Participants

Twenty-four participants were recruited for each of the four experiments for a total of ninety-six adult participants (28 male, 68 female), whose ages ranged from 18 to 41. All participants had normal or corrected to normal vision, no known abnormalities of binocular or colour vision, and gave written informed consent. Our procedures were approved by the Ethics Committee of the Department of Psychology at the University of York (identification number 184).

Apparatus and stimuli

To present synchronised stimulus modulations independently to each eye, two light engines (SpectraTuneLAB, which are thermally stable across time with active cooling according to the manufacturers: LEDMOTIVE Technologies, LLC, Barcelona, Spain), each with 10 independently addressable LED colour channels, were integrated into a customised binocular viewing system. The light engines were operated via a Python interface to their REST API [23], which supports synchronous launch and playback of spectral sequences prepared in advance and stored in JSON format. A special command was commissioned from LEDMOTIVE to allow two different stimulus files to be launched simultaneously from the two devices. The synchronisation of the spectra from the two devices was tested and showed that they were synchronised to within about 3ms.

When preparing the spectral sequences, the age of participants was used to account for the yellowing of the lenses. We used the silent substitution technique [24] to selectively stimulate specific photoreceptor classes. Silent substitution exploits the fact that each photoreceptor class has a distinct spectral tuning that overlaps with the others. Using a multiprimary system, in which the primaries (i.e. LEDs) have different spectra, it is possible to target one class of photoreceptors while maintaining the others at a constant activity level, effectively silencing them [25,26]. We calculated silent substitution solutions using the PySilSub toolbox [27], using linear algebra. The outputs of the two light engines (see Fig 1b and 1c) were calibrated using an Ocean Optics Jaz spectroradiometer, which was wavelength-calibrated to an Argon lamp and intensity calibrated using a NIST-traceable light source. Each primary was also linearised using a polynomial fit (see S1 Fig for details). We used the 10-degree cone fundamentals [28], and estimates of melanopsin absorbance spectra from CIE S 026 (discussed in a previous paper [27]) to calculate -opic irradiance.

The output from the light engines was directed through liquid light guides (LLG3-8H: Thorlabs Ltd, Cambridgeshire, UK) and diffused onto semi-opaque and highly diffusive white glass discs with a diameter of 50 mm for even illumination (34–473: Edmund Optics, York, UK). The light guide gaskets were butt-coupled to the light engine diffusers with threaded adapters (SM1A9, AD3LLG: Thorlabs Ltd, Cambridgeshire, UK) and the exiting ends of the light guides were mated with 51 mm depth optical cylinders (SM2L20: Thorlabs Ltd, Cambridgeshire, UK) via appropriately threaded adapters (AD3LLG, SM2A6: Thorlabs Ltd, Cambridgeshire, UK). The stimulus diffuser discs were retained at the front end of the optical cylinders about 51 mm from the light source, at which distance the output beam was sufficiently dispersed to afford even illumination of the diffuser when viewed from the front. To guarantee safe illumination levels, a circular neutral-density filter with the same diameter as the white glass discs (50 mm) and an optical density of 0.6 log units was placed in the optical path between the light source and the diffusers. A small circular piece of blackout material with a diameter of about 8 degrees (10 mm) was positioned centrally on the front of each diffuser disc to aid as a fusion lock, as a fixation point, and to occlude the fovea.

The diffuser discs were positioned in the objective planes of the lenses of a modified VR headset (SHINECON SC-G01, Dongguan Shinecon Industrial Co. Ltd., Guangdong, China), which was used by the participants to view the stimuli. The stimuli were two discs of flickering light with a diameter of about 30 degrees, which were fused together into a cyclopean percept resembling a donut-shaped ring of light, similar to that used in other studies [5–7,29,30]. The VR headset modifications allowed for small adjustments to account for individual differences in interpupillary distance and focal length. The use of this set up allowed us to modulate the stimuli in three different ocular configurations, similar to the ones we used in our previous study [3]: monocular, binocular and dichoptic. In the monocular configuration, the unstimulated eye still saw a non-flickering disc of mean light flux. A schematic of the stimulation system is shown in Fig 1a. Pupillometry data were collected using a binocular Pupil Core eye-tracker headset (Pupil Labs GmbH, Berlin, Germany [31]) running at 120 Hz, and the signals were recorded with the Pupil Capture software.

