Vision Research 45 (2005) 413–430
www.elsevier.com/locate/visres

Perisaccadic perception of continuous ﬂickers
Junji Watanabe a,b,*, Atsushi Noritake c, Taro Maeda b,
Susumu Tachi a, ShinÕya Nishida baGraduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, JapanNTT Communication Science Laboratories, NTT Corporation, 3-1 Morinoisato Wakamiya, Atsugi, Kanagawa 243-0198, Japanc
Graduate School of Humanities, Kwansei Gakuin University, 1-155 Ichibancho Uegahara, Nishinomiya, Hyogo 662-8501, Japanb

Received 24 July 2004

Abstract
To realize perceptual space constancy, the visual system compensates for the retinal displacement caused by eye movements. It
has been reported that the compensation process does not function perfectly around the time of a saccade––a perisaccadic ﬂash issystematically mislocalized. However, observations made with transient ﬂash stimuli do not necessarily indicate a general perisaccadic failure of space constancy. To investigate how the visual system realizes perisaccadic space constancy for continuous stimuli, we
examined the time course of localization for a perisaccadic 500 Hz ﬂicker with systematic variation of the onset timing, the oﬀset
timing and the duration. If each ﬂash in the ﬂicker is localized individually in the same way as a single ﬂash, the apparent positionand length of the ﬂicker should be predicted from the time course of mislocalization of a perisaccadic ﬂash. However, the results did
not support this prediction in many respects. A dot array (of half the length of the retinal image) was perceived when the ﬂicker waspresented during a saccade, while only a single dot was perceived when the ﬂicker was presented only before or after the saccade. A
ﬂash in a ﬂicker was localized at a diﬀerent position, depending on the onset timing, the oﬀset timing and the duration of the ﬂicker,
even if the ﬂash was presented at the same timing to the saccade. In general, our results support a two-stage localization in which thelocal geometrical conﬁguration is ﬁrst generated primarily based on the retinal information, and then localized as a whole in the egocentric or exocentric space. The localization is based on the eye position signal sampled at a time temporally distant from thesaccade, which enables precise localization and space constancy for continuous stimuli.
Ó 2004 Elsevier Ltd. All rights reserved.
Keywords: Saccade; Localization; Space constancy; Flicker; Continuous light

1. Introduction
Human observers frequently make eye movements tosee surrounding environments with the central sensitive
area of the retina. Although the eye movements shift thelocation of stationary objects on the retina, the observers do not normally perceive the displacement of the objects. The visual system compensates for the retinal*

Corresponding author. Tel.: +81 3 5841 6917; fax: +81 3 5841
8601.
E-mail address: junji@star.t.u-tokyo.ac.jp (J. Watanabe).
0042-6989/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.visres.2004.09.010

displacement in some way and realizes perceptual spaceconstancy. A widely-accepted account of this compensation is the cancellation theory (Sperry, 1950; von Holst,
1954; von Holst & Mittelstaedt, 1950), which states thatthe perceived location of an object is determined by thesummation of the retinal location of the object and theinternal information about the eye position, namely,that the retinal displacement by the eye movement iscanceled by the internal eye position signal (EPS). It
has been reported that the compensation process does
not function perfectly around the time of a saccade.
When a brieﬂy ﬂashed stimulus is presented before, during, and after a saccade, the perceived position of thestimulus is systematically mislocalized (Bockisch &414

J. Watanabe et al. / Vision Research 45 (2005) 413–430

Miller, 1999; Boucher, Groh, & Hughes, 2001; Dassonville, Schlag, & Schlag-Rey, 1995; Honda, 1989, 1990,
1991; Mateeﬀ, 1978; Matin, Matin, & Pearce, 1969; Matin, Matin, & Pola, 1970; Matin & Pearce, 1965; Schlag& Schlag-Rey, 1995). Single ﬂashes presented in darkness before saccades were mislocalized toward the direction of saccade, while those presented after saccades
were mislocalized in the opposite direction (examplesof the time courses are shown in Fig. 2). These errors
have been interpreted through the cancellation theory
as a result of a mismatch between the actual eye position
and the sluggishly changing EPS. Additionally, whenmeasured in relation to visual references, the error indicates a non-uniform mislocalization across the visualﬁeld, which resembles a compression of visual spacearound the saccadic target (Awater & Lappe, 2004;
Honda, 1993; Kaiser & Lappe, 2004; Lappe, Awater,& Krekelberg, 2000; Matin & Pearce, 1965; Morrone,
Ross, & Burr, 1997; Ross, Morrone, & Burr, 1997).
Perisaccadic space constancy has been studied bymainly using single ﬂashes, but it is debatable whether
the mislocalization of a single ﬂash indicates a general
failure of perisaccadic space constancy. In typical environments, almost every object continues to exist before
and after the saccade, and the visual system may exhibit
more robust space constancy in such a continuous environment. Furthermore, a ﬂash stimulus should not be
regarded as a general probe for perceptual localization,
since it is known that transient stimuli like a ﬂash and astimulus onset are mislocalized in various ways by thepresence of retinal motion (Eagleman & Sejnowski,
2000a, 2000b, 2000c; Kerzel, 2002; Nijhawan, 1994;
Purushothaman, Patel, Bedell, & Ogmen, 1998; Schlag,
Cai, Dorfman, Mohempour, & Schlag-Rey, 2000; Whitney & Cavanagh, 2000; Whitney & Murakami, 1998).
The localization error for a ﬂash presented near the timeof a saccade may also include some eﬀects speciﬁc to thetransient stimulus rather than indicating the generalfunction of realizing the space constancy.
Indeed, previous studies reported several cases where
the time course of mislocalizations measured with single
ﬂashes do not agree with those measured with less transient stimuli. Schlag and Schlag-Rey (1995) reported
that when a dot was continuously presented immediately before a saccade, although apparent displacementsof single ﬂashes predicted the perception of a motion
streak, subjects veridically saw a single dot (see also
Campbell & Wurtz, 1978; Holly, 1975; Mateeﬀ, 1978;
Sogo & Osaka, 2001). The streak was found to be visible
only when there was an actual stimulus movement on
the retina. As an elegant extension of this ﬁnding, Cai,
Pouget, Schlag-Rey, and Schlag (1997) showed thatwhen a single ﬂash was presented at the oﬀset of the continuous light stimuli, the ﬂash was mislocalized relative
to the continuous stimuli. Hershberger and his colleagues reported that, just as a continuous light pre-sented during a saccade produces a motion streak, arapidly ﬂickering stimulus produces the perception ofa dot array, which they called a ÔPhantom ArrayÕ
(Hershberger, 1987; Hershberger & Jordan, 1992;
Hershberger, Jordan, & Lucas, 1998; Jordan & Hershberger, 1994). They showed that the dot appeared tomove in the opposite direction of the saccade, and thatthe length of the perceived dot array was about half
the length of the retinal image. In addition, a dot ﬂashedwithin 80 ms before the saccade was seen as spatiallycoincident with the ﬁrst ﬂash of the dot array, which isinconsistent with the time course of single-ﬂash mislocalization (Jordan & Hershberger, 1994). More recently,
Sogo and Osaka (2002) found an interaction between
the apparent locations of successively presented two
ﬂashes. Speciﬁcally, when the inter-stimulus interval
was 120 ms or shorter, the apparent distance between
the two ﬂashes did not coincide with the time courseof the perisaccadic mislocalization, but was coincident
with their retinal distance. These ﬁndings suggest that
perisaccadic localization of intransient stimuli is a complex phenomenon that cannot be simply predicted fromlocalization of single ﬂashes.
To gain further insight into the principle and mechanism underlying space constancy in natural environments, the present study examined the time course of
localization for a continuous stimulus, and compared
the data with those obtained with a single ﬂash. The
stimulus we mainly used was a 500 Hz ﬂicker. Considering the temporal response of early visual mechanisms, a
500 Hz ﬂicker is indistinguishable from a physically continuous light to the visual system as long as the eye isstationary. We also repeated some experiments with aphysically continuous light (see Expts. 2 and 3). A meritof using a high-frequency ﬂicker is that it potentially
produces diﬀerent appearances for two possible typesof perceptual spreads. One is caused by retinal painting
during saccadic eye movement. In this case, since the eye
movement is very fast, the ﬂicker should be seen as anarray of dots. The other type is a dot spread potentiallyobserved before or after a saccade, caused by extra-retinal localization errors. If this spread in fact occurs, theﬂicker that stimulates the same retinal location should
be seen as a continuous light spread, rather than a dot
array. As described below, however, we never observed
the dot spread of the latter type.
In the experiments, we systematically varied theparameters that previous ﬁndings (e.g., Schlag & Schlag-Rey, 1995; Sogo & Osaka, 2001, 2002) suggested
to be potentially important: the onset timing, the oﬀset
timing and the duration. Depending on the timing ofeye movements, a ﬂickering LED was perceived either
as a single dot or a dot array. We asked subjects to point
to the position of either the dot or the left and right endsof the dot array, so as to estimate both the apparent
locations and the apparent length. In the ﬁrst experi-

