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The phantom array: a perisaccadic illusion of visual direction.

If one saccades in the dark across a point source of light blinking rapidly on and off, one will see a spatially extended series of lights called the "phantom array" (Hershberger, 1987). Certain features of the phantom array have remarkable theoretical implications regarding the nature of the shift of retinal local signs that accompanies a saccadic eye movement. The received view holds that the retina's local signs (i.e., spatiotopic coordinates) shift sluggishly, forming, as it were, one long continuous change that temporally brackets the attendant saccade (e.g., see Dassonville, Schlag, & Schlag-Rey, 1992; Matin, 1972, 1982). The phantom array, as Hershberger described it, implies otherwise. The purpose of the present study was to determine whether theoretically naive observers would describe the phenomenon as Hershberger did. Because the theoretical implications of the phantom array are only as sound as Hershberger's description, it is important to determine the replicability of that description, particularly among naive observers.

Figure 1 illustrates the phantom array as it was described by Hershberger (1987). Letting the arrow in Figure 1 represent a single, rightward, saccadic eye movement and the asterisk represent a single flashing light, the bracketed array represents the phenomenal appearance. One sees, fixed in space, a horizontal array of lights blinking on and off in sequence (from right to left) giving an impression of apparent motion, or phi, with the entire array being displaced to the right, in the direction of the attendant saccade.

The direction of the phi (from right to left) implies that the retina is moving across the flashing image faster than the retina is changing its local signs, because, if the two were changing at the same rate, the flashes would all be seen to be coming from only one location; that is, one would see a single point of light situated at its objective location, not an array. Conversely, phi in the same direction as the eye movement would signify that the retina's local signs were changing at a rate that is faster than the eye is moving.

The relatively veridical location of the last flash in the array implies that the shift of retinal local signs is essentially complete by the end of the saccade; that is, the tail end of the array appears virtually coincident with the light source.(1) Therefore, some or all of the shift of retinal local signs appears to have occurred before the eye began to move. That is, the only way for the total shift of retinal local signs to be complete or nearly so (i.e., isometric with the saccade) by the end of the saccade is for the shift of retinal local signs (the slower of the two changes occurring during the saccade) to have begun first. This presaccadic shift of retinal local signs is reflected by the discrete displacement of the first flash in the phantom array, the one comprising the right end of the array.(2)

This presaccadic shift appears to be quick as well as early. With a light source flashing at 200 Hz, as in the present study (i.e., a 1-ms flash once each 5 ms), the displacement of the first flash in the phantom array (the displacement spanning the entire array) appears to be perfectly discrete. That is, just prior to the shift in the retinal local signs, the light appears in its objective location whereas 5 ms later it appears maximally displaced. (We, the authors, have observed the same effect at 500 Hz.) This shift in retinal local signs may not be instantaneous, but it is remarkably abrupt (taking less than 2 ms at 500 Hz) and certainly much faster than the fastest saccade.

The magnitude of this discrete presaccadic shift of retinal local signs corresponds to the angular displacement of the first flash (i.e., the size of the army itself). Although we have not determined its maximum size, the phantom army typically subtends a visual angle that appears to be about half the size of the attendant saccade. Thus, at least half of the overall perisaccadic shift of retinal local signs appears to be discrete and presaccadic; further, by the end of the saccade the total shift appears to be complete. These observations are at odds with the received view that the shift is sluggish or damped.

As mentioned above, the purpose of the present research was to determine whether or not theoretically naive observers would describe the phantom array as we have done here (a preliminary account of this research was summarized in Hershberger & Jordan, 1992); obviously, the theoretical significance of the illusion depends critically upon its replicability.

We carefully interrogated each observer to determine whether he/she experienced the complex army in all of its aspects. As described above, the phantom array has the following four aspects:

1. For horizontal saccades, the array comprises a horizontal row of dots. We will refer to this aspect as ROW.

2. The dots within the array materialize in a regular sequence in the direction opposite the eye movement. We will refer to this aspect as SEQUENCE.

3. The army of dots does not appear to move in the direction of the eye movement. We will refer to this aspect as FIXED.

4. The entire array of dots appears to be located to one side of the blinking light, the side associated with the new direction of gaze. We will refer to this aspect as SIDE.

Method and Results

Participants as naive observers were 75 undergraduates enrolled in Introductory Psychology at Northern Illinois University. In order to obtain their informed consent, we told them that their task would be to describe the appearance of some lights viewed in the dark. Further, we said that they would receive bonus course credit for participating whether or not they completed the task.

