Spectral Analysis Laboratories
Blackbody Radiation
Planck 1900 · Wien 1893 · Stefan-Boltzmann
Thermal
Planck SPD Wien displacement CIE xy
Open Lab →
Atomic Emission
Balmer 1885 · Rydberg 1888 · Bohr 1913
Quantum
Rydberg formula Balmer series CIE 1931 CMF
Open Lab →
Diffraction Grating
Fraunhofer 1820 · grating equation
Optics
Grating equation Angular dispersion Resolving power
Open Lab →
Metamerism
CIE 13.3-1995 · illuminant metamerism index
Perceptual
reflectanceToXYZ CIELAB ΔE*ab 7 illuminants
Open Lab →
Visible Spectrum
380–780 nm · CIE 1931 · photopic / scotopic
Photometry
V(λ) photopic V′(λ) scotopic CIE CMF
Open Lab →
CIE Observer
Overlay Options
Keyboard shortcuts
O toggle observer (2° ↔ 10°)
Live SPD Explorer

Three modes: monochromatic wavelength, Planck blackbody, illuminant comparison. All outputs computed live via CIE observer and spectral integration.

380 nm 555 nm 780 nm
Property x̄(λ) ȳ(λ) z̄(λ) V(λ) V′(λ) Hex
800 K 6504 K 20000 K

All 7 CIE standard illuminants normalised. Bars show perceived colour chip and Y (luminance factor) for a flat 50% grey reflector.

Illuminant CCT (K) x y Perceived Hex
Export & Share
PNG exports the SPD explorer canvases. CSV copies 81-point CMF + V(λ) data. JSON includes full observer + illuminant data. Share URL encodes current wavelength, temperature, and observer.
Data content

CSV contains: wavelength (nm), CIE 1931 x̄ ȳ z̄, CIE 1964 x̄ ȳ z̄, photopic V(λ), scotopic V′(λ) for each 5 nm step (380–780 nm, 81 points).
JSON includes: observer setting, wavelength array, full CMF tables for both observers, photopic / scotopic arrays, illuminant SPDs + XYZ for all 7 illuminants.

Tip: CSV can be imported directly into spreadsheet software for custom spectral analysis. JSON can be used as a data source for external tools.
Applicable standards & principles
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.

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

CIE S 014-2 — CIE Standard Illuminants

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. Illuminant A (2856 K) follows Planck blackbody.

Reference: CIE S 014-2:2006.

Planck Radiation Law (1900)

Max Planck derived the exact spectral radiance of a blackbody: B(λ,T) = c₁/[λ⁵·(exp(c₂/λT)−1)]. All thermal emission SPDs in this laboratory are computed from this formula. Wien displacement gives the peak wavelength: λpeak·T = b = 2.898×10³ nm·K.

Reference: M. Planck, Ann. Phys. 4(3):553, 1901.

Rydberg Formula & Atomic Emission (1888)

1/λ = R·(1/n₁² − 1/n₂²) where R = 1.097 × 10⁷ m¹. The Balmer series (n₁=2) produces visible hydrogen emission lines. Each element has a unique spectral fingerprint — the basis of analytical spectroscopy.

Reference: J. R. Rydberg, 1888; N. Bohr, Phil. Mag. 26:1, 1913.

Diffraction Grating Equation (Fraunhofer 1820)

d·(sin θi + sin θm) = m·λ. Joseph von Fraunhofer invented the diffraction grating and mapped 574 dark lines in the solar spectrum. Angular dispersion dθ/dλ = m/(d·cos θm). Resolving power R = m·N = λ/Δλ.

Reference: J. von Fraunhofer, 1820.

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.

Photopic & Scotopic Luminous Efficiency

V(λ) = photopic luminous efficiency, peak 555 nm (cone-mediated daylight vision). V′(λ) = scotopic efficiency, peak 507 nm (rod-mediated night vision). Luminous flux: Φv = Km·∫ Φ(λ)·V(λ) dλ where Km = 683 lm/W (photopic) or K′m = 1700 lm/W (scotopic).

Reference: CIE 15:2004, Table T.1.

CIE 13.3-1995 — Metamerism Index

The Special Metamerism Index ΔE*ab quantifies the colour difference between two stimuli under a test illuminant when they match under the reference illuminant. Used in the Metamerism lab for factory and textile colour QC.

Reference: CIE 13.3-1995.