J. Watanabe et al. / Vision Research 45 (2005) 413–430

ment, the time course of localization for a brieﬂy ﬂashedstimulus was measured. The data formed the basis forcomparing the time course with the data from subsequent experiments. In the second experiment, we presented a ﬂickering stimulus long before a saccade
onset, and systematically changed the oﬀset timing. In
the third experiment, we systematically changed the
ﬂicker onset time, and presented the stimulus until longafter a saccade onset. In the fourth experiment, we systemically changed both the duration and onset/oﬀset
timing of the ﬂicker presented around the time of a saccade. Consistent with the previous report, our results
showed that perisaccadic mislocalization of continuous
ﬂickers was incompatible with the time course of single-ﬂash localization. Further analysis of the pattern of
mislocalization led us to a two-stage localization process––the local geometrical conﬁguration is ﬁrst generated based on the retinally-painted image, thenlocalized as a whole in the egocentric or exocentric
space.

415(a) Spatial arrangement
FPTP

8 deg saccade

S
Left end

Right end

Perceived dotted line(b) Time charts
10ms

Time

TP
Flash
random timing

Expt 1 S

FPExpt 2 S
Expt 3 S
Expt 4 S

2-3s

Saccade onset

Eyemovement

500ms
VariedFixed
Varied

Fixed

20ms

VariedVaried20ms

20, 50, 100, 200 ms

2. Experiment 1: Localization of a brieﬂy ﬂashed stimulus
In a completely dark room the subject localized theperceived position of a perisaccadically ﬂashed stimulus.
2.1. Methods
2.1.1. Subjects
Three naı¨ve male subjects with normal visual acuity
whose age ranged from 22 to 24 (referred to as Y.I.,
Y.A. and K.F.), participated in all four experiments.
2.1.2. Apparatus
A ﬁxation point (FP), a target point (TP) and a probe
stimulus (S) were arranged as shown in Fig. 1a. The FP
and TP were red light emitting diodes (LED) (diameter:
0.25 deg, luminance: 16 cd/m2). The subject was asked tomake a saccade from the FP to the TP. The distance between the FP and TP was 8 deg in visual angle. The S
was a green LED (diameter: 0.1 deg) and located at
the center of the FP and TP. The luminance of the S
was 10 cd/m2 (one subject, K.F., was also tested with
1.6 cd/m2, which was the luminance of ﬂicker stimuli
used in the following experiments). The distance fromthe subjectÕs right eyeball to the S was 150 cm. The eyeball, FP, TP and S were arranged at same vertical level.
The subject sat in a chair with the head stabilized by achin rest. The subjectÕs left eye was covered with aneye patch. Horizontal movement of the subjectÕs righteye was measured at 600 Hz by an EMR-600 (NAC
Inc.) with a resolution of 0.17 deg. The output of analog
voltage by EMR-600 and the ﬂash timing of the FP, TP,
and S were recorded by a digital I/O of an AT PC. A micro IC (PIC16F877 microchip inc.) was used to control

Fig. 1. (a) Spatial arrangement and (b) time charts of experiments. A
ﬁxation point (FP), target point (TP) and stimulus (S) were respectively
located at 4, 4, and 0 deg away from the front of the right eyeball of
the subject. The subject was asked to make an 8 deg saccade fromthe FP to TP. At the beginning of a trial, the FP was turned on. The
subject moved his gaze to the FP. After a random duration (2–3 s), theFP disappears. Immediately after the disappearance of the FP, the TP
turned on for 10 ms. The subject had to make a saccade to the TP as
quick as possible. In Expt. 1, the S was presented for 2 ms at a random
time from 10 ms to 600 ms after the oﬀset of the TP (i.e., from about
200 ms before to about 400 ms after the onset of a saccade). In Expt. 2,
the S started to ﬂicker as the FP turned on. The duration of the S wasvaried so that the termination time was set between 10 ms and 600 ms
after the oﬀset of the TP. In Expt. 3, the S started to ﬂicker at a
random time from 10 ms to 600 ms after the oﬀset of the TP, and its
disappearance time was ﬁxed to 700 ms after the oﬀset of TP (about
500 ms after the saccade oﬀset). In Expt. 4, the presentation time of the
ﬂicker was also set between 10 ms and 600 ms after the oﬀset of the TP,
and its duration was selected among 20, 50, 100 and 200 ms. In all
experiments, the subject was asked to point to the perceived location of
the S. When the subject perceived a dot, he localized it using one laser
pointer, and when a dot array was perceived, he localized the left andright ends of the dot array using two laser pointers at the same time.

the ﬂash timing of the LEDs. All experiments were performed in a completely dark room.
2.1.3. Procedure
Each block of the experiments began with a calibration procedure, in which the subject sequentially ﬁxated
upon one of ﬁve dots located at 8, 4, 0, 4, or 8 deg on
the same level as the FP, TP and S. The eye position was
calculated linearly based on the measurements for theﬁve positions. The time charts of the experiments areshown in Fig. 1b. At the beginning of each trial, theFP was turned on, and the subject moved his gazeto the FP. After a random duration (2–3 s), the FP

416

J. Watanabe et al. / Vision Research 45 (2005) 413–430

disappeared, and the TP (saccade target) turned on
immediately for 10 ms. The subject made a saccade to
the TP. The S was presented for 2 ms at a random timefrom 10 ms to 600 ms after the oﬀset of TP (i.e., fromabout 200 ms before to about 400 ms after the onset ofa saccade). The subject was asked to point to the perceived location of the S with a red laser pointer (diameter: 0.08 deg, laser: class II), which was ﬁxed on the tablein front of the subject, and could move only horizontally. The plane where the FP, TP and S were attached
was covered with graph paper (resolution 1 mm), andthe experimenter read the value from the location of
the laser beam. We asked the subject to point to the perceived location immediately to avoid potential memory
distortion of the perceived location (Sheth & Shimojo,2001). The measured value of the perceived location
was not told to the subject. In all experiments, eachexperimental block consisted of 50 trials, and each subject ran ﬁve blocks.
2.1.4. Data analysis
The same analysis of eye position data was performed
in all experiments. Since the subjects were to make an
8 deg saccade, all data samples in which the amplitudeof the saccade was over 10 deg or under 5 deg, or theduration was over 70 ms or under 20 ms, or the latency
was over 300 ms or under 60 ms, were excluded. Before
analyzing the data, a linear low pass ﬁlter (cut-oﬀ frequency 100 Hz) was applied to eliminate noise. The onset of a saccade was deﬁned as the time when thevelocity of the eye movement exceeded 40 deg/s for theﬁrst time, and the oﬀset of a saccade was deﬁned as
the time when it became less than 40 deg/s for the ﬁrst
time after the saccade onset.
2.2. Results
Table 1 describes the number of trials, amplitudes,
durations and latencies of saccades for all subjects inall experiments. These data indicate that stable saccades
were achieved. The localization data of Expt. 1 areshown in Fig. 2. The amount of mislocalization wastightly related to the time when the stimulus was ﬂashed.
For all subjects, the displacement in the same directionof the saccade began at least 200 ms before the onsetof the saccade and reached a maximum at the onset.
Soon after the onset, the mislocalization in the opposite
direction emerged, and persisted until about 200–400 ms
after the oﬀset of the saccade. The mislocalization of
Y.I. (Fig. 2a) continued slightly longer than the othersubjects. In the data of Y.A. (Fig. 2b), the mislocalization in the same direction apparently began more than
200 ms before the saccade onset, and the mislocalizationin the opposite direction after the saccade was notclearly visible. In some trials of K.F. (Fig. 2c), mislocalization in the same direction occurred even after the saccade. The last subject (K.F.) was tested also with adarker S (1.6 cd/m2, Fig. 2d), but the result was nearly
the same as the result with 10 cd/m2. Besides minor differences between individuals, the general tendencies ofTable 1
Number of trials, amplitudes, durations and latencies of performed saccades in all experiments
TrialsMean amplitudes (deg)Duration (ms)

