THRESHOLDS
NORMALIZED THRESHOLDS
50
1.0
0.5
0.0
1.0
0.5
0.0
Threshold (°)
1.5
4
6
8
Amplitude (°)
Downward
4
6
8
Amplitude (°)
1.0
0.5
0.0
-0.5
1.5
1.0
4
6
8
Amplitude (°)
20
10
0
0.0
4
4
6
8
Amplitude (°)
D
Upward
1.5
1.0
0.5
15
5
0
Undershoot
0.5
1.0
0.5
0.0
-0.5
4
6
8
Amplitude (°)
Bias (°)
1.5
4
6
8
Amplitude (°)
1.0
0.5
0.0
-0.5
4
6
8
Amplitude (°)
20
10
Overshoot
0
Underestimation
0.0
-0.5
Downward
Rightward
Percent Error of Target Location
1.0
1.5
Bias (°)
Bias (°)
4
6
8
Amplitude (°)
30
Overestimation
-0.5
Leftward
8
4° saccade
6° saccade
8° saccade
Individual subject data
Average across subjects
10
0.0
1.5
6
Saccade Amplitude (°)
ERROR OF PERCEPTUAL TARGET AMPLITUDE
Number of
Occurences
PERCEPTUAL BIASES
Bias (°)
30
−10
0.5
-0.5
C
1.5
Rightward
-10
-20
-30
70 80 90 100 110 120 130
Percent Gain of Saccade Amplitude
5 10 15
Number of
Occurences
0
Fig. 3. Perceptual performance for all subjects. A: perceptual threshold. Bar graphs represent the means and standard errors for perceptual threshold across
subjects for all target amplitudes and directions (red: 4°, green: 6°, and blue: 8°). Saccade direction had no significant effect on threshold; however, perceptual
threshold for all directions increased significantly with target amplitude. B: normalized threshold for each direction plotted against target amplitude. We derived
normalized thresholds by scaling the perceptual threshold as a percentage of the mean primary saccade amplitude for each amplitude and direction. Mean
normalized thresholds were ⬃10% of movement amplitude. C: perceptual bias. Bar graphs represent the means and standard errors for perceptual bias (amount
of displacement at chance level) across subjects for all target amplitudes and directions. D: percent gain of saccade amplitude and percent error estimation of
target location. The percent error in the estimated target location is plotted as a function of percent gain in the saccade amplitude for all saccade amplitudes and
directions. Horizontal and vertical movements are combined for each amplitude, and the larger symbols represent the respective mean percent gains in saccade
amplitude and mean percent errors in target location estimation. The histograms to the right and above the plot are the respective distributions of the percent error
and the percent gain.
2013). The present results indicate that the ability to detect
visual changes that occurred during the saccade proportionally increased in difficulty with movement amplitude. This
difficulty appears to be a systematic function of the saccade
amplitude, with the threshold of detection ⬃10% of the
movement amplitude for all directions. In addition, subjects
made saccades that fell short of the initial target location but
frequently overestimated this location, demonstrating a positive perceptual bias for targets in different directions and
amplitudes.
Influence of saccade and visual errors on perceptual
judgments. As shown in Fig. 2A, there was movement-tomovement variability in the saccade end points that scaled with
movement amplitude. We were interested in the influence, if
any, of these movement amplitude fluctuations on perceptual
performance. Previous work (Collins et al. 2009; Joiner et al.
2013; Ostendorf et al. 2010) has shown that the perception of
transsaccadic target displacement is independent of variations
in the saccade amplitude. This suggests that the CD signal of
the saccade accounts for the inherent movement-to-movement
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Threshold (°)
Threshold (°)
-0.5
Upward Saccades
Downward Saccades
Rightward Saccades
Leftward Saccades
40
Threshold as a Percentage
of Saccade Amplitude (%)
Threshold (°)
Upward
1.5
Leftward
3317
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THE EFFECT OF SACCADE METRICS ON PERCEIVED EYE LOCATION
A
FORWARD PERCEPTUAL REPORTS FOR HORIZONTAL SACCADES
100
75
6° SACCADES
R = 0.35
P = 0.13
100
R = 0.27
P = 0.24
75
100
50
50
25
25
25
0
-3 -2 -1 0 1
2 3
0
-3 -2 -1
0 1 2
3
R = 0.14
P = 0.58
75
50
B
0
-3 -2 -1 0 1
2 3
FORWARD PERCEPTUAL REPORTS FOR VERTICAL SACCADES
4° SACCADES
Percent “forward” Reports
8° SACCADES
100
75
6° SACCADES
R = 0.29
P = 0.22
100
R = 0.01
P = 0.95
75
8° SACCADES
100
75
50
50
50
25
25
25
0
-3 -2 -1 0 1 2 3
Saccadic Error (°)
variability. Here, we were interested in determining whether
this independence was consistent across different movement
directions, and more importantly, different saccade amplitudes
attributable to the correlated changes in movement variability.
