Empirical tests of the effectiveness of EnChroma multi-notch filters for enhancing color vision in deuteranomaly

Manufacturers of notch filter-based aids for color vision claim that their products can enhance color perception for people with anomalous trichromacy, a form of color vision deficiency (CVD). Anecdotal reports imply that people with CVD can have radically enhanced color vision when using the filters. However, existing empirical research largely focussed on the effect of notch filters on performance on diagnostic tests for CVD has not found that they have any substantial effect. Informed by a model of anomalous trichromatic color vision, we selected stimuli predicted to reveal the effects of EnChroma filters. Using these stimuli, we tested the ability of EnChroma filters to enhance color vision for 10 deuteranomalous trichromats in three experiments: 1. asymmetric color matching between test and control filter conditions, 2. color discrimination measured using four alternative forced-choice, and 3. color appearance measured using dissimilarity ratings to reconstruct subjective color spaces using multidimensional scaling. To investigate potential effects of long-term adaptation or perceptual learning, participants completed all three experiments at two time points, on first exposure to the filters, and after a week of regular use. We found a significant effect of the filters on color matches in the direction predicted by the model at both time points, implying that the filters can enhance the anomalous trichromatic color gamut. However, we found minimal effect of the filters on color discrimination at threshold. We found a significant effect of the filters in enhancing the appearance of colors along the red-green axis at the first time point, and a trend in the same direction at the second time point. Our results provide the first quantitative experimental evidence that notch filters can enhance color perception for anomalous trichromats.


Introduction
EnChroma glasses (EnChroma Ltd., Berkeley, California, USA; Schmeder & McPherson, 2019) are aids designed to enhance color vision for individuals with anomalous trichromatic color vision deficiency (CVD).EnChroma has gained considerable attention in mainstream and social media, and despite intermittently carrying disclaimers stating that the aids are "not a cure for color-blindness" and are "not designed to improve scores on color-blindness tests" their website has hosted articles describing the product as a "cure", alongside language and visualizations that suggest this to be the case (https://www.enchroma.com,2017, accessed via archive.org).There is a need for more scientific research to investigate the effects of EnChroma filters on anomalous color perception, specifically to test the claims made by EnChroma in marketing their products.To validate our model of the effects of EnChroma filters on color vision in anomalous trichromacy (Somers & Bosten, 2024) we empirically tested the effect of the filters on color discrimination and color appearance.
Normal human color vision is based on a comparison between the signals of three classes of retinal cone sensitive to short (S), medium (M) and long (L) wavelengths of light.Postreceptorally there are thought to be two main retinogeniculate pathways carrying color information.The L/(L + M) pathway compares the activities of the L and M cones, and the S/(L + M) pathway compares the activity of the S cones to the activities of the other two cone types.Anomalous trichromacy is a mild form of CVD affecting about 6% of men in which there are still two cone classes sensitive in the medium and long wavelength part of the spectrum, but their spectral sensitivities are much more similar than in normal trichromacy.There are two categories of anomalous trichromacy: In deuteranomaly normal M cones are replaced by variant L′ cones, and in protanomaly normal L cones are replaced by variant M′ cones.Color vision is impaired in anomalous trichromacy because the strength of L/ (L + M) cone opponent color signals are dependent on the difference between the spectral sensitivities of two inputting cone classes.In normal trichromacy there is a roughly 27 nm spectral separation (Δλ max ) between the peak sensitivities of the L and M cones, while for anomalous trichromats Δλ max can vary between 1 nm and 12 nm (Bosten, 2019;Neitz & Neitz, 2011).
Including EnChroma filters, a number of different filter-based aids have been developed and marketed that aim to improve color vision in people with CVD using several different modes of operation.Interocularly discrepant bandpass filters such as X-Chrom (Zeltzer, Ipswich, Ma, USA;Zeltzer, 1991), Chromagen (Harris, Birkenhead, UK;Harris, 1999) and Colormax (Azman, Birmingham, Al, USA) have been found to 'improve' the performance of people with CVD on diagnostic tests for CVD such as the Ishihara Plates test (Welsh et al., 1978;Paulson, 1980;Matsumoto et al., 1983;Swarbrick et al., 2001;Ilhan et al., 2020), the D15 test (Swarbrick et al., 2001;though Welsh et al., 1978 found minimal effect), and the Hardy Rand Rittler (Ilhan et al., 2020;Paulson, 1980;Welsh et al., 1978).These results indicate that interocularly discrepant filters can break metamerism between figure and ground in pseudoisochromatic plate tests for CVD by introducing a luminance difference between confusion colors that is likely to be perceived as interocular lustre (Heath, 1974;Formankiewicz & Mollon, 2009).In the D15 test they may improve performance by introducing a luminance gradient useful for ordering the test colors.Consistent with the idea that the filters offer no enhancement to color signals themselves, no significant improvement has been found for the more complex Farnsworth-Munsell 100 hue test (Welsh et al., 1978;Paulson, 1980;Matsumoto et al., 1983;Kassar et al., 1984), which involves arranging 85 colors in order of hue.
Notch filters such as EnChroma are designed to enhance anomalous trichromatic color vision by inserting a spectral notch in the filter transmission spectrum positioned to coincide with the difference between the peak sensitivities of the cone classes sensitive in the medium and long wavelength part of the spectrum.The spectral notch increases chromatic contrast by increasing the difference between the activities of the two cone classes when exposed to broadband colored light.Colorlite filters (Colorlite USA LLC, Boca Raton, Fl, USA; Ábrahám et al., 1998), which may confer a spectral notch, claim to tailor filter effects for the individual by combining multiple filter layers to selectively attenuate regions of the spectrum.The first filters to explicitly employ a spectral notch were EnChroma filters and Oxy-Iso filters (Vino Optics, US Virgin Islands; Barber & Changizi, 2012).Recently, further notch filters have been developed using dyes (Badawy et al., 2018) and using gold nanostructures (Karepov & Ellenbogen, 2020).
Much of the existing research testing the effectiveness of notch filters as an intervention for CVD has focused on identifying their impact on outcomes of diagnostic tests for CVD.Some studies have used digital tests for CVD.No significant effects of EnChroma filters have been found for the CAD test (Patterson et al., 2022), the CVA-UMinho test ( Álvaro et al., 2022) or a computerized version of the Farnsworth-Munsell 100 hue test (Almutairi et al., 2017).However, small significant effects of Oxy-Iso filters have been reported for the CAD test (Patterson et al., 2022) and of EnChroma filters on computerized versions of the Ishihara Plates test (Almutairi et al., 2017).These positive effects have been interpreted as arising from luminance differences between target and distractor colors introduced by the filters (Patterson et al., 2022).Though there are mixed results of EnChroma filters for digital tests, it is likely that the filters are less effective for screen-rendered colors than for broadband surfaces in the real world, as the notch likely coincides (at least to an extent) with the spectral gap between display red and green primaries.In support of this, modelling results reported in our accompanying paper predict that EnChroma filters have a smaller effect on the saturations of screen-rendered Munsell colors than on those of physical surfaces (Somers & Bosten, 2024).
For the physical Farnsworth-Munsell 100 hue test, no significant effects of EnChroma filters have been found for total error scores ( Álvaro et al., 2022;Gómez-Robledo et al., 2018;Kitchens & Cisarik, 2017;Pattie et al., 2022), but changes have been reported in the distribution of errors around the hue circle (Kitchens & Cisarik, 2017;Pattie et al., 2022).For the physical Ishihara Plates test there are mixed findings on the effect of EnChroma filters.Gómez-Robledo et al. (2018) reported no significant effect on the errors made, while Álvaro et al. (2022) and Varikuti et al. (2020) reported a significant reduction in errors which Álvaro et al. attributed to the induction of a luminance difference between target and surround, and Pattie et al. (2022) reported a significant reduction in errors for deuteranomals only.Martínez-Domingo et al. (2019) found a substantial reduction in errors on the Ishihara Plates test with Oxy-Iso filters, which they also attributed to induced differences in luminance between target and surround.There have not so far been many tests of the effect of EnChroma filters using custom (non-clinical) assessments of color perception in CVD with broadband surface stimuli.Two recent exceptions are studies by Álvaro et al. (2022) who found no significant effect of EnChroma filters on sorting errors for colored boardgame pieces but a significant increase in sorting time, and Marques et al. (2023) who found no significant effect of EnChroma or Oxy-Iso filters on illumination discrimination for colors sampled from natural scenes which were reproduced using a spectrally tuneable light source.
In summary, existing research on the effectiveness of notch filters for enhancing anomalous trichromatic color vision has produced mixed but mainly negative results.However, the stimuli used in existing research have mostly been restricted to those employed in standard diagnostic tests of CVD, including screen-rendered colors for which there is reason to expect that the filters may not be so effective (Somers & Bosten, 2024).Informed by predictions using our model (Somers & Bosten, 2024), we therefore set out to test the effectiveness of EnChroma filters for improving both color discrimination and color appearance using broadband colored stimuli that have spectral properties more typical of colored surfaces in everyday contexts, for which our model predicted that the filters would have a positive effect.Our participants were deuteranomals rather than protanomals because deuteranomaly is the most common form of anomalous trichromacy (over 80% of anomalous trichromats are deuteranomalous), and because our model predicted that EnChroma filters will be more effective for deuteranomals than for protanomals (Somers & Bosten, 2024).In Experiment 1 we tested the effect of EnChroma filters on color matches, where the target and matching colored surfaces were presented under different filters (an EnChroma filter and a control neutral density filter).In Experiment 2 we tested the effect of EnChroma filters on color discrimination thresholds along 7 hue axes using custom broadband painted stimuli.In Experiment 3 we tested the effect of EnChroma filters on color appearance for a set of broadband Munsell surfaces, where we reconstructed subjective color spaces using multidimensional scaling applied to sets of pairwise dissimilarity ratings.

