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  1. Kurse
  2. CIE 1931 and 1976 Chromaticity Charts — Color, Transformations and NVIS
  3. 2. Reading the 1931 chart and its limits
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Home └CIE 1931 and 1976 Chromaticity Charts — Color, Transformations and NVIS └2. Reading the 1931 chart and its limits
CIE 1931 and 1976 Chromaticity Charts — Color, Transformations and NVIS
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Kursinhalt
  • CIE charts: theory and practice
    • 1. Why color needed coordinates
    • 2. Reading the 1931 chart and its limits
    • 3. Why CIE introduced 1976 u′v′
    • 4. Transforming points and boundaries
    • 5. Mixing, white points and display gamut
    • 6. Tolerances and measurement decisions
    • 7. Guided FPD.DEV calculator laboratory
    • 8. NVIS engineering case study
    • 9. Review and glossary

2. Reading the 1931 chart and its limits

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A-P08 · Development edition / Draft

Chapter 2 of 9

Reading the 1931 chart and its limits

Identify the spectral locus and line of purples · Distinguish physical limits from display gamut · Locate chromaticities outside the physical region

Narration transcript

The curved edge is the spectral locus

Follow the moving wavelength marker around the curved boundary. Each point corresponds to an ideal monochromatic stimulus. The spacing is uneven: ten nanometers does not have the same chart distance everywhere. The visible range is not a hard switch at two universal wavelengths. Sensitivity becomes very small near the ends. Our calculations retain the CIE data from three hundred sixty to eight hundred thirty nanometers; familiar diagrams often label a shorter practical range.

The line of purples closes the boundary

The straight closing edge is called the purple boundary, or line of purples. Its interior points represent additive mixtures of the long-wavelength and short-wavelength ends. There is no single wavelength that takes you along this line. Violet on the spectral locus is different from a red-and-violet mixture. As the mixing proportion changes, the chromaticity moves along the line. Changing to nineteen seventy-six coordinates keeps that boundary straight.

Physical limits are stricter than x + y ≤ 1

The nonnegative XYZ triangle is larger than the region actual light can occupy. A point may have positive x, positive y, and x plus y below one, yet remain outside the physically realizable region. Real spectra contain nonnegative power. Their mixtures lie within the convex region generated by spectral chromaticities. A tolerance box can extend outside this region without making those impossible coordinates real. Keep the mathematical specification and the physical possibilities separate.

What neither chart can tell you

A chart point cannot tell you how bright a display is, which wavelengths it emits, or whether it flickers. Many different spectra can share a point. An ordinary monitor also cannot reproduce every color drawn on the diagram. Its colors are illustrations. At true black, X, Y and Z are all zero, so normalized chromaticity is undefined. The origin is not a special black point, and the center of the diagram is not automatically white.

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Slide 7 of 54

Reading the 1931 chart and its limits

Slide 8 of 54

The curved edge is the spectral locus

Slide 9 of 54

The line of purples closes the boundary

Slide 10 of 54

Physical limits are stricter than x + y ≤ 1

Slide 11 of 54

What neither chart can tell you

Slide 12 of 54

Chapter 2 complete

Chapter Reading

The curved edge is the spectral locus

The spectrum locus, commonly called the spectral locus, traces monochromatic chromaticities. A finite-bandwidth LED or OLED generally lies inside this boundary because its spectrum combines neighboring wavelengths. Narrower bandwidth tends to approach the locus, but a point’s distance from the boundary does not uniquely determine its bandwidth.

CIE’s retained 1 nm color-matching dataset covers 360–830 nm. This is a tabulation range, not a sharp physiological visibility cutoff. Wavelength labels are dense near some parts of the curve and sparse near others. The eye’s sensitivity, available radiance and viewing conditions matter. A spectrum locus drawn from rounded or sparse data is a numerical approximation.

Check your understanding

Does a point labeled 530 nm represent a normal broad OLED spectrum?

Show worked answer

It represents ideal monochromatic light. A broad OLED requires spectral integration.

The line of purples closes the boundary

CIE describes the purple boundary using mixtures of monochromatic stimuli at approximately 380 and 780 nm. The full-range tabulated diagram closes its locus at the retained extreme wavelengths; endpoint details depend on the adopted data range. These practical conventions should not be mistaken for a new band of spectral wavelengths.