The observers participated one at a time. They sat at a table, with their arms resting on the table and their heads supported by a chin rest. A red, light-emitting diode (LED) oscillating on and off at 200 Hz (cycle: 1 ms on and 4 ms off) was located 160 cm in front of the chin rest. At this distance, the 5-mm (diameter) LED subtended a visual angle of about .18 degrees. The LED's luminance was about 175 mL, and, oscillating at 200 Hz, it did not appear to flicker. The room was totally dark except for the LED. From an adjacent room, the experimenter communicated with the observer via an intercom.

To begin the interrogation, the experimenter asked the observers whether they could see the red light. When they replied in the affirmative, the experimenter read the first set of instructions (Instruction #1) printed below. (Because the value of our observers' answers are only as trustworthy as our method of interrogation, it is important to describe our method of interrogation in detail.)

Instruction #1: I want you to quickly look at the left corner of the room, then the right corner of the room, then back to the left corner, and so on. Once you get your eyes to either corner, keep them there for a second before looking to the other corner. I know you can't see the corners of the room but pretend that you can. While you are looking back and forth between the corners of the room, make sure that you do both of the following: (1) keep your head still, and (2) move your eyes across the red light. Don't look at the red light, just make sure your eyes move across it. While doing this task, note what happens to the red light. Continue looking from corner to corner until you have a good idea of what you are seeing. When you have a good idea of what you are seeing, comment on it. I will then ask you a few questions.

Do Naive Observers See ROW?

After the observers indicated that they had a good idea of what they were seeing, the experimenter asked them five forced-choice questions which had been designed to determine whether or not an observer was seeing a horizontal row of dots (ROW) during each eye movement. Each question in this series of five could be asked only if the questions that preceded it had been answered in a manner congruent with seeing a horizontal row of dots during the saccade. Thus, if for any of these first five questions an observer selected the answer that was noncongruent with seeing a horizontal row of dots, the experimenter repeated Instruction #1, waited for the observer to comply with the instructions, and then asked the observer the question again. If, after one repetition, the observer still selected the noncongruent response, this response was recorded as a final datum and the observer was excused. This criterion was used throughout the experiment: Observers continued through the series of questions as long as they were at least uncertain about whether or not they experienced the phenomenon as Hershberger (1987) described it. The criterion is a compromise based upon the following considerations. Questioning observers about phenomena they can not experience is futile at best, but summarily dismissing observers who are merely uncertain appears worse, because doing so would cull the potential nay sayers from the pool of observers and insidiously bias the overall results.

The first five questions and the observers' initial answers were as follows:

Q#1. Each time you move your eyes, do you see any dots or flashes? Results: 74/75 (99%) initially responded "yes."

Q#2. Each time you move your eyes do you see only one dot or more than one dot? Results: 73/75 (97%) initially responded "more than one."

Q#3. Do all the dots appear at one point in space or do they appear to be spread out? Results: 72/74 (97%) initially responded "spread out."

Q#4. Is the spatial arrangement of the dots that you see random or regular; that is, do you see a shapeless cluster of dots, or a regular pattern such as a dotted line? Results: 72/74 (97%) initially responded "a dotted line."

Q#5. Is the dotted line vertical as in up and down or horizontal as in side to side? Results: 72/74 (97%) initially responded "horizontal."

One observer never reported being able to see more that one dot during any given eye movement (i.e., twice he answered Q#2 in a noncongruent manner). Another observer, who had initially answered each question (Q#1-Q#5) in a manner congruent with seeing a horizontal row of dots, insisted that she was no longer able to see the phenomenon when it came time to answer Q#6. Both of these observers were dismissed. Thus, the number of observers going on to Q#6 was 73.

Do Naive Observers See SEQUENCE?

Once the experimenter was sure that an observer was reliably seeing a horizontal row of dots during every saccade, he then determined whether or not the dots in the row appeared to materialize in a regular sequence opposite the direction of the saccade (SEQUENCE). The experimenter accomplished this by reading Instruction #2 to the observer, followed by three more forced-choice questions, Q#6, Q#7, and Q#8.

Instruction #2: Now I would like for you to look as far to the right as possible then as far to the left as possible while keeping your head still. Continue to do this at a steady pace until you can answer the following question. (Insert the appropriate question here.)