Participants
Male participants were recruited at the University of Sussex campus.Recruitment was in person on campus by screening for CVD (n = 773), either using the Ishihara Plates Test (Ishihara, 1917), or using a shortened diagnostic procedure on an anomaloscope (Oculus; Wetzlar, Germany).Briefly, the shortened anomaloscope procedure was employed for time efficiency (considering the large number of people tested), and consisted of 3 trials in which participants were asked to find a color match between the test field (mixing red and green light) and the monochromatic reference field, but to ignore any luminance or brightness differences between the fields by adjusting only one of the two available dials.The starting mixture was alternated across trials between the two extremes of the range of possible red-green mixtures.
The color vision of 95 men who made at least one match outside the normal range in the shortened procedure was further characterised through 5 matches using the anomaloscope, where participants were allowed to adjust both the ratio of red to green of the test field and the luminance of the matching field.Potential CVD participants were not included in the study if their color vision was found to be normal trichromatic (n = 4), deuteranopic (n = 12), extreme deuteranomalous (n = 14), protanopic (n = 8), protanomalous (n = 12), or extreme protanomalous (n = 5).Men found to be deuteranomalous (n = 37) were invited to take part in the study (N.B., men found to have extreme deuteranomaly were not invited to take part).Individuals who had previously used EnChroma filters were excluded (n = 3).Of the remaining 34 deuteranomals, 10 chose to take part in the study (mean age 26).For the 10 deuteranomals who took part in the study the mean anomaloscope midpoint was 19.3 Nagel units (std: 2.7, range 14.9-24.0),and the mean matching range was 7.9 Nagel units (std: 5.3, range: 1.6-16.5).
The study received ethical approval from the Science and Technology Cross-Schools Research Ethics Committee (C-REC) at the University of Sussex (ER/LS487/4), and participants gave written informed consent before participating.The study adhered to the tenants of the World Medical Association's Declaration of Helsinki ( 2013), with the exception that it was not pre-registered.

Filters
The EnChroma filter used in all experiments was the Cx-25 filter selected as a representative example of the most common filter profile from a range of 16 EnChroma filters we measured between 2017 and 2018 (Somers & Bosten, 2024).This filter was designed for both indoor and outdoor use, and was suitable for the light levels in the testing environment.A neutral density filter (Lee Filters, Hampshire, UK) of 0.6 log unit attenuation was used as a control filter, to match the attenuation of the EnChroma filter.The transmission profiles of the EnChroma and control filters (Fig. 1a) were measured using a SpectaScan PR655 spectroradiometer (Photoresearch, Chatsworth, CA) in reference to a polytetrafluoroethylene white plaque (Sphere Optics, Uhldingen, Germany) under an LED illuminant.

