Ocular-following responses to broadband visual stimuli of varying motion coherence

Abstract

Manipulations of the strength of visual motion coherence have been widely used to study behavioral and neural mechanisms of visual motion processing. Here, we used a novel broadband visual stimulus to test how the strength of motion coherence in different spatial frequency (SF) bands impacts human ocular-following responses (OFRs). Synthesized broadband stimuli were used: a sum of one-dimensional vertical sine-wave gratings (SWs) whose SFs ranged from 0.0625 to 4 cpd in 0.05-log₂(cpd) steps. Every 20 ms a proportion of SWs (from 25% to 100%) shifted in the same direction by ¼ of their respective wavelengths (drifting), whereas the rest of the SWs were assigned a random phase (flicker), shifted by half of their respective wavelengths (counterphase), or remained stationary (static): 25% to 100% motion coherence. As expected, the magnitude of the OFRs decreased as the proportion of non-drifting SWs and/or their contrast increased. The effects, however, were SF dependent. For flicker and static SWs, SFs in the range of 0.3 to 0.6 cpd were the most disruptive, whereas, with counterphase SWs, low SFs were the most disruptive. The data were well fit by a model that combined an excitatory drive determined by a SF-weighted sum of drifting components scaled by a SF-weighted contrast normalization term. Flicker, counterphase, or static SWs did not add to or directly impede the drive in the model, but they contributed to the contrast normalization process.

Introduction

Manipulations of the strength of visual motion coherence have been widely used to study behavioral mechanisms (e.g., perception, eye movements) (Behling & Lisberger, 2020; Narasimhan & Giaschi, 2012; Pilly & Seitz, 2009; Scase, Braddick, & Raymond, 1996; Schutz, Braun, Movshon, & Gegenfurtner, 2010; Wei, Mitchell, & Maunsell, 2023) and neural mechanisms (e.g., middle temporal, medial superior temporal, lateral intraparietal areas) (Behling & Lisberger, 2023; Britten, Shadlen, Newsome, & Movshon, 1992; Britten, Shadlen, Newsome, & Movshon, 1993; Heuer & Britten, 2007; Law & Gold, 2008; Newsome & Pare, 1988; Salzman, Murasugi, Britten, & Newsome, 1992; Shadlen & Newsome, 2001) of visual motion processing. However, it is unclear which spatial frequency (SF) components of broadband stimuli are most responsible for these effects. Most studies have employed one-dimensional (1D; e.g., barcode) and/or two-dimensional (2D; e.g., random dots) broadband patterns, in which motion coherence was reduced by introducing random flicker throughout the SF space. Additionally, because visual stimulation is delivered using cathode-ray tube (CRT) and liquid-crystal display (LCD) monitors and thus inevitably involves apparent motion stimuli (i.e., discrete image steps), for a given speed of motion, high SFs often move with temporal frequencies that exceed the temporal Nyquist limit of the display, introducing spatial aliasing. As the speed of motion increases, more and more SFs are affected, further complicating the interpretation of the differences in behavioral or neuronal responses. 

Here, we introduce a novel synthesized broadband visual stimulus that is free of spatial aliasing and that makes it possible to selectively change motion coherence in isolated SF bands across a wide SF range. We presented this stimulus to human subjects while recording their ocular-following responses (OFRs), a short-latency tracking eye movement whose characteristics provide a behavioral signature of neuronal mechanisms operating at early stages of visual processing (for reviews, see Masson & Perrinet, 2012; Miles, 1998; Miles & Sheliga, 2010). 

Because our goal was to quantify how the motion signal generated by drifting stimuli is affected by the presence of non-drifting (namely, flickering, counterphase, or static) stimuli, we synthesized broadband visual stimuli by summing 1D vertical sine-wave gratings (SWs; range, 0.0625–4 cycles per degree [cpd]), some of which were then shifted by ¼ of their respective wavelengths (drifting SWs), whereas the rest underwent either random flicker (Experiments 1–3) or counterphase flicker (Experiments 4 and 5) or remained stationary (Experiments 6 and 7). We systematically varied the proportion of SWs that drifted (motion coherence), as well as the contrasts of drifting and non-drifting SWs, which allowed us to study how the OFRs varied as a function of the relative power of drifting and non-drifting components. Furthermore, by changing which SWs drifted and which did not, we were able to investigate the spatial frequency dependency of each mechanism. The results of all experiments were well fit by a model (Sheliga & FitzGibbon, 2024) that combined an excitatory drive determined by a SF-weighted sum of drifting components scaled by a SF-weighted contrast normalization term that included contributions of both drifting and non-drifting SWs. Preliminary results of this study were presented in abstract form elsewhere (Sheliga, FitzGibbon, Quaia, & Krauzlis, 2024). 

Methods

Many of the techniques will be described only briefly, as they were similar to those used in this laboratory in the past (e.g., Sheliga, Chen, FitzGibbon, & Miles, 2005). Experimental protocols were approved by the Institutional Review Committee concerned with the use of human subjects. Our research was carried out in accordance with the tenets of the Declaration of Helsinki, and informed consent was obtained for experimentation with human subjects. 

Subjects

Three subjects took part in this study: two were authors (BMS and EJF) and the third was a paid volunteer (JC) naïve as to the purpose of the experiments. All subjects had normal or corrected-to-normal vision. Viewing was binocular. 

Eye-movement recording

The horizontal and vertical positions of the right eye were recorded (sampled at 1 KHz) with an electromagnetic induction technique (Robinson, 1963). A scleral search coil embedded in a silastin ring (Collewijn, Van Der Mark, & Jansen, 1975) was placed in the right eye under topical anesthesia, as described by Yang, FitzGibbon, and Miles (2003). At the beginning of each recording session, a coil calibration procedure was performed using fixation targets monocularly viewed by the right eye. 

Visual display and stimuli

Dichoptic stimuli were presented using a Wheatstone mirror stereoscope. In a darkened room, each eye saw a computer monitor (HP p1230 21-inch CRT; HP Inc., Palo Alto, CA) through a 45° mirror, creating a binocular image 521 mm straight ahead from the eyes’ corneal vertices, which was also the optical distance to the images on the two monitor screens. Thus, the stereoscope was set up for equal vergence and accommodation demand. Each monitor was driven by an independent PC (Dell Precision 490; Dell Technologies, Round Rock, TX), but the outputs of the video card of each computer (Quadro FX 5600; NVIDIA, Santa Clara, CA) were frame-locked via NVIDIA Quadro G-Sync cards. The monitor screens were each 41.8° wide and 32.0° high with 1024 × 768-pixel resolution (i.e., 23.4 pixels per degree directly ahead of each eye), and the two were synchronously refreshed at a rate of 150 Hz. Each monitor was driven via an attenuator (Pelli, 1997) and a video signal splitter (AC085A-R2; Black Box Corporation, Lawrence, PA), allowing the presentation of black and white images with an 11-bit equidistant grayscale resolution (mean luminance of 20.8 cd/m²). Visual stimuli were seen through an ∼22° × ∼22° (512 × 512 pixels) square aperture centered directly in front of the eyes. The stimuli seen by the two eyes were always the same; we were not sure if we would need binocular manipulations to understand these responses and so opted to use the stereoscope at the outset of the project. 

