Spatial Vision, Vol. 18, No. 3, pp. 297– 316 (2005)  VSP 2005.

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A continuously lit stimulus is perceived to be shorter than a flickering stimulus during a saccade ATSUSHI NORITAKE ∗ , KOJI KAZAI, MASAHIKO TERAO and AKIHIRO YAGI Department of Psychology, Kwansei Gakuin University, Japan Received 13 April 2004; accepted 11 November 2004 Abstract—When subjects made a saccade across a single-flashed dot, a flickering dot or a continuous dot, they perceived a dot, an array (phantom array), or a line (phantom line), respectively. We asked subjects to localize both endpoints of the phantom array or line and calculated the perceived lengths. Based on the findings of Matsumiya and Uchikawa (2001), we predicted that the apparent length of the phantom line would be larger than that of the phantom array. In Experiment 1 of the current study, contrary to the prediction, the phantom line was found to be shorter than the phantom array. In Experiment 2, we investigated whether the function underlying the filled-unfilled space illusion (Lewis, 1912) instead of the function underlying the saccadic compression could explain the results. Subjects were asked to localize both endpoints of a line or an array while keeping their eyes fixated. Although the results of Experiment 2 showed that the perceived length of a line was shorter than that of an array, the function underlying the filled-unfilled illusion could not fully account for the results of Experiment 1. To explain the present results, we proposed a model for the localization process and discussed its validity. Keywords: Human; saccade; phantom array; mislocalization.

1. INTRODUCTION

Hershberger and his colleagues (Hershberger, 1987; Hershberger et al., 1998) reported that when a person makes a saccade across a flickering dot, it is perceived as an array of dots. They referred to this phenomenon as a ‘phantom array’. Furthermore, they reported that the stimulus (a flickering dot) initially jumped in the direction of the saccade, ran in the direction opposite of the saccade, and finally stopped near the actual location of the stimulus (Fig. 1A). The subjects’ perception ∗ To

whom correspondence should be addressed. E-mail: [email protected]

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Figure 1. (A) Schematic representation of the phantom array reported by Hershberger (1987). The solid arrow indicates the saccade direction; In this case, the saccade direction is rightward. A person perceives a phantom array when making a saccade across a flickering stimulus. Hershberger explained that the first-perceived dot jumps to the neighborhood of the saccade endpoint and moves in the opposite direction of the saccade discretely, and the last perceived dot is at the actual stimulus position. The horizontal level of the phantom array is the same as the level of the actual stimulus. (B) Arrangement of LEDs for the fixation, stimulus, target, and localization. Open circles indicate green LEDs, and filled circles indicate red LEDs. (C) Time courses of the fixation LED, the target LED, the stimulus LED, and the horizontal eye position. The duration of the stimulus presentation was 2 ms under the single condition or 31 ms under the flicker and the continuous conditions. The buzzer (1000 Hz) sounded at the last 1 s of the fixation point presentation. The subjects kept their eye position as long as possible after the saccade execution until the buzzer for localization sounded.

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of the distance between the first and last dots was found to be approximately half as long as the actual retinal image. It is known that when a continuously lit stimulus is presented during a saccade, a line is perceived. This phenomenon is referred to as a ‘phantom line’, which is named after the phantom array in the current study. The perceived length of the phantom line has not been investigated systematically to the best of our knowledge. One of the objectives in the current study is to compare the perceived length of the phantom array with that of the phantom line, that is, to investigate whether the difference in the visual structures could affect their perceived lengths. Ross et al. (1997) found that when a stimulus flashed beyond the saccade goal and the visual reference was always presented in a given trial, the stimulus was mislocalized against the direction of the saccade as if the visual scene were compressed to the saccadic goal. This phenomenon is referred to as a ‘saccadic compression of visual space’ (Morrone et al., 1997; Ross et al., 1997). In their study, Ross et al. briefly presented a natural scene around the time of a saccade and asked subjects to report how it appeared. The subjects reported that the natural scene appeared to be compressed when it was presented just before a saccade. Contrary to the results of Ross et al., Matsumiya and Uchikawa (2001) showed that when a stimulus made of multiple elements perceived as a constellation of multiple objects was presented before the onset of a saccade, the perceived length of the stimuli was shorter than the actual length, but saccadic compression did not occur when a stimulus made of multiple elements perceived as a single object was presented. These results suggested that the visual structure could cause differences in the perceived lengths between a single-object stimulus and a multiple-objects stimulus even if the actual lengths were the same. If saccadic compression occurs, according to Matsumiya and Uchikawa (2001), the apparent length of the phantom line will be larger than that of the phantom array because the apparent length of a stimulus perceived as multiple objects (the phantom array) should be more compressed around the onset of a saccade than that of a stimulus perceived as a single object (the phantom line). To check this assumption, in Experiment 1, we compared the length of the phantom array to that of the phantom line. Furthermore, in the current study, we reported the locations of both endpoints of the phantom array and line. Previous studies showed that when a single-flashed stimulus was presented just before, during or after a voluntary saccade in a dark room, subjects systematically mislocalized the position of the stimulus (Honda, 1989, 1990, 1991; Mackey, 1970; Mateeff, 1978; Matin et al., 1969, 1970). The magnitude of saccadic mislocalization depends on the time when the stimulus is presented relative to the saccade onset (e.g. Honda, 1989). Saccadic mislocalization starts to emerge when the stimulus is presented 100 ms before the saccade onset. The magnitude gradually increases in the direction of the saccade as the interval between the stimulus onset and the saccade onset decreases and then peaks when the stimulus is presented simultaneously with the saccade onset. The magnitude reaches