Latency (ms)Y.I.

Expt. 1
Expt. 2Expt. 3
Expt. 4, 20 ms
Expt. 4, 50 ms
Expt. 4, 100 ms
Expt. 4, 200 ms

185
181
221
184
171
169
160

7.69 (1.18)
7.65 (1.43)
7.46 (1.16)
7.13 (1.09)
7.21 (1.19)
7.24 (1.26)
7.11 (1.27)

40.6 (5.8)
40.8 (6.4)
39.4 (5.8)
40.6 (6.1)
40.5 (5.7)
40.7 (5.9)
40.3 (5.7)

220.2 (25.4)
207.7 (31.9)
212.9 (31.5)
221.1 (33.5)
222.2 (32.9)
224.8 (31.0)
222.9 (30.5)

Y.A.

Expt. 1
Expt. 2Expt. 3
Expt. 4, 20 ms
Expt. 4, 50 ms
Expt. 4, 100 ms
Expt. 4, 200 ms

206
214
171
201
181
182
183

6.92 (1.05)
7.62 (1.38)
7.54 (1.02)
6.92 (1.12)
6.96 (1.05)
6.95 (1.10)
6.95 (1.08)

39.0 (4.9)
42.6 (5.9)
41.6 (5.5)
40.0 (5.3)
40.3 (5.0)
40.0 (5.0)
39.5 (5.0)

213.5 (48.6)
212.7 (40.5)
208.8 (33.9)
212.6 (32.0)
206.0 (35.9)
219.6 (50.6)
222.5 (50.7)

K.F.

Expt. 1
Expt. 1 (1.6 cd/m3)
Expt. 2Expt. 2 (cont.)
Expt. 3
Expt. 3 (cont.)
Expt. 4, 20 ms
Expt. 4, 50 ms
Expt. 4, 100 ms
Expt. 4, 200 ms

181
166
176
153
167
176
189
184
168
169

7.17 (1.26)
7.20 (1.35)
7.60 (2.17)
7.00 (1.65)
7.29 (1.47)
7.30 (1.86)
6.98 (1.16)
6.97 (1.16)
6.87 (1.18)
7.06 (1.22)

38.0 (6.2)
36.9 (5.8)
41.0 (9.2)
35.4 (9.1)
41.9 (8.3)
35.5 (6.0)
38.5 (5.4)
38.9 (5.4)
38.3 (5.4)
39.1 (6.0)

258.4 (45.2)
248.9 (41.8)
222.4 (35.3)
218.4 (20.2)
244.3 (48.9)
230.8 (32.8)
228.7 (42.8)
223.0 (40.9)
227.5 (42.0)
223.8 (39.5)

J. Watanabe et al. / Vision Research 45 (2005) 413–430

Perceived position [deg](a)Subject: Y.I.

Subject: Y.A.

4
3
2
1
0
-1
-2
-3
-4
-200 -100 0(c)

Perceived position [deg]

(b)

417

100 200 300 400

Subject: K.F.

-200 -100 0(d)

100 200 300 400

Subject: K.F. (1.6 cd/m2)

4
3
2
1
0
-1
-2
-3
-4
-200 -100 0

100 200 300 400-200 -100 0

100 200 300 400

Flash time from saccade onset (ms)Fig. 2. Perceived positions for a brieﬂy ﬂashed stimulus. The abscissa (horizontal axis) represents the temporal diﬀerence between the ﬂash time andthe saccade onset (ms). A negative value indicates that the stimulus ﬂashes before the saccade onset. The ordinate (vertical axis) represents perceived
position (deg). Saccades were made from 4 deg to +4 deg. Lined-dots represent averages of perceived positions, which was computed for every 20 ms
interval from 200 to +100 ms and for every 40 ms interval from +100 to +420 ms. In the following ﬁgures, the averages were computed in the sameway.

the present results are coincident with the previous studies (Bockisch & Miller, 1999; Boucher et al., 2001; Dassonville et al., 1995; Honda, 1990). If each ﬂash in a
ﬂicker is localized independently in the same way as asingle ﬂash, the apparent position and length of the
ﬂicker should be predicted from these time courses.

3. Experiments 2 and 3: Localization of a continuous
ﬂicker from long before, until long after a saccade
The following experiments investigated the timecourse of localization for continuous stimuli. In the second and third experiments, a ﬂickering stimulus was presented from long before or until long after a saccade,respectively. The duration of the ﬂicker was varied.
We compared the time courses obtained in Expts. 2
and 3 with that of Expt. 1.
3.1. Procedure
In Expt. 2, the same procedure was used as Expt. 1
except for the ﬂash timing of the S. As depicted inFig. 1b, the S started to ﬂicker at 500 Hz (0.5 ms on,
1.5 ms oﬀ) as the FP turned on. The duration of the S
was varied in such a way that the S terminated during

the interval from 10 ms to 600 ms after the oﬀset of the
TP (i.e., from about 200 ms before to about 400 ms after
the onset of a saccade). According to the ﬂicker oﬀset
time, the subject perceived either a dot or a dot array.
When the subject perceived a dot, he localized it using
one laser pointer, and when a dot array was perceived,
he localized the left and right ends at the same timeusing two laser pointers.
In Expt. 3, the S started to ﬂicker during the intervalfrom 10 ms to 600 ms after the oﬀset of the TP (i.e., fromabout 200 ms before to 400 ms after the onset of a saccade). The ﬂicker oﬀset time of the S was ﬁxed at
500 ms after the onset of the saccade. According to theﬂicker onset time, the subject perceived either a dot ora dot array. The subjects localized it with one or two laser pointer(s). One subject, K.F. was also tested with
continuous light, which was presented at the same onset
and oﬀset timing as in Expts. 2 and 3, respectively. In thiscase, the subject perceived a dot or a continuous line.
The luminance of the S was 1.6 cd/m2 (which was
10 cd/m2 in Expt. 1). A darker luminance was used in
Expts. 2 and 3, because the S was presented for a longer
time than the 2 ms in Expt. 1. If a stimulus with the same
luminance was used, the subjects perceived it as brighter.
Note also that reducing the luminance of the S to
1.6 cd/m2 had only a minor eﬀect for K.F. in Expt. 1.