Synthesized broadband stimuli were used: a sum of 1D vertical SWs whose SFs ranged from 0.0625 to 4 cpd in 0.05-log₂(cpd) steps (121 SWs in total). Every 20 ms (three video frames) a proportion of SWs (from 25% to 100%) shifted in the same direction by ¼ of their respective wavelengths (drifting; 12.5 Hz), whereas other SWs were assigned a random phase (flicker), were shifted by half of their respective wavelengths (counterphase), or remained stationary (static), representing 25% to 100% motion coherence. The SF arrangement of drifting versus non-drifting SWs is illustrated in Figure 1A. For the 75% coherent stimulus, for example, shown in the second row, three of four neighboring SWs shifted in the same direction by ¼ of their respective wavelengths (marked 1), whereas the fourth SW did not shift, undergoing flicker or counterphase or remaining stationary (marked 2). On the other hand, for the 33% coherent stimulus, shown in the fifth row, two of three SW neighbors underwent flicker or counterphase or remained stationary (marked 2), whereas the third SW shifted by ¼ of its wavelength (marked 1). 

Figure 1.

 

(A) Stimulus synthesis. SW components were equidistantly spaced in log SF space (0.05 log₂ units). Values of 1 indicate drifting SW components—that is, those whose phase was shifted by ¼ of their respective wavelengths every 20 ms (12.5Hz). Values of 2 indicate non-drifting SW components—that is, those that were assigned a random phase (flicker; in Experiments 1 to 3), shifted by half of their respective wavelengths (counterphase; in Experiments 4 and 5), or remained stationary (static; in Experiments 6 and 7). (B) Sample 1D synthesized patterns shown in two successive video frames. (C) The log-Gaussian envelopes of bandpass filters applied to flicker, counterphase, and static SW components of stimuli. Two samples of 1- and 2-octave FWHM filters are shown for which the central SF was 0.5 cpd. (D) Experiment 1. Mean eye velocity profiles over time to 100% motion coherence stimuli (black dashed and dotted traces) and 50% motion coherence stimuli. Each line is associated with a different RMS contrast of the flicker SW components (grayscale). For subject BMS, each trace is the mean response to 153 to 166 repetitions of the stimulus. The abscissa shows the time from the motion stimulus onset; the horizontal thin dotted line represents zero velocity; and the horizontal thick black line beneath the traces indicates the response measurement window.

Experiments 1 to 3 explored the impact of SW components that underwent random flicker, Experiments 4 and 5 explored the impact of SW components that underwent counterphase flicker, and Experiments 6 and 7 explored the impact of static SW components. To better constrain the model (presented later) and to make certain that it provided a good fit to pure SWs, we ran Experiment 8, which investigated the OFR SF tuning for horizontally drifting single 1D vertical SWs. 

Experiment 1

In Experiment 1, 50% coherent stimuli were used (i.e., 1212 … in the convention depicted in Figure 1A). Half of the SWs shifted in the same direction by ¼ of their respective wavelengths, whereas the remaining half of SWs were assigned a random phase (flicker). Each SW was assigned an root mean square (RMS) contrast value, according to the following formula:  

\begin{eqnarray} RMS = \frac{{\sqrt {\frac{{\sum_{i = 1}^N {{{\left( {Lu{m_i} - Lu{m_{mean}}} \right)}^2}} }}{N}} }}{{Lu{m_{mean}}}} \quad \end{eqnarray}

(1)

using actual pixel luminance values (Lum).¹ The drifting SWs were all assigned the same contrast, selected from three values: 0.57%, 1.13%, or 2.26%.² The flicker SWs were also all assigned the same contrast values but were selected from five contrast values: 0.57%, 0.80%, 1.13%, 1.60%, or 2.26% (the equivalent Michelson contrasts are 0.8%, 1.13%, 1.6%, 2.26%, or 3.2%). We also tested 100% coherent stimuli: 1111…, in which all 121 SWs shifted in the same direction by ¼ of their respective wavelengths, and 1010…, in which flicker SWs of 50% coherence stimuli were omitted (i.e., 61 SWs in total). The overall (i.e., including both drifting and flickering SWs) stimulus RMS contrast ranged from 4.3% to 24.7%. Figure 1B shows an example of a rightward phase shift of a 50% coherent stimulus. Note that the appearance of the stimulus changes following such a shift (compare left and right panels of Figure 1B). A single block of trials had 42 or 28 (subject JC) randomly interleaved stimuli: three or two (subject JC) contrasts of drifting SWs, five contrasts of flicker SWs, three or two (subject JC) contrasts of control 100% coherent stimuli, and two directions of the phase shift of drifting SWs (forward or backward). 

Experiment 2

In Experiment 2, 25%, 33%, 67%, and 75% coherent stimuli were used. Non-drifting SWs were assigned a random phase (flicker). The RMS contrast of drifting SWs was set to 1.13%. The RMS contrast of flicker SWs was set to 0.57%, 0.80%, 1.13%, 1.60%, or 2.26%. For control, 100% coherent stimuli were also included which were produced by omitting flicker SWs in less than 100% coherent stimuli. The overall stimulus RMS contrasts ranged from 6.1% to 22.3%. A block of trials had 50 randomly interleaved stimuli: four levels of motion coherence, five contrasts of flicker SWs, four control 100% coherent stimuli, two directions of the phase shift of drifting SWs, plus leftward and rightward drifting 1111…, with 100% coherent stimuli from Experiment 1 serving as a common condition for the OFR amplitude normalization between Experiments 1 and 2. 

Experiment 3

Based on the amplitudes of the OFRs recorded to stimuli in Experiment 2, for each subject we picked two stimuli—a combination of motion coherence and RMS contrasts of drifting and flicker SWs—that produced OFRs with notable amplitude differences. For each subject, the values of motion coherence and contrast are shown in insets in panels of Figure 4 (M, drifting SW contrast; F, flicker SWs contrast; Coh, motion coherence). These picked stimuli were then filtered using a bandpass filter with a Gaussian envelope on a log SF scale. The filtering was applied to flicker SWs only, whereas all drifting SWs retained the original contrast. The central SF of the filter varied from 0.125 to 2 cpd in half-octave increments. All subjects ran an experiment in which the full width at half maximum (FWHM) of the filter was 1 octave, but subject BMS also ran an experiment in which the FWHM was 2 octaves. Examples of 1- and 2-octave filters (0.5-cpd central SF) are shown in Figure 1C. A block of trials had 38 randomly interleaved stimuli: two contrast/coherence combinations, nine central SFs of the filter, two directions of the phase shift of drifting SWs, plus leftward and rightward drifting 1111… 100% coherent stimuli from Experiment 1 which were used for amplitude normalization between Experiments 1 and 3. 

