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Article  |   January 2017
Sustained smooth pursuit eye movements with eye-induced reverse-phi motion
Author Affiliations
  • Arthur Portron
    Ecole Normale Supérieure, PSL Research University, Département d'études cognitives, Laboratoire des Systèmes Perceptifs (LSP), Paris, France
    arthur.portron@ens.fr
  • Jean Lorenceau
    Ecole Normale Supérieure, PSL Research University, Département d'études cognitives, Laboratoire des Systèmes Perceptifs (LSP), Paris, France
    jean.lorenceau@ens.fr
Journal of Vision January 2017, Vol.17, 5. doi:10.1167/17.1.5
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      Arthur Portron, Jean Lorenceau; Sustained smooth pursuit eye movements with eye-induced reverse-phi motion. Journal of Vision 2017;17(1):5. doi: 10.1167/17.1.5.

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Abstract

The gain and speed of smooth pursuit eye movements quickly drop whenever a moving tracked target disappears behind an occluder. The present study tests to what extent pursuit maintenance after target disappearance depends on the occluder's characteristics. In all experiments, a target moving for 2500 ms, (or 1250 ms) at 13.3°/s (or 26.6°/s), disappears behind an occluder for 700 ms (or 350 ms). Participants are asked to maintain their pursuit eye movements as long as possible after target disappearance. Experiment 1 compares smooth pursuit with four types of occluders and shows that a texture of flickering disks allows maintaining pursuit for long durations. Experiment 2 investigates the capability to maintain pursuit with occluders of varying flickering frequencies (3, 5, 10, 20, and 30 Hz). It is found that after target disappearance, smooth pursuit is maintained for longer durations with flicker at 10 and 20 Hz, relative to other flickering frequencies (3, 5, and 30 Hz). Experiment 3 tests whether disk size and disk density of a flickering occluding texture influence smooth pursuit maintenance. Finally, Experiment 4 tests the influence of the contrast distribution of the flickering disks on pursuit maintenance. Altogether, the results show that individuals can maintain smooth pursuit for long durations after target disappearance behind an occluding texture of disks flickering at temporal frequency above 5 Hz with balanced contrast. It is suggested that eye-induced reverse-phi motion responses in MT/MST neurons provide a positive visual feedback to the pursuit system, allowing generating smooth pursuit in the absence of explicit stimulus motion.

Introduction
Smooth tracking eye movements aim at maintaining the retinal image of a moving target in central vision, where visual acuity is best. This process initially requires estimating the on-going target velocity and transforming this sensory input into an oculomotor command. As soon as the eyes start to move, the retinal target velocity decreases, and the pursuit system enters a sensory-motor loop aiming at stabilizing the target on the retina by combining retinal and extraretinal signals (reviews in Barnes, 2008; Kowler, 1989; Spering & Montagnini, 2011). In everyday life, a tracked target (e.g., a flying bird) can move against a static textured background (e.g., a forest) or disappear behind occluding objects (e.g., the foliage of trees) before reappearing after a delay at a new position. During sustained pursuit, the static background against which a target is moving drifts on the retina in a direction opposite to that of the eyes, possibly eliciting motion signals in cortical motion-sensitive regions. If used in the computation of oculomotor commands, the responses to these “spurious” eye-induced visual inputs may yield an incorrect motor output, especially if the target momentarily disappears behind an occluding surface. In order to minimize motor errors, the irrelevant sensory responses to the static surrounding background should thus be canceled or suppressed as much as possible. 
Experimental evidence indicates that, on average, tracking a target moving against a static textured background is not perfect: The eye-velocity gain is reduced (by ∼10%–15%), and the phase lag is increased, indicating that contextual motion signals related to the retinal slip of the background influence, at least in part, the computation of an oculomotor command (Heinen & Watamaniuk, 1998; Niemann & Hoffmann, 1997). On the other hand, a consensual observation is that soon after a tracked target disappears—for instance when passing behind an occluding surface—the eye speed and the gain of smooth pursuit drop within 200–500 ms and intrusive or catch-up saccades quickly occur, except if the background itself moves in the same direction as the eyes (Masson, Proteau, & Mestre, 1995; Spering & Gegenfurtner, 2007). A residual eye velocity is reported after target disappearance, especially when the target reappears after a predictable delay, in which case the eye speed increases before the time of the predicted target reappearance (Becker & Fuchs, 1985; Bennett & Barnes, 2003; Churchland, Chou, & Lisberger, 2003; Fukushima, Fukushima, Warabi, & Barnes, 2013; Madelain & Krauzlis, 2003). 
These studies uncovered the many ways sensory, attentional predictive and efferent extraretinal signals are generated and combined to produce oculomotor commands that can best achieve precise object tracking (Barnes, 2008; Kowler, 1989; Spering & Montagnini, 2011). Altogether, it appears that the contribution of each of these factors is highly flexible and that the respective weights of stimulus characteristics, attention, prediction, or learning are modulated to adapt the oculomotor commands so as to produce accurate pursuit. For instance, using a reinforcement procedure in which sound beeps are triggered to intrusive or catch-up saccades, Madelain and Krauzlis (2003) showed that the ability to sustain smooth pursuit in the absence of driving motion signals improves with learning (velocity gain from 0.59 before training to 0.89 after training) supporting the idea that the modulation of pursuit by extra-retinal signals is flexible. Different individuals could, however, process the contextual background motion elicited by smooth pursuit eye movements differently to generate an oculomotor output—for instance, by weighting differently the suppression of these signals—possibly involving attentional mechanisms. 
To further probe the contribution of the eye-induced retinal slip in the generation of smooth pursuit, we used stimuli that elicit an illusory, eye-movement–dependent, motion percept that appears to drift in the same direction as the eyes. The stimulus used herein consists in static disks, randomly distributed within a rectangular surface, whose contrast polarity quickly alternates over time. When the eyes are static, the stimulus appears as faint, barely visible disks, as the time averaged luminance of the disks is close to that of the background. The illusory motion is apparent during smooth pursuit because the timely change of contrast polarity occurs in neighboring spatial retinal locations. The spatiotemporal luminance profile resulting from the combination of the retinal slip and the contrast reversals matches that of an apparent reverse-phi motion stimulus (Anstis, 1970; Anstis & Rogers, 1975; Sato, 1989), whose perceived direction is the same as that of the eyes (Figure 1). Importantly, a reversal of direction tuning is found in MT cortical neurons when stimulated with a reverse-phi motion stimulus (Krekelberg & Albright, 2005; Livingstone & Conway, 2003), in agreement with motion-energy models where direction-selective units invert their responses when stimulated by stimuli reverting their contrast over time (Adelson & Bergen, 1985; Livingstone & Conway, 2003; Mo & Koch, 2003). Consequently, the response to eye-induced visual motion elicited in MT (and possibly V1 and MST) neurons during smooth pursuit could, in principle, contribute to the computation of an oculomotor command, so as to sustain smooth pursuit for long period of time (Lorenceau, 2012). However, the observation that some participants have trouble sustaining smooth pursuit in this later study suggests that the capability to rely on eye-induced reverse-phi motion may depend on several factors: the eye speed relative to the spatiotemporal reverse-phi luminance profile, and the tuning response function of the motion selective neurons; the amount of cancellation, if any, exerted on the eye-induced retinal slip, possibly through efferent signals (Lindner & Ilg, 2006; Lindner, Schwarz, & Ilg, 2001); and finally, active inference during the disappearance of a driving target differing among individuals and populations (e.g., schizophrenic individuals and their relatives: Adams, Perrinet, & Friston, 2012; Spering, Dias, Sanchez, Schütz, & Javitt, 2013; elderly: Sharpe & Sylvester, 1978), or correlate with idiosyncratic sensitivities to different motioncarriers (Wilmer & Nakayama, 2007). 
Figure 1
 
Illustration of eye-induced reverse-phi motion moving in the same direction as the eyes: The spatiotemporal luminance profile elicited when a disk undergoing contrast reversal is displaced on the retina by pursuit eye movements matches that of a reverse-phi motion stimulus (see text for details).
Figure 1
 
