Reflectance Spectra — A (blue) · B (orange) · |A−B| (green fill)

Perceived Colour Under Each Illuminant

Metamerism Index (ΔE*_ab)

Illuminant	ΔE*ab	ΔL*	Δa*	Δb*	Status

ΔE*ab Across Illuminants

CIE xy Chromaticity Diagram — spectral locus · A (•) · B (◼) per illuminant

CIELAB a*b* Plot — A (•) · B (◼) per illuminant

Spectral Stimulus Mismatch Function

R_A(λ)·I(λ) vs R_B(λ)·I(λ) under preview illuminant. Red fill = |difference|.

XYZ Values Under D65 — CIE normalised

Spectrum	X	Y	Z	x	y	Hex	Swatch

Export & Share

PNG exports the reflectance overlay. CSV/JSON copy spectral data + ΔE values for all illuminants. Share URL encodes both spectrum control points.

Data content

CSV contains: wavelength (nm), reflectance A, reflectance B, |difference| for each 5 nm step.
JSON includes: observer setting, 16 control-point wavelengths, control values for A and B, ΔE per illuminant for all 7 illuminants.

Tip: Pin A = metameric pair via Share URL, then change B to explore how different spectra interact with each illuminant.

Applicable standards & principles

CIE 13.3-1995 — Method of Measuring and Specifying Colour Rendering

Defines the Special Metamerism Index as the ΔE*_ab colour difference between two colour stimuli under a test illuminant, after they have been matched under the reference illuminant. The test/reference illuminant pair (e.g. D65/A) is the standard way to quantify illuminant metamerism.

Reference: CIE 13.3-1995.

CIE 15:2004 — Colorimetry

The CIE 1931 2° and CIE 1964 10° Standard Observer colour-matching functions. Spectra are integrated against CMF×illuminant to obtain XYZ 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, and a Gaussian approximation for the 1964 observer.

Reference: CIE 15:2004; C. Wyman et al., JCGT 2(2), 2013.

CIE S 014-2 (D-illuminant series)

Defines the spectral power distribution of CIE daylight illuminants (D50, D55, D65, D75) based on Judd et al. eigenvector reconstruction from measured daylight spectra. D65 (6504 K) is the standard for colour science; D50 (5003 K) is the ISO 3664 graphic arts viewing standard.

Reference: CIE S 014-2:2006.

CIE 51.2-1999 — Observer Metamerism

Observer metamerism arises when two spectra that match for one observer (2°) differ for another (10°). CIE 51.2 defines a method for evaluating observer metamerism by computing ΔE between the 2° and 10° observer for the same sample under the same illuminant.

Reference: CIE 51.2-1999 (Practical Methods for the Observation of Observer Metamerism).

IEC 61966-2-1 — sRGB Colour Space

Perceived colours are rendered on screen by converting CIE XYZ to sRGB via the IEC 61966-2-1 3×3 matrix, with gamma encoding for display. Colour swatches in the illuminant comparison rows use this pipeline.

Reference: IEC 61966-2-1:1999.

CIELAB Colour Space (CIE L*a*b*)

CIELAB is the CIE 1976 perceptually uniform colour space. The ΔE*_ab Euclidean distance approximates perceived colour difference. Values below 1 are imperceptible; 1–3 noticeable to trained observers; above 6 strongly visible.

Reference: CIE 15:2004, §8.2.1.

Fluorescent Lamp Standards (CIE F-series)

The CIE defines 12 representative fluorescent illuminants (F1–F12). F2 is cool-white (4230 K), F7 simulates D65 (broadband), and F11/TL84 is a narrow triband source (4000 K) widely used in retail lighting. Fluorescent spiky SPDs cause especially strong metamerism compared to broadband daylight.

Reference: CIE 15:2004, Table T.6.

Mathematical formulations

Metamerism Condition

Two surfaces A, B are metamers under illuminant I if:

X_A = X_B, Y_A = Y_B, Z_A = Z_B

where X = (1/k) · ∑ R(λ) · I(λ) · x̄(λ) · Δλ
      Y = (1/k) · ∑ R(λ) · I(λ) · ȳ(λ) · Δλ
      Z = (1/k) · ∑ R(λ) · I(λ) · z̄(λ) · Δλ
      k = ∑ I(λ) · ȳ(λ) · Δλ

Illuminant metamerism: X_A = X_B under I₁ but X_A ≠ X_B under I₂
Observer metamerism: X_A = X_B for 2° but X_A ≠ X_B for 10°

CIELAB Colour Coordinates

f(t) = t^1/3 if t > (6/29)³
= (29/6)²·t/3 + 4/29 otherwise

L* = 116·f(Y/Y_n) − 16
a* = 500·[f(X/X_n) − f(Y/Y_n)]
b* = 200·[f(Y/Y_n) − f(Z/Z_n)]

X_n, Y_n, Z_n = white point (perfect reflector under illuminant)

ΔE*ab (Euclidean)

ΔE*_ab = √[(ΔL*)² + (Δa*)² + (Δb*)²]

Perceptual thresholds:
ΔE < 1 — imperceptible
ΔE 1–3 — noticeable to trained observer
ΔE 3–6 — visible to most observers
ΔE > 6 — strongly visible (fail)

CIE xy Chromaticity

x = X / (X + Y + Z)
y = Y / (X + Y + Z)

The (x, y) chromaticity diagram projects the 3D XYZ gamut onto a 2D plane. The spectral locus boundary represents pure monochromatic light. Metamerism appears as chromaticity shift between illuminants.