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nearly half the intended saccadic amplitude. One of the common explanations is that the mislocalization arises from an eye-position signal (EPS) that is incapable of representing an actual eye position. A discrepancy between the actual eye position and the represented EPS at a certain moment during a saccade induces localization errors, in other words, the extraretinal signal causes localization errors (For a detailed discussion, see Sogo and Osaka, 2001). Mislocalization of a visual stimulus is based on the algebraic summation of the retinal location of a visual stimulus, the EPS, and the actual eye position. Thus, the localization that is based on both the retinal location of stimuli and the EPS is called the egocentric manner or coordinate (Dassonville et al., 1995).

2. EXPERIMENT 1

A flickering stimulus or continuously lit stimulus was presented in a random order during a saccade. The timing of these stimuli varied around the time of the saccade onset. The subjects were asked to localize both endpoints of the phantom array or line. The apparent distance between the right and left endpoints of the phantom array or line was estimated by subtracting one localized point from the other localized point. The flickering-stimulus condition was called the flicker condition, and the continuously lit stimulus was called the continuous condition. In another condition, the single condition, a single-flashed stimulus was presented to obtain each subject’s saccadic mislocalization curve, and this curve was compared with the localization curves of the flickering and the continuous conditions. 2.1. Method 2.1.1. Subjects. Two males (M. M. and K. N.) and two females (Y. O. and N. I.) participated in Experiment 1. They had normal or corrected-to-normal visual acuity with binocular vision. None of them was informed of the objectives of this experiment. All subjects gave written, informed consent form to participate in the experiment. One subject (N. I.) quit participating after the experiment had begun. 2.1.2. Apparatus. The experiment was performed in complete darkness. The subjects were seated with their heads stabilized by a dental bite board. Figure 1B contains a schematic representation of the apparatus and the stimulus. Three red light-emitting diodes (LED: 0.3 degree in diameter, 8 cd/m2 ) were placed at eye level, 4 degrees to the left of the subjects’ median lines (the fixation LED at −4 degrees), at the median lines (the center LED at 0 degrees), and 4 degrees to the right of the median lines (the target LED at +4 degrees). The stimulus LED was located at +2 degrees. It flickered at 200 Hz (1 ms on, 4 ms off) for 31 ms under the flicker condition, was turned on for 31 ms under the continuous condition, or flashed for 2 ms under the single condition. The stimuli LEDs were placed 57 cm from the subject’s eyes. To localize the stimulus LED, we placed 40 green LEDs

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(the localization LED) 1.5 degrees below the stimulus LED. These LEDs extended horizontally from 4 degrees to the left of the median lines to 16 degrees to the right of them at intervals of 0.5 degrees. All subjects held a small board with three buttons positioned in the shape of a triangle. The appliances were controlled by a PC/AT-compatible computer with a digital I/O board equipped with a timer function whose accuracy was one microsecond. The horizontal eye movement of each subject’s right eye was recorded with an infrared system, Ober2 (Permobil Meditech) with a resolution of less than 0.5 degrees. The data were stored in another PC/AT-compatible computer by an A/D converter (ADM-687PCI, Microscience) with a sampling rate of 1000 Hz. These eye-position data were used to calculate the timing of the stimulus presentation from the saccade onset and to check drifts before and after saccades. 2.1.3. Procedure. The experiment began after 15 minutes of adaptation to the darkness. At the beginning of each trial, a warning buzzer (1000 Hz, 50 ms) sounded three times. Then the center LED was turned on, and the subject fixated on the center LED to perform drift correction on our custom-written software. After a delay of 1 s, the center LED disappeared. The fixation LED was turned on and presented for 2–3 s with a tone (1000 Hz) signal at the last 1 s of its presentation. The subjects were asked to keep watching the fixation LED until the target LED for guiding a saccade flashed for 10 ms. At various times before, during, or after the saccade, the stimuli (the stimulus LEDs) were presented for 2 ms under the single condition or for 31 ms under the flicker and continuous conditions (Fig. 1C). The subjects were instructed to make an 8-degree horizontal saccade to the target LED from the fixation LED as quickly as possible. The blank interval for 1000 ms was inserted after the offset of the stimulus LED, and the warning buzzer (500 Hz) sounded for 200 ms. After the buzzer sounded, one of the localization LEDs was randomly emitted to localize the perceived points. The subjects were also instructed to localize both the right and left endpoints of the phantom array or line and to localize the first-perceived endpoint first. For example, if the subjects first perceived the right endpoint of the phantom array or line, they localized its position first and then localized the other endpoint. If the subjects perceived a single dot instead of an array or a line, they localized the perceived point twice in the same position. Under the single condition conducted separately from the flicker and continuous conditions, the subjects were asked to locate the perceived point once. The subjects localized both endpoints in the following way. The localization LED moved 0.5 degrees to the right when the subjects pressed the right button on the keyboard, and it moved 0.5 degrees to the left when they pressed the left button. To locate the first endpoint of the phantom array or line, the subjects pressed the apex button. Once they localized the endpoint, its position was fixed. The number of localization LEDs turned on increased or decreased in the indicated direction to the other endpoint as the subjects pressed one of the buttons. One trial was finished