Illustration of eye-induced reverse-phi motion moving in the same direction as the eyes: The spatiotemporal luminance profile elicited when a disk undergoing contrast reversal is displaced on the retina by pursuit eye movements matches that of a reverse-phi motion stimulus (see text for details).
To get further insights into these processes, we recorded eye movements while individuals tracked a visible moving target that disappeared after a delay behind occluding surfaces of different kinds: uniform visible or invisible (same color as the background) masks and textures of static or flickering disks. Assuming that a texture of flickering disks induces reverse-phi responses in cortical motion areas while smoothly moving the eyes, we expect a greater ability to sustain smooth pursuit for long period of time in absence of a moving target. Consistent with this hypothesis, previous studies reported that participants can generate smooth pursuit eye movements against a background made of randomly distributed elements changing polarity over time (Lorenceau, 2012; Spillman, Anstis, Kurtenbach, & Howard, 1997). However, these studies did not fully characterize stimulus parameters best suited to elicit smooth pursuit and did not analyze in details the related oculomotor behavior. The present study aims at providing quantitative measurements of smooth pursuit under these conditions. In the following, we first compare the eye velocity gain before and after target disappearance behind different occluders. As the results of this first experiment indeed showed that a flickering background allows sustaining smooth pursuit after target disappearance, we investigate in more details the effects of the temporal flickering frequency on smooth pursuit in Experiment 2. Experiment 3 probes the effects of the size and density of the disks composing the static flickering texture. Finally, Experiment 4 further tests whether flicker is by itself sufficient to elicit sustained pursuit or whether the temporal distribution of the luminance contrast of the disks relative to the background influences the quality and sustainability of smooth pursuit. 
Experiment 1: Effect of occluders' characteristics on smooth pursuit after target disappearance
Methods
Participants
A total of 10 subjects, recruited in the Cognitive Science department participated in the study (age range: 22–33 years; three males). Nine of them were naive to the goal of the study and had no experience in eye-movement research. All participants were healthy and had normal or corrected-to-normal vision, and had no relevant medical and psychiatric history. All participants gave written informed consent in accord with local ethical approval (Comité de protection des personnes, Ile-de-France VI, Paris, France). 
Stimuli and apparatus
Participants sat in a cushioned chair with their heads maintained by a chinrest in order to minimize head movements. Each participant was asked to tune their posture to be comfortable by adjusting the chin and forehead rests' height and chair height. The horizontal and vertical positions of the left eye were recorded with an Eyelink 1000 system (SR Research, Ltd., Mississauga, Ontario, Canada; sampling: 1 kHz). A monitor screen (BenQ 24-in. display, 1024 × 768, 120 Hz) was positioned 80 cm from the participant's eyes. Custom software, JEDA (Lorenceau & Humbert, 1990), displayed the stimuli on the monitor screen, and recorded the temporal information linked to stimulus presentations (used for post hoc analysis). 
Each occluder was a rectangular surface (width 9.3°, height 27.2°). Two occluders were uniform and either visible (12.6 cd/m2) or invisible (same hue and luminance as the background, 14.6 cd/m2). The other two occluders were filled with static or flickering, disks (n = 300; diameter: 1.11°, contrast alternating from +6% to −6% at 5 Hz) randomly positioned on each trial (with possible overlap) on the rectangular surface. For the static texture condition, dark and light disks were mixed, so as to deliver, on average, the same luminance as the flickering texture of alternating light and dark disks (Figure 2). All these occluders were positioned at the center of the screen and presented on a uniform gray background (14.6 cd/m2; Figure 2). The target to be tracked was a gray bull's eye (ring: 0.75°, central dot: 0.37°, 11.3 cd/m2). 
Figure 2
 
Masks and textures of disks used in Experiment 1. The masks are either uniform and invisible, ([A] occlude with same hue as the background; vertical white dashed lines delineate the otherwise invisible occluder's borders), or visible (B), or textured and static (C), or flickering ([D], 5 Hz). In all conditions, the masks and texture cover 9.30° × 27.10° of visual angle. At 13.3°/s, the moving target, whose trajectory is shown by filled and dashed black lines in (A), is visible for 900 ms and invisible for 700 ms after passing behind the occluder.
Figure 2
 
Masks and textures of disks used in Experiment 1. The masks are either uniform and invisible, ([A] occlude with same hue as the background; vertical white dashed lines delineate the otherwise invisible occluder's borders), or visible (B), or textured and static (C), or flickering ([D], 5 Hz). In all conditions, the masks and texture cover 9.30° × 27.10° of visual angle. At 13.3°/s, the moving target, whose trajectory is shown by filled and dashed black lines in (A), is visible for 900 ms and invisible for 700 ms after passing behind the occluder.
Experimental design
A 9-point calibration procedure was performed before each session for each participant. A trial consisted in the presentation of a black fixation target whose position was randomly left or right of the display screen. After 500 ms, the black target turned to white and started to move horizontally at 13.3°/s. The target moved for 900 ms (11.95°), before disappearing behind an occluder during 700 ms (9.2° of visual angle) then reappeared and moved until it reached the other side of the screen. The target then reversed its direction, and moved as before until it reached its initial position. Participants were asked to track the target and to sustain smooth pursuit as long as possible, even after the target disappeared behind the occluder chosen for the trial. Thus, in each trial, participants faced two periods of occlusion, during which the moving target was not visible. Note that participants were not asked to report on their perception of the occluding background, but only to sustain their pursuit eye movements as long as possible. 
Data acquisition and analysis
Eye movement data were analyzed offline using Python custom software (Figure 3; Python 2.7.9 |Anaconda 2.3.0 (64-bit)/Copyright © 2001–2014, Python Software Foundation, All Rights Reserved). The first four trials of each session served as training trials and were discarded from further analyses. Blinks were first removed before the eye traces were smoothed with a Butterworth low-pass filter (50 Hz). Eye velocity and accelerations were then computed in two passes using a 51-points sliding window filter (Savitzky & Golay, 1964). The beginning and end of saccades were then flagged in a two-pass process, using an eye-velocity threshold (20°.s−1), followed by an eye-acceleration threshold (500°.s−2).To ensure that all saccadic activity was removed from further analyses, the data points starting 10 ms before and 10 ms after the flagged data points were replaced by NaN (not a number). All subsequent analyses were performed on saccade free eye-traces (Figure 3). Each trace was decomposed into (a) initial fixation, (b) smooth pursuit during target tracking (700-ms window starting 200 ms after motion onset), and (c) smooth pursuit after target disappearance (700-ms window, starting 900 ms after motion target onset). In the following, we analyze and compare the eye velocity gain and saccade rate during smooth pursuit, before and after target disappearance. 
Figure 3
 
Flow of eye-movement analyses. (A) Eye position during half a trial (a trial consisted in a back-and-forth motion of the target, half a trial corresponds to back-or-forth motion; the shaded area represents the occlusion period: 700 ms). (B) Eye velocity during half a trial. The dashed horizontal black line corresponds to the velocity threshold used for saccade detection (>20°/s−1). (C). Eye acceleration during half a trial. The horizontal dashed black lines shows the acceleration threshold used for saccade detection (±500°/s−2). (D) Saccade-free eye velocity during half a trial. The dark and light gray shaded areas (700 ms) delineates the pre-occlusion and occlusion periods used to compute the velocity gains.
Figure 3
 
Flow of eye-movement analyses. (A) Eye position during half a trial (a trial consisted in a back-and-forth motion of the target, half a trial corresponds to back-or-forth motion; the shaded area represents the occlusion period: 700 ms). (B) Eye velocity during half a trial. The dashed horizontal black line corresponds to the velocity threshold used for saccade detection (>20°/s−1). (C). Eye acceleration during half a trial. The horizontal dashed black lines shows the acceleration threshold used for saccade detection (±500°/s−2). (D) Saccade-free eye velocity during half a trial. The dark and light gray shaded areas (700 ms) delineates the pre-occlusion and occlusion periods used to compute the velocity gains.
The statistical analyzes compared the velocity gain, computed independently for the pre- and occlusion periods, across conditions. All statistical analysis used two-tailed tests. Effect sizes are reported as η2 (eta squared) for analyses of variance (ANOVAs) and as Cohen's d for post hoc analyzes. All analyzes were performed using R software (Version 3.2.1). 
Results
The time course of the horizontal velocity averaged across trials is shown for each participant and each condition in Figure 4. As can be seen, for all participants, eye velocity during the pre-occlusion period is similar in all four conditions, although the mean eye velocity differs across participants. Soon after target disappearance, the eye velocity quickly drops for three out of four conditions, replicating previous results (Becker & Fuchs, 1985; Bennett & Barnes, 2003; Madelain & Krauzlis, 2003; Pola & Wyatt, 1997). However, for seven out of 10 participants, the residual eye velocity in the flicker condition is higher than in the other occluder conditions. In the same way, but to a lesser extent, the residual eye velocity remains higher with the invisible occluder condition as compared to the other static occluders. In addition, it can be noted that the velocity gain decreases before a target reversing its direction, in line with previous results showing anticipatory behavior based on predictive cues (Barnes, 2008; Jarrett & Barnes, 2005). 
Figure 4
 
Mean eye velocity for each participant in the four conditions shown in the inset. Red line: invisible occluder. Yellow line: visible occluder. Orange line: static texture. Blue line: flickering texture. The gray shaded area delineates the target off period (700 ms). The target is occluded 900 ms after motion onset and reappears for 900 ms after the occlusion period.
Figure 4
 