Illuminants
A white light-emitting diode (LED) illuminant was used for Experiments 1 (color matching task) and 2 (color discrimination task) because our model predicted that it would mediate strong enhancements to chromatic contrast for both cone opponent color pathways (for further detail, see Section 3.1).The source was a S63 5DL 30 W bulb (Maplins, Rotherham, UK) with a correlated color temperature of 5.1 K and a color rendering index of 77.9.For Experiment 3 (rating task) a halogen illuminant was used, because our model predicted that the EnChroma filter would cause greater enhancements in the anomalous trichromatic equivalent of L/(L + M) saturation than in S/(L + M) saturation (see Section 5.1).This asymmetry should be advantageous in revealing an effect of the filter on perceived color dissimilarity along the L/(L + M) axis.The source was a Diall R7S 400 W bulb (Kingfisher, London) with a correlated color temperature of 2.9 K and a color rendering index of 98.9.For all experiments the illuminant was suspended 56 cm above the viewing surfaces, and illumination was restricted to the inside of the viewing box.The experiments were conducted in an otherwise dark room.Radiance spectra of the illuminants used in both experiments are plotted in Fig. 1b.

Stimuli
Using our model of the impact of EnChroma filters on anomalous trichromatic color vision we predicted the effects of the EnChroma filter on the chromaticities of candidate stimuli for the experiments.The stimuli selected were a subset of candidate stimuli selected to sample hues around the hue circle, and because our model predicted that the EnChroma filter should enhance their color contrasts along the deuteranomalous color dimension L/(L + L′) (see the separate 'Methods' for each experiment below for details of the predictions).The stimuli used in Experiments 1 (color matching, Fig. 1c, yellow points) and 3 (rating task, Fig. 1c, pink points) were a subset of 259 surfaces from the Munsell color atlas (Glossy edition, Pantone, Michigan USA) of Value 5 (Fig. 1c, black points).The spectra were obtained from an online-accessible dataset of 1600 Glossy Munsell surface reflectances (Haanpalo, n.d.) at a resolution of 1 nm for the range 380 nm to 780 nm.For further details see Sections 3.1 and 5.1.
The stimuli used in Experiment 2 (discrimination task) were custom colored surfaces created using a mixture of white and chromatic acrylic paints (Fig. 1c, blue points).The surfaces were selected from a larger number of candidates, the reflectance spectra of which were all measured using a PR655 SpectraScan spectroradiometer (Photoresearch, Chatsworth, CA) under LED illumination, in reference to a polytetrafluoroethylene white plaque (Sphere Optics, Uhldingen, Germany).Eighteen painted surfaces were selected for each of the seven hue axes tested.For further details see Section 4.1.

Apparatus
All experiments were carried out using a custom viewing box, designed to be adjustable to allow the configurations needed for each of the three experiments.The viewing apparatus had a removable central divider, and two versions of a front panel facing the participant: one with a single central viewing aperture, and one with two viewing apertures side by side.The EnChroma and control filters were embedded into frames to allow them to be affixed to the viewing apertures on either of the front panels, allowing single filter viewing or tandem filter viewing within one experimental session.As the viewing apertures were backlit in otherwise dark conditions, participants were unable to differentiate the EnChroma filter from the control filter.All sides of the apparatus were coated in Stuart Semple's Black 2.0 paint (Cultur-eHustle, Dorset, UK) to minimize stray light.Stimuli were presented manually by a researcher on the other side of the box, shielded from view by a black curtain, with only black-gloved hands visible to the participant.
Experiment 1 (color matching task) required the viewing box to be bisected, with the target alone visible through filter A, and the matching array visible through filter B. To achieve this, a central wall was added, and the participant-facing wall had two viewing apertures, to which the filters were attached.Experiments 2 (discrimination task) and 3 (rating task) required a single space to present the stimuli.No central divider was used, and a single aperture was used on the side of the box facing the participant.Experiment 3 included a training phase which required the participant to briefly point to stimuli.This was achieved using a curtained window in the lower part of the participant-facing wall.The curtain stopped any light escaping from the viewing box during the experiments.a3) Schematic illustrating the expected effect of the EnChroma filter on color matches: If the EnChroma filter enhances saturation, then a target viewed with the EnChroma filter will be matched to a more saturated target (than its Munsell chroma match) when the matching stimulus array is viewed with the control filter.(b1) Chromaticities of the targets presented with the control filter (black crosses) and chromaticities of the predicted matches from the array of surfaces with the EnChroma filter (red circles).The predicted matches are indicated by the pale blue shaded regions connecting the surfaces predicted to be matched.Also, for context, chromaticities of the targets with the EnChroma filter (red crosses), chromaticities of the predicted matching surfaces with the control filter (black circles), and chromaticities of all surfaces in the matching array with the EnChroma filter (red dots).(b2) Chromaticities of the targets presented with the EnChroma filter (red crosses) and chromaticities of the predicted matching surfaces with the control filter (black circles).The predicted matches are indicated by the pale blue shaded regions.Also, for context, chromaticities of the predicted matching surfaces under the EnChroma filter (red circles), chromaticities of the targets under the control filter (black crosses), and chromaticities of all surfaces in the matching array with the control filter (black dots).

Procedure
Two sessions were held with each participant separated by 4-8 days, before and after a period of self-directed use of the filters worn as glasses, where participants were loaned the filters and asked to use them for a minimum of 10 hours over the period.Each session included three experiments: Experiment 1 (Color Matching task), Experiment 2 (Discrimination task) and Experiment 3 (Rating task).Experiments were conducted in a random order, different across participants, and an entire experimental session lasted approximately 90 minutes.

Experiment 1: Color matching task
To measure the impact of the EnChroma filter on color appearance, we created a color matching task.Colored targets were presented under one filter (either the EnChroma filter or the control filter), and an array of colored surfaces was presented under the other filter.The observer's matches between the targets and surfaces from the array should reveal any changes in perceived hue and saturation conferred by the EnChroma filter.Our model, based on a comparison of chromaticities of surfaces under the EnChroma filter and under a control filter in an observerspecific version of the MacLeod-Boynton (1979) chromaticity diagram (Somers & Bosten, 2024), predicted that for deuteranomals, coneopponent color signals from target surfaces under the LED illuminant would be enhanced in saturation by the EnChroma filter (Fig. 2a3 for a schematic and Fig. 2b2 for precise predictions).If the visual system is able to represent these changes, target surfaces viewed through the EnChroma filter should appear more saturated, and therefore the matches selected from the matching array viewed under the control filter should be of a higher saturation than they would be if both targets and matching array were viewed under the same filter.We also tested the effects of the filters in the opposite direction, where targets were presented under the control filter and the matching array of colored surfaces under the EnChroma filter.Here, the model predicted that less saturated surfaces will be selected to match targets (because the perceived saturations of colors in the matching array will be enhanced by the EnChroma filter).

