Superior colliculus visual neural sensitivity at the lower 1 limit of natural self-induced image displacements

Visual pattern analysis relies on computations from neurons possessing spatially confined 25 receptive fields. Often, such receptive fields are orders of magnitude larger than the visual 26 pattern components being processed, as well as these components’ minute displacements 27 on the retina, whether due to small object or self motions. Yet, perception effortlessly 28 handles such visual conditions. Here, we show that in the primate superior colliculus, a brain 29 structure long associated with oculomotor control, neurons with relatively large receptive 30 fields are still sensitive to visual pattern displacements as small as 1 min arc. We used real- 31 time gaze-contingent retinal image stabilization to control the instantaneous spatio- 32 temporal luminance modulation of detailed patterns experienced by neurons, probing 33 sensitivity to the lower limit of natural self-induced image displacements. Despite a large 34 difference between pattern displacement amplitudes and receptive field sizes, collicular 35 neurons were strongly sensitive to the visual pattern consequences of the smallest possible 36 image-shifting eye movements.


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Visual pattern analysis relies on computations from neurons possessing spatially confined 25 receptive fields. Often, such receptive fields are orders of magnitude larger than the visual 26 pattern components being processed, as well as these components' minute displacements 27 on the retina, whether due to small object or self motions. Yet, perception effortlessly 28 handles such visual conditions. Here, we show that in the primate superior colliculus, a brain 29 structure long associated with oculomotor control, neurons with relatively large receptive 30 fields are still sensitive to visual pattern displacements as small as 1 min arc. We used real-31 time gaze-contingent retinal image stabilization to control the instantaneous spatio-32 temporal luminance modulation of detailed patterns experienced by neurons, probing 33 sensitivity to the lower limit of natural self-induced image displacements. Despite a large 34 difference between pattern displacement amplitudes and receptive field sizes, collicular 35 neurons were strongly sensitive to the visual pattern consequences of the smallest possible 36 image-shifting eye movements. 37 38 39 Introduction 40 41 Image analysis in the primate visual system is performed by neurons having individual 42 receptive fields (RF's) sampling confined regions of the retinal image. Outside the fovea, and 43 particularly in higher visual areas, RF's can be large. This is also the case in sensory-motor 44 structures like the superior colliculus (SC) 1-3 , which itself has a rich and diverse visual 45 repertoire 1-7 . 46 47 Integration of relatively large image regions by individual RF's raises questions about how 48 detailed visual pattern analysis can occur when the local features inside an RF are much 49 smaller than RF size. Among these questions is what nature of visual processing takes place 50 in the SC, a sensory-motor structure, when compared to other visual areas that are more 51 distant from the motor control apparatuses. For example, the SC contributes to saccade 52 generation 8 , and its diverse visual properties seem to be optimized for detecting stimuli for 53 the purpose of gaze orienting 9 . Does this mean that SC neurons are incapable of detailed 54 visual pattern analysis that may be more the purview of visual cortex? 55 56 We investigated this question by exploring whether SC neurons are sensitive to the visual 57 pattern consequences of minute image displacements over their RF's. With the head fixed, a 58 lower limit on natural self-induced retinal image motion is that caused by slow ocular 59 position drifts during gaze fixation (Fig. 1A) 10-12 . With stable external stimuli, such drifts 60 introduce image pattern displacements over individual RF's that are much smaller than the 61 RF's themselves (Fig. 1B). Thus, the local pattern features of the stimuli never really leave 62 the RF's during drifts. Yet, theoretical and perceptual work suggests that small 63 displacements associated with ocular position drifts reformat images in meaningful ways for 64 perception [13][14][15][16] . The reformatting itself is a direct consequence of eyeball rotation: it is a 65 property of the image formation process. However, for the reformatting to be effective for 66 perception, downstream neural processing stages need to be also sensitive to them. 67 Therefore, we asked whether SC neurons functionally utilize the visual reformatting afforded 68 by ocular position drifts in their activity (Fig. 1B). 