Instruction #2 was designed to accentuate the phenomena being investigated by these three questions. If, for Q#6, Q#7, or Q#8, an observer selected the response that was noncongruent with seeing the horizontal row materialize in a regular sequence opposite the direction of the saccade, the experimenter noted this, skipped the rest of the questions in this section, and proceeded to Q#9-Q#11, which were not dependent on the observer's answers to Q#6 through Q#8. However, after asking those questions (Q#9-Q#11), the experimenter reread Instruction #2, and returned to the particular question to which the observer had initially given a noncongruent answer (Q#6, Q#7, or Q#8) a second time. This circuitous procedure was followed in order to minimize the probability of the observer simply switching his or her response to satisfy the experimenter, as might be expected if a question had been repeated immediately following a noncongruent answer. If after returning to this section the observer still gave the noncongruent response, the experimenter recorded this and marked the remaining questions of this section as not answered (NA). However, if the observer now gave a congruent answer to this question, he or she was asked the remaining questions in the section as well.

Q#6. Each time you move your eyes, do some of the dots appear before others, or do they all appear at once? Results: 45 of the 73 observers (62%) initially responded "some appear before others." Of the 28 who initially responded "all at once," 15 (54%) changed their mind when asked to observe the phenomenon a second time.

Q#7. Is the sequence in which they appear random, meaning without any type of order, or is the sequence regular as in left to right or right to left? Results: Of the 60 observers asked this question, 56 (93%) initially responded, "in a regular sequence." Of the 4 who initially responded, "in a random sequence," 2 changed their mind when asked to observe the phenomenon a second time.

Q#8. You stated that the dots appear in a regular sequence. Is this sequence in the same direction or the opposite direction of your eye movement? Results: Of the 58 observers asked this question 45 (78%) initially responded "in the opposite direction." Of the 13 who initially responded "in the same direction," 8 (62%) changed their mind when asked to observe the phenomenon a second time.

Do Naive Observers See FIXED?

Question Q#9 was designed to determine whether or not the position of a single dot in the array remained fixed while the array was present (FIXED). Because this question was concerned only with the behavior of a single dot within the array, it could be asked regardless of how the observer had answered Q#6 through Q#8. The experimenter reread Instruction #2, and then asked the following question.

Q#9. You stated that each time you move your eyes you see a horizontal row of dots. Once an individual dot in the row materializes, does its location change, or does it appear fixed at that location? Results: Of the 73 observers asked this question, 28 (38%) responded "remains fixed in space." The 40 observers who responded with "changes location" were asked the following follow-up question:

Q#9a. Does the dot's location change in the same or the opposite direction of your eye movement? The experimenter asked this question because it was assumed that some observers would confuse the phi produced by the sequential materialization of the dots, with the location of a single dot. Results: Of the 45 observers asked this question, 40 (89%) responded "in the opposite direction."

Combining the results of these two questions (Q#9 and Q#9a), 68 (93%) of the 73 observers saw the dots either as being stationary or as moving in the direction opposite the eye movement.

Do Naive Observers See SIDE?

Instruction #3 and Questions Q#10 and Q#11 were designed to determine whether or not the entire army appeared on the side of the array associated with the new direction of gaze (SIDE).

Instruction #3: Now I would like you to do what I call the LEFT-TO-RIGHT-TASK. First, look at the left corner of the room. Then look rapidly to the right corner of the room. After you have done this, close your eyes and move them back to the left corner of the room. Once you are there, open your eyes and repeat the entire process. Continue doing this until you can answer the following question: (Insert the appropriate question).

The experimenter had observers perform the left-to-right eye movement in order to simplify the communication process. If the observers had kept their eyes open while producing leftward and rightward saccades they would have had to inform the experimenter about the direction of their eye movement before commenting about the location of the array.

Q#10. Each time you move your eyes, does the row of dots appear on both sides of the red light or just one side of the red light? Results: Of the 73 observers asked this question, 57 (78%) initially responded "one side." Of the 16 who initially responded "both sides," 10 (63%) changed their mind when asked to observe the phenomenon a second time.

Question Q#11 could not be asked unless the response to Q#10 had been "one side." If the observer answered Q#10 with "both sides," the experimenter repeated Instruction #3 and repeated Question Q#10; however, first the experimenter returned to any previous questions left unanswered (Q#6, Q#7, or Q#8) starting with a repetition of the one to which the observer had initially given a noncongruent answer. If when Q#10 was repeated the observer answered, "both sides," the experimenter recorded this and marked Q#11 as NA. If the observer answered Q#10 with "one side," the experimenter recorded this, and then asked the observer Q#11.