Mathematical formulations
Planck Blackbody Radiation
B(λ, T) = c₁ / [λ⁵ · (ec₂/(λT) − 1)]

c₁ = 3.74183 × 10−16 W·m²
c₂ = 1.4388 × 10−2 m·K

Wien displacement: λpeak = b/T,   b = 2.898 × 10−3 m·K
Stefan-Boltzmann: M = σ·T⁴,   σ = 5.670 × 10−8 W·m−2·K−4
CIE Tristimulus Integration
X = (1/k) · ∑ S(λ) · x̄(λ) · Δλ
Y = (1/k) · ∑ S(λ) · ȳ(λ) · Δλ
Z = (1/k) · ∑ S(λ) · z̄(λ) · Δλ
k = ∑ ȳ(λ) · Δλ

For reflectance: S(λ) = R(λ) · I(λ)
CIE 1931 2° Observer — Piecewise Gaussian
g(λ; μ, σ₁, σ₂) = exp(−½ d² / σk²)
where d = λ − μ, σk = 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.

CIE xy Chromaticity
x = X / (X + Y + Z)
y = Y / (X + Y + Z)

The spectral locus boundary represents pure monochromatic light. The Planck locus traces the chromaticity of blackbody radiators from 1000 K to 25000 K.
Rydberg Spectral Series
1/λ = R · (1/n₁² − 1/n₂²)
R = 1.09737 × 10⁷ m−1 (Rydberg constant)

Lyman series: n₁ = 1 → UV
Balmer series: n₁ = 2 → visible (H-α 656.3, H-β 486.1, H-γ 434.0, H-δ 410.2)
Paschen series: n₁ = 3 → IR
Diffraction Grating Equation
d · (sin θi + sin θm) = m · λ

Angular dispersion: dθ/dλ = m / (d · cos θm)
Resolving power: R = m · N = λ / Δλ
Free spectral range: FSR = λc / m
Littrow condition: θi = θm = arcsin(mλ/2d)
Luminous Efficacy
K = Km · ∫ V(λ) · S(λ) dλ / ∫ S(λ) dλ

Km = 683 lm/W (photopic maximum, at 555 nm)
K′m = 1700 lm/W (scotopic maximum, at 507 nm)
CIELAB & ΔE*ab
L* = 116·f(Y/Yn) − 16
a* = 500·[f(X/Xn) − f(Y/Yn)]
b* = 200·[f(Y/Yn) − f(Z/Zn)]

ΔE*ab = √[(ΔL*)² + (Δa*)² + (Δb*)²]
Academic references & citations
  1. CIE, Colorimetry, 3rd Edition, CIE 15:2004. CIE 1931 and 1964 Standard Observer CMFs, CIELAB, standard illuminants.
  2. M. Planck, “Über das Gesetz der Energieverteilung im Normalspectrum,” Ann. Phys. 4(3):553–563, 1901. The blackbody radiation law — foundation of quantum mechanics and all thermal SPD computation.
  3. 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.
  4. J. von Fraunhofer, Denkschriften der Königl. Akademie der Wissenschaften zu München, 1820. First diffraction grating; 574 solar absorption lines mapped.
  5. J. R. Rydberg, “On the structure of the line-spectra of the chemical elements,” Phil. Mag. 29(179):331–337, 1890. Generalised spectral series formula: 1/λ = R(1/n₁² − 1/n₂²).
  6. N. Bohr, “On the Constitution of Atoms and Molecules,” Phil. Mag. 26:1–25, 1913. Quantised electron orbits explain emission line wavelengths.
  7. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed., Wiley, 2000. Comprehensive reference for spectral analysis, CMFs, illuminants, metamerism.
  8. IEC, IEC 61966-2-1:1999 — sRGB Colour Space. XYZ-to-sRGB matrix and transfer function.
  9. D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral Distribution of Typical Daylight,” JOSA 54(8):1031–1040, 1964. Foundation for CIE D-series illuminant reconstruction.
  10. M. D. Fairchild, Color Appearance Models, 3rd ed., Wiley, 2013. Colour appearance, chromatic adaptation, spectral perception.
  11. CIE, CIE 13.3-1995 — Method of Measuring and Specifying Colour Rendering Properties of Light Sources. Metamerism index definition and test/reference illuminant protocol.
  12. CIE, CIE S 014-2:2006 — CIE Standard Illuminants. Formal spectral power distributions for D50, D65, and other standard illuminants.
Research & advanced analysis
CIE xy Chromaticity Diagram — spectral locus · Planck locus · 7 illuminant white points
CIE Colour Matching Functions — x̄ (red) · ȳ (green) · z̄ (blue) · 2° (—) · 10° (···)
Photopic V(λ) & Scotopic V′(λ) Luminous Efficiency
Batch Illuminant Survey

Comprehensive colorimetric analysis of all 7 CIE illuminants: chromaticity (x, y), Wien peak, perceived colour under both 2° and 10° observers, ΔE between observers, and luminous efficacy.