69 70 We employed the technique of gaze-contingent retinal image stabilization, combined with 71 grating images of different properties, to identify a direct SC neural correlate of perceptual 72 effects 13 associated with ocular position drifts. We presented gratings to the RF's of SC 73 neurons either stably on the display (and thus moving on the retina due to drifts) or using 74 gaze-contingent display updates, as was done earlier in the primary visual cortex with simple 75 spot and bar stimuli 17

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We asked whether visually-responsive SC neurons are sensitive to image pattern 90 displacements at the lower limit of natural self-induced motion. We did so by recording SC 91 neural activity from head-fixed monkeys precisely holding their gaze on a small, stable 92 fixation spot of 8.5 x 8.5 min arc dimensions. During fixation, the eyes drifted slowly 10-12 , 93 causing retinal image displacements on the order of 1 min arc magnitude (Fig. 1A), with 94 occasional larger microsaccades. The scale of retinal image displacements associated with 95 ocular position drifts, as small as the approximate distance between two individual foveal 96 cone photoreceptors, is considerably smaller than SC RF sizes, especially extrafoveally [1][2][3]9 . It 97 is also frequently much smaller than the viewed image patterns themselves. Consider, for 98 example, a gabor grating of 4.44 cycles/deg (cpd) in an RF of a neuron preferring 3.5 deg 99 eccentricity. A displacement over the RF of the grating's retinal image by 1 min arc would 100 cause minimal change to the overall luminance pattern experienced by the neuron (Fig. 1B). 101 Yet, theoretical considerations suggest that such minute pattern displacements can still 102 matter for perception 10,13-16 . We, therefore, investigated whether SC neurons are sensitive 103 to these diminutive pattern displacements.  We utilized real-time retinal image stabilization to move a visual pattern (gabor grating) in 127 lock with instantaneous eye position (Methods). We compared neural activity with a stable 128 pattern on the display (thus moving with respect to a continuously moving retinotopic RF) to 129 neural activity with a moving pattern on the display tracking the eye movements (and thus 130 rendered more stable with respect to the RF; Fig. 1C). If the SC is sensitive to visual pattern 131 consequences of retinal image displacements as small as those in Fig. 1A, B, then the neural 132 responses should differ between the two conditions. Critically, the fixation spot was always 133 stable on the display, allowing the monkeys to properly anchor their gaze independently of 134 retinal image stabilization. Indeed, the characteristics of both ocular position drifts and 135 microsaccades across all of our gaze-contingent manipulations (Methods) were unaltered by 136 whether the grating was stable on the display (control) or not (Figs. S1-S3). This is consistent 137 with evidence that, in steady-state fixation, microsaccades and ocular position drifts act to 138 optimize eye position at the fixated target [19][20][21][22] . Therefore, we experimentally controlled the 139 subtle image displacements of visual patterns over RF's ( Fig. 1), but without altering the 140 natural gaze behavior itself. 141 142 143 Superior colliculus neurons are sensitive to visual pattern displacements on the 144 order of 1 min arc 145 We first established the effectiveness of our manipulation. After identifying a visually-146 responsive neuron, we estimated its retinotopic RF hotspot location and extent (Methods). If 147 we then pegged the stimulus, via retinal image stabilization, at the estimated hotspot 148 location, then the neuron would consistently experience an optimal stimulus. This is in 149 contrast to control trials, during which fixational eye movements could, at any one moment 150 in time, displace the stimulus from the optimal RF hotspot location or otherwise blur it. 151 Thus, neural activity was expected to be elevated with retinal image stabilization (Fig. 2). 