Our previous study [3] used a temporal frequency of 2 Hz for foveal luminance flicker, and recorded EEG data simultaneously with pupillometry. Initial pilot experiments indicated that this frequency was too high to elicit measurable responses when stimulating individual photoreceptor pathways. For all experiments, we therefore used a primary flicker frequency of 0.5 Hz, as previous literature showed that this was slow enough to elicit a pupil response from all photoreceptor classes [7]. We also focussed on only recording pupillometry data as this frequency would be too slow to elicit steady-state EEG responses [32].

For all experiments, sinusoidal temporal modulations were presented against the same background spectrum (matched between the eyes), which was used to achieve silent substitution in the three photoreceptor modulation experiments. The background spectra were defined by setting all channels to half maximum output for the brighter of the two devices (STLab 1, left eye) and then using the STLab 1/STLab 2 calibration ratio to find the equivalent settings for the companion device (STLab 2, right eye). The background spectrum illuminance was about 74 lux, or 68.5 cd/m². The spectral power distributions and -opic irradiances of the background spectra for both eyes are shown in Fig 1c and 1d.

Silent substitution stimuli were prepared and calibrated for each participant with custom Python software [27] and Python scripts. Estimates of photoreceptor spectral sensitivities for each participant were constructed from the known photopigment absorbance spectra [28], taking account of the peak axial density of the respective photopigments, as well as lens [28,33,34] and macular pigment density [34,35], in accordance with the field size and age-dependent CIEPO06 observer model [36]. The melanopic and rhodopic action spectra of the 32-year-old standard observer were taken from CIE S 026 [37] and then adjusted for age-related lens transmittance with a spectral correction function, in line with the standard. Macular pigment correction was not applied to the rhodopic and melanopic action spectra because rods are not present at the fovea and ipRGCs sit above the retinal pigment layer [38].

In the light flux experiment, the stimulus intensity was increased and decreased relative to the background, which we expected to modulate all photoreceptor classes (see Fig 1e and 1i). In the L-M cone modulation experiment, we used silent substitution to increase the L-cone activity, and simultaneously decrease the M-cone activity, during the first half-cycle of the sine wave. In the second half-cycle the polarity of the modulation reversed (see Fig 1f and 1j). The maximum available L-M contrast was about 10%. In the S-cone modulation experiment, we increased and decreased S-cone-directed signals, whilst keeping activity in the other photoreceptors constant (see Fig 1g and 1k). Our system allowed a maximum contrast of 45%. Finally, in the melanopsin experiment, we modulated the activity of the melanopsin-containing intrinsically photoreceptive retinal ganglion cells, whilst keeping cone activity constant (see Fig 1h and 1l). The maximum available melanopsin contrast was 22%. We assume that the activity of rods was constant at the high background luminance intensity used here, and so did not attempt to silence rod activity in any condition, as this would have greatly reduced the available dynamic range. Splatter on nominally silenced photoreceptors was small (see Fig 1j–1l), well below the levels that would be expected to generate measurable pupil modulations, although we can observe that the rods may not be saturated in the L-M and melanopsin-directed stimuli (Fig 1j and 1l) and could intrude in these two experiments. We also estimated activation of penumbral L and M cones [5,29,39], which was minimal ( 1.5% contrast; less than splatter on the open-field cones) for melanopsin-directed stimuli. We note that the temporal frequency of our modulation (0.5 Hz) is well below the range where penumbral cone activation can elicit visible percepts, and that such percepts fade after around 1 second [29], and do not typically affect pupil responses [7].