Illuminant CCT Wien Peak x (2°) y (2°) Swatch 2° Swatch 10° ΔE (2° vs 10°) Efficacy (lm/W)
Observer Comparison — 2° vs 10° XYZ

Full XYZ tristimulus and chromaticity coordinates for each illuminant under both CIE 1931 (2°) and CIE 1964 (10°) observers.

Illuminant XYZ (2°) xy (2°) XYZ (10°) xy (10°)
Spectral Locus Data (10 nm steps)
λ (nm) x̄ ȳ z̄ x y Swatch Hex
Tool Feature Matrix
Feature Blackbody Atomic Emission Diffraction Grating Metamerism Visible Spectrum
Live spectral canvas ✓ ✓ ✓ ✓ ✓
CIE 1931 observer ✓ ✓ partial ✓ ✓
CIE 1964 10° — — — ✓ ✓
sRGB hex output ✓ ✓ ✓ ✓ ✓
XYZ / xyY output ✓ ✓ partial ✓ ✓
Multiple illuminants — — — ✓ (7) —
ΔE*ab metamerism — — — ✓ —
Peak wavelength Wien line λ diffracted λ — V(λ)
Export (PNG/CSV/JSON) ✓ ✓ ✓ ✓ ✓
Share URL ✓ ✓ ✓ ✓ ✓
Physical model Planck 1900 Rydberg 1888 Fraunhofer 1820 CIE 13.3-1995 CIE 1931
Historical Timeline — The Science of Spectra
1666
Newton — Prism Dispersion
Isaac Newton splits white sunlight into a rainbow spectrum. Invents the word “spectrum”.
1800
Herschel — Infrared Radiation
William Herschel detects heat beyond the red end of the solar spectrum.
1814
Fraunhofer — Absorption Lines
Joseph von Fraunhofer maps 574 dark lines in the solar spectrum. Invents the diffraction grating.
1859
Kirchhoff & Bunsen — Spectral Analysis
Each element has a unique emission spectrum. Discovery of caesium and rubidium.
1885
Balmer & Rydberg — Spectral Series
Balmer derives hydrogen visible series. Rydberg generalises: 1/λ = R(1/n₁²−1/n₂²).
1893
Wien — Displacement Law
λpeak·T = b. Hotter bodies peak at shorter wavelengths.
1900
Planck — Quantum Radiation Law
Max Planck derives B(λ,T) by quantising energy exchange. Birth of quantum mechanics.
1905
Einstein — Photoelectric Effect
Light consists of photons with E = hν.
1913
Bohr — Atomic Orbit Model
Quantised orbits explain emission lines at precise wavelengths.
1931
CIE — XYZ Colour Matching Functions
CIE standardises the 2° observer x̄(λ), ȳ(λ), z̄(λ).
1964
CIE — 10° Observer
Supplementary 10° observer CMFs from Stiles and Burch data.
1976
CIE — CIELAB Colour Space
Perceptually uniform L*a*b* with ΔE*ab distance metric.
1995
CIE 13.3 — Metamerism Index
Formalises ΔE*ab as the standard metamerism index.
How the Spectral Functions Connect
Function Source Used by
spdBlackbody(λ, T) Planck 1900 Blackbody lab, Illuminant A
spdD65 / spdD50(λ) CIE D-series Gaussian Metamerism, illuminant comparison
spdFluorescent(λ, v) Multi-Gaussian F-series Metamerism (F2, F7, F11)
getIlluminantArray(name, wl) Dispatcher Metamerism, illuminant comparison
cie1931(λ) / cie1964(λ) CIE CMF Gaussian All five tools
spectrumToXYZ(wl, spd, cmf) CIE integration Blackbody, atomic, metamerism
reflectanceToXYZ(wl, R, I, cmf) Product integral Metamerism
linspace(start, end, n) Uniform grid All five tools
gaussian(x, μ, σ) General Gaussian CMF, illuminant SPD, presets
Physical source → SPD(λ) [Planck, Rydberg, illuminant] ↓ CMF integration → XYZ [spectrumToXYZ · reflectanceToXYZ] ↓ XYZ → linear sRGB → gamma sRGB [3×3 matrix + γ=1/2.2] ↓ sRGB → hex colour chip [perceived colour display] ↓ XYZ → CIELAB → ΔE*ab [metamerism index only]
Research backend: CIE xy chromaticity with spectral locus & Planck locus, dual-observer CMF explorer (2° solid · 10° dashed), photopic/scotopic V(λ), batch illuminant survey with ΔE observer metamerism, spectral locus data table, tool feature matrix, historical timeline, function architecture diagram. All computation on-device with zero network dependency.