Clay & Cortex Lens tint study

Method

How the contrast is computed, what is measured, and what is not known

This page is the honest version of the pitch. It says where every number comes from and how sure we are of it.

1. The physics

A lens is a spectral transmission curve T(λ) with T ≤ 1 everywhere. It cannot add light; it can only remove light differently from the clay and from the background. The eye sees the result through three cone classes, so the question is: for this clay, this background, this illuminant and this observer, which T(λ) produces the largest usable difference in cone excitation?

The computation, per lens: the spectral radiance of the clay (its reflectance under the light that falls on it) and of the background (a sky radiance, or a reflectance under its own light) are multiplied by T(λ) and integrated against the Stockman & Sharpe (2000) 2° cone fundamentals, the basis of CIE 170-1:2006, and against the CIE 1931 ȳ function for luminance. Cone contrast of the clay against the background is (T − B)/B per cone class (Cole, Hine & McIlhagga 1993; Sankeralli & Mullen 1996); Weber luminance contrast is (Yclay − Ybg)/Ybg. Daylight spectra come from the CIE daylight model (Judd, MacAdam & Wyszecki 1964) at a colour temperature: 5500 K for a sunlit surface, 6504 K (D65) for overcast, 10 000 K for a clear sky at low elevation.

The largest single term is the light on the clay, not the lens. The same orange clay against the same blue sky has a Weber contrast of about −0.29 when the sun is behind you and −0.86 when it is ahead, and in the second case no lens improves it, because the clay is lit by the same blue skylight the lens removes. The recommender therefore asks for the sun's position, or computes it from place, time and the bearing you shoot (NOAA solar equations, ~0.1° accuracy).

2. The objective

Tracking a fast target is a luminance-channel job. Pursuit gain, latency and positional accuracy are severely impaired below two to three times luminance-contrast threshold (Spering et al. 2005); low-contrast targets are perceived as slower than they are (Thompson 1982; Stone & Thompson 1992), which for a shooter means shooting behind; and purely chromatic motion is seen poorly (Cavanagh, Tyler & Favreau 1984). So the index the recommender ranks by is

index = wlum·r(CY/θlum) + wlm·r(CLM/θlm) + ws·r(CS/θs),   r(x) = x1.5/(41.5 + x1.5)

with weights 1.0, 0.3 and 0.1. The saturating response r (Naka–Rushton form, half-response at four times threshold) keeps moving across the 1–10× band, where contrast still changes pursuit and perceived speed, and flattens beyond it, which is what stops the model recommending the darkest lens for a scene that is already at ceiling. The luminance threshold θlum rises as the background luminance behind the lens falls below about 100 cd/m² (a De Vries–Rose square-root law), which is the transmission penalty that stops it recommending a 22% lens at dusk. The thresholds, weights and knee are placeholders; the study exists to fit them.

3. What the display can and cannot do

A laptop display sits 10–56× below the luminance of a real range, and rendering the clay–sky pair as seen through a strong long-pass lens puts it outside the sRGB gamut. So the study does not show a tinted world and ask whether it looks better. It presents the cone-contrast vector a lens creates, scaled by a multiplier under adaptive control, on a neutral grey field. Under von Kries adaptation, cone contrast is the quantity that survives a change of adapting field, so this is the right thing to present; and because every lens condition looks like a faint grey-or-coloured disc, the observer cannot tell which lens a trial belongs to, and expectation cannot leak into the thresholds. The transmission cost, glare and absolute luminance are modelled, not shown.

The display is assumed to be sRGB with a D65 white. Luminance contrast is robust to that assumption; chromatic axes are less so, which is why the colour-vision result is reported as a screening flag and never as a diagnosis.