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when the second endpoint was localized. There was an interval of 1500 ms of the darkness between trials. Calibration of Ober2 was performed after every ten successive trials. Calibration of the three points was executed. The three red LEDs for the calibration were positioned at −10 degrees, at 0 degrees (the center LED), and at +10 degrees. The first-presented LED was the LED at −10 degrees, the second was at 0 degrees, and the third was at +10 degrees. Each LED was turned on for 1500 ms and off for 1000 ms. This sequence was repeated three times successively. The subjects were asked to fixate these LEDs in turn. The average voltage values of each point (−10, 0, and +10 degrees) were calculated. Each condition included 400 trials. In order to prevent subjects from adaptation to making constant 8-degrees saccades, 40 additional trials in which the center LED (4 degrees right to the fixation LED) served as a saccadic target were inserted. Under the flicker and continuous conditions, a total of 840 trials were divided into four sessions of 210 trials. Each session included 100 trials under the flicker condition, 100 trials under the continuous condition, and 10 trials under the 4-degree saccade condition. The order of these different conditions was randomized within each session. Under the single condition, a total of 420 trials were divided into two sessions of 210 trials. Each session included 200 trials under the single condition and 10 trials under the 4-degree saccade condition. When half of a session had been performed, the subjects had a 10-min rest. Three subjects performed four sessions in two weeks. The additional 40 trials (the fixation LED: 20 trials; the target LED: 20 trials) were conducted as the control condition in which subjects did not make a saccade but fixated on the fixation LED or the target LED. 2.2. Results 2.2.1. Eye movements. Digitized data of eye movements were analyzed offline to determine the saccade onset and offset and to obtain the saccadic duration, amplitude, and latency. The saccade onset and offset were defined by a velocity criterion with a threshold of 10% of the maximum speed during the saccade. Data were excluded from the following criteria: (1) the saccade latency was too short (<50 ms); (2) the saccadic latency was too long (>300 ms); (3) a subject blinked within ±500 ms of the saccade onset; and (4) a subject made a corrective saccade of more than 2 degrees or a large drift of more than 1 degree after the saccade offset. The reason for setting the criteria for saccadic latency was that the saccadic latencies in almost all trials of all subjects were longer than 50 ms and shorter than 300 ms. This distribution of very short saccadic latencies compared with those in previous studies (e.g. Honda, 1989) could be due to the fact that the warning tone sounded at the last 1 s of the fixation presentation. The ratios of rejected trials were 23.1, 33.4, and 54.8% of the total number of trials for subjects Y. O., M. M., and N. K., respectively.

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Table 1. The saccades properties of each subject in Experiment 1; saccade duration (ms), saccade latency (ms), and saccade amplitude (degree). The values in the bracket of each cell indicate standard deviation. The smaller values of saccade latency in all subjects than previous experiments (e.g. Honda, 1990) would be due to the beep sounded for the last 1000 ms of the fixation point presentation Subjects

Conditions

Saccade duration (ms)

Saccade latency (ms)

Saccade amplitude (degree)

M. M.

Single Flicker Continuous Single Flicker Continuous Single Flicker Continuous

34.8 (6.5) 34.7 (5.6) 34.8 (5.9) 41.0 (7.5) 38.0 (5.4) 38.1 (6.2) 34.6 (3.2) 33.4 (4.1) 33.5 (4.0)

78.8 (12.8) 88.9 (8.7) 98.4 (22.8) 118.5 (42.0) 91.3 (18.9) 84.3 (16.9) 87.6 (5.5) 88.9 (8.7) 90.3 (15.4)

7.6 (1.3) 7.8 (1.1) 7.7 (1.1) 6.0 (0.7) 6.4 (0.8) 6.6 (1.1) 6.9 (0.9) 6.7 (0.9) 6.6 (1.1)

N. K.

Y. O.

As shown in Table 1, the mean amplitude of all the saccades was smaller than the expected amplitude of 8 degrees under all conditions. Before making a comparison of the lengths of both endpoints between the phantom array and line, we checked the amplitudes of saccades were almost the same under both conditions. The Wilcoxon signed rank test on the saccade amplitude of trials in which the onset of the phantom array or line occurred −30 to 30 ms from the saccade onset revealed no significant difference between conditions in each subject. This result excludes the possibility that differences of perceived lengths between the phantom array and line were due to saccades’ amplitudes. 2.2.2. Perceptions under the flicker and the continuous conditions. After performing randomly chosen trials, we asked the subjects to report orally the visual structure of the stimulus they perceived (a line, an array of dots, or a single dot) and how many dots they perceived when they perceived an array. All the subjects reported that when the stimulus presentation overlapped with a saccade, they perceived an array under the flicker condition and a line under the continuous condition. When the stimulus presentation was out of the range of −30 to 30 ms from the saccade onset, they reported a single dot (see below and Fig. 4 in Section 2.2.4). They could easily discriminate whether a line or dot array was perceived when the stimulus was presented during a saccade. 2.2.3. Localization error. All the subjects showed a small mislocalization in the control trials in which they fixated on a fixation LED (Y. O.: −0.82 degrees, M. M.: −1.97 degrees, N. K.: 0.95 degrees) or a target LED (Y. O.: 0.18 degrees, M. M.: −0.79 degrees, N. K.: 0.38 degrees). Therefore, before analyzing the mislocalization of all conditions, data correction was performed using the same response bias in the control trials as that used in the previous studies (Honda, 1989;