Q#11. You said that all the dots appear on one side of the light. Which side, the right or the left? Results: Of the 67 observers asked this question, 49 (73%) initially responded, "the right side." Of the 18 observers who initially responded, "the left side," 8 (44%) changed their mind when asked a second time.

If the observer responded with "the left side" to Q#11, the experimenter returned to Instruction #2 and repeated any questions that required repetition (i.e., Q#6, Q#7, and Q#8) before repeating Instruction #3 and repeating Q#11.

Summary of the Results

The results are summarized in Table 1. All but 2 of the 75 naive observers consistently saw a horizontal row of flashing dots whenever they saccaded horizontally across the flashing LED, and even 1 of these 2 people initially appeared to see the array. Further, of the 60 observers who were able to see the temporal sequence of the flashes, all but 4 saw them flashing on and off sequentially in a direction opposite to the eye movement's, and even 2 of these 4 observers changed their mind when they were asked to examine the phenomenon a second time (i.e., they too reported seeing a direction of motion opposite to the eye movement's). Furthermore, of the 73 observers who consistently saw the horizontal row of dots, all but 5 (i.e., 93%) saw the individual dots as being stationary or as moving in a direction opposite to the eye movement's (this apparent motion appears to be the phi produced by the sequential flashes). (The 5 observers who reported that the dots moved in the same direction as the eye movement may have been reporting a displacement of the entire array rather than a motion of the individual dots, because all 5 of these observers subsequently reported that they saw the array displaced to the right when they looked to the right.) Finally, only 6 (8%) of 73 observers consistently saw the array as straddling the location of the LED. The other 67 observers saw it located to one side of the LED, with only 10 (15%) of these 67 observers consistently locating it on the side opposite the new direction of gaze. That means that 57 (85%) of these 67 observers saw the entire array on the side associated with the new direction of gaze.
Table 1

Relative Numbers of Observers Answering Questions in a Fashion
Consistent With Hershberger's Description of the Phantom Array

Q#/ASPECT FIRST TIME SECOND TIME COMBINED

Q#1 ROW 99% (74/75) 100% (1/1) 100% (75/75)
Q#2 ROW 97% (73/75) 50% (1/2) 99% (74/75)
Q#3 ROW 97% (72/74) 100% (2/2) 100% (74/74)
Q#4 ROW 97% (72/74) 100% (2/2) 100% (74/74)
Q#5 ROW 97% (72/74) 100% (2/2) 100% (74/74)
Q#6 SEQUENCE 62% (45/73) 54% (15/28) 82% (60/73)
Q#7 SEQUENCE 93% (56/60) 50% (2/4) 97% (58/60)
Q#8 SEQUENCE 78% (45/58) 62% (8/13) 91% (53/58)
Q#9 FIXED 38% (28/73) 89% (40/45) 93% (68/73)
Q#10 SIDE 78% (57/73) 63% (10/16) 92% (67/73)
Q#11 SIDE 73% (49/67) 44% (8/18) 85% (57/67)

Note. Q#9 was not asked a second time. Instead, observers saying
they saw movement were asked the direction of the movement: Q#9a.


Conclusions and Implications

As a rule, the vast majority of our naive observers reported seeing the phantom array essentially as Hershberger (1987) described it. Irrespective of whether the minority of incongruent answers represent fundamental individual differences or merely experimental noise, it is clear that the phantom array is a robust perceptual phenomenon that is replicable across most observers.

The fact that the phantom array observed in this experiment was generated by a 1-ms flash occurring once every 5 ms implies that the first half of the overall shift of retinal local signs (the part manifesting itself as the discrete displacement of the first flash in the array) occurs within a 5-ms interval.

This discrete shift occurs very early as well as very abruptly. We have determined the perisaccadic moment of the discrete shift by psychophysically timing the first flash in the phantom array (Jordan & Hershberger, 1994). We found that the first flash occurs at least 80 ms before the attendant saccade when, presumably, the oculomotor system discretely alters a neural reference signal specifying intended direction of gaze. Our 80-ms finding is precisely consistent with Becker and Jurgens' (1975) earlier report that the amplitude of a saccade may be altered by retinal information presented as late as 80 ms prior to the saccade. This remarkable coincidence suggests that the shift in the spatiotopic coordinates of the retina may be synchronized with the finalization of the intention to orient the eye in a particular direction. In a similar vein, Duhamel, Colby, and Goldberg (1992) have found that the retinal receptive fields of neurons in the parietal cortex of monkeys undergo a shift in the direction of an impending saccade well before the onset of the saccade. They documented their finding with data illustrating a parietal shift that occurred exactly 80 ms before the attendant saccade.