4. The study

  1. The observer's isoluminant point. The red–green axis is defined so that its two poles have the same luminance for the standard observer; but people with normal colour vision weight their L and M cones over a several-fold range (Carroll, Neitz & Neitz 2002; Hofer et al. 2005), so for most of them one pole is slightly brighter than the other, and a red–green threshold measured along the standard axis is partly a brightness detection. That is small for a normal observer and decisive for a red–green-weak one, who could otherwise pass the screening on the brightness leak. So the session first measures each observer's own null by heterochromatic flicker photometry (Ives 1912; Wagner & Boynton 1972): the two poles alternate at about 15 Hz, above the rate at which colour differences can be seen to flicker, so only a brightness difference flickers (Lee, Martin & Valberg 1988), and the observer adds or removes an equal L+M increment until the flicker is least; three settings from random starting points, median taken, spread recorded. Task 1's red–green axis is rotated to that null, and the L:M weight ratio it implies is reported. The blue–yellow axis keeps its standard null, since S cones contribute nothing measurable to flicker luminance (Eisner & MacLeod 1980). A flicker null and a static-detection null can differ by a few percent; that residual is stated, not hidden.
  2. Cone-contrast thresholds on three cardinal directions (luminance, L−M along the observer's own null, S) with a 1° disc at 3° eccentricity for 300 ms, four-alternative location, ZEST adaptive placement (King-Smith et al. 1994), 36 trials per axis. In the tradition of the cone contrast test (Rabin, Gooch & Ivan 2011).
  3. Clay-sized moving target, luminance only: a 15-arcmin disc (a 110 mm clay at 25 m) crossing fixation at 20°/s for 150 ms in one of four directions, four-alternative direction judgement, 48 trials.
  4. Lens conditions: the same moving disc carrying the cone-contrast vector each of six lens classes produces for a chosen scene, scaled by a multiplier under adaptive control, interleaved, 40 trials per lens. The threshold multiplier per lens is the measurement. The session compares it with what the model predicts from tasks 1 and 2 (Kendall's τ) and with a standard-observer prediction, and reports the luminance contrast the disc had at each lens's threshold, which shows directly whether colour is contributing.
  5. Preference: the scene rendered approximately as seen through each lens, rated 1–7. Reported separately, because preference is what people buy on and it is not the same thing as performance.

Screen scale is calibrated by matching a bank card (ISO/IEC 7810 ID-1, 85.60 × 53.98 mm) and viewing distance by the blind-spot method (Li, Joo, Yeatman & Reinecke 2020), cross-checked against a self-report. Durations are presented in whole frames and the achieved duration is logged; a dropped frame rejects the trial. Thresholds are fitted by maximum likelihood with a fixed slope (Wichmann & Hill 2001 for why the lapse rate is bounded), with parametric bootstrap intervals, and any threshold outside the range of stimuli actually shown is marked "not measurable" rather than reported.

Gates, stated in advance. Test–retest ICC ≥ 0.7 on each threshold before any individual claim. Model-predicted versus measured lens ranking τ ≥ 0.6 across observers before the personal layer is used in the recommender. A field study with real lenses and a process-measure primary (reaction time or gaze acquisition) before any performance claim. Until then, the recommender's outputs are predictions of contrast, and nothing else.

5. Where the spectra come from

6. Provenance and independence

Lens names appear because people shop by name. Inclusion is not endorsement. The ranking is computed from the physics above and is independent of any commercial arrangement; if affiliate links are ever added they will be labelled, and the ranking code runs entirely in your browser (/js/scene.js, /js/colour/), so what it does can be read from this site. The rules that bind any future commercial link, including that a ranking is never for sale, are published at Clay & Cortex: the rules.