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Sogo and Osaka, 2001). When a target was presented before the execution of a saccade, we subtracted the mean error in control trials in which subjects kept watching the fixation LED from the mislocalization magnitude. When a target was presented after the end of a saccade, the mislocalization magnitude was also corrected by using the mean error when the subject kept watching the target LED. Finally, to correct the mislocalization of a target presented during a saccade, the mean of the errors obtained in the two kinds of control trials was used. These corrections did not influence the results of statistical tests for the comparison of the length between the phantom array and the phantom line because the same values of the left endpoint and the right endpoint in a given trial shifted in the same direction. Figure 2A shows the saccadic mislocalization curve under the single condition. Each point in Fig. 2A indicates the mean of each 10 ms consisting of 8–40 samples from −5 to +5 ms of the plotted positions. For example, the plotted dots at −75 ms to the saccade onset indicate the mean from −80 to −70 ms. Mislocalization curves were observed in all subjects, as has been reported in previous studies (Honda, 1989; Mateeff, 1978; Matin and Matin, 1972). When the stimulus was presented before the saccade onset, the systematic mislocalization in all subjects began to shift in the direction of the saccade at −80 ms before the saccade onset, and the maximum magnitude of the mislocalization was marked at the time of the saccade onset. The similarity in this and the previous studies (e.g. Honda, 1989) indicates that the very short latencies of the saccade in Experiment 1 did not influence the property of the mislocalization curve. Figure 2B shows the localization of both endpoints under the flicker condition as a function of the timing of the target presentation with respect to the saccade onset. Figure 2C shows the localization under the continuous condition. In these figures, each point consists of 6–50 samples and indicates the mean of each 10 ms from −5 to +5 ms of the plotted positions, as in the single condition. The dissociation between the right and left endpoint-mislocalization curves started at 30 ms before the saccade onset and continued up to 30 ms after that. These results indicate that when the stimulus duration of 31 ms overlapped with the duration of a saccade execution, the subjects observed a phantom array or line. In other words, a retinal sweep of the stimulus only during a saccade is necessary for the subjects to perceive a phantom array or line (Sogo and Osaka, 2001). On the other hand, the right and left endpoints were localized at almost the same positions earlier than −30 ms before the saccade onset and later than +40 ms after the saccade onset. This indicates that the subjects perceived the flickering stimulus or the continuously lit stimulus as a single dot (see below and Fig. 4 in Section 2.2.4). To verify that the right endpoint was the first-perceived one, as has been reported by Hershberger (1987), we calculated the ratio of trials in which subjects reported that the right endpoint was the first-perceived one to all trials included in each 10 ms bin from −30 to +30 ms relative to the saccade onset. Figure 3 shows the ratio of trials in which subjects reported that the first-perceived endpoint was the right one.

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Figure 2. Localization errors of subjects Y. O., M. M. and N. K. under the single (A), the flicker (B) and the continuous (C) conditions when they made a rightward saccade. The horizontal axis indicates the time of stimulus onset from the saccade onset. A negative value means that the stimulus onset was before the saccade onset. The vertical axis indicates a localization error in degrees. A negative or positive value means that the localization of the stimulus was left or right to the actual stimulus position, respectively. The presentation duration under the flicker (B) and the continuous (C) conditions was 31 ms. Each dot represents the average value of which window span is 10 ms from −5 to 5 ms at plotted positions. An open circle indicates right-endpoint localization, and a cross indicates left-endpoint localization.

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Figure 3. The ratio of trials in which subjects reported that the right endpoint was the first perceived to all trials included in each 10 ms bin from −30 ms to +30 ms relative to the saccade onset. The vertical axis represents the ratio and the horizontal axis represents the time of stimulus onset to saccade onset.

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As shown in this figure, all subjects reported that after the saccade onset, the right endpoint was the first-perceived one. It should be noted that the magnitude of the mislocalization of the left endpoint of the phantom array or line from 0 to 30 ms in subjects Y. O. and M. M. reached 2 degrees in the direction opposite to the saccade. These results do not agree with those by Jordan and Hershberger (1994) (see Fig. 4 in their paper). They reported that the subjects perceived the left endpoints of the phantom array near the actual stimulus position. This disagreement might be due to the difference in methods between the study of Jordan and Hershberger (1994) and our study. Their task was to report where a flash that was presented around the time of a rightward saccade appeared relative to the phantom array, and the subjects were forced to choose one of the following five alternatives: The flash had appeared at (1) the leftmost end of the phantom array; (2) the rightmost end of the phantom array; or (3) (4) (5) the inner left, middle, or inner right aspects of the phantom array, respectively. In contrast, in Experiment 1, we asked subjects to localize the endpoints of the phantom array or line. The localization manner of left endpoints could be the exocentric manner. The exocentric manner means that the spatial and temporal relation to other objects on the retina affected the localization of the object (Sogo and Osaka, 2001). In Experiment 1, the left endpoints of the phantom array and line were perceived after the right endpoints of the phantom array and line. Therefore, the previous stimulation to the left endpoints could be the visual reference. However, in the current study, it would not the case. Sogo and Osaka (2002) showed that in an exocentric situation where the two flashes whose inter-stimulus interval (ISI) was 120 ms or shorter were presented around the time of a saccade, the perceived distance between them was equal to the actual distance between these flashes on the retina. In the current study, because the ISIs were 5 ms under the flicker condition, the perceived lengths of the phantom array should have been equal to the actual distance between two endpoints made by sweep of the stimuli on the retina. However, the perceived lengths were around half the actual distance on the retina. Therefore, the locations of the left endpoints could not be predicted by purely exocentric manner. 2.2.4. Comparing the phantom array with the phantom line. When subjects’ eyes are stationary, the critical flicker frequency (CFF) is usually around 60 Hz for normal people (Hecht and Schlaer, 1936), and it is reduced after some adaptation to darkness (White et al., 1976). Under the flicker condition, therefore, the subjects observed the flickering stimulus as a single light continuously lit as long as the eyes were stationary because of the 200 Hz flicker and the adaptation to darkness. When the subjects made a saccade, on the other hand, they could see an array or a line because each light fell on a different part of the retina during the saccade. In Fig. 4, the open squares and filled circles indicate the mean lengths of the phantom array and line by subtracting the right endpoint from the left endpoint

