Selects the x̄ ȳ z̄ colour matching functions displayed in the CMF canvas.
Spectral Band & CMF Overlay
Hover or drag across the canvas to move the wavelength cursor. The rainbow strip shows the perceived colour of each monochromatic wavelength. Curves show the selected CMF and optional overlays.
Photopic V(λ) vs Scotopic V′(λ)
LMS Cone Fundamentals
Wavelength Detail
CMF Data Table (5 nm step)
Active row highlighted in yellow| λ (nm) | x̄(λ) | ȳ(λ) | z̄(λ) | V(λ) | V′(λ) | L(λ) | M(λ) | S(λ) | Hex |
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CSV contains: wavelength (nm), CIE x̄ ȳ z̄,
photopic V(λ), scotopic V′(λ), LMS cone fundamentals,
sRGB hex for each 5 nm step (380–780 nm, 81 points).
JSON includes: observer setting, current wavelength, full grid with
CMF, V(λ), V′(λ), LMS, hex for all 81 points.
Visible Range & the Electromagnetic Spectrum
The visible spectrum spans approximately 380–780 nm. Shorter wavelengths (below 380 nm) are ultraviolet (UV); longer wavelengths (above 780 nm) are near-infrared (NIR). Within the visible range, wavelength is perceived as hue: violet at 380 nm through blue, cyan, green, yellow, orange to red at 780 nm.
CIE 15:2004 — Colorimetry & Standard Observer
In 1931 the CIE standardised how a “normal” observer perceives any spectral distribution. Three primaries R, G, B were mixed until subjects matched a monochromatic test light at each wavelength. The resulting colour matching functions x̄(λ), ȳ(λ), z̄(λ) allow any SPD to be condensed to three tristimulus values. This tool uses the Wyman et al. (2013) piecewise Gaussian analytical approximation for the 1931 observer, valid 380–780 nm with <0.06% RMS error.
The 1964 10° observer covers a wider retinal area (relevant for large surfaces or industrial colour measurement). The 2012 (Stockman–Sharpe) observer refines the 2° data with modern cone fundamentals.
Reference: CIE 15:2004; C. Wyman et al., JCGT 2(2), 2013.
Photopic vs Scotopic Vision & the Purkinje Effect
Photopic vision (bright conditions, >3 cd/m²) uses three cone types — L (~560 nm), M (~530 nm), S (~420 nm). The combined sensitivity curve V(λ) peaks at 555 nm (yellow-green) with Km = 683 lm/W.
Scotopic vision (dim conditions, <0.001 cd/m²) relies on rods only. The scotopic efficiency V′(λ) peaks at 507 nm (blue-green) with Km′ = 1700 lm/W. This is the Purkinje shift: at dusk, blue-greens look relatively brighter than reds compared to daylight.
LMS Cone Fundamentals
The three cone types in the human retina are named by the wavelength they respond to most strongly: L (long, ~560 nm), M (medium, ~530 nm), and S (short, ~420 nm). The LMS cone fundamentals are the basis functions that, after a 3×3 linear transform, yield the XYZ tristimulus values.
About 8% of men have anomalous L or M cone sensitivity (red–green colour vision deficiency). About 0.003% of people have no S cones (tritanopia).
IEC 61966-2-1 — sRGB Colour Space
All colour chips in this laboratory are rendered via the IEC 61966-2-1 sRGB colour space: linear RGB from 3×3 XYZ matrix, then gamma encoding (γ ≈ 1/2.2). Out-of-gamut colours are normalised by maximum channel before encoding.
Reference: IEC 61966-2-1:1999.
Dominant Wavelength
The dominant wavelength is the spectral wavelength that, when mixed with the reference white (D65), matches the chromaticity of the test stimulus. It is found by drawing a line from D65 through the test point on the CIE xy diagram and extending to the spectral locus. For non-spectral (purple) colours, the complementary wavelength is reported instead.
CIE Tristimulus Integration
CIE 1931 2° Observer — Piecewise Gaussian
Source: C. Wyman, P.-P. Sloan, P. Shirley, JCGT 2(2), 2013.
CIE xy Chromaticity Coordinates
Luminous Efficacy
LMS Cone Fundamentals (Gaussian approximation)
sRGB Conversion (IEC 61966-2-1)
CIELAB & ΔE*ab
- CIE, Colorimetry, 3rd Edition, CIE 15:2004. CIE 1931 and 1964 Standard Observer CMFs, CIELAB, standard illuminants.
- C. Wyman, P.-P. Sloan, P. Shirley, “Simple Analytic Approximations to the CIE XYZ Color Matching Functions,” JCGT 2(2):1–11, 2013. Piecewise Gaussian approximation used for the CIE 1931 observer in this lab.
- A. Stockman, L. T. Sharpe, “The spectral sensitivities of the middle- and long-wavelength-sensitive cones derived from measurements in observers of known genotype,” Vision Research 40:1711–1737, 2000. Cone fundamentals underlying the CIE 2012 observer.
- G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed., Wiley, 2000. Comprehensive reference for visible spectrum, CMFs, luminous efficiency, chromaticity.
- IEC, IEC 61966-2-1:1999 — sRGB Colour Space. XYZ-to-sRGB matrix and transfer function used for all hex colour output.
- M. D. Fairchild, Color Appearance Models, 3rd ed., Wiley, 2013. Colour appearance, chromatic adaptation, cone fundamentals, Purkinje shift.
- D. B. Judd, G. Wyszecki, Color in Business, Science and Industry, 3rd ed., Wiley, 1975. Historical reference for photopic/scotopic vision, Fraunhofer lines, spectral nomenclature.
- CIE, CIE S 014-1:2006 — Colorimetric Observers. Formal definition of the CIE standard colorimetric observers.
- W. S. Stiles, J. M. Burch, “N.P.L. colour-matching investigation: Final report (1958),” Optica Acta 6:1–26, 1959. 10° observer data underlying CIE 1964.
- E. R. Hunt, M. R. Pointer, Measuring Colour, 4th ed., Wiley, 2011. Practical colorimetry, dominant wavelength, LMS transforms.
CMF values, photopic/scotopic sensitivity, and LMS cone response at the midpoint of each named spectral band, computed with the currently selected observer.
| Band | Range | x̄ | ȳ | z̄ | V(λ) | V′(λ) | L | M | S | Hex |
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CMF values at 14 test wavelengths under all three CIE observers. ΔE*ab computed in CIELAB between 1931↔1964 and 1931↔2012 to quantify observer metamerism.
| λ | x̄ (31) | ȳ (31) | z̄ (31) | 1931 | 1964 | 2012 | ΔE 31↔64 | ΔE 31↔12 |
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| λ (nm) | x̄ | ȳ | z̄ | x | y | Swatch | Hex |
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