152 Alternatively, if we pegged the stimulus at a sub-optimal location relative to the RF during 153 retinal image stabilization, then the neuron's activity was expected to decrease, because in 154 control trials, eye movements could momentarily bring the stimulus to a more optimal RF 155 position (Fig. S4). These effects are similar to those observed in V1 with the retinal image 156 stabilization technique and simple spot and bar stimuli 17,23,24 , and they meant that we were 157 now in a good position to explore, in more detail, the visual pattern consequences of minute 158 ocular position drifts on SC image representations. 159 160 In all of our subsequent analyses, we only focused on situations like in Fig. 2, with an 161 optimally placed RF stimulus, and also with primarily extrafoveal neurons with RF's larger 162 than the scale of ocular position drifts; this was the relevant scenario for the questions 163 raised by Fig. 1B. We also excluded all epochs around microsaccades (Methods), because 164 retinal image stabilization with discretized display update times (Methods) is expectedly 17 165 least effective for these faster eye movements (but see  Retinal image stabilization of a stimulus at the RF hotspot location consistently elevated SC 187 neural activity, suggesting sensitivity to local image pattern statistics within the RF's (like 188 those schematized in Fig. 1B). In Fig. 3A, we plotted the normalized population activity after 189 the onset of a 4.44 cpd grating in the RF's, either in control or with full retinal image 190 stabilization. We found a persistently elevated sustained response (after an initial visual 191 burst due to stimulus onset) for as long as the stimulus was stabilized over the RF's (compare 192 control to retinal image stabilization firing rates). Given the spatial scale of our image 193 displacements associated with ocular position drifts and the predicted luminance 194 modulations that they introduced (Figs. 1A, S1, S3C-F), this implies that SC neurons can 195 indeed detect minute image pattern displacements much smaller than RF sizes, and also 196 smaller than the pattern features themselves (Fig. 1B). Figure    showing individual neuron firing rates as well as spiking statistics in the different conditions). 283 Thus, it was always ocular position drifts orthogonal to the local pattern orientations that 284 resulted in the largest neural modulations. 285 286 Therefore, not only are SC neurons sensitive to image pattern displacements on the order of 287 magnitude of 1 min arc, but they are also differentially sensitive as a function of the relative 288 difference between the image displacement directions and the underlying pattern 289 orientations. We previously demonstrated this to be the case in the SC for the image 290 displacements associated with significantly larger microsaccades 25 , but the smaller scale of 291 ocular position drifts (Fig. 1A, B) suggests an even finer ability of SC neurons to represent 292 and react to detailed visual patterns (Fig. 1B). The SC can indeed contribute to the 293 theoretically-predicted perceptual effects associated with slow ocular position drifts (e.g. 294 13,15 ). 295 296 297 298 299 300 The results so far suggest that SC neurons are sensitive to image pattern features that can be 319 significantly smaller than the neurons' RF sizes (Fig. 1B). However, with a pattern at the 320 optimal RF location, the scale of luminance modulations caused by ocular position drifts (Fig.  321 1B) should depend on both the spatial detail of the pattern itself as well as the spatial scale 322 of the retinal image displacements caused by eye movements (Fig. S3A, B). Therefore, given 323 the ocular position drift sizes that we observed (Figs. 1A, S1, S3C-F), we expected to observe 324 the largest effects of retinal image stabilization with high spatial frequency patterns ( Fig.  325 S3A, B). This was indeed the case. In our experiments, we also tested low (0.56 cpd) and 326 intermediate (

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When comparing the high to the middle spatial frequency, the difference in modulation indices was smaller than 351 in B (but the modulation indices with 4.44 cpd were still higher than with 2.22 cpd; 20.86% versus 13.27%).