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Figure 4. Apparent lengths between the right and left endpoints under the flicker and continuous conditions of subjects Y. O., M. M. and N. K. The vertical axis represents the distances between the right and left endpoints of the perceived array under both conditions. The error bar means one standard error. The distances were calculated by subtracting the left endpoint position from right endpoint position, always resulting in a positive value. Each dot indicates the average value of the perceived length on the y-axis and the stimulus onset from the saccade onset on the x-axis. The dots consist of 6–50 trials in which the window span is 10 ms. The horizontal gray bar indicates the stimulus presentation time with the dot located at 5 ms after the saccade onset.

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in each 10 ms bin where more than 6 points were included from −5 to +5 ms relative to the presented point. The vertical axis indicates the apparent length of the phantom array or line in visual degrees. The horizontal axis indicates the presentation timing of the stimulus from the saccade onset. Figure 4 shows that the length of the phantom array was longer than that of the phantom line around the time of saccade onset. The difference was largest at the saccade onset, reaching 1 degree. The difference was observed from −20 to +20 ms in subject Y. O., from 0 to +10 ms in subject M. M., and from 0 to +30 ms in subject N. K. (p < 0.05, Wilcoxon signed rank test). The maximal length of the phantom array was nearly one-half the magnitude of the intended saccade amplitude as reported in previous studies (Hershberger, 1987; Jordan and Hershberger, 1994). The maximal length of the phantom line was shorter than that of the phantom array (Y. O.: 77.6%, N. K.: 78.3%, M. M.: 80.3%). 2.3. Discussion In Experiment 1, we first investigated whether the difference in the visual structures between the phantom array and line influences the apparent lengths. As we mentioned above, there was no difference in saccadic amplitudes between the flicker and the continuous conditions. Therefore, the lengths of the retinal sweep of the stimuli under both conditions were almost the same. Nevertheless, the perceived lengths of the phantom array were significantly longer than those of the phantom lines (Fig. 4). These results are in apparent contradiction to those of Matsumiya and Uchikawa (2001) that predicted a shorter length of the phantom array than that of the phantom line. There was a difference in whether an exocentric visual reference was presented, which could have caused the different results between our study and the study of Matsumiya and Uchikawa (2001). In their study, the horizontal line that was always shown in a given trial served as a visual reference to a target. On the other hand, the current experiment was conducted in a dark room, and no visual reference appeared in a given trial. Although there is a possibility that each element of the phantom array or line could serve as the visual reference by itself, as discussed above, the previous stimulation of the left endpoints would not serve as exocentric visual references. Awater and Lappe (2004) mentioned that when supplementary visual references as well as saccadic targets were shown, a saccadic compression was present, and that there was a uniform mislocalization but no saccadic compression when no visual reference was shown. Furthermore, Lappe et al. (2000) showed that post-saccadic visual references are most effective in inducing the saccadic compression. Thus, the function underlying the saccadic compression could not describe our result showing that the perceived lengths of the phantom array were longer than those of the phantom line. Instead of the saccadic compression phenomenon, the function underlying ‘an illusion of the filled-unfilled space’ (Lewis, 1912) could describe the present results.

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It has long been said that the perceived distance between the two endpoints of an array of dots is larger than that between two dots when these stimuli are fixated on, even though the distances between both endpoints of these stimuli are the same. The former is referred to as filled space, and the latter as unfilled space. This phenomenon is referred to as an illusion of filled-unfilled space or an illusion of interrupted distance (Beagley, 1985; Lewis, 1912). If a line works as the unfilled space, the perceptual system of the phantom array or line could be identical to the function underlying the illusion of filled-unfilled space. To check this possibility, we conducted Experiment 2. 3. EXPERIMENT 2