Mean eye velocity for each participant in the four conditions shown in the inset. Red line: invisible occluder. Yellow line: visible occluder. Orange line: static texture. Blue line: flickering texture. The gray shaded area delineates the target off period (700 ms). The target is occluded 900 ms after motion onset and reappears for 900 ms after the occlusion period.
To get better insights into these results, we computed the saccade rate and the average velocity gain (ration of eye velocity to target velocity), using a mean pre-occlusion eye velocity computed over 700 ms (200–900 ms) and a mean eye velocity computed relative to the invisible moving target during the occlusion period (time window: 900–1600 ms; Figure 5A, B). 
Figure 5
 
Left panel: (A) Time-averaged velocity gain during the occlusion period as a function of the time averaged velocity gain before occlusion. Symbols indicate the different experimental conditions (see inset legend); each colored line represents the velocity gains of a single participant for all conditions. Right panel: (B) Mean velocity gain for each condition, for the pre-occlusion (gray outline) and occlusion period (black outline). Stars indicate the significant effects of the occluders type on the velocity gains during the occlusion period (***p < 0.0001). (C) Mean saccade rate for each condition during occlusion period. Error bars represent 1 SE. See text for details.
Figure 5
 
Left panel: (A) Time-averaged velocity gain during the occlusion period as a function of the time averaged velocity gain before occlusion. Symbols indicate the different experimental conditions (see inset legend); each colored line represents the velocity gains of a single participant for all conditions. Right panel: (B) Mean velocity gain for each condition, for the pre-occlusion (gray outline) and occlusion period (black outline). Stars indicate the significant effects of the occluders type on the velocity gains during the occlusion period (***p < 0.0001). (C) Mean saccade rate for each condition during occlusion period. Error bars represent 1 SE. See text for details.
Pre-occlusion velocity gain
To determine whether the eye velocity gain measured before the occlusion period differs for the different occluder conditions, we performed a repeated-measures ANOVA on the mean eye velocity gain computed before the occlusion period (time window: 200–900 ms). This analysis revealed a significant effect of the occluder type, F(3, 27) = 6.083, p < 0.001, η2 = 0.012 (Figure 5B). A multiple comparison procedure (Tukey's honest significant difference [HSD] tests) revealed significant differences between the invisible and flicker occluder conditions relative to the gray and textured occluder conditions, with however, a small effect size (Cohen's d < 0.2). The mean velocity gain for the flicker condition is 0.89 ± 0.10; 0.91 ± 0.07 for the invisible condition; 0.87 ± 0.10 for the gray condition; and 0.87 ± 0.10 for the textured condition (Figure 5B). The velocity gain is significantly greater for the flicker and invisible conditions relative to the gray and textured conditions (p < 0.05). No significant difference is found between the flicker and invisible conditions (p > 0.05), and between the gray and textured conditions (p > 0.05). These differences suggest that the peripheral viewing of the occluders had a small, but significant, influence on the initial velocity gain. 
Velocity gain during the occlusion period
The mean velocity gain during the occlusion period is plotted in Figure 5 for each participant in each condition as a function of the mean velocity gain before the occlusion period. Several observations are worth noting: (as) large interindividual differences exist in the velocity gain measures, before, as well as during, the occlusion period; (b) the pre-occlusion velocity gain is largely independent of the experimental conditions for participants that perform at a high level (gain above 0.9, n = 6), but participants with lower gain values (below 0.9, n = 3) are more variable and perform differently as a function of the conditions, with larger gains for the invisible occluder condition; (c) velocity gains during the occlusion period are smaller than during the pre-occlusion gains, replicating previous results showing that eye velocity quickly drops after the driving moving signal is removed (Becker & Fuchs, 1985; Eckmiller & Mackeben, 1978); (d) the eye velocity tend to increase just before target reappearance, as reported in previous studies (Bennett & Barnes, 2003); and (e) the occlusion gains are larger for the flicker condition, except for two participants who performed similarly in the invisible and flicker conditions (green & light blue lines). Figure 5b shows the eye velocity gains averaged across participants for each condition. 
A repeated-measures ANOVA performed on the velocity gain revealed significant differences between conditions during occlusion period: F(3, 27) = 101.2, p < 0.0001, η2 = 0.17. Multiple comparisons (Tukey's HSD tests) showed that the velocity gain was higher in the flicker texture condition as compared to all other conditions (velocity gains: 0.58 ± 0.16; 0.48 ± 0.11; 0.39 ± 0.11; and 0.36 ± 0.09 for flicker, invisible, gray, and textured conditions, respectively, p < 0.0001, Cohen's d > 0.8). 
Saccade rate during the occlusion period
We computed the saccade rates (number of saccades per second) during the occlusion period (Figure 5C), and conducted a repeated-measures ANOVA on these values. This analysis revealed an overall significant effect of the occluder conditions, F(3, 27) = 32.61, p < 0.0001, η2 = 0.06). Multiple comparisons indicate that the saccade rate is less for the flicker relative to all other conditions (saccade rate: 1.11 ± 0.58 sac.s−1; 2.13 ± 0.45 sac.s−1; 2.42 ± 0.42 sac.s−1; 2.61 ± 0.54 sac.s−1, for the flicker, invisible, gray, and textured conditions, respectively, p < 0.01, Cohen's d > 0.5). 
Overall, this first experiment indicates that smooth pursuit maintenance after target disappearance depends upon the structure of the occluding surface. In particular, the capability to maintain a high velocity gain for a long duration after target disappearance with a texture of flickering disks suggests that participants relied upon the processing of the eye-induced reverse-phi motion. 
Experiment 2: Effect of temporal flickering frequency and target speed on pursuit maintenance
Although Experiment 1 showed that a flickering textured background facilitates pursuit maintenance after target disappearance, previous observations (Spillman et al., 1997) suggest that the flicker frequency and/or the eye speed modulate pursuit maintenance after target disappearance. One reason for a potential effect of flicker frequency and eye speed is that they both modify the spatiotemporal luminance profile elicited on the retina when smoothly pursuing a moving target and/or when maintaining pursuit without any visible moving target. Considering both the spatial and temporal integration responses of direction-selective neurons, and their functional limits (Braddick, Ruddock, Morgan, & Marr, 1980; Mikami, Newsome, & Wurtz, 1986; Watson & Ahumada, 1985), there could exist particular spatiotemporal distributions that optimally elicits an eye-induced reverse-phi response (e.g., in MT neurons; Krekelberg & Albright, 2005; Mikami et al., 1986), although populations of directional neurons with different spatiotemporal motion-energy profiles could respond differently to different stimulation conditions. Also note that because generating pursuit eye movements with too slow and too high target speeds is difficult or impossible (e.g., for very high speeds), the range of temporal frequencies well suited to elicit reverse-phi motion response is also limited. Further, different initial tracking eye velocities constrains the retinal slip occurring when entering the occlusion period, and thus the spatiotemporal luminance profile of the flickering texture on the retina. Thus, the initial eye-induced reverse-phi responses could depend on the conjunction of the initial eye velocity and of the flickering frequency. To investigate this hypothesis, we measured the eye velocity gain before and after target disappearance, using two target speeds (13.3°/s and 26.6°/s), and different flicker frequencies (3, 5, 10, 20, and 30 Hz). 
Methods and stimuli
A subset of subjects (six out of 10) who participated in Experiment 1 took part in Experiment 2. Overall, the experimental settings are the same as in Experiment 1, except for the following: two target speeds were used (13.3°/s and 26.6°/s); only the flicker condition of Experiment 1 was tested. Four flickering frequencies (3, 10, 20, and 30 Hz) were used for the 13.3°/s speed (The 5-Hz temporal frequency of Experiment 1 was not retested); five temporal frequencies (3, 5, 10, 20, and 30 Hz) were used in the 26.6°/s. condition. Thus, a session comprised nine experimental conditions (20 trials per conditions, 180 trials per session). As doubling the target speed reduces the pre- and the occlusion periods by a factor of 2, the occlusion period only lasts 350 ms with a speed of 26.6°/s (as compared to 700 ms with a target moving at 13.3°/s). As before, participants were asked to track a bulls-eye target during the pre-occlusion period and to maintain smooth pursuit during the occlusion period. 
Results
The raw eye traces were analyzed as in Experiment 1 (see Data analyses section). The mean velocity gains averaged across trials and time are shown in Figure 6 for the two tested speeds with flickering frequency as a parameter. Each value was computed on the entire occlusion period (700 ms for 13.3°/s and 350 ms for 26.6°/s). On average, pursuit maintenance with a high gain after target disappearance is longer than what is generally reported, confirming the peculiar effect of a flickering texture background that helps maintaining smooth pursuit for long durations. We then computed the mean eye velocity gain and saccade rate for each participant and each flickering frequency for each of the two target speeds (Figure 6). For a target moving at 13.3°/s, the velocity gain is higher (Figure 6A), and the saccadic rate is lower (Figure 6B), for medium (10–20 Hz), as compared to low and high flickering frequencies (3–30 Hz). On average, a small advantage is found for a flickering frequency of 10 Hz. This band-pass pattern is observed for all participants. For a faster target speed (26.6°/s), the distribution of the eye velocity gain as a function of the flickering frequency is high pass (Figure 6C), with larger gains for the higher flickering frequencies (30 and 20 Hz), and smaller values for lower frequencies (3, 5, and 10 Hz). The distribution of saccades (Figure 6D) follows the inverse pattern. Comparing low and high target speeds further indicates that the eye velocity gain during the occlusion period is larger for a fast speed. Also note that, despite participants showing a similar pattern of results, large interindividual differences also exist. 
Figure 6
 