It has been recognized ever since Matin and Pearce's (1965) seminal research that retinal local signs begin to shift during the latency of impending saccades, well before the eye starts to move. What has not been widely recognized is that this change in local signs involves a large, discrete shift that occurs abruptly, apparently when the intention to orient the eye in a particular direction changes abruptly.

The discrete presaccadic shift accounts for only about half of the overall perisaccadic shift of retinal local signs because, as illustrated in Figure 1, the phantom array subtends a visual angle equaling roughly half that of the attendant saccade. The remaining half occurs either during or at the end of the saccade. The immobility of the flashes comprising the phantom array implies the latter. That is, if the retina's local signs were shifting at the time that the flashes were being painted upon the retina, the resultant positive afterimage of each flash should appear to move in the direction of that shift, and they do not. However, the retinas' motion across the image of each flash should also provide the fast magnocellular channels of the visual system (see Livingstone & Hubel, 1988) with an effective stimulus for motion - in a direction opposite to the eye's movement. This motion is not apparent either. Perhaps the two types of motion, being in opposite directions, tend to mask or offset each other; that is, the retinal motion may mask or offset the extraretinal "motion" comprising the shift of local signs. As a result, the only motion that remains visible is the apparent motion generated by the succession of several flashes. Would the extraretinal motion be visible if the retinal motion were removed? What if the image were a negative afterimage, immobile on the retina? A negative afterimage might very well appear to move during a saccadic eye movement, reflecting a gradual shift in retinal local signs. We know that a saccade changes the apparent visual direction of a negative afterimage (Grusser, 1986); the questions to be addressed are whether or not this change necessarily occurs during the saccade and whether or not it mediates a perception of continuous, as opposed to stroboscopic, motion.

Using negative afterimages that lasted for several minutes, Grusser, Krizic, and Weiss (1987) found that afterimages do sometimes appear to move in a continuous fashion when the eye moves saccadically, but only sometimes, particularly at the end of the saccade: Their subjects attended to a small foveal afterimage while saccading horizontally back and forth in the dark between two loudspeakers situated 39 [degrees] apart. At a frequency of less than 1 saccade per second, all subjects perceived movement. Further, most subjects "reported having the impression that the center of gaze was on target earlier than the afterimage" (p. 221). This implies that this gradual shift of retinal local signs is delayed relative to the saccade itself. In other words, the perisaccadic shift may be altogether discontinuous, with the first half occurring before the onset of the saccade (the part that discretely displaces the first flash in the phantom array) and the last half occurring during or at the very end of the saccade. If this is the case, then it follows that a foreshortening of the time between successive saccades could have dramatic effects upon the perceived visual direction of afterimages, even though the saccades themselves remained unchanged. This is what Grusser et al. (1987) found: When their subjects saccaded at a gradually increased rate, the apparent angular distance traversed by the afterimage gradually decreased until finally at a frequency of about four saccades per second all subjects saw one stationary afterimage located about midway between the speakers. In other words, the afterimage was continuously displaced from each of the two terminal eye positions by an angular amount equal to 50% of the saccade - remarkably like the first flash in the phantom array.

We have assumed, heretofore (Hershberger, 1987; Hershberger & Jordan, 1992; Jordan & Hershberger, 1994) that the entire perisaccadic shift is mediated by a single, efferent type of eyeposition signal. However it seems more likely that the two parts of the overall shift (i.e., the first half and the second half) may be mediated by two different eye-position signals, both efferent.(3) Invoking Robinson's (1975) closed-loop model of the oculomotor system, we suggest that the first eye-position signal is the oculomotor system's reference signal specifying intended eye orientation, and that the second is an efference copy representing actual eye orientation.(4)

Assuming that the two shifts involve two different types of extraretinal signal, it is reasonable to suppose that perceived direction of gaze corresponds to a simple average of the two (this also implies that each contributes one half of the overall perisaccadic shift). For example, when Grusser et al.'s (1987) subjects saccaded alternately left and right at 4 Hz, these two signals appeared to be, effectively, 180 degrees out of phase, so that the perceived direction of gaze remained straight ahead.