3.1. Method 3.1.1. Subjects. Twelve subjects, including two subjects who had participated in Experiment 1 (Y. O. and N. K.), participated in this experiment. They had normal or corrected-to-normal visual acuity with binocular vision. Two of them were authors and therefore knew the objectives of this experiment, but the others were not informed. All subjects gave written consent to participate in this experiment. 3.1.2. Experimental design. In Experiment 2, the experimental design had three factors: length, eye position, and stimulus type. The length factor consisted of two different lengths of stimuli, 4 degrees and 8 degrees. We called these the SHORT and the LONG conditions, respectively. We also manipulated the eye positions for fixation. The fixation points were located at −4 degrees, 0 degrees (subjects’ median line), and +4 degrees, which were referred to as the LEFT, the CENTER, and the RIGHT conditions, respectively. The stimulus types were a line, an array of seven dots, and an array of two dots, which were referred to the LINE, the 7-dot, and the 2-dot condition, respectively. The diameter of each dot under the 7-dot and the 2-dot conditions was 0.3 degrees, which was the same as the property of the stimuli in Experiment 1. The center of each stimulus was located at 0 degrees and jittered less than 0.5 degrees in every trial. Each dot under the 7-dot condition was placed on the simulated saccade curve based on the saccadic parameters of Experiment 1. Therefore, seven dots were assigned at −2.00, −1.61, −1.03, 0.00, +1.03, +1.61, and +2.00 degrees under the SHORT condition and at −4.00, −3.43, −2.23, 0, +2.23, +3.43, and +4.00 degrees under the LONG condition. Each condition consisted of 20 trials repetition; therefore, the total number of trials was 360. Each block consisted of 40 trials, and the subjects performed nine blocks in a day. The sequence in which the length and the stimulus-type factors were included was randomized in a given block, and the eye-position factor was pseudo-randomized across subjects. 3.1.3. Apparatus. The experiment was performed in complete darkness. Subjects were seated with their heads stabilized by a chinrest. Instead of being shown

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in the LEDs, all stimuli of this experiment were presented on a 21-inch CRT monitor (Calix, TOTOKU) with a resolution of 1152 × 864 pixels and a 100 Hz refresh rate. The luminance of stimuli was the same as in Experiment 1. The distance from a subjects’ eye to the monitor was 32 cm. The horizontal eye movement of each subject’s dominant eye was sampled at 250 Hz with EyelinkII (SR research Ltd.) which has a resolution of less than 0.5 degrees. We wrote a customized program in Matlab (Mathworks), using the Psychophysics Toolbox and Eyelink Toolbox extensions (Brainard, 1997; Cornelissen et al., 2002; Pelli, 1997; see http://psychtoolbox.org/). The program running under Macintosh G4 (Apple) controlled the timing of stimuli presentation and the EyelinkII to obtain these eye positions. The program also could detect fixation error and determine the mouse position at the time of localizations for both endpoints of a stimulus. 3.1.4. Procedure. Each trial began with the presentation of a white center dot for drift correction. The subjects were instructed to push a button when they fixated on the center dot for drift correction. Then a red filled circle (8 cd/m2 ) was displayed at eye level. The subjects were instructed to fixate on this point until the localization pointer appeared, even if this point disappeared. After a delay of 1 or 1.5 seconds, the target point was displayed at the same eye level and the fixation point simultaneously disappeared. The fixation and target positions depended on the conditions of the eye-position factor. Under the LEFT condition, the fixation was displayed at −4 degrees and the target was at 4 degrees. Under the RIGHT condition, the fixation was displayed at 4 degrees and the target was at −4 degrees. The target position was at 4 degrees and the fixation was centered under the CENTER condition. Then, the stimulus was presented for 30 ms. There was some delay (100–300 ms) between the disappearance of the fixation point and the presentation of the stimulus. After 500 ms, a pointer for localizations appeared in a random position on the monitor. Until the appearance of the localization pointer, subjects had to keep fixating on the fixation dot. The pointer was controllable by a mouse that the subjects used in a right-handed manner. The subjects were asked to click two positions depending on the order in which they perceived endpoints of the stimulus. When the subjects perceived both endpoints of the stimulus simultaneously, they clicked the two positions in an arbitrary order. One trial was finished when the second endpoint was localized. The ITI was 1000–1500 ms. Calibration of three horizontal points was performed before each block began. If the subject’s eye position was out of the 1-degree window surrounding the fixation dot, a beep sounded to inform the subjects that they were breaking the fixation. Then a blank screen appeared, and the next trial started. The erroneous trial was inserted into a random position of the residual sequence. We calculated the perceived lengths in all trials, the mean values of the 20 repetitions in any given condition for each subject, and the grand average and standard error across subjects.

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3.2. Results and discussion In Fig. 5, bars indicate the perceived length of each stimulus type in degree on the vertical axis and the conditions are represented on the horizontal axis. The line represents standard errors across subjects. We performed a three-way analysis of variance (ANOVA) using within-subjects factors of length (SHORT and LONG), eye position (LEFT, CENTER, and RIGHT), and stimulus type (LINE, 7-dot, 2-dot) on the grand average of the lengths. The statistical results indicated significant effects on the length factor (F (1, 11) = 1247, p < 0.01), the stimulus-type factor (F (2, 22) = 41.1, p < 0.01), and an interaction between these two factors (F (2, 22) = 10.3, p < 0.01), but not the eye-position factor (F (2, 22) = 0.861, p = 0.44). To check whether these stimulus types could modulate the perceived lengths, we performed a post-hoc test on the stimulus-type factor. A comparison of the three conditions (LINE, 7-dot, and 2-dot) revealed that there were significant differences in length between the LINE and the 7-dot conditions and between the 2-dot and the 7-dot conditions, but not between the LINE and the 2-dot conditions. These results indicate that the perceived length under the 7-dot condition was longer than those of the other two conditions and that the perceived length under the LINE condition was very similar to that under the 2-dot condition. Thus, these results correspond to the unfilled condition in the Lewis study (Lewis, 1912). In Fig. 5, we show that the perceived lengths were almost the same as the actual lengths (4 degrees under the SHORT condition and 8 degrees under the LONG condition), regardless of the LONG and the SHORT conditions. As mentioned above, the perceived lengths under the 7-dot condition were longer than those of the other two conditions, and the perceived length under the LINE condition was very similar to that under the 2-dot condition. These tendencies were not affected by eye position.