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J. Watanabe et al. / Vision Research 45 (2005) 413–430

Fig. 3b. Since the last ﬂash (left end) was presented longafter the saccade, the two ends are both plotted to theﬂicker onset time (right end). In Fig. 3a and b, all ﬁlled
circles are plotted corresponding to the time when theﬂash was presented, and the crosses are not. Fig. 3cshows the apparent line length of the dot array obtainedin Expts. 2 and 3 relative to the saccade amplitude.
When a dot is perceived, the value is zero.
In Expt. 2 (ﬂicker oﬀset-variable condition, Fig. 3aand c), all subjects perceived just a dot near the veridical
position (0 deg) before the saccade. After the saccade onset, a dot array began to spread, then the length of the
dot array saturated at the time of the saccade oﬀset. This
indicates that the dot spread only during the saccade.
Although there were some individual diﬀerences, thelength of the dot array was about half the saccade
amplitude, as reported by Hershberger (1987). The perceived length was always smaller than the length painted
on the retina. As to the perceived positions of the right3.2. Results

Perceived position (deg)Expts. 2 and 3 are referred to respectively as ‘‘ﬂicker
oﬀset-variable condition’’ and ‘‘ﬂicker onset-variablecondition’’ in Fig. 3. The results of Expt. 2 are shownin Fig. 3a. Since the ﬂicker onset time was ﬁxed, theapparent location of the ﬁrst ﬂash (right end) and thelast ﬂash (left end) are both plotted to the ﬂicker oﬀset
time (as discussed at the end of this section, we assumed
that the dot, which appeared ﬁrst, was located at theright end of the perceived line and the dot, which appeared last, was located at the left end). For example,
when a stimulus continued to ﬂicker until 100 ms after
the onset of the saccade, the subject Y.I. perceived a
dot array and pointed to the right and left ends at theposition of about +2.0 deg and 1.5 deg, respectively.
In Fig. 3a, the indicated positions both are plotted at
100 ms in the abscissa and at each perceived positionin the ordinate. The results of Expt. 3 are shown in

4
3
2
1
0
-1
-2
-3
-4

Subject: Y.I.

-200 -100

Subject: Y.A.

0

100 200 300 400-200 -100

Subject: K.F.

0100 200 300 400-200 -1000

100 200 300 400-200 -1000

100 200 300 400

Perceived position (deg)Flicker offset time from saccade onset (ms)

4
3
2
1
0
-1
-2
-3
-4
-200 -1000

100 200 300 400-200 -100 0 100 200 300 400
Flicker onset time from saccade onset (ms)Fig. 3. The perceived positions of right and left ends in Expt. 2 (a) and Expt. 3 (b). The abscissas represent the temporal diﬀerence of the ﬂicker oﬀset
or ﬂicker onset time to the saccade onset (ms). The ordinates represent the perceived position of either the dot or dot array (deg). In (a), the crosses
represent the right ends of the perceived dot arrays, and the ﬁlled circles represent the left ends. The diamonds represent averages of the left ends. The
two ends are both plotted to the ﬂicker oﬀset time (the presentation time of the last ﬂash). In (b), the crosses represent the left ends of the perceived
dot arrays, and the ﬁlled circles represent the right ends. The triangles represent averages of the right ends. The two ends are both plotted to theﬂicker onset time (the presentation time of the ﬁrst ﬂash). (c) The apparent line length of the dot array obtained in Expts. 2 and 3 relative tothe saccade amplitude. The abscissa represents the same value as in (a) and (b). The ordinate represents the relative length of perceived dot array tothe saccade amplitude. When a dot is perceived, the value is zero. The diamonds and triangles are means of the data from Expts. 2 and 3. (d)Averages of perceived positions in Expts. 1 (dots), 2 (diamonds) and 3 (triangles). The abscissa represents the temporal diﬀerence of the ﬂash
presentation time to the saccade onset (ms). Ordinates represent perceived position (deg).

Relative length

J. Watanabe et al. / Vision Research 45 (2005) 413–430

419

Flicker offset-variable
Flicker onset-variable

0.8
0.6
0.4
0.2
0

Perceived position (deg)-200 -1000

100 200 300 400-200 -100 0 100 200 300 400-200 -100
Flicker offset time from saccade onset for (ms)Flicker onset time from saccade onset for (ms)0

100 200 300 400

Flash
Flicker offset-variable
Flicker onset-variable

4
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Flash time from saccade onset for (ms)Flicker offset time from saccade onset for (ms)Flicker onset time from saccade onset for(ms)

0

100 200 300 400

Fig. 3 (continued )and left ends after the saccade onset, there were diﬀerences among individuals. Y.I. perceived the left end displaced in the opposite direction of the saccade. As the
ﬂicker oﬀset time extended after the saccade, the perceived position of the left end gradually approached
the veridical position (i.e., 0 deg). In the data of Y.A.,
the displacement in the opposite direction continued until more than 400 ms after the saccade onset. K.F. always
perceived the left end nearly at the veridical position.
In Expt. 3 (ﬂicker onset-variable condition, Fig. 3b
and c), all subjects perceived a dot array when the S
started to ﬂicker before the saccade oﬀset. The maximum length of the dot array was also about half the saccade amplitude. At the saccade onset, the length started
to diminish, and became zero at the saccade oﬀset.
When the S started to ﬂicker after the saccade oﬀset,
the subjects perceived a single dot at the veridical position (0 deg). In spite of the variation of the ﬂicker onset
time, the left end of the dot array (or the single dot) was
localized roughly at the veridical position. For subjects
Y.A. and K.F., the right end was perceived at 4 deg before the saccade, and suddenly shifted to zero after thesaccade onset. For subject Y.I., the magnitude of mislocalization of the right end gradually increased during the
pre-saccadic period, while the relative length of the dot

array was nearly constant. This is because this subject
had a tendency to make small saccades when the S
was presented long before the saccade.
Fig. 4 shows the results obtained with using a continuous light for subject K.F. Overall, the results were
nearly the same as those obtained with a 500 Hz ﬂicker.
The similarity between the two stimulus conditions canbe regarded as justiﬁcation of our choice of using a
500 Hz ﬂicker as a probe for investigating space constancy in continuous environments.
In the above analyses, we assumed that the ﬁrst dot of
the ﬂicker should be seen at the right end of the perceived dot array and the last dot should be seen at theleft end. Indeed, as Hershberger and Jordan (1992) reported, all subjects in our experiments perceived eithera displacement in the opposite direction to the saccadeor no movement. Additionally, a pilot experiment was
conducted to clarify the relationship between the perceived location and the physical temporal order of eachﬂash in the dot array. A ﬂickering stimulus, whose ﬁrst
or last dot had a diﬀerent color (the ﬁrst or last dot wasred, others were green), was presented around the timeof a saccade. The subjects perceived a dot array only
during the saccade, and when rightward saccades were
made, all subjects always perceived the ﬁrst red ﬂash

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4
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2
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0
-1
-2
-3
-4

0.8

Perceived position (deg)-200 -100 0 100 200 300 400
Flicker offset time from saccade onset (ms)Relative length

Perceived position (deg)Subject: K.F. (Continuous light)

Flicker offset-variable
Flicker onset-variable

0.6
0.4
0.2
0

4
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-200 -100 0 100 200 300 400
Flicker offset time from saccade onset for (ms)Flicker onset time from saccade onset for (ms)-200 -100 0 100 200 300 400
Flicker onset time from saccade onset (ms)Fig. 4. The results obtained with a continuous light, for subject K.F. The perceived positions of right and left ends obtained in Expt. 2 (a) and Expt. 3(b), and the apparent line length (c).

at the right end and the last red ﬂash at the left end of
the perceived dot array, respectively. When leftward saccades were made, vice versa. These observations demonstrate that each dot in the dot array physically spread in
the opposite direction of the saccade.
3.3. Discussion
Can the perisaccadic localization of ﬂickers, obtainedin Expts. 2 and 3, be explained by the time course of
localization of single ﬂashes, obtained in Expt. 1? In
Fig. 3d, the apparent position of the last ﬂash in Expt.
2 (ﬁlled circles of Fig. 3a) and the apparent position of
the ﬁrst ﬂash in Expt. 3 (ﬁlled circles of Fig. 3b) are plotted together with the averaged position of single ﬂashes
in Expt. 1 (Fig. 2). Since all these data are correctly plotted to the horizontal time axis, the three time courses
should overlap if each ﬂash of a ﬂicker was localized
individually along with the time courses of localization
for a single ﬂash. It is obvious that Fig. 3d does not support this prediction. Consequently, as to the perceived
position, the prediction of individual localization ofeach ﬂash does not coincide with our results.