Figure 4 shows the relationship between perceptual performance (the percentage of forward perceptual reports) and the
saccade error (the difference between the original target location and the primary saccade end point). Positive saccade
errors indicate that the target was in front of the saccade
(hypometric saccade); negative values indicate that the target
was behind the saccade (hypermetric saccade). As in our
previous study (Joiner et al. 2013), we binned the saccade
errors into 20 bins of equal size and then calculated the
percentage of forward reports within each bin. In agreement
with previous work (Collins et al. 2009; Joiner et al. 2013;
Ostendorf et al. 2010), we found no significant relationship
between perceptual judgments and saccade variability (P ⱖ
0.13 in all cases). Importantly, this was true for saccades to
targets located at different directions and amplitudes. Thus,
although there was an increase in saccade variability with
movement amplitude, perceptual performance remained independent of variations in the saccade amplitude.
The movement-to-movement fluctuations of the saccade
amplitude and the random shift of the target (both in magnitude
and direction) resulted in various visual errors at target reappearance that subjects could potentially use to guide the perceptual report. We therefore examined the influence of these
visual errors on perceptual performance. The visual error was
quantified by determining the vector between the eye position
at the time of target reappearance and the shifted target location. Figure 5A plots the percentage of correct perceptual
reports as a function of visual error for horizontal and vertical
saccades. For each subject, we sorted the visual error within
bins ⬃1.25° wide and determined the average percentage of
0
-3 -2 -1 0 1 2 3
Saccadic Error (°)
0
R = 0.06
P = 0.81
-3 -2 -1 0 1 2 3
Saccadic Error (°)
correct responses across subjects. In most cases, the percentage
of correct responses for both horizontal and vertical saccades
was greatest for the largest visual errors (ⱖ⫾2.5°) but declined
as the visual error decreased. Figure 5B displays the average
percentage of correct perceptual reports across subjects for
small (ⱕ⫾0.75°) and large visual errors (negative: ⬍⫺0.75°,
positive: ⬎0.75°) for the different saccade directions and
amplitudes. As shown in the figure, the percentage of correct
responses was significantly greater than chance level (50%,
P ⬍ 0.01 in all cases), even for the small visual error range
(ⱕ⫾0.75°). For large errors (⬍⫺0.75° and ⬎0.75°), we found
a significant difference between movement amplitudes but not
between movement directions (2-way ANOVA, P ⬍ 0.01 for
the main effect of saccade amplitude and P ⱖ 0.07 for the main
effect of saccade direction, for both cases). That is, for the
same error range, perceptual performance decreased with amplitude, but this decrease was similar for horizontal and vertical
saccades. In contrast, for small visual errors between ⫾0.75°,
we did not find a significant difference between movement
amplitudes, but perceptual performance was significantly different between movement directions (2-way ANOVA, P ⫽
0.79 for the main effect of saccade amplitude and P ⫽ 0.04 for
the main effect of saccade direction). In other words, the
perceptual response tended to be more accurate for vertical
movements when subjects experienced these small visual errors, but there was not a consistent change in performance
across movement amplitudes.
It should be noted that any significant difference in performance between movement directions and amplitudes for the
different magnitudes of visual error reported above is nominal
compared with the overall ability of subjects to report the
correct shift direction (⬎75% in all cases). This overall similarity in performance makes it difficult to distinguish the
contribution of the CD signal to the perceptual report, espe-
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Fig. 4. Relationship between saccade error
and perceptual decision. The saccade error
was the difference between the original target
location and the eye position after the saccade. Positive saccade errors represent hypometric movements (the target was in front of
the saccade end point). The percentage of
forward perceptual reports is plotted as a
function of saccade error for horizontal (A)
and vertical (B) saccades. Each column displays the results for saccades to the 4°, 6°, and
8° targets. The regression line is represented
by the thick colored trace and the respective
correlation coefficient, and significance values are displayed in the top right of each plot.