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Sensitivity to drift-scale pattern displacements still occurs in extrafoveal and 356 lower visual field neurons with larger receptive fields 357 In prior theoretical and perceptual work 13,15 , the image pattern consequences of ocular 358 position drifts were primarily, and understandably, considered from a foveal perspective. 359 However, our results above suggest that even eccentricities with larger RF's ( Fig. 1B) may 360 still utilize the visual formatting afforded by slow fixational eye movements in SC visual 361 neural coding. Therefore, we exploited the fact that we sampled neurons from a wide range 362 of eccentricities (Fig. S9), and we specifically analyzed extrafoveal neurons to ask if they 363 were still sensitive to our retinal image stabilization manipulations. These extrafoveal SC 364 neurons clearly showed modulations (Fig. 6A) that were very similar to those observed for 365 the entire neural population (Figs. 3-5): greater elevation with retinal image stabilization for 366 high than low spatial frequencies. 367 368 We then separated the neurons into 3 groups based on their preferred eccentricities (<1 369 deg, 1-3 deg, and >3 deg). In all cases, full and horizontal retinal image stabilization (with 370 vertical gratings) had higher positive neural modulation indices than vertical retinal image 371 stabilization (Fig. 6B). Specifically, the full and horizontal retinal image stabilization 372 modulation indices in Fig. 6B were statistically significantly different from zero (p<0.0026 in 373 each panel; 1-sample t-test; neuron numbers shown in Fig. 6B), but the vertical retinal image 374 stabilization modulation indices were not. Moreover, the modulation indices were higher for 375 high rather than low spatial frequencies (Fig. 6C); each comparison of high (4.44 cpd) to low 376 (0.56 cpd) spatial frequency modulation indices in Fig. 6C was statistically significant 377 (p<0.032 in each panel; 2-sample t-test; neuron numbers shown in Fig. 6C  Another test of the effects of RF sizes in our retinal image stabilization manipulations was to 405 also check upper and lower visual field SC neurons. This is so because, in the very same 406 animals, we previously documented a substantial difference in SC RF sizes above and below 407 the horizontal meridian, with lower visual field RF's being significantly larger 9 . Here, we 408 found that even such lower visual field neurons, with significantly larger RF's than upper 409 visual field neurons 9 , still showed all the same hallmarks of neural modulations described 410 above (Figs. S10, S11). Thus, visual reformatting of the SC neural code by slow ocular 411 position drifts extends well beyond the fovea and affects extrafoveal and lower visual field 412 neurons with larger RF's (Fig. 1B)  We found that individual SC neurons, even with large RF's, are sensitive to minute 481 displacements of visual patterns caused by ocular position drifts on the order of 1 min arc in 482 amplitude. We were particularly motivated by the question of whether the diverse visual 483 capabilities of the primate SC, which are becoming increasingly evident, include being 484 sensitive to local feature patterns that are significantly smaller than the RF's themselves (Fig.  485 1B). Thus, we investigated whether subtle shifts of these patterns caused by ocular position 486 drifts, representing the lower limit of natural self-induced image displacements, can reliably 487 and systematically modulate SC neural activity. We employed retinal image stabilization to 488 experimentally control the location and motion of a given pattern over the RF at any one 489 moment in time. If the RF's grossly integrated information all over their spatial extents, then 490 subtle shifts of a given pattern (Fig. 1B) should not have resulted in altered neural responses. 491 In contrast, we found robust neural modulations, which were also direction-dependent. 492 Thus, even though SC neurons may have large RF's, they still exhibit sensitivity to highly local 493 image features. This idea is consistent with the notion that the primate SC can contribute to 494 visual scene analysis 4,5,26 and object processing 6,27-30 in a variety of ways. 495 496 Our results are relevant with respect to theoretical predictions on how eye position drifts 497 can reformat visual images by introducing temporal fluctuations of image luminance at any 498 one position on the retina [13][14][15][16]31 . Such image reformatting happens by virtue of a physical 499 rotation, albeit small, of the eyeball when viewing a stationary image. However, for such a 500 reformatting to actually influence perception in a meaningful way, then neural elements 501 downstream of the retina must be sensitive to its consequences. With small foveal RF's, say 502 in the lateral geniculate nucleus or primary visual cortex, this idea might be expected 503 because small ocular position drifts can displace stimuli in and out of the equally small RF's; 504 that is, the scale of image shifts is similar to the scale of foveal (and perifoveal) RF sizes. 