How about the perception of the dot spread? If eachﬂash in the ﬂicker is localized individually in the same
way as a single ﬂash, the apparent length of the stimulus
may be predicted from the results of Expt. 1: for instance, in Expt. 2, the dot may start to spread about
200 ms before the saccade and, in Expt. 3, a dot spreadmay be perceived until about 200 ms after the saccade.
However, our results did not support these predictions.
Fig. 3c indicates that the dot spread during the saccade,but not before and after the saccade. Thus, predictions
based on the individual localization of each ﬂash cannot
explain both the perceived position and length of perisaccadic ﬂickers.
Our results are compatible with the study by Schlag
and Schlag-Rey (1995), which reported that the apparent elongation of a continuously ﬂashing stimulus did
not occur before a saccade, as well as with the study
by Sogo and Osaka (2001), which made a similar observation with a ﬂicker (frequency 200 Hz, duration 80 ms)
presented before a saccade.
We observed that as long as the eyes are stationary
before and after the saccade, a continuous ﬂicker wasperceived as a single dot, and that when the ﬂicker is

J. Watanabe et al. / Vision Research 45 (2005) 413–430

the time course of mislocalization for continuous stimuli
is inﬂuenced by the conﬁguration process as well. Thisdiﬀerence might produce dissociations we found in theabove experiments.
Consider next the localization process for continuous
ﬂicker in more detail. We agree with the suggestion by
Schlag and Schlag-Rey (1995) that the perceived location of each shape is not continuously updated with achange in non-retinal information. Localization is likely
to be determined by the localization cues sampled at agiven point in time, or those averaged over a given period. However, given the eye position signal changes
overtime, which eye position signal is used for localization? If the eye position signal for a single ﬂash is sampled at the time of ﬂash presentation, it is possible thatthe eye position signal for a continuous ﬂicker is also
sampled at a transient event such as ﬂicker onset or
ﬂicker oﬀset. To test this hypothesis, we calculated the
expected position of the ﬁrst and last ﬂash in a ﬂicker,
when the eye position signal is sampled at the time ofthe ﬂicker onset (onset-based localization) or ﬂicker

presented during the saccade, it was perceived as a dot
array. This dot array is likely originated from a retinal
image physically drawn by the ﬂicker. Notice also in
Fig. 3c that the apparent length of a fully-developed
dot array, expressed in terms of the ratio to the saccade
amplitude, was quite stable within each subject, regardless of a large change in temporal conditions of ﬂicker
presentation. These ﬁndings led us to a hypothesis thatthe representation of local geometrical conﬁguration between stimulus elements (e.g., a dot or a dot array) is
ﬁrst established based mainly on retinal information,and then the local geometrical conﬁguration is localized
as a whole in the egocentric or exocentric coordinates.
Although the observed shrinkage of a dot array to a half
length of the retinal image may indicate some eﬀects of
non-retinal information on shape perception (see Section 5.2 for further discussion), they could be consideredseparately from the eﬀects on the following localization
process. According to our hypothesis, the time course of
mislocalization for single ﬂashes is dependent mainly on
the characteristics of the localization process only, but

Perceived position (deg)Subject: Y.I.

421

Onset-based localization
Offset-based localization
Subject: K.F.

Subject: Y.A.

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100 200 300 400

Perceived position (deg)Onset-based localization
Offset-based localization
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100 200 300 400-200 -1000

100 200 300 400-200 -1000

100 200 300 400

Fig. 5. Comparison of the results of Expts. 2 (diamonds) and 3 (triangles) with the positions predicted from localization based on ﬂicker onset(squares), and ﬂicker oﬀset (crosses). In (a), the perceived position of the last ﬂash in Expt. 2 is compared. In (b), the perceived position of ﬁrst ﬂash in
Expt. 3 is compared. The abscissa represents the temporal diﬀerence of the ﬂash presentation time to the saccade onset (ms). Ordinates represent
perceived or predicted position (deg).

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J. Watanabe et al. / Vision Research 45 (2005) 413–430

oﬀset (oﬀset-based localization). The following are theequations for our proposed model.

4. Experiment 4: Localization of a continuous ﬂicker
with varying onset, oﬀset and duration

Onset-based localization

4.1. Procedure

X first ðt1 ; t2 Þ ¼ F ðt1 Þ

In Expt. 4, we changed the presentation timing andduration of the ﬂicker. The same procedure as Expt. 1
was employed except for the ﬂash timing of the S. The
duration of the ﬂicker was selected from among 20,
50, 100 and 200 ms. As depicted in Fig. 1b, the S waspresented within the time interval from 10 ms to
600 ms after the oﬀset of the TP (i.e., from about
200 ms before and to 400 ms after the onset of the saccade). For instance, a 200 ms ﬂicker started at a random
time from 10 ms to 400 ms after the oﬀset of the TP. The
subjects were asked to point to the perceived dot, orends of the dot array with one or two laser pointer(s).
The luminance of the S was 1.6 cd/m2, which was thesame as the luminance in Expts. 2 and 3. Although theapparent intensity of the stimulus might change as
the ﬂickering duration varied, for the perception of thestimulus near the time of the saccade, the subjects could
not distinguish the four conditions of duration. Whenthe ﬂicker of the S ended before the saccade or started
after the saccade, subjects perceived a single dot that
was apparently quite similar to a single ﬂash of 10 cd/
m2 as used in Expt. 1. In this experiment, the four conditions (20, 50, 100, 200 ms) were randomized in a block.

X last ðt1 ; t2 Þ ¼ F ðt1 Þ  Lðt1 ; t2 ÞOﬀset-based localization
X first ðt1 ; t2 Þ ¼ F ðt2 Þ þ Lðt1 ; t2 Þ
X last ðt1 ; t2 Þ ¼ F ðt2 Þ
Assume that the S ﬂickers from time t1 to t2 (time to thesaccade onset), F(t) as the time course of localization fora single ﬂash, L(t1, t2) as the perceived length, Xﬁrst as thepredicted position of the ﬁrst ﬂash (right end), and Xlast
as the predicted position of last ﬂash (left end). In either
case, the position of ﬁrst and last ﬂash can be easily predicted by the perceived position of a single ﬂash and perceived length of the ﬂicker. If the localization is based on
the stimulus onset, as Schlag and Schlag-Rey (1995) suggested, the predicted position of the ﬁrst ﬂash in a ﬂicker
coincides with the perceived position of a single ﬂash attime t1, and the predicted position of last ﬂash is determined by both the perceived position of a single ﬂash attime t1 and the perceived length. On the other hand, if
the localization is based on the stimulus oﬀset, the predicted position of the last ﬂash coincides with the perceived position of a single ﬂash at time t2, and the ﬁrst
ﬂash is determined by both the perceived position of asingle ﬂash at time t2 and the perceived length.
In Fig. 5a, the perceived positions of the last ﬂash in
Expt. 2 were compared with the predicted time coursesof the onset- and oﬀset-based localization. For the ﬂickering stimulus ending before the saccade, the perceived
positions overlap with the predicted time course of theonset-based localization. For the ﬂickering stimulus
continuing until after the saccade, on the other hand,the perceived positions were closer to, or nearly coincide
with, the time course of the oﬀset-based localization.
In Fig. 5b, the perceived positions of the ﬁrst ﬂash in
Expt. 3 were compared with the predicted time coursesof the onset- and oﬀset-based localization. For all timings, the perceived positions overlap with the predicted
time course of the oﬀset-based localization.
These results suggest that when a ﬂicker ends before
the saccade, the localization is based on the ﬂicker onset,
but when the ﬂicker continues until after the saccade,the localization is based rather on the ﬂicker oﬀset. In
either case, the eye position signal is sampled at a time
temporally distant from the saccade. To test the generality of these tendencies, both the onset and oﬀset ofthe ﬂicker were systematically changed in the next
experiment.