Mean velocity gains (A and C) and saccade rates (B and D) of each participant (dotted lines) for a target speed of 13.3°/s (top) and 26.6°/s (bottom), as a function of flicker temporal frequency. The velocity gains averaged across participants is also shown (black line). See text for details.
Figure 6
 
Mean velocity gains (A and C) and saccade rates (B and D) of each participant (dotted lines) for a target speed of 13.3°/s (top) and 26.6°/s (bottom), as a function of flicker temporal frequency. The velocity gains averaged across participants is also shown (black line). See text for details.
To get additional insights into this pattern of results, we conducted statistical analyses as in Experiment 1. We first considered the velocity gain during the pre-occlusion period, before analyzing the velocity gain after target disappearance. 
Pre-occlusion velocity gain
To study the possible effects of the flickering texture during the pre-occlusion tracking period, we computed the velocity gain on a time window starting 200 ms after motion onset (200–900 ms for a target speed of 13.3°/s and 200–450 ms for a target speed of 26.6°/s). For the velocity condition 13.3°/s, an ANOVA reveals significant differences between the flickering frequency conditions, F(3, 15) = 8.723, p < 0.0001, η2 = 0.026. Post hoc Tukey HSD tests further indicate that the velocity gain is significantly higher for 10 and 20 Hz (p < 0.001) at this target speed, as compared to 30 and 3 Hz (velocity gains: 0.91 ± 0.07; 0.93 ± 0.07; 0.92 ± 0.08; and 0.88 ± 0.08 for 30, 20, 10, and 3 Hz, respectively). The effect sizes for these comparisons were overall small (Cohen's d < 0.5). 
The same analyses performed for a target speed of 26.6°/s also revealed a significant effect of the flickering frequency, F(4, 20) = 129.3, p < 0.0001, η2 = 0.034. Post hoc Tukey's HSD tests (p < 0.01) show that the velocity gain in the 3-Hz condition is significantly lower than for the other flickering frequencies (velocity gain: 0.77 ± 0.11; 0.79 ± 0.11; 0.77 ± 0.13; 0.73 ± 0.13; and 0.67 ± 0.12 for 30-, 20-, 10-, 5-, and 3-Hz conditions, respectively). The size effects depend upon the comparisons between flickering frequencies: for the comparison between 3 Hz and 30, 20 or 10 Hz, d is greater than 0.8 corresponding to a large effect size. The size effect for the comparison between 5- and 3-Hz conditions is a medium effect (Cohen's d > 0.5). Finally, the velocity gain for 20 Hz is significantly larger than for 5 Hz (p < 0.05, Cohen's d > 0.3). 
Velocity gain during the occlusion period
For the slowest speed (13.3°/s), repeated-measures ANOVA conducted on the average velocity gains showed significant effects of temporal frequency, F(3, 15) = 104.99, p < 0.0001, η2 = 0.13). Tukey's HSD tests revealed that all comparisons between flickering frequencies are significant (p < 0.0001), except for the comparisons between 20 and 10 Hz (velocity gains: 0.65 ± 0.14; 0.76 ± 0.13; 0.77 ± 0.14; and 0.59 ± 0.15 for 30, 20, 10, and 3 Hz, respectively). The effect sizes reported for each significant comparisons were large (Cohen's d > 0.8). 
For the fastest speed (26.6°/s), the ANOVA computed on the velocity gain during the occlusion period revealed significant differences between conditions, F(4, 20) = 39.75, p < 0.0001, η2 = 0.11. Tukey's HSD tests (p < 0.001) clarify the origin of these effects, which mainly originate from a difference between the highest frequencies (30 and 20 Hz) and the lower frequencies (10, 5, and 3 Hz; velocity gains: 0.80 ± 0.14; 0.84 ± 0.12; 0.76 ± 0.14; 0.69 ± 0.16; 0.64 ± 0.16 for 30-, 20-, 10-, 5-, and 3-Hz conditions, respectively). The effect sizes depend upon the performed comparisons: The effect size is large (Cohen's d > 0.8) for comparisons between 3 Hz and either 30, 20, or 10 Hz. For comparisons between 5 Hz and either 30, 20, or 10 Hz, the effect sizes are respectively large for the comparison between 3 and 30 or 20 Hz (Cohen's d > 0.8), and a medium effect for the comparison between 10 and 5 Hz, (0.5 < Cohen's d < 0.8). No significant difference in velocity gain is found between 30 and 20 Hz. 
Saccade rates during the occlusion period
An ANOVA conducted on the normalized saccade rates (Figure 6B, D) for a target speed of 13.3°/s revealed a significant effect of flickering frequency, F(3, 15) = 31.15, p < 0.0001, η2 = 0.08, with saccade rate decreasing with flickering frequency (saccade rate: 1.86 ± 0.6 sac.s−1; 1.25 ± 0.45 sac.s−1; 1.25 ± 0.55 sac.s−1; and 2.03 ± 0.43 sac.s−1, for 30, 20, 10, and 3 Hz, respectively. Post hoc Tukey's tests indicate that the differences in saccade rates are significant (p < 0.0001, Cohen's d < 0.13), except for the comparison between 10 and 20 Hz. 
For a target speed of 26.6°/s, an ANOVA gave similar results, F(4, 20) = 31.15, p < 0.000, η2 = 0.02). Post hoc Tukey's tests revealed significant changes in saccade rate between high frequencies (up to 10 Hz) and low frequencies (5 and 3 Hz; saccade rates: 1.46 ± 0.62; 1.57 ± 0.80; 1.63 ± 0.79; 1.95 ± 0.71; and 2.15 ± 0.84, for 30, 20, 10, 5, and 3 Hz, respectively). Post hoc Tukey's tests revealed significant differences in saccade rate between 30 and 5 or 3 Hz (p < 0.01), between 20 and 3 Hz (p < 0.01), and between 10 and 3 Hz (p < 0.05). The effect sizes for each significant comparison correspond to a medium effect (0.5 < Cohen's d < 0.8), except for the comparison between 30 and 3 Hz, where the effect size is large (Cohen's d > 0.8). 
Interaction between target speed and temporal flicker frequency
The statistical analyzes also revealed a significant interaction between the velocity gains computed for the two speeds (13.3°/s and 26.6°/s), F(8, 40) = 46.38, p < 0.0001, confirming that the distribution of the velocity gains are different as a function of the temporal flicker frequencies. As the period over which the velocity gains were computed are different (700 vs. 350 ms), which could account for the observed differences, we performed the same analyses using a similar time windows (350 ms) for both speeds. The results (data not shown) are qualitatively similar, and the statistical analyses of the velocity gains again show a significant interaction between target speed and temporal flicker frequency, F(8, 40) = 6.706, p < 0.0001, indicating that the different time windows used in the previous analyzes do not account for the observed differences. 
Interindividual differences
We also analyzed the interindividual differences. A repeated-measures ANOVA using participants as a main factor on the average velocity gains show large interindividual differences, F(5, 40) = 201.1, p < 0.0001, η2 = 0.32. 
Overall, the results of this experiment show that sustained pursuit after target disappearance is easier for appropriate combinations of the initial eye speed and the temporal flickering frequency of the texture. 
Experiment 3: Effect of disk density and disk size
The results of Experiment 2 suggest that pursuit maintenance is facilitated when there exists a match between the eye speed just before target disappearance and the spatiotemporal luminance profile elicited by eye movements on the retina. As this spatiotemporal luminance profile depends on both the temporal and spatial characteristics of the slipping retinal stimulus, this experiment investigates the effect of different spatial distributions and sizes of the disks composing the flickering texture. 
Methods and stimuli
Five subjects participated in Experiment 3 (two of which participated in Experiment 2. One participant was removed from further analyses due to a technical problem in data acquisition). Overall, the experimental settings are the same as in Experiments 1 and 2, except for the following: Three target speeds (6°/s, 13.3°/s, and 26.6°/s) and only one temporal frequency (10 Hz) are used, based on the results of Experiment 2. The number of disks, (i.e., disk density), composing the flickering texture was varied (n = 100, 200 and 300) and three different disk sizes were tested (d = 0.55°, 1.11°, and 1.65°, Figure 7A). Thus, a session comprised nine experimental conditions (10 trials per conditions, 90 trials per session; the density and the disk size conditions were tested in different consecutive sessions, for a total of 360 trials per subject). The task was the same as in the two previous experiments. Note that the conditions using 300 disks of 1.11°, a target speed of 13.3°/s or 26.6 °/s, and a temporal frequency of 10 Hz were already tested in Experiment 2
Figure 7
 