References

  1. Stockman, A. & Sharpe, L. T. (2000). The spectral sensitivities of the middle- and long-wavelength-sensitive cones derived from measurements in observers of known genotype. Vision Research, 40, 1711–1737.
  2. CIE 170-1:2006. Fundamental chromaticity diagram with physiological axes, Part 1. Commission Internationale de l'Éclairage.
  3. Judd, D. B., MacAdam, D. L. & Wyszecki, G. (1964). Spectral distribution of typical daylight as a function of correlated color temperature. JOSA, 54, 1031–1040.
  4. Cole, G. R., Hine, T. & McIlhagga, W. (1993). Detection mechanisms in L-, M-, and S-cone contrast space. JOSA A, 10, 38–51.
  5. Sankeralli, M. J. & Mullen, K. T. (1996). Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms. JOSA A, 13, 906–915.
  6. Rabin, J., Gooch, J. & Ivan, D. (2011). Rapid quantification of color vision: the cone contrast test. Investigative Ophthalmology & Visual Science, 52, 816–820.
  7. Ives, H. E. (1912). Studies in the photometry of lights of different colours. I. Spectral luminosity curves obtained by the equality of brightness photometer and the flicker photometer under similar conditions. Philosophical Magazine, 24, 149–188.
  8. Wagner, G. & Boynton, R. M. (1972). Comparison of four methods of heterochromatic photometry. Journal of the Optical Society of America, 62, 1508–1515.
  9. Lee, B. B., Martin, P. R. & Valberg, A. (1988). The physiological basis of heterochromatic flicker photometry demonstrated in the ganglion cells of the macaque retina. Journal of Physiology, 404, 323–347.
  10. Eisner, A. & MacLeod, D. I. A. (1980). Blue-sensitive cones do not contribute to luminance. Journal of the Optical Society of America, 70, 121–123.
  11. Carroll, J., Neitz, J. & Neitz, M. (2002). Estimates of L:M cone ratio from ERG flicker photometry and genetics. Journal of Vision, 2(8), 531–542.
  12. Hofer, H., Carroll, J., Neitz, J., Neitz, M. & Williams, D. R. (2005). Organization of the human trichromatic cone mosaic. Journal of Neuroscience, 25, 9669–9679.
  13. Cavanagh, P., Tyler, C. W. & Favreau, O. E. (1984). Perceived velocity of moving chromatic gratings. JOSA A, 1, 893–899.
  14. Thompson, P. (1982). Perceived rate of movement depends on contrast. Vision Research, 22, 377–380.
  15. Stone, L. S. & Thompson, P. (1992). Human speed perception is contrast dependent. Vision Research, 32, 1535–1549.
  16. Spering, M., Kerzel, D., Braun, D. I., Hawken, M. J. & Gegenfurtner, K. R. (2005). Effects of contrast on smooth pursuit eye movements. Journal of Vision, 5(5):6.
  17. King-Smith, P. E., Grigsby, S. S., Vingrys, A. J., Benes, S. C. & Supowit, A. (1994). Efficient and unbiased modifications of the QUEST threshold method. Vision Research, 34, 885–912.
  18. Wichmann, F. A. & Hill, N. J. (2001). The psychometric function: I. Fitting, sampling, and goodness of fit. Perception & Psychophysics, 63, 1293–1313.
  19. Li, Q., Joo, S. J., Yeatman, J. D. & Reinecke, K. (2020). Controlling for participants' viewing distance in large-scale, psychophysical online experiments using a virtual chinrest. Scientific Reports, 10:904.
  20. Naka, K. I. & Rushton, W. A. H. (1966). S-potentials from luminosity units in the retina of fish (Cyprinidae). Journal of Physiology, 185, 587–599.
  21. Wolffsohn, J. S., Cochrane, A. L., Khoo, H., Yoshimitsu, Y. & Wu, S. (2000). Contrast is enhanced by yellow lenses because of selective reduction of short-wavelength light. Optometry and Vision Science, 77, 73–81.
  22. Erickson, G. B., Horn, F. C., Barney, T., Pexton, B. & Baird, R. Y. (2009). Visual performance with sport-tinted contact lenses in natural sunlight. Optometry and Vision Science, 86, 509–516.
  23. Christie, C. J., Nellemann, S., Davies, T., Fourie, J. L. & Davy, J. P. (2023). Sunglass tint does not impact the indoor catching performance of cricket fielders. Frontiers in Sports and Active Living, 5:1188270.
  24. Improving filter recommendations: the role of individual light sensitivity in ecological conditions (2026). Frontiers in Psychology, doi 10.3389/fpsyg.2026.1755789.
  25. Meeus, J. (1998). Astronomical Algorithms, 2nd ed., ch. 25, as implemented in the NOAA solar calculator.
  26. IEC 61966-2-1:1999. Multimedia systems and equipment: colour measurement and management, Part 2-1: default RGB colour space, sRGB.

The design appraisal behind this study, with the computed contrasts for eleven scenes and nine idealised filters, is docs/tint-filter-appraisal.md in the project repository.