4.2. Results
The results are shown in Fig. 6. The apparent positions of the right and left ends, each corresponding to
the position of the ﬁrst and the last ﬂash, are plotted
as functions of presentation timing. For instance, if a
100 ms ﬂicker was presented from 100 ms to 0 ms, thepositions of the right and left ends are plotted at
100 ms and 0 ms in the abscissa, respectively. Whenthe subject reported a single dot, the two data are plotted on the same position in the ordinate. The average
positions of the right and left ends, together with the single-ﬂash positions of Expt. 1, are plotted separately for
four diﬀerent durations in Fig. 6a–d.
When the stimulus duration was 20 ms (Fig. 6a), thetime courses of localization for the ﬁrst and last ﬂashes
were similar. For longer durations (Fig. 6b–d), however,
the two time courses signiﬁcantly deviate from eachother. In the pre-saccadic range, the mislocalizationsof the ﬁrst ﬂashes were larger, while in the post-saccadic
range those of the last ﬂashes were larger. In addition,neither of them exactly matches the time course for asingle ﬂash.
A notable deviation, observed for all the stimulus
durations, was that there was no post-saccadic displacement in the opposite direction of the saccade when the
ﬂicker started after a saccade (t > 40 for ﬁrst ﬂashes

J. Watanabe et al. / Vision Research 45 (2005) 413–430

423

(a)
Subject: Y.I.

Subject: Y.A.

Subject: K.F.

Flash condition

Perceived position (deg)

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Perceived position (deg)(b)
Flash condition

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100 200 300 400-200 -1000

100 200 300 400-200 -1000

100 200 300 400

Perceived position (deg)(c)
Flash condition

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100 200 300 400-200 -1000

100 200 300 400-200 -1000

100 200 300 400(d)Flash condition

Perceived position (deg)

4
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1
0
-1
-2
-3
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100 200 300 400-200 -1000

100 200 300 400

Flash time from saccade onset for-200 -1000

100 200 300 400

(ms)

(e)
20 ms
50 ms
100 ms200 msRelative length

0.8
0.6
0.4
0.2
0
-200 -1000

100 200 300 400-200 -1000

100 200 300 400-200 -1000

100 200 300 400

Flicker offset time from saccade onset (ms)Fig. 6. The results of Expt. 4. (a–d) The average perceived position of the right end (ﬁrst ﬂash of a ﬂicker) and the left end (last ﬂash of a ﬂicker) when
the duration was 20, 50, 100 or 200 ms. The abscissa represents the temporal diﬀerence of the ﬂash time to the saccade onset (ms), and the ordinate
represents perceived position (deg). The triangles and diamonds represent the right ends and left ends of the ﬂicker. The circles are averages ofperceived position in Expt. 1. (e) The apparent line length of the dot array relative to the saccade amplitude. The abscissa represents the temporal
diﬀerence of termination time of the S to the saccade onset. The ordinate represents the relative length to the amplitude of the saccade. The circles,
up-triangles, diamonds and down-triangles represent the results obtained for 20, 50, 100 and 200 ms conditions, respectively.

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J. Watanabe et al. / Vision Research 45 (2005) 413–430

and t > 40 + d for the last ﬂashes, where t is time on theabscissa and d is duration of the ﬂicker). In the data of
Y.A., the time courses of the ﬁrst and last ﬂashes werequite similar to that of a single ﬂash, because this subject
did not show post-saccadic displacement even with single ﬂashes.
In Fig. 6e, the apparent line length of the dot array
relative to the saccade amplitude is plotted as a functionof the temporal diﬀerence from the ﬂicker oﬀset time of
the S to the saccade onset. The results indicate that the
dot array was observed only when the S ﬂickered during
a saccade. For example, for the 200 ms condition, theapparent length was greater than zero from 0 ms (whenthe ﬂicker ended just before the saccade) to 240 ms(when the ﬂicker started at the end of the saccade). Notethat the duration of the saccade was about 40 ms. For
the 20 ms condition, the maximum length was smaller
than those of the other conditions. This could be ascribed to the stimulus duration being shorter than the
duration of a saccade. For the 50, 100 and 200 ms conditions, the maximum length was almost constant withineach subject (0.5–0.7).
4.3. Discussion
In Fig. 6, the results of Expt. 4 again demonstrate
clear dissociations in the time courses of localization
among the ﬁrst and last ﬂashes of ﬂickers and single
ﬂashes. They are localized at diﬀerent positions, evenwhen they are presented at the same timing to the saccade, namely at the same position on the retina. Fig.
6e also shows that all subjects perceived a dot array during the saccade, but not before and after the saccade.
These results, together with those of Expts. 2 and 3, indicate that the individual localization of each ﬂash in a
ﬂicker cannot explain the localization of ﬂickers, andthat the perceived geometrical conﬁguration is mainly
generated by the retina-originated information.
The results of Expts. 2 and 3 (Fig. 5) suggest thatwhen a ﬂicker ends before the saccade, the localization
is based on the ﬂicker onset, but when the ﬂicker continues until after the saccade, the localization is based
rather on the ﬂicker oﬀset. To test whether the same ruleaccounts for the results of Expt. 4, we compared the obtained data with the predicted time courses of onset- andoﬀset-based localizations in Fig. 7a–h.
When a ﬂicker started and ended before the saccade(t1 <  d, or t2 < 0; left no-colored range, given S ﬂickers
from time t1 to t2 for d = t2  t1), only a single dot wasperceived. The time course of the perceived position inthis range roughly overlaps the predicted time courseof the onset-based localization, but not the oﬀset-based
localization. On the other hand, when a ﬂicker started
after the saccade (t1 > 40 or t2 > 40 + d; right no-coloredrange), only a dot was perceived again, but the timecourse of the perceived position is closer to the predicted

time course of the oﬀset-based localization. Between
these two ranges (d < t1 < 40 or 0 < t2 < d + 40) colored in Fig. 7, the subject made a saccade while a ﬂicker
was presented, and perceived a dot array. In this time
range, whether the localization is based on the onset
or oﬀset is not clearly discernible.
To quantitatively evaluate how well the perceived
positions in each time range can be predicted by onsetand oﬀset-based localizations, we calculated the following values:
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Donset ¼ M½ðd 2onset Þ ¼ M½ðP onset  P Þ2 
Doffset ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
M½ðd 2offset Þ ¼ M½ðP offset  P Þ @ ¼ M½ðd 2offset  d 2onset Þ=ðd 2offset þ d 2onset ÞHere, M[. . .] denotes taking the mean. P represents theperceived position, and Ponset and Poﬀset are the predicted position based on the ﬂicker onset and oﬀset,
respectively. Donset and Doﬀset (deg) represent the prediction error of onset- and oﬀset-based localization. Whenthe value of Donset or Doﬀset is small, the onset- or oﬀsetbased localization is close to the perceived position.
When localization index o is positive (i.e., d 2onset is smaller than d 2offset ), the onset-based localization is closer, andwhen the value is negative (i.e., d 2offset is smaller thand 2onset ), the oﬀset-based localization is closer. Fig. 8
shows Donset and Doﬀset, and the localization indexes oin three time sections for the averaged data of all subjects. The ﬁrst time section denoted as ‘‘Before’’ inFig. 8 includes the cases where the ﬂicker started andended before or during the saccade (the left no-colored
and left blue-colored ranges in Fig. 7: these two subranges showed similar tendencies). In this time section,o is positive for all durations. Thus, when the ﬂicker
started before the saccade but did not last until theend of the saccade, the localization was performed based
rather on the onset of the stimulus. The second time section denoted as ‘‘Before/After’’ in Fig. 8 is the casewhere the ﬂicker started before and ended after the saccade (yellow-colored range in Fig. 7). In this time section, while o is slightly positive for 100 ms, it was
negative for 200 ms. That is, when a saccade was madeduring the presentation of a 200 ms ﬂicker, the localization was based on the stimulus oﬀset. The third time section denoted as ‘‘After’’ in Fig. 8 includes the cases
where the ﬂicker started during or after the saccadeand ended after the saccade (the right blue-colored
and the right no-colored ranges in Fig. 7: these two
sub-ranges showed similar tendencies). For all durations, o is negative, indicating oﬀset-based localizationin this time section.
The ﬁnding that the localization was based on the
ﬂicker onset in the ‘‘Before’’ section, while on the ﬂicker