Methods
23 surfaces were selected as targets from the subset of Munsell surfaces of Value 5 (Glossy edition, Pantone, Michigan USA).The chromaticities of targets used in trials 1-12, where targets were viewed under the control filter, are plotted in Fig. 2b1, and the chromaticities of targets used in trials 13-23, where targets were viewed under the EnChroma filter, are plotted in Fig. 2b2.Munsell surfaces with the most similar chromaticities (nearest neighbours) to each target when calculated in the opposite filter condition were identified as potential matches.EnChroma matches (red circles) to targets presented under the control filter (black crosses) are plotted in Fig. 2b1, and control filter matches (black circles) for targets presented under the EnChroma filter (red crosses) are plotted in Fig. 2b2.Since the side-by-side viewing of stimuli under both filter conditions allows minimal adaptation, the predictions were based on modelled chromaticities that were not corrected to a common white point.The chromaticities of the surfaces in the matching array that included all Value 5 Munsell surfaces other than Neutral 9.5 (N = 221) are plotted in Fig. 2b1 and 2b2 (small points).
The target and matching array were presented in either side of a bisected box, with separate viewing apertures to each side containing the EnChroma and control filters (Fig. 2a1).On each trial a single target was presented in one half of the viewing apparatus and the participant was required to verbally identify a color match using coordinates written next to the surfaces of the matching array presented in the other half of the viewing apparatus.The matching array was split between two boards (Fig. 2a2), and the participant was presented with both boards sequentially and in a random order on each trial.There were no time limits and participants were permitted to view the target and matching arrays repeatedly.If no single surface was a perfect match, the closest match or range of matches was requested.Four participants repeated the trials twice, completing 46 trials per session, before the procedure was shortened to reduce participant fatigue.The remaining 6 participants carried out 23 trials per session.The two filter conditions, control and experimental, were unknown to participants, and the order of filter conditions and trials was randomized.

Results
The average color matches selected for each target in each filter condition are plotted in Fig. 3, along with our model predictions.The results show that the observed color matches broadly follow the predictions, implying that EnChroma filters increase the perceived saturation of the surfaces.When targets were presented with the control filter and the matching array with the EnChroma filter (Fig. 3a1-a3), the matches were systematically closer to the achromatic centre of the set of Munsell Stimuli in a deuteranomalous version of the MacLeod-Boynton (1979) chromaticity diagram than the targets, implying that surfaces of lower saturation were matched to targets with higher saturation.When targets were presented with the EnChroma filter and the matching array with the control filter (Fig. 3b1-b3) participants consistently selected surfaces with higher saturation as matches to lower saturation targets.
From the results we extracted a measure of the effect of the EnChroma filter along the color axis of interest, the L/(L + L′) color axis that is impaired in deuteranomaly compared to the L/(L + M) color axis in normal trichromacy.Specifically, we extracted the change in absolute L/ (L + L′) relative to the achromatic point (Munsell Neutral 9.5).With this metric, positive values indicate that the EnChroma filter has caused L/(L + L′) saturation to increase.Matched-pairs t-tests conducted on average matches (averages of 12 matches to targets presented with the control filter and 12 matches to targets presented with the EnChroma filter) showed that the EnChroma filter caused a significant increase in absolute L/(L + L′) (t = 15.3, p < 0.001 for the pre-habituation session; t = 16.1, p < 0.001 for the post-habituation session).
Fig. 3c shows the mean changes in absolute L/(L + L′) between target and matched surfaces, plotted against the changes in absolute L/(L + L′) predicted by our model.The figure shows a relationship between the sizes of observed changes in L/(L + L′) and those predicted by the model, and a Spearman's correlation revealed that the relationship is significant (ρ = 0.71, p < 0.001 for the pre-habituation session; ρ = 0.68, p < 0.001 for the post-habituation session).The mean observed change in absolute L/(L + L′) (0.0026 for the pre-habituation session; 0.0023 for the posthabituation session) was similar to that predicted by the model (0.0019), though matched pairs t-tests between model predictions and average matches (across participants) for the 24 stimuli showed that the EnChroma filter significantly outperformed the model for the prehabituation session only (t = 2.78, p = 0.01 for the pre-habituation session; t = 1.32, p = 0.2 for the post-habituation session).
There was a significant correlation between the mean changes in absolute L/(L + L′) and the unfiltered L/(L + L′) chromaticities of the targets (ρ = 0.41, p = 0.045 for the pre-habituation session; ρ = 0.42, p = 0.044 for the post-habituation session).This implies that enhancements in perceived saturation caused by the EnChroma filter increase with the saturation of the colored surfaces.
To investigate the effect of habituation to the filters, a paired t-test was conducted on the mean absolute changes in L/(L + L′) conferred by the EnChroma filter relative to the control filter.No significant effect of habituation condition was found (t = 1.6, p = 0.12).

Experiment 2: Discrimination task
To measure the impact of EnChroma filters on color discrimination, we created a custom four-alternative forced choice color discrimination task using physical surfaces.Participants viewed stimuli through the EnChroma filter and the control filter in different conditions.Our model predicted that the EnChroma filter should confer increases in coneopponent color signals in all color directions away from the white point for surfaces under the LED illuminant (Fig. 4c).In the experiment we therefore tested for corresponding increases in sensitivity to saturation with the EnChroma filter in all color directions.

Methods
The stimuli for the discrimination task were surfaces hand-coated in Pablo acrylic paints (Tannegate Ltd., Surrey, UK), set into black frames, presenting three white squares and one colored target square in a 2x2 arrangement (Fig. 4a), to allow rapid manual randomization of the target surface's location (by manual rotation) within the set of four.The saturation of the target surfaces within the stimulus set increased monotonically for an average of 31.7 levels from white in seven hue directions (Fig. 4c and 4d show the first 18 levels, but the number of levels differed between axes between 23 and 40).Example reflectance spectra from the 10th target for each of the hue directions are shown in Fig. 4b.Fig. 4c shows, plotted relative to the white of the distractor quadrants, the chromaticities of all target surfaces under the control filter (black circles) and under the EnChroma filter (red circles).The chromaticities of the surfaces under the EnChroma filter are further from the white point in L/(L + L′) than the chromaticities of the surfaces under the control filter (Fig. 4d), indicating that the EnChroma filter should enhance their perceived saturation.