505 However, whether larger RF's (e.g. extrafoveally), and particularly within an area that is 506 more traditionally investigated from the perspective of motor control like the SC, can still 507 benefit from such reformatting was not equally clear. We found this to be the case, adding 508 to the increasingly rich repertoire of visual capabilities of the primate SC described in the 509 literature. Thus, visual reformatting by ocular position drifts for the benefit of perception 510 can extend also beyond the fovea, and it has direct neural consequences downstream of the 511 retina. 512 513 An additional interesting implication of our results concerns the degree of correlation 514 between the two eyes during ocular position drifts. We experimentally stabilized our grating 515 images based on the motion of only one eye (Methods), and we still observed very 516 systematic neural modulations. This means that there must have been at least a minimal 517 amount of correlation between the motions of the two eyes. Otherwise, our retinal image 518 stabilization conditions would have created disparities between the left and right eye images 519 that might have blurred the gratings too much. This would not have necessarily increased 520 the gain and directional sensitivity of neural responses with retinal image stabilization like 521 we saw. Therefore, it will be important in future work to better investigate binocular 522 coordination in ocular position drifts during gaze fixation. Indeed, the question of whether 523 ocular position drifts are correlated (either positively or negatively) between the two eyes 524 has been investigated in the past, with a variety of observations and interpretations 12,32 . It 525 has also been previously shown that primates are capable of controlling slow eye 526 movements with speeds and position changes similar to those obtained with ocular position 527 drifts during fixation 20,33,34 . 528 529 In yet additional future experiments, stabilization based on only one eye motion could be 530 exploited experimentally to investigate the strength of binocular and monocular visual input 531 integration in the SC. Specifically, it is known that most of the SC is binocular 1,35-37 . However, 532 it could be that some neurons' activity may be dominated by one eye input or the other. 533 Therefore, in follow up experiments, one can repeat our study but with stabilization, in 534 separate trials, based on the separate eyes (e.g. stabilization in one trial based on right eye 535 motion and stabilization in another trial based on left eye motion). If a particular SC neuron 536 is functionally dominated by input from one eye, then stabilization with one of the eyes 537 should cause larger modulations than stabilization based on the motion of the other eye. 538 This would allow investigating potential ocular dominance of visual information in individual 539 neurons in the awake monkey SC. Moreover, with sufficient mapping across the SC 540 topographic map using such an experiment, it may then be possible to find individual zones 541 in the SC that are potentially dominated (while remaining generally binocular) by visual input 542 from one eye or the other, similar to the finding of orientation tuning zones in the mouse SC 543 38,39 . 544 545 Since microsaccades are a component of fixational eye movements, it is also likely that they 546 cause similar visual modulations to ocular drifts, but with different spatial and temporal 547 parameters due to the faster and larger nature of microsaccades. This is exactly what we 548 saw recently in the SC 25 , and it is also consistent with calculations of the different 549 spatiotemporal consequences of saccades on visual images relative to ocular position drifts 550 40 . In any case, it is highly unlikely that microsaccades explain our results in the current 551 study, because we excluded these movements from analysis. Also, the microsaccade 552 characteristics were not altered by our retinal image stabilization manipulations but the 553 neural activity was. Therefore, our experiment isolated the effects of the smaller and slower 554 ocular position drifts on SC activity. 555 556 In all, our results highlight the importance of investigating active vision 41 in the SC 42 and in 557 other visual areas 18,43,44 , whether by careful analysis of the image consequences of eye 558 movements on the retina with stable targets (as in Fig. 7) or by experimentally altering the 559 normal visual-motor loop by gaze-contingent manipulation (as in Fig. 3). This would be even 560 more important by using rich visual stimuli -like gratings, textures, and patterns -and even 561 natural images.