Experiment 4

For Experiment 4, 25%, 33%, 50% (subject BMS only), 67% (subject BMS only), and 75% coherent stimuli were used. Non-drifting SWs shifted by half of their respective wavelengths (counterphase). The RMS contrast of drifting SWs was set to 1.13% or 0.57% (subject BMS). The RMS contrasts of counterphase SWs were set to 0.57%, 0.80%, 1.13%, 1.60%, or 2.26%. The overall stimulus RMS contrasts ranged from 3.1% to 21.9%. A block of trials had 32 or 52 (subject BMS) randomly interleaved stimuli: three or five (subject BMS) levels of motion coherence, five contrasts of counterphase SWs, two directions of the phase shift of drifting SWs, plus leftward and rightward drifting 1111… 100% coherent stimuli from Experiment 1 which were used for amplitude normalization between Experiments 1 and 4. 

Experiment 5

Based on the amplitudes of the OFRs recorded to stimuli in Experiment 4, we picked one or two (subject BMS) stimuli: a combination of motion coherence and RMS contrasts of drifting and counterphase SWs. The values of motion coherence and contrast used are shown in insets to panels of Figure 6 (M and C, drifting SW and counterphase SW contrasts, respectively; Coh, motion coherence). The stimuli were then filtered using a bandpass filter that was Gaussian on a log SF scale. The filtering was applied to counterphase SWs only, whereas all drifting SWs retained the original contrast. The central SF of the filter varied from 0.125 to 2 cpd in half-octave increments; the FWHM was 1 octave. A block of trials had 20 or 38 (subject BMS) randomly interleaved stimuli: one or two (subject BMS) contrast/coherence combinations, nine central SFs of the filter, two directions of the phase shift of drifting SWs, plus leftward and rightward drifting 1111… 100% coherent stimuli from Experiment 1 which were used for amplitude normalization between Experiments 1 and 5. 

Experiment 6

For Experiment 6, 25%, 33%, 50% (subject BMS only), 67% (subject BMS only), and 75% coherent stimuli were used. Non-drifting SWs remained stationary. The RMS contrast of drifting SWs was set to 1.13%. The RMS contrasts of static SWs were set to 0.57%, 0.80%, 1.13%, 1.60%, or 2.26%. The overall stimulus RMS contrasts ranged from 6.2% to 22.4%. A block of trials had 32 or 52 (subject BMS) randomly interleaved stimuli: three or five (subject BMS) levels of motion coherence, five contrasts of flicker SWs, two directions of the phase shift of drifting SWs, plus leftward and rightward drifting 1111… 100% coherent stimuli from Experiment 1 which were used for amplitude normalization between Experiments 1 and 6. 

Experiment 7

Based on the amplitudes of the OFRs to stimuli that were recorded in Experiment 6, we picked one or two (subject BMS) stimuli: a combination of motion coherence and RMS contrasts of drifting and static SWs. The values of motion coherence and contrast that were used are shown in insets to panels of Figure 8 (M and S, drifting SWs and static SWs contrasts, respectively; Coh, motion coherence). The stimuli were then filtered using a bandpass filter that was Gaussian on a log SF scale. The filtering was applied to static SWs only, whereas all drifting SWs retained the original contrast. The central SFs of the filter varied from 0.125 to 2 cpd in half-octave increments; the FWHM was 1 octave. A block of trials had 20 or 38 (subject BMS) randomly interleaved stimuli: one or two (subject BMS) contrast/coherence combinations, nine central SFs of the filter, two directions of the phase shift of drifting SWs, plus leftward and rightward drifting 1111… 100% coherent stimuli from Experiment 1 which were used for amplitude normalization between Experiments 1 and 7. 

Experiment 8

Horizontally drifting 1D vertical SWs had five or six (subject BMS) different SFs (range, 0.0625–1 cpd or 0.0625–2 in octave increments) and three different RMS contrasts (2.8%, 5.6%, and 11.3%; corresponding to 4%, 8%, and 16% Michelson contrast). Gratings shifted ¼ wavelength every 20 ms (i.e., 12.5-Hz temporal frequency [TF]). A block of trials had 32 or 38 (subject BMS) randomly interleaved stimuli: five or six (subject BMS) SFs, three contrasts, two phase shift directions, plus leftward and rightward drifting 1111… 100% coherent stimuli from Experiment 1 which were used for amplitude normalization between Experiments 1 and 8. 

Procedures

Experimental paradigms were controlled by three PCs, which communicated via Ethernet (TCP/IP protocol). The first PC utilized real-time experimentation (Rex) software (Hays, Richmond, & Optican, 1982), which provided the overall control of the experimental protocol, acquisition, display, and storage of the eye-movement data. Two other PCs utilized the Psychophysics Toolbox extensions of MATLAB (MathWorks, Natick, MA) (Brainard, 1997; Pelli, 1997) and generated the visual stimuli. 

At the start of each trial a central fixation target (diameter 0.25°) appeared at the center of the otherwise uniform gray (luminance, 20.8 cd/m²) screen. To proceed, the subject's eye had to be continuously positioned within 2° of the fixation target for a randomized period of 600 to 1000 ms. The fixation target was then replaced by the first image of a stimulus sequence randomly selected from a look-up table, and three video frames (i.e., 20 ms) later motion commenced. In 200 ms, the screen turned to uniform gray (luminance, 20.8 cd/m²), marking the end of the trial and the start of an intertrial interval. The subjects were asked to refrain from blinking or shifting fixation except during the intertrial intervals but were given no instructions relating to the stimuli presented. A new fixation target appeared after a 500-ms intertrial interval, signaling a new trial. If no saccades were detected (using an eye velocity threshold of 18°/s) for the duration of the trial, then the data were stored; otherwise, the trial was aborted and repeated within the same block. Data collection occurred over several sessions until each condition had been repeated an adequate number of times to permit good resolution of the responses (through averaging); the exact number of trials per condition is indicated in the legends of all figures that show experimental data. 