Percent “forward” Reports
4° SACCADES
THE EFFECT OF SACCADE METRICS ON PERCEIVED EYE LOCATION
A
AVERAGE CORRECT PERCEPTUAL REPORTS FOR HORIZONTAL AND VERTICAL SACCADES
Percent Correct Reports
Horizontal Saccades
Vertical Saccades
100
100
75
75
50
-4
-2
0
2
4
50
-4
4° Saccades
B
-2
2
0
4
Visual Error (°)
6° Saccades
8° Saccades
AVERAGE CORRECT PERCEPTUAL REPORTS FOR DIFFEFRENT ERROR SIZES
Large Positive Visual Errors
Small Visual Errors
Large Negative Visual Errors
100
100
100
75
75
75
50
Horizontal
Vertical
50
Horizontal
Vertical
50
Horizontal
Vertical
Fig. 5. Visual error and perceptual judgment of shifted targets. The visual error with respect to the shifted target was quantified by taking the difference between
the eye position at the time of target reappearance and the location of the shifted target. A: percentage of correct perceptual reports is plotted as a function of
visual error for horizontal and vertical saccades for each target amplitude (red: 4°, green: 6°, and blue: 8°). B: bar graphs for the average percentage of correct
reports for large negative (⫺2.25° to ⫺0.75°), small (⫺0.75° to 0.75°), and large positive visual errors (0.75° to 2.25°). Error bars show SE.
cially for large visual errors that likely provide a noticeable cue
of the correct shift direction. A more revealing analysis of the
CD accuracy is provided by examining the perceptual performance when small visual errors were in the direction opposite
the shift direction. That is, we examined performance of
subjects on trials when the correct perceptual response was not
aligned with the limited visual information (visual errors
ⱕ⫾0.75°). We found on this subset of trials that subjects were
still able to report the correct shift direction significantly
greater than chance level (⬎70% correct perceptual reports of
for all amplitudes and directions, P ⬍ 0.01). Thus these results
for visual errors suggest that subjects were not solely relying
on retinal information to form the perceptual judgment and that
the extraretinal information of the saccade provided by the CD
is a highly accurate representation of the movement vector.
DISCUSSION
Understanding how humans perceive transsaccadic displacements of objects in the visual scene provides insights into the
neural mechanisms that facilitate stable visual perception. In
this study, we employed a forced choice task to quantify the
effects of saccade amplitude and direction on the perception of
transsaccadic changes in the saccade target location. We assessed two characteristics of perceptual performance, the perceptual bias (the postsaccadic estimate of the target location)
and the perceptual threshold (the amount of target shift at
which detection rose sufficiently above chance level). We
found that the perceptual threshold 1) scaled with saccade
amplitude with no significant main effect of direction and 2)
was ⬃10% of the saccade amplitude across the different
saccade metrics studied. In addition, on the basis of the bias
measures, we show that subjects mostly overestimated the
target position despite the saccades generally falling short of
the target amplitude. Finally, we examined the role of the
saccade and visual errors on the ability to make a correct
perceptual report of the transsaccadic target displacement. Our
results show that 1) perception was independent of the saccade
variability for all movement directions and amplitudes tested
and 2) subjects were able to detect the target shift both when
the visual error was in agreement and opposite to the targetshift direction at a level significantly higher than chance. Taken
together, our experimental data suggest that the compensation
for saccade-induced disruptions to visual input is a process that
1) has an uncertainty proportional to the magnitude of the
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Visual Error (°)
Percent Correct Reports
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THE EFFECT OF SACCADE METRICS ON PERCEIVED EYE LOCATION
between the two movement directions, there are several differences between the two studies that may partially explain this
inconsistency. First, although both tasks assess CD, there is a
significant difference in the task requirements. In the doublestep task, the subject must update the movement plan based on
the CD information of the initial movement. In the perceptual
task utilized here, the subject must make a perceptual judgment
based on the CD of the initial movement. Thus, although the
tasks may utilize the same internal CD signal, the task demands
(motor planning vs. perceptual evaluation) require that this
information be utilized differently. Thus the subsequent neural
processes that use this CD information in each respective
paradigm may negate any direct comparisons between tasks.