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Experimental animals and ethics approvals 757 We recorded superior colliculus (SC) neural activity from two adult, male rhesus macaque 758 monkeys (N and P) aged 7 years, and weighing 8 kg and 7 kg, respectively. The experiments 759 were approved by ethics committees at the regional governmental offices of the city of 760 Tübingen. 761 762 763 Laboratory setup and animal preparation 764 The experiments were conducted in the same laboratory as that described in earlier 765 publications 3,9,45  Behavioral task 782 We employed a gaze fixation task in which we presented static gabor gratings of different 783 spatial frequencies within the receptive fields (RF's) of the recorded neurons. Unlike in our 784 earlier work with spatial frequency mapping in the SC 5,53 , we maintained the stimulus on the 785 display for much longer during fixation 54 . Specifically, once we identified the size and 786 location of an RF, we designed a gabor of suitable size to fill the RF. The grating always had 787 high contrast (100%) and one of three different spatial frequencies (0.56, 2.22, or 4.44 cpd), 788 which were varied across trials (the phase of the gabor was also random from trial to trial). 789 790 A trial started with the onset of a central white fixation dot over a gray background. After 791 the monkey fixated the spot in a stable manner for a random interval spanning a few 792 hundred milliseconds, the grating appeared in the RF and remained on for approximately 793 1500 ms. The fixation spot was small (8.5 x 8.5 min arc), and it had a luminance of 72 cd/m 2 . 794 The gray background had 21 cd/m 2 luminance. If the monkey successfully fixated the spot 795 for the entire duration of the trial, it was rewarded with fruit juice, and another trial was 796 initiated after a short blank-screen interval. 797 798 Four different trial types were interleaved. In the control condition, both the fixation spot 799 and grating were stable on the display. This condition was analyzed for microsaccade-800 induced visual reafferent responses in a recent study 25 , as well as for interactions between 801 spiking activity and microsaccade kinematics 54 . The sustained firing rates during 802 microsaccade-free fixation, as well as all the remaining three trial types of the task, were 803 never described in any other publications. The additional trial types constituted our retinal 804 image stabilization manipulations (Fig. 1). In full retinal image stabilization (Fig. 1C), the 805 grating (from the moment it appeared until trial end) was moved in lockstep with 806 instantaneous eye position (see next section). The fixation spot always remained stable on 807 the display to help anchor gaze properly and not alter the eye movement statistics (Figs. S1-808 S3). This was necessary because we wanted to isolate the influences of (slow) fixational eye 809 movements on neural activity and, therefore, had to ensure that the eye movements 810 themselves were occurring as naturally as possible. In horizontal retinal image stabilization 811 (Fig. 1D), the vertical position of the grating was kept constant on the display and unchanged 812 from control; the horizontal position of the grating was moved in lockstep with horizontal 813 eye position. Finally, in vertical retinal image stabilization (Fig. 1E), the horizontal position of 814 the grating was stable on the display and similar to the control condition, whereas the 815 vertical position of the grating was moved in synchrony with vertical eye position. 816 817 In a subset of experiments, we replaced the vertical gratings with horizontal ones, in order 818 to explore the relative relationship between eye movement directions and image pattern 819 orientations (e.g. Fig. 4). 820 821 We collected approximately 18 trial repetitions per condition per neuron. 822 823 824 Retinal image stabilization 825 We first calibrated eye position measurements using methods described earlier 19 . Briefly, at 826 the beginning of every session, the monkeys fixated (multiple times) a series of 19 locations 827 on the display for at least 1000 ms. We then measured raw voltages during stable fixation 828 from each location. To convert the raw voltages to degrees of angular rotation, we used a 829 multi-order polynomial including both the horizontal and vertical raw voltages, as well as 830 cross-channel interaction terms 19 . 