Data analysis

The calibration procedure provided eye position data fitted with second-order polynomials and later used to linearize the horizontal eye position data recorded during the experiment. Eye-position signals were then smoothed with an acausal sixth-order Butterworth filter (3 dB at 30 Hz), and mean temporal profiles were computed for each stimulus condition. Trials with microsaccadic intrusions (that had failed to reach the eye velocity cut-off of 18°/s used during the experiment) were deleted. We utilized position difference measures to minimize the impact of directional asymmetries and boost the signal-to-noise ratio: the mean horizontal eye position with each leftward motion stimulus was subtracted from the mean horizontal eye position with the corresponding rightward motion stimulus. As rightward eye movements were positive in our sign convention, OFRs in the direction of stimulus motion resulted in positive pooled measures. Mean eye velocity was estimated by subtracting position difference measures 10 ms apart (central difference method) and evaluated every millisecond. Response latency was estimated by determining the time elapsed since the appearance of the second stimulus frame (i.e., the first one in which phases of drifting SWs shifted) to when the mean eye velocity first exceeded 0.1°/s. The initial OFRs to a given stimulus were quantified by measuring the changes in the mean horizontal eye position signals (OFR amplitude) over the initial open-loop period (i.e., over the period up to twice the minimum response latency). This window always commenced at the same time after the appearance of the second stimulus frame (stimulus-locked measures) and, for a given subject, was the same in all experiments (64–128 ms for BMS, 73–146 ms for EJF, and 62–124 ms for JC). Bootstrapping was used for statistical data evaluation and to construct 68% confidence intervals of the mean in the figures (these intervals were smaller than the symbol size in many cases and, therefore, not visible on many graphs). 

Results

Experiments 1 to 3 explored the impact of random flicker SW components. The contrasts of drifting and flickering SWs were manipulated in Experiment 1. Experiment 2 manipulated the motion coherence level. In Experiment 3 the random flicker was bandpass filtered to identify the SF components that were primarily responsible for the effect of random flicker on the OFRs. 

Experiment 1

Figure 1D shows examples of mean eye velocity profiles in response to 100% (dashed and dotted black traces) and 50% (grayscale coding of velocity traces) motion coherence stimuli for subject BMS. With 100% motion coherence stimuli, removing half of the SWs (i.e., 1010… stimuli; 61 SWs in total) had a marginal effect, as the dashed and dotted black traces lie very close to each other. However, the presence of flicker SWs resulted in much weaker responses: the higher the contrast of flicker SWs, the lower the velocities of recorded OFRs. These effects are quantified in Figure 2, which shows changes in the OFR amplitudes. Figures 2A to 2C plot the amplitudes for 100% motion coherence stimuli in three subjects. In Figure 2 and subsequent figures, the symbols show the actual data points, whereas the lines represent model fits (introduced and described later in the text; see Model section). As seen in the Figure 1D example traces, removing half of drifting SWs did not have much of an effect. In all three subjects, filled black (1111… stimulus) and open gray (1010… stimulus) circles largely overlapped for three different contrasts of drifting SWs. A fourfold increase in the contrast of drifting SWs had modest (and idiosyncratic) effects on the OFR amplitudes; the OFRs of subject BMS did show an increase with drifting SW contrast, but the other two subjects exhibited no clear dependence. On the other hand, 50% motion coherence stimuli produced OFRs that showed clear dependence on the contrast of both flickering and drifting SWs (Figures 2D to 2F): (a) for any given contrast of drifting SWs, higher contrasts of flickering SWs resulted in weaker OFRs; and (b) for any given contrast of flickering SWs, higher contrasts of drifting SWs resulted in stronger OFRs. 

Figure 2.

 

Experiment 1. Symbols indicate data, and lines indicate Equation 2 fits. (A–C) Dependence of mean OFR amplitude on the contrast of drifting SW components for three subjects, with 100% motion coherence stimuli, 61 SW components (gray), and 121 SW components (black). (D–F) Dependence of mean OFR amplitude on the contrast of flicker SW components for three subjects for stimuli whose drifting components had one of three different contrasts (symbol- and color-coded). All stimuli had 50% motion coherence (i.e., half of the spectral components drifted and half flickered). Each column has data from a different subject: subject BMS (153–166 trials per condition), subject EJF (75–95 trials per condition), and subject JC (141–151 trials per condition).

Experiment 2

In this experiment, 25%, 33%, 67%, and 75% motion coherence stimuli were tested. The remaining (i.e., 75%, 67%, 33%, and 25%, respectively) non-drifting SWs underwent a random phase change (flicker). Figure 3A shows examples of mean eye velocity profiles of subject EJF in response to stimuli of different motion coherence for cases when contrasts of drifting and flickering components were the same (1.13%)—that is, pure motion coherence effects: lowering motion coherence weakened the OFRs. Figures 3B to 3D clearly show that the OFR amplitudes depended on both the contrast of flickering SWs and motion coherence: (a) for a given motion coherence level, higher flicker contrasts resulted in weaker OFRs; and (b) for a given flicker contrast, higher motion coherence resulted in stronger OFRs. As a control, 100% motion-coherent stimuli were constructed by omitting all SWs that would flicker in the 25%, 33%, 50%, 67%, and 75% motion coherence stimuli. The OFRs to such stimuli are plotted in Figures 3E to 3G as a function of the number of drifting SWs in the stimulus: 31, 41, 61, 81, or 91. Despite a threefold difference in the number of summed SWs, the OFR changes in three subjects were minor and idiosyncratic, emphasizing the importance of flickering SWs in reducing the amplitude of the OFRs to stimuli of less than 100% motion coherence. To understand how different SF components of broadband stimuli might contribute to these results, we next confined the flickering components to limited SF bands. 

Figure 3.

 

Experiment 2. Symbols indicate data, and lines indicate Equation 2 fits. (A) Mean eye velocity profiles over time to stimuli of different motion coherence. In all cases, the contrast of drifting and flicker components was 1.13%. For subject EJF, each trace is the mean response to 82 to 116 repetitions of the stimulus. The abscissa shows the time from the motion stimulus onset, the horizontal thin dotted line represents zero velocity, and the horizontal thick black line beneath the traces indicates the response measurement window. (B–D) Dependence of mean OFR amplitude on the contrast of flicker SW components for different motion coherence stimuli (symbol- and color-coded). The 50% coherence data (red diamonds) are replotted from Figure 2. (E–G) Dependence of mean OFR amplitude on the number of drifting SW components in 100% motion coherence stimuli. Stimuli were constructed by omitting all flicker SWs in 25%, 33%, 50%, 67%, and 75% motion coherence stimuli; subject BMS (146–154 trials per condition), subject EJF (89–119 trials per condition), and subject JC (117–134 trials per condition). For each subject, two stimuli picked for Experiment 3 are shown as an open green circle and open orange square.