Procedure

Before the start of each experiment, participants adjusted the objective planes of the lenses with the help of the experimenter until the stimulus was in focus and they perceived the two pieces of blackout material as one fused disc. Pupil responses to binocular temporal contrast modulations were examined in a factorial design that combined six ocular conditions and five temporal contrast levels: 6, 12, 24, 48 and 96% of the available dynamic range. This design, similar to that used in our previous studies [3,40,41], was applied in four separate experiments, each with a different mode of photoreceptor stimulation. In the first three conditions, the discs flickered at 0.5 Hz, in either a monocular, binocular or dichoptic arrangement. In the dichoptic condition the non-target eye saw a flickering fixed contrast of 48% of the available dynamic range. In the remaining three conditions (the cross-frequency conditions) one eye’s disc flickered at 0.4 Hz, and the other eye’s disc flickered at 0.5 Hz. This included monocular responses at 0.4 Hz, as well as binocular (one eye sees each frequency at the target contrast) and dichoptic (target stimulus flickering at 0.5 Hz, mask contrast of 48% at 0.4 Hz in the other eye) arrangements. We counterbalanced presentation of the target stimulus across the left and right eyes. The full set of conditions is summarised in Table 1.

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Table 1. The six ocular conditions used in each of the four experiments. The target eye was modulated at the target contrast (one of five levels); the response was measured at the frequency or frequencies indicated. Target-eye assignment was counterbalanced across the left and right eyes.

https://doi.org/10.1371/journal.pone.0356765.t001

The experiments were conducted in a windowless room, in which the only source of light was the modified VR headset. The participants sat as close as possible to the VR headset, leaving enough space for the eye-tracker to record the eyes. Each experiment was carried out in a single session of around 45–60 minutes, divided into three blocks of 15–17 minutes each. In each block, there were a total of 60 trials lasting 15 seconds each (12s of stimulus presentation, followed by 3s of interstimulus interval). The participants were given no task other than look at the black fixation dot while trying to minimise their blinking during the presentation period. For all experiments other than the light flux condition, participants adapted to the unmodulated background luminance for two minutes before stimulation began.

Before the start of the L-M experiment, participants completed a luminance nulling perceptual calibration procedure in L-M cone space on an Iiyama VisionMaster^TM Pro 510 display (800 x 600 pixels, 60 Hz refresh rate). During the task, participants were presented with a disc flickering within the L-M cone space (between magenta and cyan). Using a trackball, participants adjusted the angle in cone space to find their subjective isoluminant point, which resulted in changing the flickering intensity of the stimulus until the amplitude of the flicker appeared to be minimised. The result was used to modify the requested contrasts during stimulus preparation so as to account for individual differences affecting perceived illuminance, principally the L:M cone ratio [42,43].

Data analysis

The pupillometry data were analysed using the same method we used in our previous study [3]. The data were converted from mp4 videos to a csv text file using the Pupil Player software [31], which estimated pupil diameter for each eye on each frame using a 3D model of the eyeball. The individual data were then loaded into R for analysis, where a ten-second waveform for each trial in each eye was extracted (excluding the first two seconds after stimulus onset). We interpolated across any dropped or missing frames to ensure regular and continuous sampling over time. The Fourier transform was calculated for each waveform, and all repetitions of each condition were pooled across eye and then averaged. Finally, data were averaged across all participants to obtain the group results. We used coherent averaging and at each stage we excluded data points with a Mahalanobis distance exceeding D = 3 from the complex-valued mean [44]. For monocular stimulation, we confirmed that the consensual response was equivalent to the response in the stimulated eye. For all experiments, we used a bootstrapping procedure with 10⁴ iterations to estimate standard errors across participants. All analysis and figure construction was conducted using a single R-script, available online, making this study fully computationally reproducible: https://osf.io/gdvt4/.

Computational model and parameter estimation

To quantitatively summarise our data, we used the same model described in our previous study [3]. The model has the same general form as the first stage of the contrast gain control model proposed by Meese and colleagues [22], but omits the second stage. For the previous model that we used [3], the exponent of the numerator and denominator had fixed values of 2 and (implicitly) 1. Here, we allow these parameters (called p and q) to be free, to allow different shapes of contrast response function, e.g., accelerating or saturating.

In words, the model works as follows. Each eye produces an excitatory response that grows with the contrast in that eye. This response is then divided by a term that includes the contrast in the other eye, so that stimulating one eye reduces the response to the other. The two suppressed monocular signals are summed to give the binocular response. The weight sets the strength of this interocular suppression: values below 1 give weak suppression, and therefore stronger binocular facilitation, whereas values near or above 1 give strong suppression, which can produce ocularity invariance or, when suppression is strong enough, a binocular response that is smaller than the monocular one. The responses of the left eye and right eye channels are as follows:

(1)

(2)

where L and R are the contrast signals from the left and right eyes, p and q are exponents, Z is a saturation constant that shifts the contrast-response function laterally, and is the weight of suppression from the other eye.