831 832 We then employed our real-time gaze-contingent display system 19,20,46 . In this system, we 833 sampled and processed eye positions at 1 KHz using a real-time control system, and we 834 updated the display at 120 Hz (constrained by the display technology). In retinal image 835 stabilization trials, after every display refresh time, we sampled new eye positions and 836 processed them. We then calculated the position of the grating according to the new eye 837 positions, and we updated the display at the next frame refresh. Thus, our retinal image 838 stabilization trials discretized eye positions at 120 Hz (the bottleneck imposed by the display 839 refresh rate). Such a rate is suitable for successful retinal image stabilization with slow eye 840 movements, as shown previously by our 19,20 and other 13,17,55,56 laboratories. In fact, even 841 with microsaccades, Fig. S5 shows that the microsaccade-related reafferent responses were 842 reduced by retinal image stabilization at 120 Hz. This means that while the microsaccades 843 were still a bit too rapid for the display's 120 Hz frequency, the stimulus was still moved 844 sufficiently rapidly to catch up with the real microsaccade and reduce the retinal slip of the 845 grating by the eye movement (and, therefore, the associated reafferent response). 846 847 Finally, eye coil systems often exhibit a slow drift in their measurements, which is much 848 slower than ocular position drifts (we confirmed this by comparing initial fixation positions 849 across trials and assessing a time constant of eye coil system drift, which was more than two 850 orders of magnitude slower than within-trial ocular position drifts). Therefore, at the 851 beginning of every trial, we performed a drift correction that was applied for all subsequent 852 eye position measurements within a trial. We did this by averaging eye position in the final 853 50 ms before gabor onset and using this measurement as a reference to which we compared 854 all subsequent eye positions in the trial. In post-hoc analyses, if there was a microsaccade in 855 the drift correction measurement interval, the trial was excluded from further analysis. 856 857 858 Eye movement data analysis 859 We detected saccades and microsaccades as described previously 25,46,57 . We used the 860 detections for two primary purposes. First, we established that microsaccade properties 861 were not altered by our retinal image stabilization manipulations (Fig. S2). Second, for our 862 neural analyses, we excluded all data starting from 10 ms before microsaccade onset until 90 863 ms after microsaccade end. This was done in order to avoid movement-induced reafferent 864 responses from the analyses (Fig. S5). We also inspected all trials for blinks, and we removed 865 all blink intervals, including a period of 50 ms before and a period of 50 ms after each of 866 them. 867 868 Our microsaccade analyses (Fig. S2) included microsaccade rate, directions, and main 869 sequence 58 relationship between movement amplitude and peak velocity. For microsaccade 870 rate, we used a running window of 25 ms width and moved in steps of 2 ms. Within each 871 such time window, we counted the fraction of trials in which the window contained 872 microsaccades across trials of a given condition. For microsaccade directions and main 873 sequence relationships, we considered all microsaccades in the sustained fixation interval 874 that we were interested in for our neural analyses (>300 ms after stimulus onset; see Neural 875 data analysis below), and we plotted the distribution of movement vector angles (for the 876 direction analysis) or the scatter of movement peak velocity versus movement radial 877 amplitude (for the main sequence analysis). We performed all of these analyses separately 878 for each of the four stimulus conditions (control and three retinal image stabilization  879 versions), and we then compared the results to confirm that retinal image stabilization did 880 not significantly alter the statistics of microsaccades. 881 882 To confirm that retinal image stabilization also did not alter absolute eye position (i.e. the 883 combination of ocular position drifts and microsaccades), we also plotted the raw eye 884 positions (in sustained fixation; >300 ms after stimulus onset) across all trials in each 885 condition (Fig. S1). 886 887 We also analyzed ocular position drifts more specifically. For example, for Fig. S3C-F, we first 888 excluded all microsaccades and their pre-and post-movement periods mentioned above. 889 We then considered all sustained fixation intervals starting from 300 ms after stimulus onset 890 in each trial. For every interval in between two successive microsaccades (which we called a 891 saccade-free fixation interval), we measured mean eye position and subtracted it from every 892 sample of eye position within the same interval. This gave us the instantaneous deviation of 893 eye position from the mean position during the particular saccade-free interval of interest. 