Experiment 3

For each subject, based on the amplitudes of the OFRs recorded to stimuli in Experiment 2, we picked two stimuli—combinations of motion coherence and RMS contrasts of drifting and flickering SWs—which produced OFRs with notable amplitude differences. In Figure 3, those are shown for each subject as an open green circle and open orange square. The numerical values of motion coherence and contrast are also listed in an inset in Figure 4 (M, drifting SW contrast; F, flickering SW contrast; Coh, motion coherence). A bandpass filter (1-octave FWHM Gaussian on a log SF scale) was then applied to flickering SWs of these stimuli, whereas drifting SWs retained the original contrast. The OFR amplitudes are shown in Figures 4A to 4C as a function of the central SF of the filter. Open and filled symbols plot OFRs to each one of two picked stimuli. The effects were SF dependent; flicker at intermediate SFs (0.3–0.6 cpd) was most disruptive, resulting in the lowest OFR amplitudes. Figure 4D shows additional data from subject BMS with a 2-octave FWHM filter with a very similar pattern of amplitude changes. 

Figure 4.

 

Experiment 3. Symbols indicate data, and lines indicate Equation 2 fits. Dependence of mean OFR amplitude on the central SF of the filter applied to flicker SW components. (A–C) One-octave FWHM filter in three subjects: subject BMS (167–189 trials per condition), subject EJF (116–134 trials per condition), and subject JC (106–127 trials per condition). (D) Two-octave FWHM filter in subject BMS. For each subject, two stimuli from Experiment 2 were picked (filled and open black circles). The numerical values of their motion coherence and contrast are listed in an inset, where M represents motion contrast; F, flicker contrast; and Coh, motion coherence.

Having investigated the effect of flickering components, we then turned to non-drifting SW components of a different nature: counterphase (i.e., 180°) phase shifts (Experiments 4 and 5) and static SWs (Experiments 6 and 7). Experiments 4 and 6 manipulated the motion coherence level. In Experiments 5 and 7 the non-drifting components were confined to isolated SF bands. 

Experiment 4

In Experiment 4, 25%, 33%, and 75% (also 50% and 67% in subject BMS) motion coherence stimuli were tested. The remaining non-drifting SWs underwent a counterphase shift. Figure 5 shows that the OFR amplitudes depended on both counterphase SW contrast and motion coherence. The overall pattern indicates that, for a given motion coherence level, higher counterphase contrasts tended to induce weaker OFRs, and, for a given counterphase contrast, higher motion coherence tended to induce stronger OFRs, with the effects saturating at the extremes. 

Figure 5.

 

Experiment 4. Symbols indicate data, and lines indicate Equation 2 fits. (A–C) Dependence of mean OFR amplitude on the contrast of counterphase SW components for stimuli of different motion coherence (symbol- and color-coded) for three subjects: subject BMS (132–141 trials per condition), subject EJF (139–162 trials per condition), and subject JC (117–130 trials per condition). Stimuli picked for Experiment 5 are shown as an open green circle and open orange square.

Experiment 5

For each subject, we picked one or two (subject BMS) stimuli from Experiment 4. Those are shown in Figure 5 as an open orange square and open green circle (subject BMS). The numerical values of motion coherence and contrast are also listed in an inset in Figure 6. A bandpass filter (1-octave FWHM Gaussian on a log SF scale) was applied to counterphase SWs of these stimuli, whereas drifting SWs retained the original contrast. Figures 6A to 6C show OFR amplitudes as a function of the central SF of the filter. The effects were SF dependent, although the dependence was different from that observed in Experiment 3, as the OFR amplitudes declined for lower central SFs of the filter. 

Figure 6.

 

Experiment 5. Symbols indicate data, and lines indicate Equation 2 fits. (A–C) Dependence of mean OFR amplitude on the central SF of the filter applied to counterphase SW components in three subjects: subject BMS (174–186 trials per condition), subject EJF (158–176 trials per condition), and subject JC (152–166 trials per condition). One or two (subject SMS) stimuli from Experiment 4 were picked (filled and open black circles). The numerical values of their motion coherence and contrast are listed in an inset, where M indicates motion contrast; C, counterphase contrast; and Coh, motion coherence.

Experiment 6

For Experiment 6, 25%, 33%, and 75% (also 50% and 67% in subject BMS) motion coherence stimuli were tested. The remaining non-drifting SWs remained stationary. Figure 7 shows that the OFR amplitudes depended on both static SWs contrast and motion coherence. For any given motion coherence level, higher contrast of static SWs resulted in weaker OFRs, and, for any given contrast of static SWs, higher motion coherences resulted in stronger OFRs. 

Figure 7.

 

Experiment 6. Symbols indicate data, and lines indicate Equation 2 fits. (A–C) Dependence of mean OFR amplitude on the contrast of static SW components for different motion coherence stimuli (symbol- and color-coded) for three subjects: subject BMS (146–154 trials per condition), subject EJF (120–141 trials per condition), and subject JC (126–144 trials per condition). Stimuli picked for Experiment 7 are shown as an open green circle and open orange square.

Experiment 7

For each subject, we picked one or two (subject BMS) stimuli from Experiment 6. These are shown in Figure 7 as an open orange square and open green circle (subject BMS). The numerical values of motion coherence and contrast are also listed in an inset in Figure 8. A bandpass filter (1-octave FWHM Gaussian on a log SF scale) was applied to static SWs of these stimuli, whereas drifting SWs retained the original contrast. Figures 8A to 8C show OFR amplitudes as a function of the central SF of the filter. The dependencies were like the ones observed in Experiment 3 with flicker SWs, as static SWs at intermediate SFs (0.3–0.6 cpd) were the most disruptive, resulting in the lowest OFR amplitudes. 

Figure 8.

 

Experiment 7. Symbols indicate data, and lines indicate Equation 2 fits. (A–C) Dependence of mean OFR amplitude on the central SF of the filter applied to static SW components in three subjects: subject BMS (166–178 trials per condition), subject EJF (152–173 trials per condition), and subject JC (103–121 trials per condition). One or two (subject SMS) stimuli from Experiment 6 were picked (filled and open black circles). The numerical values of their motion coherence and contrast are listed in an inset, where M indicates motion contrast; C, counterphase contrast; and Coh, motion coherence.