Spectral Mismatch Function

ΔS(λ) = R_A(λ)·I(λ) − R_B(λ)·I(λ)

= [R_A(λ) − R_B(λ)] · I(λ)

Metamers have ΔS(λ) ≠ 0 but ∑ ΔS(λ)·CMF(λ) = 0. When I(λ) changes, ∑ ΔS(λ)·CMF(λ) ≠ 0 → metamerism failure.

CIE 1931 2° Observer — Piecewise Gaussian

g(λ; μ, σ₁, σ₂) = exp(−½ d² / σ_k²)
where d = λ − μ, σ_k = σ₁ if d < 0 else σ₂

x̄(λ) = 1.056·g(599.8,37.9,31.0) + 0.362·g(442.0,16.0,26.7) − 0.065·g(501.1,20.4,26.2)
ȳ(λ) = 0.821·g(568.8,46.9,40.5) + 0.286·g(530.9,16.3,31.1)
z̄(λ) = 1.217·g(437.0,11.8,36.0) + 0.681·g(459.0,26.0,13.8)

Source: C. Wyman, P.-P. Sloan, P. Shirley, JCGT 2(2), 2013.

Blackbody Radiation (Illuminant A)

B(λ, T) = c₁ / [λ⁵ · (e^c₂/(λT) − 1)]

c₁ = 3.74183 × 10⁻¹⁶ W·m²
c₂ = 1.4388 × 10⁻² m·K
Illuminant A: T = 2856 K

Academic references & citations

CIE, Colorimetry, 3rd Edition, CIE 15:2004. CIE 1931 and 1964 Standard Observer CMFs, CIELAB, standard illuminants.
CIE, Method of Measuring and Specifying Colour Rendering Properties of Light Sources, CIE 13.3-1995. Special metamerism index definition and test/reference illuminant protocol.
CIE, A Method for Assessing the Quality of Daylight Simulators for Colorimetry, CIE 51.2-1999. Observer metamerism evaluation methodology.
C. Wyman, P.-P. Sloan, P. Shirley, “Simple Analytic Approximations to the CIE XYZ Color Matching Functions,” Journal of Computer Graphics Techniques, 2(2):1–11, 2013. Piecewise Gaussian approximation used in this tool.
IEC, Multimedia systems and equipment — Part 2-1: Default RGB colour space — sRGB, IEC 61966-2-1:1999. XYZ-to-sRGB matrix and transfer function.
G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Edition, Wiley, 2000. Definitive reference on metamerism, colour matching, and illuminant SPDs.
R. S. Berns, Billmeyer and Saltzman’s Principles of Color Technology, 4th Edition, Wiley, 2019. Practical colour technology including industrial metamerism testing.
M. D. Fairchild, Color Appearance Models, 3rd Edition, Wiley, 2013. Colour appearance, chromatic adaptation, and metamerism perception.
R. W. G. Hunt, M. R. Pointer, Measuring Colour, 4th Edition, Wiley, 2011. Measurement methods, observer variability, and metamerism applications.
D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral Distribution of Typical Daylight as a Function of Correlated Color Temperature,” Journal of the Optical Society of America, 54(8):1031–1040, 1964. Foundation for CIE D-series illuminant reconstruction.
CIE, CIE S 014-2:2006 — Colorimetry — Part 2: CIE Standard Illuminants. Formal spectral power distributions for D50, D65, and other standard illuminants.

Research & batch analysis

Cross-Illuminant Metamerism Matrix

ΔE*_ab between spectra A and B computed under every illuminant for both CIE 1931 (2°) and CIE 1964 (10°) observers. The “\u0394 Obs” column shows how much the metamerism index differs between observers.

Illuminant	A swatch	B swatch	ΔE (2°)	ΔE (10°)	Δ Obs

Observer Metamerism — 2° vs 10°

How does the same spectrum appear to the 2° vs 10° observer under each illuminant? This table computes ΔE between the 1931 and 1964 colour for the same object, revealing field-size metamerism.

Illuminant	ΔE A (2° vs 10°)	ΔE B (2° vs 10°)	Assessment

Research backend provides: Reflectance × illuminant spectral integration with CIE 1931 / 1964 CMFs, ΔE*_ab metamerism index, CIE xy chromaticity positions, CIELAB a*b* coordinates, spectral stimulus mismatch function, cross-illuminant & cross-observer metamerism survey, full CSV/JSON/PNG export. All computation on-device with zero network dependency.