(A) Examples of the texture backgrounds used in Experiment 3. Velocity gains for each participant (colored dashed lines) during the occlusion period computed for the different flickering textures with (B) varying disk sizes and (C) varying disk density, for three target speeds. Black symbols represent the velocity gains averaged across participants.
Figure 7
 
(A) Examples of the texture backgrounds used in Experiment 3. Velocity gains for each participant (colored dashed lines) during the occlusion period computed for the different flickering textures with (B) varying disk sizes and (C) varying disk density, for three target speeds. Black symbols represent the velocity gains averaged across participants.
Results
As before, the mean velocity gain was computed separately for the pre- (data not shown) and target occlusion periods. The right panel of Figure 7 shows the visual mean velocity gains during the occlusion period as a function of disk size (Figure 7B) and of disk density (Figure 7C) for the three target speeds. As it can be seen, the velocity gains depend little on either disk size or disk density. Also note that the mean velocity gains remain high for three participants while one participant, who had small velocity gains during the pre-occlusion period, performs poorly. 
Effects of disk density and disk size
Two repeated-measures ANOVAs were conducted, one for the disk density conditions and one for the disk size conditions. These analyses did not reveal any significant effect of disk density, F(2, 8) = 0.173, p > 0.05, and for disk size, F(2, 8) = 0.726, p > 0.05. 
Effect of velocities
In contrast, the velocity gains were significantly larger with faster target speeds in the disk density, F(2, 8) = 7.651, p < 0.0001, η2 = 0.016, and in the disk size conditions, F(2, 8) = 9.207, p < 0.0001, η2 = 0.02, extending the results of Experiment 2. Post hoc Tukey's HSD tests conducted to characterize the effect of target speed for disk density conditions indicate no significant differences between 26.6°/s and 13.3°/s, consistent with the results of Experiment 2. Comparisons between 13.3°/s and 6°/s (p < 0.001) and between 26.6°/s and 6°/s (p < 0.01) were significant (Cohen's d > 0.5). 
For the disk size conditions, post hoc Tukey's HSD tests again indicate a significant effect of target speed between 13.3°/s and 6°/s (p < 0.001, Cohen's d > 0.5) and between 26.6°/s and 6°/s (p < 0.01, Cohen's d < 0.2). No significant difference in velocity gain is found between 13.3°/s and 26.6°/s. 
Overall, the result of this experiment indicates that the velocity gain during pursuit maintenance after target disappearance is not significantly modulated by the spatial characteristics—disk size or density—of the flickering texture. 
Experiment 4: Effect of luminance contrast on pursuit maintenance
In Experiments 1, 2, and 3, alternations of bright and dark disks correspond to a balanced change in contrast polarity relative to the background. However, whether an exact balance of contrasts of different polarity is necessary to elicit reverse-phi percepts and/or neuronal responses is unknown. Previous studies used either a “dissolve” procedure to alternate contrast (Anstis & Rogers, 1975), stroboscopically flashed stimuli (Behrens & Grüsser, 1979), or quick alternations of black and white high-contrast elements (Sato, 1989; Spillman et al., 1997). One cannot exclude that a dynamic change of contrast is by itself sufficient to facilitate pursuit maintenance after target disappearance, without any specific contribution of both a change in polarity and balanced contrast relative to the background. To address this issue, we replicated Experiment 1 with a flickering texture together with five different contrast combinations (Figure 8). The different luminance/contrast combinations were chosen so as to compare both the effects of contrast polarity and of contrast amplitude on pursuit maintenance. 
Figure 8
 
Mean velocity gains computed over the first 700 ms of the occlusion period as a function of the mean velocity gains computed over the last 700 ms of the occlusion period, for three flickering frequencies. Each symbol (A–E) represents a different luminance contrast. Contrast is computed as (L1t1-L2t2)/Lb, with L1t1 corresponding to a disk luminance, L1, at time t1, L2t2 corresponding to a disk luminance, L2, at time t2, and Lb the background luminance. Balanced condition (A) +6%/−6%; Imbalanced conditions (B) +6%/−28%; (C) +31%/−6%; (D) +31%/+6%; (E) −6%/−28%. The velocity gains are larger during the first 700 ms than during the last 700 ms. Velocity gains are larger at higher temporal frequencies and a balanced contrast (A) involving a change in contrast polarity. Error bars represent 1 SE.
Figure 8
 