894 In Fig. S3C, E, we then binned all such deviations across all fixation intervals and obtained a 895 distribution of how much ocular position drifts altered eye position. For Fig. S3D, F, we also 896 took the standard deviation of eye position within each microsaccade-free fixation interval. 897 We then plotted the distribution of these measurements across all such intervals in Fig. S3D, 898 F. Our purpose in both cases was to highlight that the slow ocular position drifts had similar 899 characteristics whether we ran control or retinal image stabilization trials (Fig. S3C-F), and 900 also to predict the amounts of luminance modulations over the retina that were expected 901 from our gratings and ocular position drift amplitudes (Fig. S3A, B). 902 903 904 Neural data analysis 905 We recorded from 61 individually isolated SC neurons, which were first characterized online 906 using delayed visually-guided and memory-guided saccade tasks 9,45,53 . The initial 907 characterization allowed classifying the neurons as being visual or visual-motor, as well as 908 assessing the neurons' RF sizes and locations. After establishing that a recorded neuron was 909 visually-responsive, we ran the main behavioral task described above with the grating placed 910 at the optimal RF position (except for some test examples like in Fig. S4). We included all 911 visually-responsive neurons in our analyses, without further classification into visual or 912 visual-motor categories. This was because our results were similar regardless of whether a 913 neuron was purely visual or visual-motor in nature (the results were also highly consistent 914 across the population; for example, Fig. S6A, B). 915 916 In both monkeys, we tested the neurons with vertical gratings. In monkey N, we additionally 917 tested 35 neurons with horizontal gratings (27 of these neurons had both vertical and 918 horizontal gratings tested together within the same session). 919 920 We analyzed neural data by counting spikes during the sustained fixation interval or by 921 converting spike times into firing rate estimates (with a Gaussian convolution kernel of s 40 922 ms). We defined the sustained fixation interval as the time from 300 ms to 1400 ms after 923 grating onset. The lower bound of this time interval (300 ms) was chosen to avoid the initial 924 visual onset response of the neurons (occurring immediately after grating onset); the upper 925 bound was chosen to maximize the numbers of neurons that we could pool in the analyses. 926 We did not notice a difference in the onset response strength (the initial visual burst after 927 grating onset) across our different retinal image stabilization manipulations relative to 928 control. Therefore, we did not analyze initial visual responses further. Rather, we were 929 interested in assessing how subtle image displacements (i.e. during sustained presence of a 930 stimulus within the RF's) affected SC neural activity. Our chosen interval of more than 1 931 second (300 ms to 1400 ms from stimulus onset) was sufficient to do that. 932 933 As stated above, in all of our analyses, except for Fig. S5, we excluded all neural activity 934 associated with microsaccades, in order to avoid contamination by microsaccade-induced 935 reafferent responses 25 (Fig. S5 shows an example of such responses). We replaced all 936 intervals starting from 10 ms before microsaccade onset to 90 ms after microsaccade end by 937 not-a-number labels such that these intervals were not included when computing across-938 trial averages of firing rates or when computing inter-spike intervals. Note that all of our 939 neurons were not microsaccade-related in the sense of emitting a motor burst at movement 940 onset; they, therefore, did not exhibit prolonged buildup of discharge up to 100 ms before 941 microsaccade onset 59,60 . This justified our choice of pre-microsaccadic mask interval (also 942 see Fig. S5A). 943 944 For summarizing population firing rates (e.g. Fig. 3A), we first calculated the within-neuron 945 average firing rate across trial repetitions of a given spatial frequency in the control 946 1107 1108 1109 Figure S4 Validating the retinal image stabilization technique by forcing a grating position at a sub-optimal RF 1110 position (away from RF center). The schematic shows the experimental manipulation that we applied for this 1111 neuron. We presented a grating stimulus displaced away from the preferred RF location indicated by the dashed 1112 yellow circle. Therefore, the stimulus was near the RF, but at a sub-optimal position. Forcing this position during 1113 retinal image stabilization significantly reduced the sustained response of the neuron. This is the complement of 1114 the example neuron results shown in Fig. 2, in which forcing a stimulus at the best receptive field location 1115 elevated the neural response relative to control.