The responses from the two eyes are then summed binocularly:

(3)

where k is a noise parameter, and R_max scales the overall response amplitude. The models were fit using a hierarchical Bayesian framework implemented in Stan [45]. The data for each photoreceptor type and response frequency was fit separately, for a total of 8 model fits. We did not fit the two eyes separately. Target-eye assignment was counterbalanced across participants, and responses were pooled across eye before fitting, after confirming that the consensual response matched the response in the stimulated eye (see Data analysis). The prior for the parameter was Gaussian, with a mean of 1 and standard deviation of 0.5. Priors for the other free parameters were also Gaussian, with mean values based on previous work [3]. All free parameters were constrained to be positive (and the saturation constant Z to be at least 1), so these Gaussian priors were truncated at those bounds. The model was hierarchical and was fitted to the individual-participant amplitudes rather than to the group averages: each participant had their own set of parameters, drawn from group-level distributions whose means we report and compare across conditions. We ran 16 chains of 64,500 iterations each, discarded the first 2,000 iterations of each as warm-up, and thinned by a factor of 10, giving 103,200 retained samples per fit (over 10⁶ samples before thinning). The group-level parameters converged well in every fit (split- and effective sample size > 3,000). In the melanopsin first-harmonic fit a few participant-level exponent and suppression parameters reached ; the group-level suppression weight, which is our parameter of interest, had . As a summary of fit, we report the root-mean-square error between the group-mean data and the model prediction for each fit in Table 2.

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Table 2. Convergence diagnostics and fit statistics for the eight model fits. Maximum split- is taken across all parameters; minimum effective sample size (ESS) is taken across the group-level parameters; RMSE is the root-mean-square error between the group-mean data and the model prediction.

https://doi.org/10.1371/journal.pone.0356765.t002

Physiological interpretation of the pathway and harmonic differences

Our four experiments modulate different photoreceptor classes, and the differences between them are open to physiological interpretation. We are cautious about attributing responses to discrete physiological mechamisms because silent substitution isolates photoreceptor contrast rather than an anatomically separate neural pathway: the targeted photoreceptor signals converge with others downstream, and we did not explicitly silence the rods although their contribution at the mean luminance levels used is expected to be small.

The light flux stimulus modulates several photoreceptor classes together and produced by far the largest pupil response. Its weak first-harmonic suppression is consistent with strong binocular facilitation, but because several receptors are co-modulated this condition cannot tell us which retinal input dominates. The isoluminant L-M stimulus targets a cone-opponent signal rather than luminance, and showed the strongest first-harmonic suppression, with a binocular response weaker than the monocular one. This may indicate stronger binocular normalisation for cone-opponent input, though our data cannot localise whether this interaction arises in retinal, pretectal or other subcortical circuitry.

The S-cone stimulus produced a relatively large second harmonic. This could reflect nonlinearity or asymmetry in how S-cone increments and decrements are converted into a pupil response, rather than a separate oscillatory mechanism. For example, it is well known that there are asymmetries in the number of S-cone on- and off- bipolar cells in the retina [51,52]. The melanopsin-directed responses were delayed in phase relative to the cone-directed responses, which is broadly consistent with the slower phototransduction of the ipRGCs. But the ipRGCs also receive cone and rod input, and our stimulus isolates melanopsin contrast rather than an anatomically independent pathway, so the delay need not arise from melanopsin phototransduction alone.

The meaning of the differences we observe between the 0.4 and 0.5 Hz responses is unclear. The pupil is a temporally filtered and nonlinear system, so a modest change in frequency can alter response phase, waveform asymmetry and harmonic content. Some of the difference may also reflect noisier estimates or imperfect model fit. We therefore do not attribute the 0.4 versus 0.5 Hz differences to distinct physiological mechanisms. A limitation that applies across all of these comparisons is that the four experiments used separate groups of 24 participants, so differences between the photoreceptor-directed conditions are partly between-group differences.