The ideal boundary mixtures are limiting cases. Ordinary displays use finite-bandwidth primaries and reproduce only a subset of purple chromaticities. The word purple also covers interior colors, not only boundary points. A magenta screen pixel is usually a mixture of the display’s red and blue primaries; it need not lie on the outer purple boundary. Equal powers do not in general put the point at the geometric midpoint.

Check your understanding

Why is there no “purple wavelength” for a point halfway along this edge?

Show worked answer

That point is a mixture of separated spectral components, not a monochromatic stimulus.

Physical limits are stricter than x + y ≤ 1

The familiar horseshoe and its closing purple boundary show the practical colorimetric limit for nonnegative spectra under the chosen observer. Computationally, the convex hull of the sampled spectral chromaticities is a useful physical-region approximation, also used by the calculator. Tiny local irregularities of tabulated data should not be interpreted as new producible colors.

The axes themselves are coordinate limits, not spectral limits. A triangle with vertices (0,0), (1,0) and (0,1) describes nonnegative normalized XYZ; many points in it still cannot be generated by light. Imaginary XYZ primaries are mathematical basis vectors. A manufacturer’s bounding rectangle is an allowed coordinate envelope, not proof that every corner can occur.

The marked example is (0.01, 0.90) in xy, which transforms to approximately (0.00290, 0.58781) in u′v′. Although x, y and z=0.09 are all positive, no nonnegative light spectrum can generate it for this observer. The colored interior is the physically realizable chromaticity region; its on-screen colors are illustrative approximations.

Check your understanding

Can x=0.01, y=0.90 be produced by light, even though x+y=0.91<1?

Show worked answer

No. This point lies outside the physical chromaticity region for the CIE 1931 2° observer. It transforms to u′=0.00290, v′=0.58781 and remains outside in the 1976 chart.

What neither chart can tell you

Chromaticity is not a full color-appearance model. Adaptation, surround, luminance, contrast, field size and observer differences influence appearance. Two samples can match in xy at one condition and differ perceptually at another. Normalized plots discard intensity; dimming an invariant spectrum leaves its point unchanged, although actual devices may shift spectrum when dimmed.

At X=Y=Z=0, both xy and u′v′ formulas produce 0/0. Near black, measurement noise and stray light can make reported chromaticity unstable. A browser’s plotted fill uses an sRGB approximation with clipping or normalization; it cannot demonstrate the physical appearance of an out-of-gamut green, a radiance level or NVIS performance.

Check your understanding

Where is black on the chromaticity diagram?

Show worked answer

Black has no defined chromaticity; it is not the (0,0) point.

Open FPD.DEV CIE calculator Glossary

Sources and calculation assumptions

CIE 1931 2° observer. Coordinate conversions describe the same stimulus; chart colors are illustrative sRGB approximations. CIE dataset and adapted charts: CC BY-SA 4.0, modified by FPD.DEV. Chromaticity alone does not establish NVIS spectral compatibility.

  1. CIE data — CIE (2019), 1931 2° color-matching functions; 360–830 nm, 1 nm. CC BY-SA 4.0.
  2. CIE 1976 definitions — CIE e-ILV 17-23-073: UCS transformation and 1960 relationship.
  3. Purple boundary — CIE e-ILV 17-23-058.
  4. Spectral locus — CIE e-ILV 17-23-056.
  5. Dominant and complementary wavelength — CIE e-ILV 17-23-062 and 17-23-063.
  6. CIELUV — CIE e-ILV 17-23-074; ISO/CIE 11664-5:2024.
  7. Standard observers — ISO/CIE 11664-1:2019 overview.
  8. History — Fairman, Brill & Hemmendinger (1997), Color Research & Application 22, 11–23.
  9. History reconstruction — Broadbent (2004), Color Research & Application 29, 267–272.
  10. Color discrimination — MacAdam (1942), JOSA 32, 247–274.
  11. sRGB — ICC Three Component Color Encoding Registry.
  12. NVIS standard — MIL-STD-3009 base 2001; Notice 2 validation 2024; Figure 2 and Tables II–V.
  13. Standard reader — FPD.DEV retained MIL-STD-3009 reader.
  14. Calculator — FPD.DEV RGB / CIE Calculator A-P14; reused local delivery copy.
  15. Narrated case study — Engineering Shorts 04 A-P19, published 1 November 2026; illustrative spectral model.
  16. CIE tristimulus calculation — ISO/CIE 11664-3; spectral distributions are inputs to XYZ calculation
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