Fig. 3.
Results of Experiment 1. (a1-a3) Predicted and observed average matches (over the 10 participants) where targets were presented with the control filter and the matching arrays were presented with the EnChroma filter.On each panel the black crosses are the chromaticities of targets with the control filter, the red open circles are the chromaticities of matching surfaces predicted by our model, and the red filled circles are the observed chromaticities of the mean matches to each target.Panel (a1) shows results for the first session (pre-habitation), panel (a2) shows results for the second session (post-habituation), and panel (a3) shows results averaged over both sessions.N.B., Chromaticities for all surfaces are plotted as they are under the control filter so that the differences in saturation between targets and matches are visible.(b1) -(b3) Predicted and observed matches where targets were presented with the EnChroma filter and the matching arrays were presented with the control filter.On each panel the red crosses are the chromaticities of targets with the EnChroma filter, the black open circles are the chromaticities of matching surfaces predicted by our model, and the black filled circles are the observed chromaticities of the mean matches to each target.Panel (b1) shows results for the first session (pre-habitation), panel (b2) shows results for the second session (post-habituation), and panel (b3) shows results averaged over both sessions.N.B., Chromaticities for all surfaces are plotted as they are under the contol filter so that the differences in saturation between targets and matches are visible.In a four-alternative forced choice task, participants were asked to identify the colored surface on each trial.Stimuli were presented manually in a 1-up 1-down staircase procedure.Staircases began with the maximally saturated stimulus from each color axis.Staircases were terminated after 5 reversals.One staircase was run for each of the 7 color sets, and all 7 color sets were completed under one filter condition before changing the filter.The order of color sets and filter conditions were randomized.Each participant completed the task four times, once under each filter condition in the pre-habituation session and again in the post-habituation session.

Results
For each staircase, discrimination threshold was calculated as the average of the saturation levels at the 5 reversals.Changes in L/(L + L′) discrimination thresholds between the control filter and the EnChroma filter conditions are plotted in Fig. 5.We conducted a 3-way repeated measures ANOVA with factors for filter condition, hue condition and habituation condition.There was no significant main effect of filter (F = 0.64, p = 0.45), a significant main effect of hue (F = 25.5, p < 0.001), and no significant main effect of habituation (F = 0.38, p = 0.56).There was a significant interaction between hue and filter (F = 10.95,p < 0.001), but none of the other interactions showed significant effects.
To explore the significant interaction between hue and filter we conducted post-hoc paired t-tests for each hue between the EnChroma and control filters, averaged across habituation conditions.Once adjusted for multiple comparisons using a Bonferroni correction, only red and orange showed a significant difference in L/(L + L′) thresholds between filter conditions.For red, L/(L + L′) thresholds were significantly reduced with the EnChroma filter compared to the control filter (t = 4.36, p = 0.0018, α = 0.0071), while for orange they significantly increased (t = -3.5, p = 0.0070, α = 0.0071).To further explore the significant interaction between hue and filter, we conducted paired ttests on the difference scores between filter conditions, averaged across habitation conditions on results for the 7 hues.Following a Bonferroni correction for multiple comparisons, changes in threshold with the EnChroma filter compared to the control filter were larger for red than for all colors other than green (4.6 ≤ t ≤ 6.0, 0.0002 ≤ p ≤ 0.001).
We generated a set of predicted thresholds using the observed mean thresholds under the control filter condition to predict mean thresholds under the EnChroma filter condition.Specifically, we interpolated the chromaticities under the two filters at the observed threshold with the control filter and found the difference between the interpolated chromaticites.These predictions are plotted in Fig. 5 as the wide grey bars.There was no significant correlation between the observed changes in threshold between the EnChroma and control filter conditions and the model predictions (ρ = -0.036,p = 0.96).
In summary, the results of Experiment 2 imply that EnChroma filters may be able to reduce discrimination thresholds for particular hues, but we did not find evidence that they improved color sensitivity around the hue circle.

Experiment 3: Rating task
The rating task aimed to test whether EnChroma filters enhance the appearance of colors varying in L/(L + L′).We used a rating task where participants had to rate pairwise dissimilarities within a set of colored surfaces.We then reconstructed a geometrical map of the underlying stimulus space using multidimensional scaling, where any enhancement in color appearance along the L/(L + L′) axis is expected to increase the spacing along the equivalent axis in the MDS-reconstructed space.

Methods
Thirteen Munsell surfaces of high (N = 9) and low chroma (N = 4) were selected to provide a range of chromaticities in the MacLeod Boynton chromaticity diagram.We chose a halogen illuminant because our model predicted that under halogen the EnChroma filter would increase L/(L + L′) saturation more than S/(L + L′) saturation (Fig. 6a).We reasoned that a selective change by the filter in L/(L + L′) saturation should increase dissimilarity ratings along the L/(L + L′) axis relative to the + L′) axis.This we to show clearly in the results than similar changes in perceived saturation for both axes, because in that scenario participants could downscale their rating scale (e.g., if restricted to a scale from 0 to 9) to accommodate larger color differences across all stimuli, which might undo any changes in perceived saturation that may otherwise be observed.
For each filter condition, participants were first presented with all stimuli simultaneously to familiarize them with the range of available color differences (Fig. 6b).Participants were instructed to rate identical pairs as 0 and the most different as 9, and were asked to identify pairs they would give dissimilarity ratings of 0, 9 and 5.No feedback was given during this phase or any phase of the experimentthe familiarization process was intended to increase the consistency of the ratings and help participants make full use of the available rating scale.During the rating task two surfaces were viewed on each trial, presented manually by an experimenter wearing black sleeves and black gloves, and otherwise hidden from view.Participants were asked to give a verbal rating for how dissimilar each pair of surfaces appeared, on the scale from 0 to 9. The set of pairs included 4 duplicates to establish a baseline of surfaces rated against themselves.Two ratings were collected for each pair, giving 160 ratings in total.The stimuli were viewed through a single aperture, where experimental and control filters were used in separate repetitions of the task (Fig. 6c), conducted in randomized order.