4. GENERAL DISCUSSION

In the current study, we conducted two experiments on the perceived lengths of stimuli such as a line or an array during saccadic eye movements (Experiment 1) and fixation (Experiment 2). We found that the perceived lengths under line stimulus conditions were shorter than those under array stimulus conditions in both experiments. As shown in the results, the maximum perceived length of the phantom array or line was around half the actual image length on the retina when subjects made a saccade (Experiment 1) but not when the eyes were stationary (Experiment 2). As mentioned in the Section 2.3 Discussion, the saccadic compression cannot explain results of Experiment 1. The filled-unfilled illusion can account for the tendency that the perceptual length of an array was longer than that of a line, but not fully account for the results of Experiment 1 because the ratio of length under the LINE

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Figure 5. Apparent lengths between the right and left endpoints when subjects’ eyes were stationary. The vertical axis indicates distances, in degrees, between the right and left endpoints of the perceived arrays or lines. The horizontal axis indicates conditions of the stimulus-type factor (LINE, 7-dot, and 2-dot). Each bar indicates the mean value of 12 subjects under the condition and the error bars represent one standard error. Each condition of the length factor is referred to as LONG and SHORT. As shown in the legend, the grating of the bar represents the conditions of the eye-position factor; light gray, black, and dark gray indicate a fixation point was left, center, and right, respectively.

condition to that under the 7-dot condition (95% as shown in Fig. 5) was higher than the ratio of the phantom-line length to the phantom-array length (80% as shown in Fig. 3). To account for the present data, therefore, we propose a model for the localization processes that assumes two steps.

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The first step is the temporal package step: within a temporal window, the stimulations of the retina at different times are packed into one configuration, even though they are not simultaneously presented. The second step is the remapping step: the retinal coordinate is translated into the spatial coordinate. This remapping process is vulnerable to effects by saccadic eye movements. When we fixate a given point, the remapping process works well, that is, the location of the point in the retina coordinate corresponds to that in the spatial coordinate. On the contrary, when we make a saccade, the remapping is distorted, resulting in the saccadic mislocalization or compression. The fact that there was a similar tendency for perceptual lengths of an array or a line between Experiments 1 and 2 indicates that the temporal package step precedes the remapping step. If each element of the stimuli such as a flicker or a continuous light had been individually processed in real time, the locations of both endpoints of the phantom array and line on the retina should have been the same, that is, the perceived lengths between the phantom array and line should have been the same. According to our model, both in Experiments 1 and 2, the filled-unfilled illusion influenced the temporal package process, inducing the tendency for the perceptual length of an array to be longer than that of a line. In Experiment 1, however, the saccade modulated the length of the array or line at the remapping step after the filled-unfilled illusion had occurred at the temporal package step. Thus, in terms of length, the ratio of the LINE condition to the 7-dot condition in Experiment 2 was different from the ratio of the phantom line to the phantom array in Experiment 1. These processes at the first and second steps of our model are in good agreement with the findings of psychophysical and physiological studies. For example, the configuration such as gestalt or figure-ground segregations is first processed in V1/V2 area (e.g. Super et al., 2003), and the perisaccadic remapping is processed in higher areas such as the parietal area (e.g. Duhamel et al., 1992). Recently, Tolias et al. (2001) found that more than one-third of V4 neurons showed that the receptive field (RF) shrunk around the time of a saccade and shifted toward the saccade target. Although the mechanism of how these neurons are related to perisaccadic remapping is still unclear, it is possible that these V4 neuronal activities influence the perisaccadic shrinkage or compression. The perisaccadic compression induced by the remapping process may not always occur. As shown in the study of Matsumiya and Uchikawa (2001), some stimuli having the special properties such as the filled rectangle were not affected by the perisaccadic remapping process. The remapping process may be completed after a saccade in Experiment 1. Since we assumed a temporal window in which some elements were packed into one configuration perceptually, the remapping process would be delayed at least for the duration of the temporal window. Some studies have shown that events after a saccade modulated the localization of stimuli or the perceptions of an object’s location in observers’ represented space. For instance, Lappe et al. (2000) showed that a presentation of the visual reference beside a stimulus induced the maximum effect of saccadic compression, as mentioned above. Deubel et al. (1996)

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showed that the postsaccadic target blanking prevented saccadic suppression of displacement. We speculated that the completion of the remapping process seemed to wait for a trigger of saccade offset in our case, because the processing in real time for the localization should cost too much for the visual system and contradicts our results. Although our model may be valid, it remains unclear how long is the duration of the configuration time window, or what properties of configuration within a temporal window are affected by the remapping process around the time of a saccade. These questions remain open for future research. Acknowledgements We express appreciation to Paul Dassonville, and an anonymous reviewer for review of the manuscript and excellent suggestions, Kiyoshi Fujimoto, Masayoshi Nagai, Kanamori Nobuhiro, Junji Watanabe, Hideyuki Ando, and Hiroko Fukuda for useful comments. This research was supported by grants from Japan Society for the Promotion of Science (JSPS) Research Fellowship for Yong Scientist, the original Industrial Technology Research and Development Promotion program from the New Energy and Development Organization (NEDO) of Japan, and the Ministry of Education, Science, Sports and Culture of Japan.