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425

Onset-based localization

Subject: Averaged

Offset-based localization

Perceived position (deg)

(a)

(b)

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Perceived position (deg)0100 200 300 400

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0100 200 300 400

(f)

(e)
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(h)

(g)
Perceived position (deg)-200 -100

(d)

(c)

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100 200 300 400-200 -100

Time from saccade onset (ms)Fig. 7. Comparison of the results of Expt. 4 (triangles and diamonds for the ﬁrst and last ﬂash in a ﬂicker) with the positions predicted fromlocalization based on the ﬂicker onset (squares), and the ﬂicker oﬀset (crosses), each being referred to as onset- and oﬀset-based localization. The
averaged data of three subjects are shown. The abscissa represents the temporal diﬀerence of the ﬂash time to the saccade onset (ms). The ordinate
represents perceived or predicted position (deg). The left white area represents the time range when the ﬂicker started and ended before the saccade.
The left blue-colored area represents the time range when the ﬂicker started before and ended during the saccade. The yellow-colored area represents
the time range when the ﬂicker started before and ended after the saccade. The right blue-colored area represents the time range when the ﬂicker
started during and ended after the saccade. The right white area represents the time range when the ﬂicker started and ended after the saccade.

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J. Watanabe et al. / Vision Research 45 (2005) 413–430

Subject: Averaged
Duration 20ms

DonsetDoffset1

Localization Index

2
0

1
0

-1
Duration 50ms

1

2
0

1
0

-1
Duration 100ms

1

2
0

1
0

-1
Duration 200ms

1

2
0

1
0

Before Before/After After-1

Before Before/After After

Fig. 8. Evaluation of similarity of the onset- and oﬀset-based localization to the perceived position for the averaged data of three subjects. The time
ranges are classiﬁed into three time sections, ‘‘Before’’ section when the ﬂicker started before and did not continue until after the saccade (40  d > t1
or 40 > t2; ﬂicker is presented from t1 to t2 and d is duration of the ﬂicker), ‘‘Before/After’’ section when the ﬂicker started before and ended after thesaccade (40  d < t1 < 0 and 40 < t2 < d), and ‘‘After’’ section when the ﬂicker started during or after the saccade (0 < t1 or d < t2). The data of thecases when the ﬂicker started and ended during the saccade in the 20 ms condition, when the ﬂicker started before and ended after the saccade in the
50 ms condition, and when the ﬂicker started before and ended during the saccade in the 200 ms condition are excluded, because these time ranges are
too short to calculate averages. Donset (square) and Doﬀset (cross) for each time section are shown in the left column, and localization index oare shown in the right column. In each condition, the data of the ﬁrst and last ﬂash are added together. The standard deviations among individuals
are also presented.

oﬀset in the ‘‘After’’ section, is consistent with a rule thata ﬂash temporally distant from the saccade was used for
localization. In the ‘‘Before/After’’ section, both the onset- and oﬀset-based localization were equally possible,and diﬀerent results were obtained for the 100 and
200 ms conditions.
The results of Expt. 4 also show another interesting
trend: when the ﬂicker starts after the saccade (rightno-colored range in Fig. 7, also see Fig. 6), the perceived
location was almost veridical, showing no post-saccadic
displacement in the opposite direction of the saccade.
Although this tendency can be in part predicted by the
localization based on the last ﬂash, the perceived location
was more veridical than predicted, especially for the results of Y.I. in the short (i.e., 20, 50 ms) duration conditions. We interpret this ﬁnding as an indication that a
ﬂicker presented after the saccade is localized based on
the eye position signal later than the physical stimulus
termination. This is a reasonable strategy if it enabled

subjects to use more reliable eye position signal for localization of remembered target. Even if that is the case,however, one may wonder how can the visual system tellvery brief ﬂickers from single ﬂashes? We speculate that a
ﬂicker stimulating the same retinal position may generatea Ôno-motionÕ signal that tells the visual system that thestimulus did not move on the retina. Then the visual system can localize the ﬂicker based on the stable eye position signal sampled suﬃciently after the saccade. On theother hand, a ﬂash does not generate such a Ôno-motionÕ
signal. Since the visual system cannot tell how the ﬂash
moved, the system has to use an erroneous instantaneouseye position signal near the time of the saccade.
In summary, the results of Expt. 4 indicate a trendthat the perisaccadic localization of a ﬂicker is basedon the eye position signal sampled at a time temporally
distant from the saccade: when the ﬂicker starts before
and does not continue until after the saccade, the localization is based on the eye position signal sampled at the

J. Watanabe et al. / Vision Research 45 (2005) 413–430

ﬂicker onset, while when the ﬂicker starts during or after
the saccade and ends after the saccade, the localization
is based on the eye position signal sampled at the ﬂicker
oﬀset or later. This tendency is consistent with the results of Expts. 2 and 3.

5. General discussion
5.1. Two-stage localization of perisaccadic ﬂickers
When a ﬂash is presented around the time of a saccade,the apparent position is shifted (as shown in Fig. 2). Thismislocalization has been explained by the cancellation
theory, which postulates that it is generated by the integration of the retinal image and the dumped internal
eye position signal (EPS) (Honda, 1989, 1990; Mateeﬀ,
1978). Based on this theory, Hershberger (1987) interpreted the perception of a dot array for repetitively presented ﬂashes (ﬂicker) during a saccade as a result of
position compensation for each individual ﬂash. However, the present study shows that the perceived lengths
and positions for perisaccadic ﬂickers do not coincidewith the prediction from the time course of localization
for a perisaccadic single ﬂash (Expts. 1–4). This ﬁnding
clearly rejects a simple cancellation theory as an explanation of localization of perisaccadic continuous ﬂickers.
Instead, we proposed a two-stage localization process. Namely, the representation of local geometrical
relationships between stimulus elements is ﬁrst established based primarily on retinal information, then thelocal geometrical relationship is localized as a whole in
the egocentric or exocentric coordinates. This hypothesis is supported not only by the dissociation between
ﬂashes and ﬂickers, but also by the ﬁnding that the perceived shape is mainly based on the retina-originatedinformation (Expts. 2–4; see also Schlag & Schlag-Rey,
1995; Sogo & Osaka, 2001). As long as a ﬂicker stimulates the same retinal area, a single dot is perceived. A
dot array is perceived only when it is drawn on the retina
by an eye movement. Although the length of the dot array does not correspond to the retinal size (Hershberger,
1987), it is quite stable within each subject in spite oflarge variations in perceived position (Expts. 2–4). It
should be also noted that if all ﬂashes of a ﬂicker are
localized individually, as Hershberger assumed, the retinal signal and eye position signal should be integrated ntimes when the ﬂashes are presented n times. In contrast,
our two-stage mechanism is much more economical,
since it integrates the two signals only once per saccade.
Concerning how the perceived shape is localized, ourresults indicate that the localization is based on the eye
position signal sampled at a time temporally distantfrom the saccade. For a stimulus that ends by the timeof the saccade onset, the localization is based on theeye position signal sampled at the stimulus onset, as