Data analysis
Data processing was done using custom code written in Matlab (MathWorks Inc., Massachusetts, USA).Trial duplicates were averaged before the tied rank of the rating for each pair was found.Non-metric multidimensional scaling was performed on the resulting ranked dissimilarity matrices, specifying 2-dimensional MDS solutions, which represent the set of perceived dissimilarities as 2-dimensional Euclidean distances.
To relate the reconstructed maps of stimuli in the MDS solutions and the predictions made in the MacLeod Boynton chromaticity diagram, Procrustes analysis was used to optimally align the dimensions of the MDS solution with the cardinal axes of the deuteranomalous variant of the MacLeod Boynton chromaticity diagram (see Boehm et al., 2014).We allowed reflection and rotation in the Procrustes analysis, but not scaling, so the relative positions of the stimuli within the MDS solution remained unchanged, as did the relative distances between stimuli along orthogonal axes.The Procrustes-transformed coordinates of the stimuli in the MDS solutions were averaged across participants to give group average results.

Results
The average two-dimensional MDS solutions across participants are shown in Fig. 7a1 and 7a2.The general pattern of solutions agrees with that observed in previous studies which aimed to measure color appearance in anomalous trichromats for a stimulus set using MDS (e.g., Boehm et al., 2014;Paramei & Cavonius, 1999): desaturated surfaces are close together near the centre of the solution, and saturated hues are organised systematically in a hue circle towards the edge of the solution.
Group average MDS solutions for the two filter conditions are superimposed in Fig. 7a1 and 7a2.If the EnChroma filter enhances perceived L/(L + L′) saturations, then we would expect to see the surfaces along Dimension 1 further away from the achromatic point at the centre of the MDS solution in the EnChroma filter condition (solid circles) than in the control filter condition (open circles).
Fig. 7b shows the differences between filter conditions the absovalues along the Dimension 1 of the MDS solution (which has been aligned with L/(L + L′) by Procrustes transformation).Thus, positive differences occur when the surface is further from the achromatic centre of the MDS solution under the EnChroma filter than under the control filter, and negative values occur in the converse situation.Positive values imply enhancement to perceived L/(L + L′) saturation in the EnChroma filter condition relative to the control filter condition.The figure shows that most surfaces show small positive differences, consistent with an enhancement to perceived saturation by the EnChroma filter.To test the effect of the filters we conducted one-sample t-tests on the mean difference scores across surfaces between the EnChroma and control filter conditions.The t-tests showed that difference scores were significantly greater than 0 for the pre-habituation session (t = 2.30, p = 0.047), and there was a non-significant trend in the posthabituation session (t = 2.18, p = 0.057).
To investigate the effect of surface we conducted one-way ANOVAs on the difference scores for each surface.No significant effects of surface were found (F(12,117) = 1.64, p = 0.09 for the pre-habituation session; F(12,117) = 0.19, p > 0.99 for the post-habituation session).