Mean velocity gains computed over the first 700 ms of the occlusion period as a function of the mean velocity gains computed over the last 700 ms of the occlusion period, for three flickering frequencies. Each symbol (A–E) represents a different luminance contrast. Contrast is computed as (L1t1-L2t2)/Lb, with L1t1 corresponding to a disk luminance, L1, at time t1, L2t2 corresponding to a disk luminance, L2, at time t2, and Lb the background luminance. Balanced condition (A) +6%/−6%; Imbalanced conditions (B) +6%/−28%; (C) +31%/−6%; (D) +31%/+6%; (E) −6%/−28%. The velocity gains are larger during the first 700 ms than during the last 700 ms. Velocity gains are larger at higher temporal frequencies and a balanced contrast (A) involving a change in contrast polarity. Error bars represent 1 SE.
Method and stimuli
The general settings were as in Experiment 2, except for the following: The flickering frequency of the textured occluder was either 3, 5, or 10 Hz. Five combinations of contrast/luminance were used, together with a constant background luminance (31.5 cd/m−2; see Figure 8). Each disk alternated between two luminance levels: (A) 33.6/29.4 cd/m2 (light/dark); (B) 33.6/22.4 cd/m2, (light/DARK); (C) 41.5/ 29.4 cd/m2 (LIGHT/dark); (D) 41.5/33.6 cd/m2 (LIGHT/light); (E) 29.4/22.4 cd/m2 (dark/DARK). Contrast polarity changes over time in the three first luminance combinations (A, B, and C) with the first combination (A) using balanced luminance contrast relative to the background. For the remaining combinations (D and E), the contrast polarity relative to the background is constant. Each participant (n = 4) performed 20 trials per Luminance × Frequency conditions (300 trials per subject). Only a leftward moving target (speed 13.3°/s) was used. The duration of the occlusion period was increased (up to 1400 ms) by increasing the size of the occluder (width on horizontal axis: 18.6°) to test whether pursuit can be maintained for such a long duration. 
Results
As before, the mean velocity gain was computed separately for the pre- (data not shown) and target occlusion periods. As the occlusion period was increased (up to 1400 ms) for a target speed of 13.3°/s, we analyzed separately two successive periods of 700 ms in order to compare the present results with those of the previous experiments, so as to determine whether pursuit gain declines over time with such a long duration. Figure 8 presents the mean velocity gain computed for the first 700 ms as a function of the mean velocity gain for the last 700 ms, for the different contrast and frequency conditions. As it can be seen, the mean velocity gain during the first 700 ms ranges from 0.6 to 0.9, and from 0.3 to 0.6 during the last 700 ms, depending on the conditions. Several aspects of this figure deserve comments: First, the velocity gain clearly depends on both the flickering frequency and on the different contrast/luminance combinations. The larger gains are obtained for a temporal frequency of 10 Hz and a balanced contrast involving changes of polarity over time. For this condition, the gain is very high (0.85) during the first 700 ms, and slightly decreases during the last 700 ms (0.65). Second, the velocity gain is low for the 3-Hz conditions (Figure 8, left panel), with little influence of the luminance contrast distributions. Third, the velocity gain varies with both contrast and temporal frequency for the 5-Hz condition (Figure 8, middle panel) and the 10-Hz condition (Figure 8, right panel), with higher velocity gains for the low-contrast balanced conditions involving a change in contrast polarity over time (Condition A). 
A three-way ANOVA on the velocity gains with contrast distribution, temporal frequency, and period (first vs. last 700 ms) as main factors indicate significant effects of contrast, F(4, 12) = 12.70, p < 0.0001, η2 = 0.03; temporal frequency, F(2, 8) = 24.06, p < 0.05, η2 = 0.03; and period, F(1, 4) = 33.665, p < 0.0001, η2 = 0.22. The interaction between temporal frequency and contrast is also significant, F(14, 42) = 3.251, p < 0.01, η2 = 0.017. 
Effects of contrast
Post hoc multiple comparisons confirm the effect of luminance contrast on the velocity gain, in particular between Condition A (balanced low contrast) and the other conditions (velocity gain: 0.65 ± 0.09; 0.57 ± 0.12; 0.56 ± 0.12; 0.53 ± 0.12; and 0.52 ± 0.11 mean velocity gains for conditions A, B, C, D, and E, respectively; p < 0.05 between Conditions A and B; p < 0.0001 between Condition A and C, D, and E). The comparison between Condition B and E is also significant (p < 0.05). All effect sizes for these significant comparisons are large (Cohen's d > 0.8). 
Effects of flickering frequency
The flickering frequency of the texture background also modulates the velocity gain. The significant effects found between 10 and 5 Hz (p < 0.01; velocity gains: 0.61 ± 0.09 and 0.57 ± 0.05) and between 5 and 3 Hz (p < 0.001; velocity gains: 0.57 ± 0.05 and 0.52 ± 0.02) are medium effects (0.5 < Cohen's d < 0.8), while the significant effect between 10 and 3 Hz (p < 0.0001; velocity gains: 0.57 ± 0.09 and 0.47 ± 0.01) is a large effect size (Cohen's d > 0.8). 
Interaction between contrast and frequency conditions
Comparisons of the effects of contrast and temporal frequency, confirmed that the gain is significantly larger for the Condition A (balanced contrast) at 10 Hz relative to any other contrast/frequency combinations (p < 0.05). The effect sizes are large for all the comparisons tested (Cohen's d > 0.8). 
Overall, the results indicate that the luminance contrast distribution of the dynamic textured background has significant effects on pursuit maintenance. In particular, a balanced low contrast (+6%) flickering texture allows maintaining smooth pursuit with a high velocity gain for a long duration (Condition A10, circle symbol on right panel in Figure 8). 
General discussion
This study investigates the conditions under which smooth pursuit eye movements can be maintained after a moving tracked target disappears behind an occluding mask. Experiment 1 compares several masking occluders and shows that the maintenance of smooth pursuit after target disappearance depends of the spatiotemporal characteristics of the occluder. The velocity gain is lower for a static texture and an visible occlude and better for an invisible and a flickering background, the latter allowing to maintain smooth pursuit for longer durations. Experiments 2, 3, and 4 aimed at characterizing which features of such flickering background are best suited for pursuit maintenance. Experiment 2 tests different combinations of temporal frequencies and target speeds, and shows that pursuit maintenance (velocity gain) is facilitated at moderate-to-high temporal frequencies, but depends on combinations of both the initial target speed and the flickering temporal frequencies. Experiment 3 shows that pursuit maintenance does not significantly depend upon the density or size of the disks composing the flickering texture. Finally, Experiment 4 tests different combinations of flickering contrast distributions and shows that smooth pursuit is facilitated at a low luminance contrast with balanced changes in contrast polarity over time. 
Relationships with previous studies
These findings are in line with previous results showing that visual surrounding contexts influence the capability to generate and maintain smooth pursuit, with or without a visible moving target. For instance, a static high-contrast background reduces the velocity gain during the initiation or steady state phase of target tracking (Collewijn & Tamminga, 1984; Keller & Kahn, 1986; Kimmig, Miles, & Schwarz, 1992; Masson et al., 1995; Niemann & Hoffman, 1997; Spering & Gegenfurtner, 2007). The present results replicate these findings when the occluders are static (visible or invisible homogenous occluders, or static textured background), although there also are significant differences between them (Experiment 1; Figure 4). 
Some studies reported that dynamic visual background contexts permit to endogenously generate smooth pursuit (or Optokinetic Nystagmus [OKN]). These studies used either counterphase flickering gratings (Pomerantz, 1970), dynamic random noise patterns (MacKay, 1961; Spillman et al., 1997; Ward & Morgan, 1978), stroboscopically illuminated random dots (Adler & Grüsser, 1979; Behrens & Grüsser, 1979; review in Grüsser, 1986) or a textured background similar to that used herein (Lorenceau, 2012). The present results with a flickering textured occluder are in line with these previous studies, in particular with regard to the temporal frequency range best suited to sustain smooth pursuit. 
To account for their observation that smooth pursuit can be generated and sustained when watching stroboscopically illuminated random dot patterns, Behrens and Grüsser (1979) wrote: “It appears to be essentially the efference copy of the motor command signals controlling the eyes or the gaze which lead to the apparent movement perception and not the spatio-temporal correlation of the afferent visual signals elicited by each flash.” The authors then discussed the appearance of their stimuli and note that “the perceived structural reorganization of the moving random dot pattern and the appearance of the apparent stripes are not caused by any efference copy mechanisms and that they are related to the changes in the retinal stimulus position.” The authors further suggested that “eye pursuit movements across a stationary stroboscopically illuminated random dot pattern lead to a neuronal reorganization of the signals caused by the visual noise”' and call for “a memory mechanism interposed between the receptors and the more central neuronal movement system.” 
Hypothetical neural mechanisms
Neurophysiological evidence indicate that generating and maintaining smooth pursuit involves subcortical, cortical, and cerebellar circuits (reviews in Krauzlis, 2004, 2005; Lisberger, 2010, 2015; Thier & Ilg, 2005) and several functional and computational models have been proposed to account for both the behavioral data and the underlying circuits (Barnes & Asselman, 1991; Keller & Heinen, 1991; Krauzlis, 2004; Lisberger, Morris, & Tychsen, 1987; Pack, Grossberg, & Mingolla, 2001; Robinson, Gordon, & Gordon, 1986). These studies emphasize the role of MT and MST in segregating a moving target from the static background, necessary for the computation of target velocity (Fukushima et al., 2013; Ilg & Thier, 2003; Newsome, Wurtz, & Komatsu, 1988; Xiao, Barborica, & Ferrera, 2007). Neurons in MT and MST then directly send projections onto the frontal eye field (FEF) that plays a major role in generating pursuit eye movements (e.g., Fukushima et al., 2013; MacAvoy, Gottlieb, & Bruce, 1991; see Ilg & Thier, 2008, Krauzlis, 2005, for reviews). In light of the present results showing reliable effects of the low-level properties of the occluders characteristics, we suggest that the retinal slip elicited by smooth pursuit with a flickering textured background evokes reverse-phi responses in cortical motion areas (e.g., V1, MT, and MST) corresponding to the very direction of the eyes. That smooth pursuit maintenance is facilitated for medium-to-high temporal frequencies with a low-contrast flickering texture changing polarity over time favors the idea that the spatiotemporal luminance profile induced by the retinal slip is processed by magnocellular direction-selective neurons responding to reverse-phi motion (Krekelberg & Albright, 2005), allowing smooth pursuit maintenance by enabling a positive sensori-motor feedback loop. Although it may seem surprising that low contrast strongly facilitates pursuit maintenance, it is compatible with the recruitment of MT neurons in the dorsal pathway that receive most of their inputs from magnocellular neurons having high-contrast sensitivity (e.g., Merigan & Maunsell, 1990). Further note that with such low-contrast and high-temporal frequency, the responses of parvocellular neurons that could provide positional information related to the static disks, should be small. Thus, the salience of position cues—drifting in a direction opposite to that of the eyes- that could counteract smooth pursuit—should be reduced. 
We schematically illustrate the outcomes of different eye velocity and flickering frequency combinations in Figure 9, assuming a single population of directional motion-energy like neurons with receptive fields of fixed spatial and temporal preferences. In this figure, the space–time and spatial representations of the retinal stimulus (top rows) depend on both eye-speed and temporal flickering frequency (bottom rows), such that the reverse-phi response amplitude in the nonpreferred direction is modulated by these factors. In this view, the spatial and temporal integration characteristics of these neurons (e.g., Braddick et al., 1980; Kumbhani, El-Shamayleh, & Movshon, 2015; Mikami et al., 1986) constrain the antipreferred reverse-phi responses, and consequently the capability to maintain smooth pursuit for long durations. 
Figure 9
 
Illustration of the effects of flicker frequency and eye-speed on retinal slip (a single disk is shown for clarity). (A) Space–time plot of the retinal position of a static disk during pursuit. (B) Spatial retinal layout of a flickering disk during over two temporal cycles during pursuit. (C) Schematic receptive field of a directional selective neuron. Neurons with different spatiotemporal integration characteristics would respond differently. (D–E) Relations between eye speed and temporal flickering frequency: For a fixed flicker frequency, increasing eye speed increases the spatial spread of a flickering disk on the retina. At a fixed eye speed, increasing flickering frequency decreases the temporal spread of contrast alternations. (F) Putative reverse-phi responses as a function of eye speed and/or temporal frequency.
Figure 9
 