Model

The data of Experiments 1 to 7 were fit by the following equation:  

{\begin{eqnarray} && \textit{OFR} = \frac{{{C^n}}}{{{C^n} + C_{50}^n}} \nonumber \\ && {*}\;\frac{{{{\left( \mathop \sum \nolimits_{i = 1}^{{N_{( M )}}} {{\left[ {OF{R_i}\;{\rm{*}}\;{{\left( {{W_{i( M )}}{\rm{*}}{C_{i( M )}}} \right)}^k}} \right]}^m} \right)}^{\frac{1}{m}}}}} {\begin{array}{l} \mathop \sum \nolimits_{i = 1}^{N_{( M )}} \left(W_{i( M )}\;{\rm{*}}\;C_{i( M )} \right)^k+ \mathop \sum \nolimits_{j = 1}^{N_{(F,C,{\rm{\ or\ }}S)}} \left(W_{j(F,C,{\rm{\ or\; }}S)}\;{\rm{*}}\;C_{j(F,C,{\rm{\ or\;}}S )} \right)^k\end{array}}\!\!\nonumber\\ \end{eqnarray}}

(2)

 

which is reminiscent of a model proposed earlier to account for the short-latency eye movements to motion and disparity of broadband visual stimuli (Sheliga & FitzGibbon, 2023; Sheliga & FitzGibbon, 2024; Sheliga, Quaia, FitzGibbon, & Cumming, 2022), but contains extra terms in the denominator (F, C, or S) to account for a contribution of flicker, counterphase, and static SWs. In the model, these additional terms neither add to nor impede the eye movement drive, but instead contribute to the global contrast normalization process. Drifting SW components, on the other hand, provide the drive as well as contribute to the contrast normalization, labeled (M). 

OFR_i is the response to a given SW component, derived from the log-Gaussian fit to the OFR SF tuning:  

\begin{eqnarray} OFR ( {S{F_i}} ) = {\lambda _{SF}}\;{\rm{*}}\;{{\rm{e}}^{ - \frac{{{{\left[ {{\rm{lo}}{{\rm{g}}_2}( {S{F_i}} ) - {\rm{lo}}{{\rm{g}}_2}( {{{\rm{\mu }}_{SF}}})} \right]}^2}}}{{2\;{*}\;{\rm{\sigma }}_{{\rm{SF}}}^2}}}} \quad \end{eqnarray}

(3)

where SF_i is a spatial frequency of this SW component, and λ_SF, μ_SF, and σ_SF are the first three free parameters of the model. OFR_i is multiplied by the contrast of that component in the image, C_i(M), and its weight, W_i(M), normalized by the weighted sum of the contributions of all SW components present in the stimulus, which include not only drifting SWs but also flicker SWs (C_j(F) and W_j(F); see Experiments 1 to 3), counterphase SWs (C_j(C) and W_j(C); see Experiments 4 and 5), and static SWs (C_j(S) and W_j(S); see Experiments 6 and 7). Each SW component contribution is raised to the power k, the fourth free parameter of the model. A competition between contributions of the components is modeled by a power-law summation, m being the fifth free parameter. C is the overall RMS stimulus contrast. Inverted cumulative Gaussian functions of log SF were used to model the weights of drifting (W_M) and counterphase (W_C) SW components. An inspection of shapes of the dependencies in Figure 6 and our recent modeling data for motion of white noise visual patterns (Sheliga & FitzGibbon, 2024) suggested that the weight functions for drifting and counterphase components might be similar. We, thus, constrained the offsets and sigmas of the weight functions for drifting and counterphase components to be the same (μ_MC and σ_MC, respectively):  

\begin{eqnarray} && {W_M}( {S{F_i}} ) = 1 - \frac{1}{2} {\rm{*}}\left[ {1 + erf\left( {\frac{{{\rm{lo}}{{\rm{g}}_2}( {S{F_i}} ) - {\rm{lo}}{{\rm{g}}_2} ( {{{\rm{\mu }}_{MC}}} )}}{{sqrt( 2 )\;{\rm{*}}\;{{\rm{\sigma }}_{MC}}}}} \right)} \right] \qquad \end{eqnarray}

(4a)

 

\begin{eqnarray} && {W_C}( {S{F_j}} ) = {{\rm{\lambda }}_C}{\rm{*}} \left\{ {1 - \frac{1}{2}\;{\rm{*}}\;\left[ {1 + erf\left( {\frac{{{\rm{lo}}{{\rm{g}}_2}\left( {S{F_i}} \right) - {\rm{lo}}{{\rm{g}}_2} ( {{{\rm{\mu }}_{MC}}} )}}{{sqrt( 2 )\;{\rm{*}}\;{{\rm{\sigma }}_{MC}}}}} \right)} \right]} \right\} \quad \end{eqnarray}

(4b)

 

The W_M function lacks a scaling free parameter (it is set to 1), because W_M appears in both the numerator and the denominator of Equation 2 and, thus, is canceled out. This is not the case for W_C, which is present only in the denominator, hence an additional free parameter, λ_C, in Equation 4b. Thus, μ_MC, σ_MC, and λ_C are the sixth, seventh, and eighth free parameters of the model. A Gaussian function of log SF was used to model the weights of flicker (W_F) and static (W_S) SW components. An inspection and comparison of shapes of the dependencies in Figure 4 and Figure 8 suggested that the weight functions for flicker and static SWs might be very similar. We, thus, constrained the offsets and sigmas of Gaussian weight functions for flicker and static SWs to be the same (μ_FS and σ_FS, respectively):  

\begin{eqnarray}{W_F}\left( {S{F_j}} \right) = {{\rm{\lambda }}_F}\;{\rm{*}}\;{e^{ - \frac{{{{\left[ {{\rm{lo}}{{\rm{g}}_2}\left( {S{F_j}} \right) - {\rm{lo}}{{\rm{g}}_2}\left( {{\mu _{FS}}} \right)} \right]}^2}}}{{2\;{\rm{*}}\;\sigma _{FS}^2}}}} \quad \end{eqnarray}

(5a)

 

\begin{eqnarray}{W_S}\left( {S{F_j}} \right) = {{\rm{\lambda }}_S}\;{\rm{*}}\;{e^{ - \frac{{{{\left[ {{\rm{lo}}{{\rm{g}}_2}\left( {S{F_j}} \right) - {\rm{lo}}{{\rm{g}}_2}\left( {{{\rm{\mu }}_{FS}}} \right)} \right]}^2}}}{{2\;{\rm{*}}\;\sigma _{FS}^2}}}} \quad \end{eqnarray}

(5b)

where μ_FS, σ_FS, λ_F, and λ_S are the ninth, 10th, 11th, and 12th free parameters, respectively, of the model. C₅₀ and n are the last two, 13th and 14th, free parameters of the model. For pure SWs, Equation 2 would simplify to:  

\begin{eqnarray} OF{R_{SW}} = {{\rm{\lambda }}_{SW\left( {MAX} \right)}}\;{\rm{*}}\;\frac{{{C^n}}}{{{C^n} + C_{50}^n}} \quad \end{eqnarray}

(6)

which is the Naka–Rushton equation (Naka & Rushton, 1966), which has been used to describe OFR contrast dependencies to pure SW gratings in the past (Barthelemy, Perrinet, Castet, & Masson, 2008; Miura et al., 2006; Quaia, Optican, & Cumming, 2017; Quaia, Optican, & Cumming, 2018; Quaia, Sheliga, Fitzgibbon, & Optican, 2012; Sheliga et al., 2005; Sheliga, Quaia, FitzGibbon, & Cumming, 2013). Thus, C₅₀ and n are the Naka–Rushton semi-saturation contrast and power term, respectively; λ_SW(MAX) is the maximal attainable response for the sine wave of a given SF, calculated using Equation 3. To ensure that Equation 2 provided a good fit to pure drifting SW gratings, we ran Experiment 8, the OFR SF tuning for horizontally drifting 1D vertical SW gratings. The data are shown in Figure 9, in which the gratings of different contrast are color and symbol coded (see inset). We then fit the data of Experiments 1 to 7 and Experiment 8 using a single set of free parameters. 