REFERENCES Awater, H. and Lappe, M. (2004). Perception of visual space at the time of pro- and anti-saccades, J. Neurophys. 91, 2457–2464. Beagley, W. (1985). Interaction of Mueller-Lyer with filled-unfilled space illusion: An explanation of Mueller-Lyer asymmetry, Perception and Psychophysics 37, 45–49. Brainard, D. H. (1997) The psychophysics toolbox, Spatial Vision 10, 433–436. Cornelissen, F. W., Peters, E. and Palmer, J. (2002). The eyelink toolbox: Eye tracking with MATLAB and the psychophysics toolbox, Behavior Research Methods, Instruments Computers 34, 613–617. Dassonville, P., Schlag, J. and Schlag-Rey, M. (1995). The use of egocentric and exocentric location cues in saccadic programming, Vision Research 35, 2191–2199. Deubel, H., Schneider, W. X. and Bridgeman, B. (1996). Postsaccadic target blanking prevents saccadic suppression of image displacement, Vision Research 36, 985–996. Duhamel, J. R., Colby, C. L. and Goldberg, M. E. (1992). The updating of the representation of visual space in parietal cortex by intended eye movements, Science 255, 90–92. Hecht, S. and Shlaer, S. (1936). Intermittent stimulation by light. V. The relation between intensity and critical frequency for different part of the spectrum, J. Gen. Physiol. 19, 965–979. Hershberger, W. (1987). Saccadic eye movements and the perception of visual direction, Perception and Psychophysics 41, 35–44. Hershberger, W. A., Jordan, J. S. and Lucas, D. R. (1998). Visualizing the perisaccadic shift of spatiotopic coordinates, Perception and Psychophysics 60, 82–88. Honda, H. (1989). Perceptual localization of visual stimuli flashed during saccades, Perception and Psychophysics 45, 162–174. Honda, H. (1990). Eye movements to a visual stimulus flashed before, during, or after a saccade, in: Attention and Performance, Jeannerod, M. (Ed.), Vol. 13, pp. 567–582. Erlbaum, Hillsdale, NJ, USA.

316

A. Noritake et al.

Honda, H. (1991). The time courses of visual mislocalization and of extraretinal eye position signals at the time of vertical saccades, Vision Research 31, 1915–1921. Jordan, J. S. and Hershberger, W. A. (1994). Timing the shift in retinal local signs that accompanies a saccadic eye movement, Perception and Psychophysics 55, 657–666. Lappe, M., Awater, H. and Krekelberg, B. (2000). Postsaccadic visual references generate presaccadic compression of space, Nature 403, 892–895. Lewis, E. (1912). The illusion of filled and unflilled space, Brit. J. Psychol. 5, 36–55. MacKay, D. (1970). Mislocation of test flashes during saccadic image displacements, Nature 227, 731–733. Mateeff, S. (1978). Saccadic eye movements and localization of visual stimuli, Perception and Psychophysics 24, 215–224. Matin, L. and Matin, E. (1972). Visual perception of direction and voluntary saccadic eye movements, Bibliotheca Ophthalmologica 82, 358–368. Matin, L., Matin, E. and Pearce, D. G. (1969). Visual perception of direction when voluntary saccades occur: I. Relation of visual direction of a fixation target extinguished before a saccade to a flash presented during the saccade, Perception and Psychophysics 5, 65–80. Matin, L., Matin, E. and Pola, J. (1970). Visual perception of direction when voluntary saccades occur: II. Relation of visual direction of a fixation target extinguished before a saccade to a subsequent test flash presented before the saccade, Perception and Psychophysics 8, 9–14. Matsumiya, K. and Uchikawa, K. (2001). Apparent size of an object remains uncompressed during presaccadic compression of visual space, Vision Research 41, 3039–3050. Morrone, M. C., Ross, J. and Burr, D. C. (1997). Apparent position of visual targets during real and simulated saccadic eye movements, J. Neurosci. 17, 7941–7953. Pelli, D. G. (1997). The VideoToolbox software for visual psychophysics: Transforming numbers into movies, Spatial Vision 10, 437–442. Ross, J., Morrone, M. C. and Burr, D. C. (1997). Compression of visual space before saccades, Nature 386, 598–601. Sogo, H. and Osaka, N. (2001). Perception of relation of stimuli locations successively flashed before saccade, Vision Research 41, 935–942. Sogo, H. and Osaka, N. (2002). Effects of inter-stimulus interval on perceived locations of successively flashed perisaccadic stimuli, Vision Research 42, 899–908. Super, H., van der Togt, C., Spekreijse, H. and Lamme, V. A. (2003). Internal state of monkey primary visual cortex (V1) predicts figure-ground perception, J. Neurosci. 23, 3407–3414. Tolias, A. S., Moore, T., Smirnakis, S. M., Tehovnik, E. J., Siapas, A. G. and Schiller, P. H. (2001). Eye movements modulate visual receptive fields of V4 neurons, Neuron 29, 757–767. White, K. D. and Baker, H. D. (1976). Foveal CFF during the course of dark adaptation, J. Opt. Soc. Amer. 66, 70–72.