Discussion
We conducted 3 experiments to measure the impact of an EnChroma filter on color discrimination and color appearance for deuteranomalous trichromats.In Experiment 1 we gathered asymmetric matches between target and matching Munsell surfaces under opposite (EnChroma versus control) filter conditions.We found that the EnChroma filter increased the perceived saturations of the Munsell surfaces to about the same extent as that predicted by our model (Fig. 3).This result is not unexpected.Since our predictions were built on an observer-specific model of metameric color matches, it would have been surprising if we had not been able to measure perceptually the enhancements in saturation we predicted.Nonetheless, the results imply, at least under the conditions of the experiment, that EnChroma filters do enhance the perceived saturation of broadband colors for deuteranomalous trichromats.
In Experiment 2, we measured the effect of an EnChroma filter on color discrimination in deuteranomalous trichromats.The results indicated that color discrimination thresholds were significantly reduced only for red stimuli, and not for orange, yellow, green, teal or purple stimuli.Our results do not provide support for the idea that EnChroma filters confer a generalized increase in color sensitivity, but they do imply that they have the potential to increase sensitivity to some color differences (e.g., for the broadband reds we tested).Is it possible that our experiment has missed broader effects on color discrimination by EnChroma filters?Since we conducted a within-participants study where discrimination under both filter conditions was assessed within the same session, our 'predictions' for the effect of the EnChroma filter on color discrimination thresholds were created post-hoc, based on observed color discrimination thresholds in the control filter condition (Fig. 5).For all stimuli other than the reds, the predicted effects of the EnChroma filter were modest and may simply have been too small to measure in our sample of 10 deuteranomals.It is possible that EnChroma could have caused larger changes in perceived saturation for surfaces that have different spectral features than those of our custom painted surfaces.Another stimulus consideration lies in the saturations of the tobe-discriminated colors.There is evidence that the contrast response functions of anomalous trichromats are steeper than those of normal trichromats at high (physical) red-green contrasts (Knoblauch et al., 2020;Boehm et al., 2021;Robinson et al., 2023).It is therefore possible that discrimination thresholds for saturated colors may be better facilitated by EnChroma filters than at the white point where we measured discrimination thresholds.Thus, different stimuli in Experiment 2 could have revealed, and, given the results of Experiment 1, could have been expected to reveal, broader impacts of EnChroma filters on color discrimination.
In Experiment 3 we measured the effect of an EnChroma filter on color appearance in deuteranomalous trichromats by asking participants to make pairwise ratings of color dissimilarity, and using MDS to reconstruct perceptual color spaces.We found a small but statistically significant effect of the EnChroma filter on increasing perceived color differences along the impaired L/(L + L′) color axis, for the prehabituation testing session and a similar sized trend in the posthabituation session.The results imply that EnChroma filters have the potential to enhance color appearance for deuteranomals.We selected as our illuminant a halogen for this experiment, because its dominance of light at long wavelengths mediated greater predicted enhancements in L/(L + L′) saturations than in S/(L + L′) saturations (Fig. 6).We reasoned that this asymmetry would help us to measure the effect of EnChroma filters.Generalised enhancement of perceived saturation for all color axes may have led participants to simply alter their rating scales, meaning that MDS would not be able to reveal the enhancement.On the other hand, a selective enhancement along one axis should allow measurable changes in ratings restricted to one color axis.However, it is possible that changes in perception are not determined by the absolute sizes of change in chromaticity conferred by EnChroma filters, but by percentage changes.Though the absolute changes in stimulus chromaticity by EnChroma are much greater along the L/(L + L′) axis than along the S/(L + L′) axis, the restricted gamut of S/(L + L′) under the long wavelength-biased halogen illuminant means that the percentage changes are similar for both axes.Thus, it is still possible that changes in rating scales between filter conditions could have affected our results and restricted our ability to detect changes in color appearance using the method.
What was the effect of habituation to the filters through a week of regular use?We conducted our perceptual tasks over two sessions.In the first session participants had not previously tried EnChroma filters.The second session was conducted after a week of habitual use.Habituation made little difference to the results for any of the three experiments.What influence of habituation should be expected?The effects of EnChroma filters on color vision should be influenced by color contrast adaptation (Krauskopf et al., 1982;Webster & Mollon, 1991), but we should expect different influences of contrast adaptation between the three tasks.For the asymmetric matching task in Experiment 1, there was little opportunity to adapt to the filters because there was continuous switching between the two filter conditions through different apertures throughout trials as the color matches were made.For Experiment 3, color contrast adaptation is expected to reduce perceived color contrast with the EnChroma filter, undoing or partially undoing any initial color contrast enhancements conferred (see Ilic et al., 2022 for a test of this conjecture for analagous contrast enhancement via wide gamut displays).In our experiment, if color contrast adaptation is long term over the habituation period, it would be expected to reduce perceived color contrast for our stimuli in both filter conditions, meaning that no change in the comparison of color contrasts between filter conditions should be expected between habituation conditions.If it is short term, however, it might be expected to counter any color contrast enhancements by the EnChroma filter in both sessions, leading to no measurable effects of the filter.The pattern of results we observea small effect of EnChroma filters on color contrast in both habituation conditionsis compatible with incomplete contrast adaptation, meaning that contrast adaptation does not entirely undo in color appearance the increases L/(L + L′) saturation conferred by EnChroma filters.It is worth noting that if users make sporadic rather than habitual use of the filters they might not experience as much reduction in contrast gain by contrast adaptation, and the filters' effects may be better preserved over time.For Experiment 2, color contrast adaptation is expected to increase color discrimination thresholds (Krauskopf et al., 1982).However, we observed the same reduction in discrimination thresholds for reds with the EnChroma filter in both habituation conditions.Though our available evidence to arbitrate between different accounts is limited, the results of Experiment 2 favour no effect of habituation on contrast adaptation.
Any color contrast adaptation to enhancements in chromatic contrasts conferred by EnChroma filters is likely to interact with the phenomenon of postreceptoral compensation in anomalous trichromatic color vision (Regan & Mollon, 1997;Boehm et al., 2014;Tregillus et al., 2021).Postreceptoral compensation is thought to occur when the full range of neural levels available to represent color in the cortex are exploited to amplify the reduced range of color contrasts achieved by comparing the activities of anomalous trichromats' L and L′ (or M′ and M) cones compared to those achieved by comparing the activities of normal trichromats' L and M cones.Postreceptoral compensation is thought to relatively normalize color appearance along anomalous trichromats' impaired color axes without affecting color discrimination thresholds (Boehm et al., 2014;Vanston et al., 2021), because the underlying contrast adaption should not impact the signal to noise ratios that determine color discrimination (Boehm et al., 2014(Boehm et al., , 2021)).The existence of postreceptoral compensation calls into question predictions for the effects of EnChroma filters on cone-opponent chromaticities of the type we have modelled (Somers & Bosten, 2024).If color appearance is already maximally compensated for anomalous trichromats by endogenous postreceptoral compensation, then there may be limited capacity in the cortical representation of color for external filter aids to enhance color appearance still further.Postreceptoral compensation may be one reason why the effect on color appearance of EnChroma filters that we observed in the results of Experiment 3 is relatively modest, and why others have not typically found positive effects of the filters.
The alternative scheme of perceptual learning (Seitz, 2017) might predict an effect of habituation on the impact of EnChroma filters on color contrast perception opposite to that predicted by contrast adaptation.Repeated exposure to EnChroma filters might enhance color contrast perception post-habituation if perceptual learning drives the observer to "tune in" to new relevant color signals.A recent paper by Werner et al. (2020) found, unexpectedly, that repeated use of EnChroma filters causes an enhancement to perceived red-green contrast when anomalous trichromatic participants are subsequently tested without the filter, an effect that they initially attributed to perceptual learning, but later to a reduction in contrast gain following adaptation that reduces multiplicative noise and therefore increases contrast response (Knoblauch, 2022).The results of our Experiment 2 do not provide support for color contrast enhancements in the post-habituation session that could result from perceptual learning, which would apply to both filter conditions (e.g., Fig. 5).For Experiment 3, such an effect would not reveal itself in the difference in distances in the MDS solution aligned with L/(L + L′) between filter conditions.A similar argument applies to Experiment 1: if the effect of perceptual learning applies to both filter conditions in the post-habituation condition, it would not affect color matches between filters.
Though we have tested the effect of EnChroma filters on naturalistic broadband-colored stimuli intended to be at least somewhat representative of reflective surfaces in real-world environments, our results are specific to our particular test conditions.Our companion paper (Somers & Bosten, 2024) has predicted, using a modelling approach, that the extent of color contrast enhancements by EnChroma filters varies with factors including illumination, observer and filter model.However, in that paper we predicted generally positive effects of the filters on L/(L + L′) for all the illuminants, filter models and deuteranomalous observers we included.In that sense our findings should be qualitatively, if not quantitatively, generalizable to most broadband colored surfaces.
The results of our three experiments allow us to conclude more positively than most authors of previous studies about the effects of EnChroma filters on color perception in anomalous trichromacy.We found that the EnChroma filter influenced metameric color matches as predicted, implying that they generally enhance perceived color contrast.We found that EnChroma filters have the potential to reduce color discrimination thresholds (though the effects we observed in Experiment 2 were restricted to reds).For color appearance we found evidence of a small enhancement in color appearance along the color axis impaired in anomalous trichromacy.It is important to note that our positive results do not imply that EnChroma filters have the potential to create "new color experiences" that are unachievable without the filters.Since filters cannot alter the spectral composition of monochromatic light, the spectrum locus of monochromatic lights which ultimately bounds the anomalous trichromatic color gamut cannot be altered by EnChroma filters or by any other spectrally-selective filter.The results of our sister modelling paper imply that the more desaturated gamut of broadband colored stimuli such as those typically encountered in natural scenes is enhanced by EnChroma filters.The results of the current paper show that EnChroma filters can have the predicted positive impact on anomalous trichromats' color perception of these real-world broadband stimuli.It is in this sense that EnChroma filters can be considered effective.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Filter transmission spectra, spectral power distributions of illuminants and chromaticities of all stimuli.(a) Transmission spectra of the Cx-25 Enchroma filter used for all experiments and of the control neutral density filter.(b) Normalized spectral power distributions of the illuminants: LED (Experiments 1 and 2) and halogen (Experiment 3).(c) Chromaticities of all stimuli.Target stimuli used in Experiment 1 are plotted in yellow, stimuli used in Experiment 2 are plotted in blue, and stimuli used in Experiment 3 are plotted in pink.In black are the chromaticities of all Munsell surfaces of Value 5 which were used as matching stimuli in Experiment 1. Chromaticities are plotted for the stimuli under the LED illuminant relative to the achromatic point, defined as Munsell Neutral 9.5.