The received view, held for the better part of 30 years, is that the perisaccadic shift of retinas' local signs is sluggish, forming, as it were, one long continuous change that temporally brackets the attendant saccade (e.g., see Dassonville et al., 1992; Marin, 1972, 1982). Although the overall shift does indeed appear to be prolonged, the phantom array indicates that this overall shift is discontinuous, comprising two components (at least), the first of which is extremely abrupt. From the present experiment we know that this presaccadic component has a time constant of 5 ms or less - because the point light source painting the phantom arrays flashed at 200 Hz.

1 The "last flash" in the array may comprise a series of flashes all of which are seen at the same location in the phantom array - in the present example, at the far left end of the army.

2 As will become obvious later in the paper, the "first flash" is actually a series of flashes all of which are seen at the same location in the phantom array - in the present example, the far right end of the array.

3 We are not the first to consider a hybrid eye-position signal. However, all others have involved afference-efference hybrids (Matin, 1972, 1976a, 1976b; Shebilske, 1977; Skavenski, 1972, 1976; Steinbach, 1987).

4 We are using the expression "efference copy" as Robinson (1975) did in describing his closed-loop model of the oculomotor system. Robinson's closed-loop model of the oculomotor system utilizes two separate indices of the variable being controlled, as do all servo systems: a feedback signal and a reference signal. The feedback signal in Robinson's model is an efference copy; it comprises corollary discharges from premotorneurons in the brainstem indicating actual eye position. The reference signal in Robinson's model is a centralized command signal that specifies the intended value of the feedback signal; that is, intended eye position. Regrettably, these two types of neural signals (commands and copies) are frequently confused in the literature, perhaps because von Hoist and Mittelstaedt (1950) did not fully appreciate the importance of the difference when they first coined the expression "efference copy," as Mittelstaedt (1958) later acknowledged.

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DUHAMEL, J-R., COLBY, C. L., & GOLDBERG, M. E. (1992). The updating of the representation of visual space in parietal cortex by intended eye movements. Science, 255, 90-92.

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GRUSSER, O.-J., KRIZIC, A., & WEISS, L.-R. (1987). Afterimage movement during saccades in the dark. Vision Research, 27, 215-226.

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HERSHBERGER, W. A., & JORDAN, J. S. (1992). Visual direction constancy: Perceiving the visual direction of perisaccadic flashes. In E. Chekaluk & K. R. Llewellyn (Eds.), The role of eye movements in perceptual processes (pp. 143). Amsterdam: Elsevier/North Holland.

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MATIN, L. (1976b). Saccades and extraretinal signal for visual direction. In A. Monty & J. W. Senders (Eds.), Eye movements and psychological processes (pp. 205-219). New York: Erlbaum.

MATIN, L. (1982). Visual localization and eye movements. In W. A. Wagenaar, A. H. Wertheim, & H. W. Leibowitz (Eds.), Symposium on the study of motion perception. New York: Plenum.

MATIN, L., & PEARCE, D. G. (1965). Visual perception of direction for stimuli flashed during voluntary saccadic eye movements. Science, 148, 1485-1488.

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SHEBILSKE, W. L. (1977). Visuomotor coordination in visual direction and position constancies. In W. Epstein's Stability and constancy in visual perception (pp. 23-69). New York:Wiley.

SKAVENSKI, A. A. (1972). Inflow as a source of extraretinal eye position information. Vision Research, 12, 221-229.

SKAVENSKI, A. A. (1976). The nature and role of extraretinal eye-position information in visual localization. In A. Monty & J. W. Senders (Eds.), Eye movements and psychological processes (pp. 277-287). New York: Erlbaum.

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VON HOLST, E., & MITTELSTAEDT, H. (1950). Das Reafferenzprinzip. Naturwissenshaften, 37, 464-476.

J. Scott Jordan is now at Saint Xavier University, Chicago, IL 60655. Correspondence should be addressed to Wayne A. Hershberger, Department of Psychology, Northern Illinois University, DeKalb, IL 60115. Electronic mail may be sent via Internet to WAH@NIU.EDU.
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Author:Hershberger, Wayne A.; Jordan, J. Scott
Publication:The Psychological Record
Date:Jan 1, 1998
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