Figure 9.

 

Experiment 8. Symbols indicate data, and lines indicate Equation 2 fits. (A–C) Dependence of mean OFR amplitude on SF of pure drifting SW gratings in three subjects: subject BMS (80–90 trials per condition), subject EJF (59–88 trials per condition), and subject JC (95–110 trials per condition). The data for gratings of different contrast are symbol and color coded (see rectangular inset).

Equation 2 provided very good fits to the data of Experiments 1 to 8: r² = 0.959, 0.945, and 0.931 for subjects BMS, EJF, and JC, respectively. Analyzing the values of the best-fit free parameters, we noticed that σ_SF, σ_MC, and σ_SF were quite similar, whereas λ_F and λ_S were close to 1. Constraining σ_SF, σ_MC, and σ_SF to be the same (σ_SF = σ_MC = σ_SF = σ) and equating λ_F and λ_S to 1 (λ_F = λ_S = 1) caused minimal deterioration of the fits (–0.3%, –0.1%, and –0.3% for subjects BMS, EJF, and JC, respectively). These fits (based on 10 free parameters) are shown in Figures 2 to 9. Figure 10 presents the OFR SF tuning functions (Figure 10A), normalized Naka–Rushton functions (Figure 10B), drifting and counterphase weight functions (Figure 10C), and flicker and static weight functions (Figure 10D) for the three subjects. Table 1 lists the best-fit values of free parameters. Though the best-fit values of m were close to 1, constraining m to equal 1 (i.e., assuming a linear summation) led to a statistically significant deterioration of fits in all subjects: p < 10^–9; F(1, 175) = 44.7, F(1, 116) = 143.2, and F(1, 109) = 107.8 for subjects BMS, EJF, and JC, respectively. Equating k to 1 resulted in a deterioration of fits in all subjects, as well: p < 10^–6; F(1, 175) = 244.5, F(1, 116) = 38.5, and F(1, 109) = 27.2 for subjects BMS, EJF, and JC, respectively. As Figure 10C and Table 1 (free parameter λ_C) show, counterphase SWs appear to have much smaller weights than drifting SWs. Indeed, equating λ_C to 1 resulted in a statistically significant deterioration of fits: p < 10^–15; F(1, 175) = 403.4, F(1, 116) = 152.3, and F(1, 109) = 93.7 for subjects BMS, EJF, and JC, respectively. 

Figure 10.

 

Model. (A) OFR SF tuning. (B) Normalized Naka–Rushton functions. (C) Drifting and counterphase weight functions. (D) Flicker and static weight functions. Functions for different subjects are color coded (see rectangular inset).

Table 1.

 

The best-fit values of Equation 2 free parameters.

 

Discussion

It has long been known that motion coherence affects motion direction discrimination and speed estimates in humans and nonhuman primates (Braddick et al., 2001; Britten et al., 1992; Pilly & Seitz, 2009; Roitman & Shadlen, 2002; Schutz et al., 2010) and alters the eye speed both at the initiation of pursuit and during steady-state tracking (Behling & Lisberger, 2020; Behling & Lisberger, 2023; Schutz et al., 2010). Furthermore, single unit activity correlates with changes in stimulus coherence in the preferred directions of neurons in macaque middle temporal, medial superior temporal, and lateral intraparietal cortical areas (Britten et al., 1992; Britten et al., 1993; Heuer & Britten, 2007; Roitman & Shadlen, 2002; Shadlen & Newsome, 2001). A limitation of these studies is that they employed broadband 1D and 2D stimuli in which lowering motion coherence introduced random flicker throughout the SF space, making it very difficult to understand the cause of the changes in neural activity and behavior. Making further progress along these lines requires manipulating motion coherence while also controlling how the non-moving components behave. 

Here, we did just that by introducing a broadband visual stimulus in which the contribution of individual spectral components to motion was tightly controlled and free from spatial aliasing, allowing us to identify how each component contributed to behavioral performance. Using stimuli that included SW components that underwent drift, random flicker, or counterphase modulation or were stationary, we showed that both the magnitude of the effect and the most impactful spectral components differed depending on the nature of the non-drifting SW components. 

We found that, with the large stimuli we used, the drive from drifting components was strongest at low SFs, between 0.1 and 0.3 cpd (Figure 9), as already reported (for reviews, see Masson & Perrinet, 2012; Sheliga & FitzGibbon, 2024). Adding non-drifting components reduced this drive (Figures 3, 5, and 7), the more so the higher the contrast of individual components and the larger their number (i.e., the lower the motion coherence). The relative impact of non-drifting components was stronger the lower the contrast of the drifting components (Figure 2). We also found that the disruptive effect of flickering and static components on the OFRs induced by drifting components was similar in strength (Figures 3 and 7) and SF tuning (Figures 4 and 8), whereas counterphase modulated components were generally less effective (Figure 5, other things being equal) and had very different SF tuning (Figure 6), with low SFs being more effective. 

We were able to describe reasonably well the results of all of the experiments using a model that predicts the OFR magnitude based on the spectral content of the stimulus, including drifting, flickering, counterphase modulated, and static components. This model is an extension of the one we proposed earlier to account for the generation of the short-latency eye movements in response to stimuli that included only drifting components (Sheliga & FitzGibbon, 2023; Sheliga & FitzGibbon, 2024). The model posits that the magnitude of OFRs is determined by two factors: an excitatory drive, equal to a weighted sum of contributions from drifting SW components, scaled by a global contrast normalization mechanism. The output of the operation of these two factors is then nonlinearly scaled by the total contrast of the stimulus. Flicker, counterphase, and static SWs contribute only to the global contrast normalization process, whereas drifting SW components provide the drive and contribute to contrast normalization. Normalization weight functions for drifting and counterphase SWs were successfully fit by inverted cumulative Gaussian functions of log SF (Figure 10C), whose parameters were the same apart from the scale: The counterphase weights were much weaker. Gaussian functions of log SF were instead used to fits the normalization weight functions for flickering and static SWs (Figure 10D). The best-fit parameters for the two Gaussians were the same, although equal scaling is likely coincidental. In this study, flicker was generated at 50 Hz, although from pilot studies we know that higher flicker TFs would produce less suppression (see also Quaia et al., 2017, who found stronger suppression from a static mask than one flickering at 150 Hz). The SF associated with maximal efficacy for the flicker and static components was considerably higher than the SF that induced the strongest OFRs (compare Figure 10D and Figure 10A), in agreement with a previous study that evaluated the suppression induced by a single static SW grating on the OFRs induced by a single moving SW grating (Quaia et al., 2017). 