Second, in the shift-detection task, the perceptual decision is
made for foveal information, whereas, in the double-step task,
the CD is used to make a movement to a peripheral goal. One
possible method to reconcile this difference between tasks is to
conduct a perceptual task during which the transsaccadic perceptual judgment is made for a peripheral target rather than at
the fovea. This may reveal perceptual differences between the
horizontal and vertical CD similar to that previously demonstrated for movement planning (Joiner et al. 2010).
Gain of the saccade CD and possible effects on the perception of visual space. Our assessment of perceptual bias suggests that subjects misjudged the postsaccadic location of the
target, often reported as a higher amplitude than the presaccadic distance. This overestimation was 1) present despite the
saccades undershooting the saccade target and 2) similar across
the three saccade amplitudes studied. Previous reports of target-shift detection with a postsaccade blank period have also
shown positive bias measures from fitted psychometric curves
(Collins et al. 2009; Ostendorf et al. 2010; Wexler and Collins
2014). A positive bias suggests that the gain of the saccade CD
is ⬍1. For example, when the targets were not shifted (shift of
0°), subjects generally perceived the target as moving opposite
the movement direction. Thus, on the basis of the CD, subjects
expected a greater undershoot than that experienced; a small
forward shift is necessary for the subject to perceive that the
target is stationary. Additionally, we found no significant
relationship between the mean saccade gain and the perceptual
bias (P ⬎ 0.06 in all cases), suggesting that the accuracy of the
CD is not dependent on the accuracy of the saccade.
Although we did not assess the estimated target location
during the initial fixation period, the positive perceptual bias
exhibited by our subjects could also be interpreted as an
expansion of visual space. That is, if there was an accurate
initial estimation of the target location, the exhibited positive
bias suggests that this estimated distance increased following
the saccade. Such an expansion would be in disagreement with
other transsaccadic perceptual studies that have shown compression of visual space at the saccade goal; flashed stimuli
around the movement goal are perceived closer to the saccade
end point than the true distance (Kaiser and Lappe 2004; Lappe
et al. 2000; Morrone et al. 1997; Ross et al. 1997). This is true
even for adapted saccades; perceptual localization of stimuli is
influenced by the movement adaptation (Awater et al. 2005;
Bruno and Morrone 2007; Collins et al. 2007; Zimmermann
and Lappe 2010). Several differences in the experimental
paradigms and how perception is assessed may account for the
discrepancy with previous reports. First is the strong role
saccadic suppression plays in the perception of visual space.
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motor signal and 2) is comparable for movements with different metrics.
Threshold linked to saccade generation. The systematic
increase in threshold with saccade amplitude is in line with
several previous human and monkey visual perception studies.
Li and Matin (1990, 1997) showed that the threshold for
transsaccadic displacements in the direction of the saccade
increased linearly with target amplitude for horizontal saccades
ranging from 4° to 12°, Recently, Joiner et al. (2013) reported
a similar increase in threshold over a comparable range of
horizontal target amplitudes (8° to 16°) in monkeys. What does
this systematic increase in perceptual threshold reveal about
the underlying neural mechanisms? Recall that the threshold is
the displacement amount required to perceive the target jump
direction at a percentage greater than chance level. This
amount should increase with any rise in noise associated with
the decision process; i.e., a larger signal (target shift) is
required to overcome any additional noise obscuring the detection of a target shift. A process with noise that increases in
near constant proportion with the movement amplitude (signaldependent noise, SDN) should demonstrate an approximately
constant normalized relationship with the movement amplitude
(a constant coefficient of variation). The finding that there is an
approximate constant threshold percentage of 10% across the
saccade amplitudes studied may reflect the SDN previously
demonstrated for saccade generation (Goossens and van Opstal
2012). As shown in Fig. 2A, previous studies that examined the
spatial variability of saccade end points demonstrated that, as
the amplitude increased, there was an accompanying increase
in motor command variance, reflected as an increase in saccade
end point scatter (Abrams et al. 1989; Leigh and Zee 2006; van
Beers 2007; van Opstal and van Gisbergen 1989). This reflects
that the neural variability associated with the saccade motor
command is linearly proportional to the mean command magnitude (SDN), as supported by several behavioral, physiological, and theoretical studies (Goossens and van Opstal 2012;
Harris and Wolpert 1998, 2006; Hu et al. 2007; van Beers
2007, 2008). Thus the observed changes in perceptual threshold with amplitude may reflect the corresponding SDN associated with the respective motor commands; perceptual decisions based on the CD representation of increasingly noisy
motor commands require larger external changes (target shifts)
to form consistent judgments, but this increase is in near
constant proportion to the original motor command.