Illustration of the effects of flicker frequency and eye-speed on retinal slip (a single disk is shown for clarity). (A) Space–time plot of the retinal position of a static disk during pursuit. (B) Spatial retinal layout of a flickering disk during over two temporal cycles during pursuit. (C) Schematic receptive field of a directional selective neuron. Neurons with different spatiotemporal integration characteristics would respond differently. (D–E) Relations between eye speed and temporal flickering frequency: For a fixed flicker frequency, increasing eye speed increases the spatial spread of a flickering disk on the retina. At a fixed eye speed, increasing flickering frequency decreases the temporal spread of contrast alternations. (F) Putative reverse-phi responses as a function of eye speed and/or temporal frequency.
The fact that stroboscopically illuminated random dot patterns (Behrens & Grüsser, 1979) or flashed pattern of different types (Adler & Grüsser, 1979), lacking explicit contrast reversals, can also serve as a substrate to maintain pursuit eye movements is not necessarily in contradiction with the present interpretation, as fast sequences of brief flashes of high-contrast stimuli contain Fourier components in all directions able to elicit ambiguous motion responses (Derrington & Goddard, 1989). We, however, note that the duration of smooth pursuit is longer, and the velocity gains are higher in this, as compared to previous studies, presumably because our stimuli optimize, at least in part, the reverse-phi motion responses in motion areas. 
Other issues
Several issues remain, which we address below. 
Why does the pursuit velocity gain decreases over time if smooth pursuit itself elicits a perceived motion in the same direction as the eyes?
In all experiments, the eye speed decreased soon after target disappearance, including in the flickering condition where positive feedback signals can help sustaining smooth pursuit. Several reasons may explain this observation. First, note that despite the flickering disks being the physical substrate of the perceived reverse-phi motion, they are static, and thus drift in a direction opposite to the eyes on the retina. (Only the illusory motion is consistently moving in the direction of the eyes). The retinal slip could decrease the velocity gain, as observed when pursuing a target against a static texture (Heinen & Watamaniuk, 1998; Kimmig et al., 1992; Spering & Gegenfurtner, 2007). This diminution could also result from an inappropriate match between the eye velocity induced by the moving target before occlusion, and the temporal flickering frequency of the occluding texture, such that the reverse-phi neuronal responses elicited by smooth pursuit do not correspond to the eye-induced perceived speed (Experiment 2). This mismatch could, in principle, yield a decreased eye speed, as well as an increased eye speed, depending on the speed tuning of neurons responding to the reverse-phi stimulus and the eye velocity. We further note that lowering the contrast of tracked moving targets results in lower velocity gain (Spering, Kerzel, Braun, Hawken, & Gegenfurtner, 2005), which, in the present study, can have opposite effects: A low contrast flickering texture (as used in Experiment 1, 2, 3, and in Condition A of Experiment 4) should entail a decreased velocity gain, but also decrease the salience of the contextual static disks that may impair the pursuit gain. Finally, we note that neuronal populations in motion areas have different spatiotemporal and speed tuning preference, some not matching the optimal eye-induced retinal spatiotemporal luminance profile. Responses from these neurons, possibly signaling a motion opposite to that of the eyes, could also account for the decreasing velocity gain observed here. 
Why is smooth pursuit maintenance not modulated by the size and density of the flickering disks?
The lack of effects of disk size in Experiment 3 is somewhat surprising, in the light of other studies showing that smooth pursuit depends on the size (or spatial frequency, or duty cycle) of the elements composing the stimuli (Behrens & Grüsser, 1979; Sato, 1989; Spillman et al., 1997). These previous studies used high-contrast stimuli consisting of mixed dark and light elements quickly changing contrast polarity over time. With such stimuli, neighboring elements with opposite contrast polarity falling within a receptive field of a direction-selective neuron elicit little or no reverse-phi response. Only those neurons tuned to the spatial frequency of the flickering stimulus should give reliable reverse-phi responses, such that the pooled response from all neurons is spatial frequency—or size—dependent. In contrast, with the uniform distribution of contrast used herein, neurons with different receptive field sizes can integrate motion signals over varying scales and distances. This could allow recruiting more neurons responding to reverse-phi motion independently of disk size, which would then feed the oculomotor system with reliable and consistent motion signals. 
In this view, it is worth noting that MT neurons with large receptive fields are built by combining inputs from neurons with smaller receptive fields that respond to local motion. When conflicting motion signals are used to stimulate MT cells, they preferentially respond to local, but not global, motion (Hedges, Stocker, & Simoncelli, 2011; Kumbhani et al., 2015). With the uniform distribution of contrast polarity used here, local and global motion responses are consistent and can contribute similarly to pursuit maintenance. 
What are the origins of the large interindividual differences observed herein?
We, as others, observed large interindividual differences in the quality of smooth pursuit, both before and after the occlusion period. (We note that these differences can also account for the decreasing velocity gain during the occlusion period, because participants with slow eye-speed before the occlusion period would fail to elicit appropriate reverse-phi responses during occlusion. As a matter of fact, those participants who did not track the visible target accurately were often those who failed to maintain pursuit for a long duration during the occlusion period, see Figure 5). However, these interindividual differences are intriguing by themselves, and indicate that smooth pursuit is not mastered equally well by participants. The possible reasons for these differences are many: differences in sensory (Wilmer & Nakayama, 2007), attentional (Ferrera & Lisberger, 1995), or motor components (for instance, some individuals may jointly move their head and their eyes to track a moving target in real life, with idiosyncratic balance between both types of movements; Fuller, 1992) are likely to differ across individuals, as is the case in some pathologies, such as in schizophrenic patients and their relatives (Adams et al., 2012; Spering et al., 2013). 
Another source of variability is the intrinsic sensitivity of each participant to the characteristics of the reverse-phi stimulation, especially contrast and temporal frequency. For instance, the same contrast polarity was arbitrarily set for all participants before the experiments. As no attempt was made to ensure that dark and light disks were of balanced perceived contrast relative to the background, the salience of position cues could have been different for each participant. Similarly, we did not attempt to adjust the flickering temporal frequency of the stimulus to maximize the perception of reverse-phi motion. As participants were not asked to report their perception of the flickering background on each trial—to avoid they direct their attention away from the tracked target—one cannot evaluate whether a reverse-phi motion was perceived during tracking or whether the disks were visible when the eyes were static. We, however, note that several studies (e.g., Beutter & Stone, 2000; Stone, Beutter, & Lorenceau, 2000; Watamaniuk & Heinen, 1999) found strong links between perception and pursuit, and that pursuit and perception co-vary on a trial-by-trial basis during a simultaneous psychophysical and oculomotor task (Stone & Krauzlis, 2003; also see Liston & Stone, 2014). Based on these studies, one can hypothesize that the velocity gain and the perception of reverse-phi motion during the occlusion period are correlated. 
What is the spatial extent of motion pooling that permits pursuit maintenance, and where is it located?
The present study did not attempt to characterize the spatial extent and spatial locations in the visual field that are necessary and sufficient to sustain smooth pursuit with a flickering textured stimulus. Such study would need not only to manipulate the spatial distribution of the flickering texture across space, but also to control for the attentional spread that could modulate this contextual influence. However, it is worth noting that the velocity gains measured before the occlusion period in Experiment 1 were different for the different conditions, suggesting that the occluders, although seen in eccentric vision, can influence pursuit gain across large distances. 
Are the present results specific to the rectilinear horizontal smooth pursuit tested herein?
The present experiments privileged the study of rectilinear predictable horizontal smooth pursuit, mainly because it allowed generating longer pursuit, given the aspect ratio of the display screen used here. Although it is known that horizontal and vertical smooth pursuit differ (Collewijn & Tamminga, 1984; Rottach et al., 1996), we think the mechanism proposed to underlie the capability to sustain smooth pursuit is general, and does not depend on a particular direction (except if considering motion anisotropies in the visual field; e.g., Van de Grind, Koenderink, Van Doorn, Milders, & Voerman, 1993). The finding that it is possible to generate smooth pursuit in any direction on a flickering background is supported by a recent study (Lorenceau, 2012), where smooth pursuit eye movements could be used to produce digits, letters and words that imply continuous changes in pursuit direction. One aim of the present study was to better characterize the conditions under which such endogenous generation of smooth pursuit eye movements is easiest. The experimental set-up used here seems well suited to optimize the stimulus characteristics best suited to each individual and/or to determine whether an individual will be able to use smooth pursuit to generate eye traces for communication purposes. 
Conclusion
This study presents four experiments designed to characterize the parameters that allow sustaining smooth pursuit eye movements in the absence of an explicitly moving target. In line with previous studies, we find that a temporally modulated textured background elicits an eye-induced retinal slip that move in the same direction as the eyes, providing a motion signals that then feeds the oculomotor system. These results suggest that retinal motion signals elicited by eye movements evoke cortical responses, presumably in MT and MST, that contribute to the computation an oculomotor pursuit command online. 
Acknowledgments
This work was supported by a grant from the French ANR n°2012-TECS-0009-01 to JL. AP was supported by a grant from Région Ile-de-France. 
Commercial relationships: none. 
Corresponding author: Arthur Portron; Jean Lorenceau. 
Email: arthur.portron@ens.fr; jean.lorenceau@ens.fr. Address: Ecole Normale Supérieure, PSL Research University, Département d'études cognitives, Laboratoire des Systémes Perceptifs (LSP), Paris, France. 
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Figure 1
 