The model is descriptive, meaning that it only describes the functional relationship between the input image and the magnitude of the induced OFRs, and it is thus difficult to map its parameters directly onto brain areas involved in OFR generation. In particular, contrast normalization, usually modeled in a form similar to the one we used (Simoncelli & Heeger, 1998) has been shown to take place at almost every level of early visual processing, including the retina (Shapley & Victor, 1978), lateral geniculate nucleus (particularly in its magnocellular layers) (Solomon, Peirce, Dhruv, & Lennie, 2004), primary visual cortex (Albrecht & Geisler, 1991; Carandini & Heeger, 1994; Carandini, Heeger, & Movshon, 1997), and middle temporal area (Britten & Heuer, 1999; Heuer & Britten, 2002). Determining how each stage contributes to the overall effect is thus quite difficult, and even in neurophysiological studies it is rarely possible to discern what is inherited from previous stages of processing and what is computed locally. 

There are, however, some tentative inferences that we can make from our results. First, the similarity between the normalization weight functions of drifting and counterphase modulated SWs suggests that these effects might be mediated by the same population of neurons. Because the effect of counterphase modulation is weaker than that of drifting stimuli, but still quite robust, we suggest that direction-selective neurons in V1 might be responsible. They have been shown (Snowden, Treue, Erickson, & Andersen, 1991) to respond less to counterphase modulated gratings than to drifting gratings, but not as strongly suppressed as MT neurons, which often do not respond to counterphase modulated gratings at all. Second, the normalization induced by flickering and static gratings might be generated by neurons that are not direction selective, either in V1 or at earlier stages of processing (responses to static stimuli are weak and transient in the middle temporal area) (Albright, 1984; Quaia, Kang, & Cumming, 2022). When motion coherence is varied in stimuli in which individual drifting and flickering components have the same contrast, the relationship between motion coherence and OFR magnitude is approximately linear (not shown), as are the responses of neurons in area MT (Britten et al., 1993) and medial superior temporal area (Heuer & Britten, 2007), supporting the idea that these neurons are ultimately responsible for OFR generation (Masson & Perrinet, 2012; Miles, 1998). 

There is a now a rich history of recording OFRs, even restricting one's focus to studies in humans with stimuli moving in a single direction. Responses to individual sine gratings (or narrowband stimuli) have been measured repeatedly, and the relationships between their magnitude (and in many cases also latency) and the spatial frequency (Gellman, Carl, & Miles, 1990; Meso, Gekas, Mamassian, & Masson, 2022; Sheliga et al., 2005), temporal frequency (Gellman et al., 1990; Meso et al., 2022; Sheliga, Quaia, FitzGibbon, & Cumming, 2016; Sheliga, Quaia, FitzGibbon, & Cumming, 2020), contrast (Barthelemy et al., 2008; Barthelemy, Vanzetta, & Masson, 2006; Quaia et al., 2017; Sheliga et al., 2005), binocularity (Quaia et al., 2018), size (Barthelemy et al., 2006; Sheliga, Quaia, Cumming, & Fitzgibbon, 2012), location (Quaia et al., 2012; Sheliga et al., 2012), aspect ratio (Sheliga, Quaia, FitzGibbon, & Cumming, 2015), and speed (Meso et al., 2022; Simoncini, Perrinet, Montagnini, Mamassian, & Masson, 2012) of the stimulus have been described and modeled. The same is true for center–surround interactions (Barthelemy et al., 2006; Quaia et al., 2012; Quaia et al., 2017; Sheliga, Fitzgibbon, & Miles, 2008; Sheliga et al., 2013), as well as dichoptic interactions (Quaia et al., 2017). The interaction effects of spatially superimposing two or three components have also been thoroughly investigated (Meso et al., 2022; Quaia et al., 2017; Sheliga et al., 2008; Sheliga, Kodaka, FitzGibbon, & Miles, 2006; Sheliga et al., 2020). More recently, the value of using tightly controlled broadband stimuli has been recognized, and several studies (Meso et al., 2022; Sheliga et al., 2016; Sheliga et al., 2020; Simoncini et al., 2012; this paper) have described how the interactions between the components of the stimuli shape the OFR. 

It would be thus desirable to achieve a synthesis of all these studies and to bring together all the models that have been proposed so far, but this process is unfortunately fraught. A major obstacle is represented by the limited overlap between the part of the vast stimulus space covered by the various studies. Take, for example, this study (and the model presented, which accounts for the results presented here and for several previous results from our group) and a recent study (Meso et al., 2022) in which it has been shown that spectral components that encode different speeds tend to suppress each other and lead to sublinear summation (similarly to what we reported here), whereas spectral components that move at the same speed tend to sum linearly or even show enhancement. Because in our study all of the drifting components had the same TF and thus a different speed and the non-drifting components did not have any speed, our model is incapable of reproducing their results (note that there is no TF anywhere in our model or its parameters), so there is no simple way to reconcile them. A larger problem is that all of the models presented so far are essentially descriptive, and even when they are implemented as a cascade of two or more stages these do not map in any natural way to the known anatomy and physiology of the early visual system. We believe that the most promising way forward would be to develop models that are image computable (i.e., that take as inputs the stream of images that are presented to the subject, not the parameters, such as TF, SF, size, etc., that define the stimulus), and that map to the various stages of visual processing that are known to mediate OFRs (at the very least the retina and lateral geniculate nucleus, V1, middle temporal, and medial superior temporal areas). Much of the progress in understanding the visual system (both its dorsal and ventral stream) has been based on such models, and it is unlikely that we will be able to gain a deeper understanding of how OFRs are shaped (or perception emerges) without adopting to an architecture that mimics the brain. The data and the model we presented here will be useful in constraining and validating such a model, which will allow us to gain a mechanistic understanding of how the various parts of the visual system shape the OFRs we recorded. 

Acknowledgments

Supported by the Intramural Research Program of the National Eye Institute at the National Institutes of Health. 

Commercial relationships: none. 

Corresponding author: Boris M. Sheliga. 

Email: [email protected]. 

Address: Laboratory of Sensorimotor Research, National Institutes of Health, Bethesda, MD 20892-4435, USA. 

Footnotes

1  In the text and figures (but not in the model that we introduce below), we express it as a percentage, as the values are usually very small.

Footnotes

2  Drifting SWs of 0.57% RMS contrast were not run in subject JC, as his OFRs were very small at this contrast.