Unlike their red-green results, the published colour-blindness models split on blue and yellow. Across 20,000 random colour pairs, the 2009 model of Machado, Oliveira and Fernandes and the 1997 model of Brettel, Viénot and Mollon share 34% of the pairs either one squeezes into a near match in the blue-yellow (tritan) case, against 69–88% for red-green, Viénot's 1999 model included. Machado's authors, in a sentence a 2021 DaltonLens review quotes, say they did not try to model tritanopia; on our grid of 4,913 screen colours, their full-severity tritan matrix lands a mean ΔE*ab, the standard CIELAB colour difference, of 15.9 from Brettel's output.
Chrome's developer tools and Firefox's accessibility inspector both base their simulations on Machado's paper. Our figures measure the model; we did not test either browser.
A projection and a cone shift redraw each pixel by separate routes
All three models work from the three cone types' sensitivities, the LMS space. Brettel's 1997 paper projects each colour onto two half-planes. Its protan and deutan anchors, a 475 nm blue and a 575 nm yellow, come from reports of people with an inherited deficiency in one eye. The tritan anchors, a 660 nm red and a blue-green near 485 nm, came from a single reported case of acquired tritanopia in one eye. The 1999 paper folds the half-planes into one plane and covers protan and deutan only.
The authors' page for Machado's model describes a physiologically based model that shifts the affected cone's sensitivity, tabulated as 3×3 matrices. By our check, its full-severity protan and deutan matrices flatten colour space onto a plane, though not by projection, and its full-severity tritan matrix flattens nothing (determinant 0.236).
A gamma shortcut paints the red-green views about ten ΔE*ab units off
Screen values are gamma-encoded. Viénot's paper decodes them to linear light in its equation (1) and re-encodes in equation (7); Brettel set up a linear display. Machado's page does not say. The R package colorspace applied Machado's matrices to gamma-encoded values until version 2.1-0, "following the illustrations of Machado et al. 2009".
On our grid, Machado's full-severity matrices applied to gamma-encoded values shift the output by a mean ΔE*ab of 10.7 for protanopia and 10.3 for deuteranopia, more than Machado and Brettel differ on red-green. For the tritan matrix the shortcut costs under 8, about half the gap between the two models.
Red-green models produce largely the same confusable pairs
Machado's protanopia and deuteranopia sit a mean ΔE*ab of 3.5 to 6.1 from Brettel's, depending on the neutral grey chosen. Brettel's and Viénot's own models differ from each other by 9.3 for protanopia and 10.7 for deuteranopia. We call a pair collapsed when a CIEDE2000 difference of 5 or more falls below 5, a working line of our own; by it, the red-green models share 69–88% of collapsed pairs.
An error red #dc2626 and a success green #16a34a start 72.5 apart in CIEDE2000. Simulated deuteranopia brings them to 7.9 under Machado, 8.7 under Brettel and 7.1 under Viénot. The models part on greys instead: Brettel's paper uses an equal-energy neutral, which is not the sRGB white, so a mid grey of 128 comes out pink, at 139, 127, 128 under protanopia. Given a D65 neutral, Brettel keeps them grey, as Machado does.
That near collapse is what WCAG success criterion 1.4.1, Use of Color, targets. At Level A in WCAG 2.2, approved in October 2025 as ISO/IEC 40500:2025, it requires that "Color is not used as the only visual means of conveying information". Red and green stay allowed.
Machado's tritan matrix generates its own set of blue-yellow confusions
Machado's paper, as quoted in the DaltonLens review, calls its tritanomaly simulation an approximation and says the authors "restrain our model from trying to model tritanopia". We could not open the 5.5 MB paper to check. The authors' page describes severity 1.0 as dichromacy for all three types.
On our pairs, Machado's tritan matrix collapses 214 where Brettel's collapses 453, or 460 with a D65 neutral, and the two sets overlap by about a third. Neither output is ground truth. Brettel's paper states "A tritanopic subject was not available"; Machado's page reports validation with groups of people with colour-vision deficiency without naming the types.
An unflagged approximation built the blue-yellow view in our simulator
Our colour-blindness simulator uses Machado's matrices. It already decoded sRGB to linear light with the IEC 61966-2-1 curve, and its anomaly views matched the authors' severity-0.5 rows exactly. Until 2 October 2026, though, its full-severity matrices were rounded to three decimals, three tritan entries wrongly, up to 1.66 ΔE*ab from the authors' table. The tritan views carried no warning about their reliability, the anomaly views were fixed at a severity of 0.5 without being labelled as such, and a prevalence note cited a 0.4% figure for women without specifying it was for European populations.
The fix, made on 2 October 2026, uses the authors' table to six decimals, adds a severity slider from 0.1 to 1.0 shown on every label, and marks both tritan views less reliable. It also reports clipping: the full-severity tritan matrix pushes 2,049 of our 4,913 grid colours off the screen's range.
A fixed severity setting sketches one point on a continuous scale
Machado's table runs from 0.0, no deficiency, to 1.0, dichromacy, in steps of 0.1, and the authors equate dichromacy with anomalous trichromacy at a severity of 20 nm. On our grid the setting moves the output more than the choice of red-green model: deuteranomaly at 0.1 and at 0.5 differs by a mean ΔE*ab of 17.3.
Screenings in Singapore and Kaohsiung record fewer affected girls than European figures
These screenings used different tests and samples, so they do not compare directly. Diagnosis and grading are done with clinical tests by an eye-care professional.
| Population and source (year published) | Sample and test | Result as published |
|---|---|---|
| Singapore men born 1962, at National Service registration (Singapore Med J, 1980) | 27,225, Ishihara | 4.430% partial red-green defects |
| Singapore schoolchildren aged 13–15 (Chia et al., 2008) | 1,249, Ishihara | boys 5.3%, girls 0.2% |
| Kaohsiung school screening (Kuo et al., 2023) | size not in abstract, Ishihara | congenital red-green: males 3.46%, females 0.14% |
| Sichuan University, 2022 freshman intake (Gao and Tian, 2023) | 17,303, colour vision plates (Version 6) | all defects: males 4.11%, females 0.16% |
| Medical students and health staff, Seremban, Malaysia (2006) | 1,427, test not in abstract | males 6.7%, females 0.4% |
The 1980 study gave Chinese 4.547%, Malays 4.612% and Indians 2.676%; the 2008 study found no significant difference among boys, at 5.4%, 4.9% and 4.9% (P = 0.97). The 1980 paper notes that Ishihara charts cannot detect tritan defects, so the three Ishihara studies count red-green only. The 2008, 2023, 2006 and Birch figures come from PubMed abstracts read on 2 October 2026. The studies we could read include none from Hong Kong, Indonesia, the Philippines, Thailand or Vietnam.
Birch's 2012 review puts European prevalence at about 8% of men and 0.4% of women, and 4% to 6.5% among Chinese and Japanese men, adding that "the male: female prevalence ratio is markedly different in Europeans and Asians". The female figures from Singapore and Kaohsiung, 0.2% and 0.14%, are half or less of that European 0.4%; the women in Seremban's staff sample match it.
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