Illustration of eye-induced reverse-phi motion moving in the same direction as the eyes: The spatiotemporal luminance profile elicited when a disk undergoing contrast reversal is displaced on the retina by pursuit eye movements matches that of a reverse-phi motion stimulus (see text for details).
Figure 1
 
Illustration of eye-induced reverse-phi motion moving in the same direction as the eyes: The spatiotemporal luminance profile elicited when a disk undergoing contrast reversal is displaced on the retina by pursuit eye movements matches that of a reverse-phi motion stimulus (see text for details).
Figure 2
 
Masks and textures of disks used in Experiment 1. The masks are either uniform and invisible, ([A] occlude with same hue as the background; vertical white dashed lines delineate the otherwise invisible occluder's borders), or visible (B), or textured and static (C), or flickering ([D], 5 Hz). In all conditions, the masks and texture cover 9.30° × 27.10° of visual angle. At 13.3°/s, the moving target, whose trajectory is shown by filled and dashed black lines in (A), is visible for 900 ms and invisible for 700 ms after passing behind the occluder.
Figure 2
 
Masks and textures of disks used in Experiment 1. The masks are either uniform and invisible, ([A] occlude with same hue as the background; vertical white dashed lines delineate the otherwise invisible occluder's borders), or visible (B), or textured and static (C), or flickering ([D], 5 Hz). In all conditions, the masks and texture cover 9.30° × 27.10° of visual angle. At 13.3°/s, the moving target, whose trajectory is shown by filled and dashed black lines in (A), is visible for 900 ms and invisible for 700 ms after passing behind the occluder.
Figure 3
 
Flow of eye-movement analyses. (A) Eye position during half a trial (a trial consisted in a back-and-forth motion of the target, half a trial corresponds to back-or-forth motion; the shaded area represents the occlusion period: 700 ms). (B) Eye velocity during half a trial. The dashed horizontal black line corresponds to the velocity threshold used for saccade detection (>20°/s−1). (C). Eye acceleration during half a trial. The horizontal dashed black lines shows the acceleration threshold used for saccade detection (±500°/s−2). (D) Saccade-free eye velocity during half a trial. The dark and light gray shaded areas (700 ms) delineates the pre-occlusion and occlusion periods used to compute the velocity gains.
Figure 3
 
Flow of eye-movement analyses. (A) Eye position during half a trial (a trial consisted in a back-and-forth motion of the target, half a trial corresponds to back-or-forth motion; the shaded area represents the occlusion period: 700 ms). (B) Eye velocity during half a trial. The dashed horizontal black line corresponds to the velocity threshold used for saccade detection (>20°/s−1). (C). Eye acceleration during half a trial. The horizontal dashed black lines shows the acceleration threshold used for saccade detection (±500°/s−2). (D) Saccade-free eye velocity during half a trial. The dark and light gray shaded areas (700 ms) delineates the pre-occlusion and occlusion periods used to compute the velocity gains.
Figure 4
 
Mean eye velocity for each participant in the four conditions shown in the inset. Red line: invisible occluder. Yellow line: visible occluder. Orange line: static texture. Blue line: flickering texture. The gray shaded area delineates the target off period (700 ms). The target is occluded 900 ms after motion onset and reappears for 900 ms after the occlusion period.
Figure 4
 
Mean eye velocity for each participant in the four conditions shown in the inset. Red line: invisible occluder. Yellow line: visible occluder. Orange line: static texture. Blue line: flickering texture. The gray shaded area delineates the target off period (700 ms). The target is occluded 900 ms after motion onset and reappears for 900 ms after the occlusion period.
Figure 5
 
Left panel: (A) Time-averaged velocity gain during the occlusion period as a function of the time averaged velocity gain before occlusion. Symbols indicate the different experimental conditions (see inset legend); each colored line represents the velocity gains of a single participant for all conditions. Right panel: (B) Mean velocity gain for each condition, for the pre-occlusion (gray outline) and occlusion period (black outline). Stars indicate the significant effects of the occluders type on the velocity gains during the occlusion period (***p < 0.0001). (C) Mean saccade rate for each condition during occlusion period. Error bars represent 1 SE. See text for details.
Figure 5
 
Left panel: (A) Time-averaged velocity gain during the occlusion period as a function of the time averaged velocity gain before occlusion. Symbols indicate the different experimental conditions (see inset legend); each colored line represents the velocity gains of a single participant for all conditions. Right panel: (B) Mean velocity gain for each condition, for the pre-occlusion (gray outline) and occlusion period (black outline). Stars indicate the significant effects of the occluders type on the velocity gains during the occlusion period (***p < 0.0001). (C) Mean saccade rate for each condition during occlusion period. Error bars represent 1 SE. See text for details.
Figure 6
 
Mean velocity gains (A and C) and saccade rates (B and D) of each participant (dotted lines) for a target speed of 13.3°/s (top) and 26.6°/s (bottom), as a function of flicker temporal frequency. The velocity gains averaged across participants is also shown (black line). See text for details.
Figure 6
 
Mean velocity gains (A and C) and saccade rates (B and D) of each participant (dotted lines) for a target speed of 13.3°/s (top) and 26.6°/s (bottom), as a function of flicker temporal frequency. The velocity gains averaged across participants is also shown (black line). See text for details.
Figure 7
 
(A) Examples of the texture backgrounds used in Experiment 3. Velocity gains for each participant (colored dashed lines) during the occlusion period computed for the different flickering textures with (B) varying disk sizes and (C) varying disk density, for three target speeds. Black symbols represent the velocity gains averaged across participants.
Figure 7
 
(A) Examples of the texture backgrounds used in Experiment 3. Velocity gains for each participant (colored dashed lines) during the occlusion period computed for the different flickering textures with (B) varying disk sizes and (C) varying disk density, for three target speeds. Black symbols represent the velocity gains averaged across participants.
Figure 8
 
Mean velocity gains computed over the first 700 ms of the occlusion period as a function of the mean velocity gains computed over the last 700 ms of the occlusion period, for three flickering frequencies. Each symbol (A–E) represents a different luminance contrast. Contrast is computed as (L1t1-L2t2)/Lb, with L1t1 corresponding to a disk luminance, L1, at time t1, L2t2 corresponding to a disk luminance, L2, at time t2, and Lb the background luminance. Balanced condition (A) +6%/−6%; Imbalanced conditions (B) +6%/−28%; (C) +31%/−6%; (D) +31%/+6%; (E) −6%/−28%. The velocity gains are larger during the first 700 ms than during the last 700 ms. Velocity gains are larger at higher temporal frequencies and a balanced contrast (A) involving a change in contrast polarity. Error bars represent 1 SE.
Figure 8
 
Mean velocity gains computed over the first 700 ms of the occlusion period as a function of the mean velocity gains computed over the last 700 ms of the occlusion period, for three flickering frequencies. Each symbol (A–E) represents a different luminance contrast. Contrast is computed as (L1t1-L2t2)/Lb, with L1t1 corresponding to a disk luminance, L1, at time t1, L2t2 corresponding to a disk luminance, L2, at time t2, and Lb the background luminance. Balanced condition (A) +6%/−6%; Imbalanced conditions (B) +6%/−28%; (C) +31%/−6%; (D) +31%/+6%; (E) −6%/−28%. The velocity gains are larger during the first 700 ms than during the last 700 ms. Velocity gains are larger at higher temporal frequencies and a balanced contrast (A) involving a change in contrast polarity. Error bars represent 1 SE.
Figure 9
 
Illustration of the effects of flicker frequency and eye-speed on retinal slip (a single disk is shown for clarity). (A) Space–time plot of the retinal position of a static disk during pursuit. (B) Spatial retinal layout of a flickering disk during over two temporal cycles during pursuit. (C) Schematic receptive field of a directional selective neuron. Neurons with different spatiotemporal integration characteristics would respond differently. (D–E) Relations between eye speed and temporal flickering frequency: For a fixed flicker frequency, increasing eye speed increases the spatial spread of a flickering disk on the retina. At a fixed eye speed, increasing flickering frequency decreases the temporal spread of contrast alternations. (F) Putative reverse-phi responses as a function of eye speed and/or temporal frequency.
Figure 9
 
Illustration of the effects of flicker frequency and eye-speed on retinal slip (a single disk is shown for clarity). (A) Space–time plot of the retinal position of a static disk during pursuit. (B) Spatial retinal layout of a flickering disk during over two temporal cycles during pursuit. (C) Schematic receptive field of a directional selective neuron. Neurons with different spatiotemporal integration characteristics would respond differently. (D–E) Relations between eye speed and temporal flickering frequency: For a fixed flicker frequency, increasing eye speed increases the spatial spread of a flickering disk on the retina. At a fixed eye speed, increasing flickering frequency decreases the temporal spread of contrast alternations. (F) Putative reverse-phi responses as a function of eye speed and/or temporal frequency.
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