Fig. 2 .
Fig. 2. Methods for Experiment 1. (a1) Diagram showing the apparatus for presenting target and matching stimulus array in different filter conditions.(a2) The two arrays of matching Munsell surfaces.(a3) Schematic illustrating the expected effect of the EnChroma filter on color matches: If the EnChroma filter enhances saturation, then a target viewed with the EnChroma filter will be matched to a more saturated target (than its Munsell chroma match) when the matching stimulus array is viewed with the control filter.(b1) Chromaticities of the targets presented with the control filter (black crosses) and chromaticities of the predicted matches from the array of surfaces with the EnChroma filter (red circles).The predicted matches are indicated by the pale blue shaded regions connecting the surfaces predicted to be matched.Also, for context, chromaticities of the targets with the EnChroma filter (red crosses), chromaticities of the predicted matching surfaces with the control filter (black circles), and chromaticities of all surfaces in the matching array with the EnChroma filter (red dots).(b2) Chromaticities of the targets presented with the EnChroma filter (red crosses) and chromaticities of the predicted matching surfaces with the control filter (black circles).The predicted matches are indicated by the pale blue shaded regions.Also, for context, chromaticities of the predicted matching surfaces under the EnChroma filter (red circles), chromaticities of the targets under the control filter (black crosses), and chromaticities of all surfaces in the matching array with the control filter (black dots).
Fig.3.Results of Experiment 1. (a1-a3) Predicted and observed average matches (over the 10 participants) where targets were presented with the control filter and the matching arrays were presented with the EnChroma filter.On each panel the black crosses are the chromaticities of targets with the control filter, the red open circles are the chromaticities of matching surfaces predicted by our model, and the red filled circles are the observed chromaticities of the mean matches to each target.Panel (a1) shows results for the first session (pre-habitation), panel (a2) shows results for the second session (post-habituation), and panel (a3) shows results averaged over both sessions.N.B., Chromaticities for all surfaces are plotted as they are under the control filter so that the differences in saturation between targets and matches are visible.(b1) -(b3) Predicted and observed matches where targets were presented with the EnChroma filter and the matching arrays were presented with the control filter.On each panel the red crosses are the chromaticities of targets with the EnChroma filter, the black open circles are the chromaticities of matching surfaces predicted by our model, and the black filled circles are the observed chromaticities of the mean matches to each target.Panel (b1) shows results for the first session (pre-habitation), panel (b2) shows results for the second session (post-habituation), and panel (b3) shows results averaged over both sessions.N.B., Chromaticities for all surfaces are plotted as they are under the contol filter so that the differences in saturation between targets and matches are visible.(c) Scatter plot showing the change in absolute L/(L + L′) relative to the achromatic point Munsell neutral 9.5 (i.e., positive values indicate that the perceived saturation of the target increases with the EnChroma filter) against the same quantity predicted by our model.The error bars indicate 95% confidence intervals.Results for the prehabituation session are shown in orange and results for the post-habituation session are shown in blue.The black dashed line indicates y = x.

Fig. 4 .
Fig. 4. Methods for Experiment 2 (color discrimination).(a) Apparatus and stimuli for Experiment 2. A single aperture was used and the different filter conditions were conducted sequentially in a random order.Stimuli were custom painted surfaces mounted in black perspex that could be manually rotated to randomize the target position.(b) Reflectance spectra for an example stimulus from each hue axis 10th most saturated).(c) Chromaticities of all stimuli with the control filter (black and with the EnChroma filter (red points).(d) Bar chart showing absolute L/(L + L′) relative to the white point with the control filter (black dots and colored bars) and the EnChroma (red dots).

Fig. 6 .
Fig. 6.Methods for Experiment 3. (a) Chromaticities of the Munsell surfaces used in Experiment 3 with the control neutral density filter (crosses) and with the EnChroma filter (solid circles).The surfaces are plotted in an equivalent of the MacLeod-Boynton (1979) chromaticity diagram constructed for a deuteranomal.The set of surfaces for each filter condition is plotted relative to its respective white point (defined as Munsell neutral 9.5).(b) Example stimuli used in Experiment 3. (c) Apparatus for Experiment 3: One filter was inserted at a time and the test run twice (in a randomized order) for the EnChroma and control filter conditions.

Fig. 7 .
Fig. 7. Results of Experiment 3: Rating task.(a1-a2) MDS solutions based on the average dissimilarity matrices (over the 10 participants), transformed by Procrustes analysis so that the X and Y axes coincide as closely as possible with the stimulus chromaticities plotted in Fig. 6a.This means that 'Transformed Dimension 1′ corresponds to the L/(L + L′) axis and 'Transformed Dimension 2′ corresponds to the S/(L + L′) axis.(a1) shows results for the pre-habituation session and (a2) shows results for the post-habituation session.Data points are colored according to their chromaticities, and are numbered as in Fig. 6a.(b) Predicted and observed changes in L/(L + L′) saturation conferred by the EnChroma filter.The colored bars show the differences between the absolute positions of the stimuli along 'Transformed Dimension 1′ of the MDS solutions between the EnChroma filter and the control filter conditions.Positive values represent enhancements of perceived L/(L + L′) saturation by the EnChroma filter relative to the control filter (the stimulus is further from the centre of the MDS solution with the EnChroma filter than with the control filter), whereas negative values represent reductions of perceived L/(L + L′) saturation by the EnChroma filter relative to the control filter.The striped bars show results from the pre-habituation session and the solid bars from the post-habituation session.The perceived changes are expressed as difference scores from the positions in the MDS solutions (left y-axis).Error bars are 95 % confidence intervals.The grey bars show the model predicted changes in L/(L + L′) saturation (Δ|L/(L + L′)|) by the EnChroma filter compared to the control filter, scaled to have the same mean as that of the experimental results.Predicted saturation enhancements are positive and saturation reductions are negative on the scale (right y-axis).Please note that the distances plotted in Panel (b) which are based on the means across MDS solutions for individual participants may not match the distances in the panels plotted in panels (a1) and (a2) which show group average MDS solutions.