427

Schlag and Schlag-Rey (1995) suggested. However,when the stimulus is visible even after the saccade, thelocalization is based on the eye position signal sampled
at the stimulus oﬀset or a time closer to the time of judgment. These ﬁndings are consistent with the notion thatthe visual system avoids using erroneous eye positionalsignals around the saccade to attain better space constancy across saccades.
Jordan and Hershberger (1994) presented a ﬂicker
stimulus during a saccade to have their subjects perceivea dot array. When they presented a ﬂash at the same
retinal position within 80 ms before the saccade, the subject perceived it as spatially coincident with the ﬁrst ﬂash
of ﬂicker, as opposed to the standard time course of
localization of a pre-saccadic ﬂash. Although this observation led Jordan and Hershberger to propose that the
EPS changes discretely and not gradually (DiscreteEPS model), it can be explained by our hypothesis, givenin the ﬁrst stage, the ﬂash and the ﬂicker are temporallygrouped together, and represented in the common retinal coordinates.
Sogo and Osaka (2002) examined perisaccadic localization of two ﬂashes with systematic changing of the inter-stimulus interval. They found that when the intervals
were longer than 120 ms, the perceived position of eachﬂash followed the time course of single-ﬂash localization,
while when the intervals were shorter than 120 ms, the relative position of the two ﬂashes was determined byretinotopic information. While Sogo and Osaka (2002)
interpreted 120 ms as a critical point where subjects
change the strategy of localization, we rather regard
120 ms as the length of the temporal window for temporalgrouping. That is, the stimuli whose stimulus onset asynchronies are within 120 ms are grouped together, andlocalized as one image. If the interval is longer, the stimuli
are analyzed separately, and localized individually.
The temporal window of grouping may vary depending on the stimulus condition. Using a bright display,
Ross et al. (1997) and Morrone et al. (1997) found an
apparent vernier oﬀset of two collinear half-bars presented at the same position at diﬀerent times with an inter-stimulus interval of 75 ms. Speciﬁcally, when the twobars were presented immediately before the saccade onset
at the middle of the ﬁxation and saccadic targets, the second bar appeared to be shifted towards the saccadic target(i.e., in the direction of saccade), as expected from mislocalization of single bars. That is, unlike a continuous
ﬂicker, the two bars separated in time only by 75 ms wereindependently localized. Similarly, in the completely darkroom, Park, Schlag-Rey, and Schlag (2003) found an
apparent verier oﬀset of two physically aligned spots thatwere temporally separated by only 50 ms.
Cai et al. (1997) reported that when a ﬂash was presented immediately before a saccade while a light wascontinuously presented until the ﬂash termination time,
subjects perceived misalignment of the ﬂash relative to428

J. Watanabe et al. / Vision Research 45 (2005) 413–430

the continuous light. This observation can be explained
also by our hypothesis, given the two stimuli were nottemporally grouped together and localized separately
based on each onset timing. The assumption that a ﬂash
and a continuous stimulus are processed separately,even when their presentation timings are physicallyoverlapped, is further supported by their study on theﬂash-lag eﬀect (Cai & Schlag, 2001).
According to our hypothesis, a sequence of stimuli on
the retina is not egocentrically localized in real time, but
after the determination of local geometric conﬁguration
via grouping of retinal information over time. Even whena ﬂicker starts before the saccade, if it continues until longafter the saccade as in Expt. 3, the localization is based on
the post-saccadic spatial coordinates. This means that theinterpretation of the past events is dependent on theinformation obtained afterwards up to the time when
the judgment is made. Although this conclusion may
sound paradoxical, it is a principle widely recognized inmany perceptual phenomena, including time perception(Dennett & Kinsbourne, 1992; Libet, Wright, Feinstein,& Pearl, 1979; Nishida & Johnston, 2002), backward
masking (Bachmann, 1994; Breitmeyer, 1984), temporalﬁlling-in (Kamitani & Shimojo, 1999), and the ﬂash-lag
eﬀect (Eagleman & Sejnowski, 2000a, 2000b, 2000c; Krekelberg & Lappe, 2000).
5.2. Reduction of perceived length
Given that perception of geometrical shapes is basedon retinal information, why is the length of the dot array
reduced relative to the retinal spread of the ﬂicker?
One possibility is that the visual persistence is notlong enough to sustain the whole ﬂicker sequence, sothat the ﬁrst ﬂash disappears before the last ﬂash is presented. Indeed, Burr and Morrone (1996) reported a
reduction in temporal impulse response during a saccade, and Bedell and Yang (2001) referred to the reduced visual persistence as a possible cause of reduced
length of motion streak induced by a saccade. However,this account is rejected by the pilot experiment describedin Section 3.2, which indicates that the subjects could see
the ﬁrst ﬂicker on one end and the last ﬂash on the otherend of the dot array.
Several studies have shown that perisaccadic stimuli
are localized toward the saccade target, as if the visual
space is compressed (Awater & Lappe, 2004; Honda,
1993; Kaiser & Lappe, 2004; Matin & Pearce, 1965;
Morrone et al., 1997; Ross et al., 1997). This phenomenon is most evident when the perisaccadic stimulus islocalized relative to a post-saccadic visual reference(Lappe et al., 2000), but recent data (Awater & Lappe,
2003; Ma-Wyatt, Morrone, & Ross, 2002), suggestingthat compression is present also in the dark. While theperisaccadic space compression strongly occurs for stimuli presented immediately before a saccade, it can also

occur for those presented during a saccade. Thus, it ispossible to ascribe the reduction in the apparent lengthof the dot array to the perisaccadic space compression.
It is also possible to regard the apparent shrinkage ofthe dot array as a result of partial cancellation of retinal
slip induced by saccadic eye movement. If the cancellation were perfect, the observer would veridically perceivea single dot. The original cancellation theory states thatthe internal EPS compensates for the change in retinal
position, but the compensation is not perfect since thechange in EPS is slower than the actual eye movement.
By assuming that a dot array is produced after cancellation of the retinal shift of each ﬂash in the ﬂicker by thesluggishly changing EPS sampled in real time, one canaccount not only for why the apparent length of dot array shrinks, but also for why the perceived length isroughly equal to the distance between the apparent positions of single ﬂashes presented at the saccade onset andoﬀset. However, as we have discussed, several lines ofevidence support the notion that the EPS is integrated
for localization only after a geometrical shape is determined. To resolve this apparent contradiction, we speculate that a computation similar to compensation by the
EPS might be performed oﬄine after generation of a geometrical shape from the retinal image. Castet, Jeanjean,and Masson (2002) reported that retinal motion induced
by a saccade is perceptible. If the visual system has estimates for the speed of retinal motion (Sretina) and the
speed of EPS change (SEPS), the retinal slip can be compensated for by scaling the retinal image in the orientation of the saccade by a factor (Sretina  SEPS)/Sretina.
This hypothesis however remains highly speculative at
the moment and merits future study.
Finally, Sogo and Osaka (2002) reported that when
two ﬂashes were presented within a short interval (e.g.,
80 ms), the distance between the two dots coincides withthe retinal distance, although we observed that when aﬂicker was presented for about the same duration, only
half of the retinal length was perceived. Although we do
not clearly know the reason behind this discrepancy, we
propose a couple of possibilities. One is a potential difference of the stability of shape perception between two
dots and a dot array (Matsumiya & Uchikawa, 2001).
Another possibility is that successive ﬂashes presented
in the ﬂicker condition stimulate motion sensors, andgive an estimate of the retinal speed, much more eﬀectively than the two dots do. If the shrinkage of the dot
array is indeed based on the estimation of retinal speed,
as we suggested above, the shrinkage may not occur forthe two dots.

6. Conclusion
The perceived position and length of a ﬂicker presented around the time of a saccade did not coincide

J. Watanabe et al. / Vision Research 45 (2005) 413–430

with the prediction based on the individual localization
along with the time course of localization for single
ﬂashes. Our results suggest a two-stage localization
process, in which the representation of local geometricalconﬁguration is ﬁrst established based primarily on retinal information, and then the conﬁguration is localized
as a whole in the egocentric or exocentric coordinates.
The localization is based on the eye position signal sampled at a time temporally distant from the saccade,which enables precise localization and space constancy
for continuous stimuli.

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