Our finding that the thresholds for target-displacement detection were similar across movement directions is in agreement with our previous study that showed that subjects made
accurate motor adjustments based on the CD of horizontal,
vertical, and oblique saccades (Joiner et al. 2010). Although
general performance in this paradigm was comparable between
the two movement directions, the second saccade compensation in the double-step task following a vertical saccade was
significantly less than that following a horizontal movement.
This implied that the movement information conveyed by the
CD of vertical movements was generally less accurate. On the basis
of this finding and the different neural origins for the motor
commands and presumably the CD for horizontal and vertical
saccades (Leigh and Zee 2006), we initially hypothesized that
transsaccadic perceptual performance would also be distinct
when reliant on the CD of vertical saccades. Although we
found no significant difference in the perceptual measures
THE EFFECT OF SACCADE METRICS ON PERCEIVED EYE LOCATION
the unpredictability of the target shift allowed us to examine
the influence of the postsaccadic visual error on perception.
Although there were variations in performance for different
directions and magnitudes of visual error, subjects reported the
correct direction of the transsaccadic target shift significantly
greater than chance level (⬎75% correct perceptual reports) for
all saccade directions and amplitudes (Fig. 5). We found that
this was true for small visual errors (ⱕ⫾0.75°), for which the
report would likely be a guess if totally reliant on such a
limited amount of visual information. In addition, when these
small errors were opposite the true shift direction (the shift
direction and visual error were misaligned), performance was
also significantly higher than the level expected when purely
based on the visual error. This again suggests that subjects used
the CD of the saccade to make the perceptual judgment rather
than the visual displacement observed at target reappearance
and that the CD provides a dependable and accurate representation of the saccade movement vector.
Conclusion. Internal information on the metrics of impending saccades likely plays a critical role in the perception of a
stable world. Transsaccadic perceptual tasks allow an assessment of the neural processes that compensate for the saccadeinduced disruptions to visual input and the CD signals hypothesized to facilitate these mechanisms. In the present study, we
report behavioral results that suggest that these processes are
uniformly applied for different movement metrics (amplitudes
and directions) and consistently independent of saccade variability. In addition, performance was significantly more accurate than that allowed by a simple guessing strategy and similar
across different movement directions for the same magnitudes
of visual error, even when the visual information was in
conflict with the true environmental change. Future studies that
systematically examine the combined effect of different saccade (horizontal, oblique, and vertical) and visual change
directions (on and off axis) on perception may allow an
estimation of the perceptual sensitivity field of these compensatory mechanisms and offer a more complete characterization
of the underlying neural signals.
ACKNOWLEDGMENTS
We are grateful for the advice and discussions with our colleagues Christian
Quaia and Edmond Fitzgibbon.
GRANTS
This work was supported by a grant from the National Eye Institute (R00
EY021252) to W. M. Joiner.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the authors.
AUTHOR CONTRIBUTIONS
Author contributions: S.B. performed experiments; S.B., L.C.J.B., and
W.M.J. analyzed data; S.B., L.C.J.B., M.S.P., and W.M.J. interpreted results of
experiments; S.B., L.C.J.B., and W.M.J. prepared figures; S.B., L.C.J.B., and
W.M.J. drafted manuscript; S.B., L.C.J.B., M.S.P., and W.M.J. edited and
revised manuscript; S.B., L.C.J.B., M.S.P., and W.M.J. approved final version
of manuscript; W.M.J. conception and design of research.
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