Chromaticity – Color Quality of Light Independent of Luminance

Chromaticity is a cornerstone of color science and photometry, describing the quality of a color as perceived by humans—specifically in terms of its hue and saturation, independent of luminance (brightness). This distinction allows for precise specification, comparison, and reproduction of color, regardless of how light or dark a color appears. Chromaticity is central to applications in lighting, display technology, manufacturing, and scientific research.

Theoretical Foundations

Trichromatic Theory and Color Matching Functions

Human color vision is based on the responses of three types of cone cells in the retina, each sensitive to different parts of the visible spectrum. The trichromatic theory forms the basis for representing any color as a mixture of three primaries. Through color matching experiments, standard color matching functions (CMFs) were derived, quantifying the average human response to spectral colors. These functions underpin the CIE colorimetric system.

The CIE defines a standard observer (initially with a 2° field of view in 1931, later extended to 10° in 1964 and further refined in 2015) based on a large body of psychophysical data. Using the standard observer and CMFs, the color of any light can be expressed as a set of tristimulus values (X, Y, Z), calculated as weighted integrals of the light’s spectral power distribution.

[ X = k \int \Lambda(\lambda) \overline{x}(\lambda) d\lambda ] [ Y = k \int \Lambda(\lambda) \overline{y}(\lambda) d\lambda ] [ Z = k \int \Lambda(\lambda) \overline{z}(\lambda) d\lambda ]

Chromaticity coordinates are then derived by normalizing these values:

[ x = \frac{X}{X + Y + Z} ] [ y = \frac{Y}{X + Y + Z} ]

This process removes the luminance (Y) component, isolating the color’s hue and saturation.

Chromaticity Diagrams

Chromaticity diagrams are two-dimensional plots that represent all perceptible colors based on their chromaticity coordinates. The most widely used are those defined by the International Commission on Illumination (CIE).

CIE 1931 (x, y) Chromaticity Diagram

The CIE 1931 (x, y) diagram is the classic chromaticity representation. It displays the full range of visible colors for the standard observer as a horseshoe-shaped region. The curved edge—the spectrum locus—corresponds to pure spectral colors, while the straight purple line connects the extremes.

The white point (x, y) = (0.333, 0.333) is marked. The horseshoe boundary is the spectrum locus of monochromatic light.

The diagram includes:

• White points (e.g., Illuminant E, D65) for reference
• The Planckian locus tracing blackbody radiators and defining correlated color temperature (CCT)
• Chromaticity regions for standard colors and regulatory compliance

Uniform Chromaticity Scales

The CIE 1931 diagram is not perceptually uniform—equal distances do not correspond to equal perceived color differences. The CIE addressed this with improved diagrams:

• CIE 1960 (u, v) diagram: Used for CCT and Duv, now largely historical.
• CIE 1976 (u’, v’) UCS diagram: Offers improved perceptual uniformity, making it preferable for defining color tolerances and binning LEDs. MacAdam ellipses (regions of indistinguishable color difference) become nearly circular in this diagram.
• CIE 2015 (s, t) UCS: Based on a 10° observer for better large-area color matching, especially in architectural lighting.

Chromaticity, Hue, Saturation, and Luminance

Chromaticity characterizes a color’s hue (the shade, such as red or green) and saturation (intensity or purity), but not luminance (brightness). This separation is critical in color science:

For example, white, gray, and black all have the same chromaticity but differ in luminance. Two light sources with identical chromaticity coordinates will appear as the same color; only their brightness will differ.

Calculation and Measurement

Stepwise Chromaticity Determination

1. Measure the Spectral Power Distribution (SPD):
   Use a spectroradiometer to capture the intensity of light at each wavelength.

2. Apply CIE Color Matching Functions:
   Integrate the SPD with the CMFs to calculate tristimulus values ((X, Y, Z)).

3. Normalize for Chromaticity Coordinates:
   Compute (x, y) (or their equivalents in other diagrams) to represent chromaticity.

4. Plot on Chromaticity Diagram:
   Visualize the color and compare to standards.

Instruments

• Spectroradiometers: Provide high-precision SPD measurements.
• Colorimeters: Use filters to approximate CIE functions for faster, but less precise, measurements.

Chromaticity Tolerances and MacAdam Ellipses

MacAdam ellipses define regions on a chromaticity diagram within which color differences are visually undetectable. These are critical for:

• Quality control and manufacturing
• Setting color tolerances for LEDs and displays
• Regulatory compliance (e.g., ANSI, IEC standards)

In perceptually uniform diagrams (e.g., CIE 1976 UCS), these ellipses are nearly circular, simplifying tolerance setting.

Applications and Use Cases

Lighting Technology

Chromaticity is essential in specifying and sorting (binning) LEDs, lamps, and luminaires to ensure color consistency. Standards like ANSI C78.377 define chromaticity bins for common correlated color temperatures (CCTs). Chromaticity data guarantees lamp replacements match existing installations.

Display Technology

Chromaticity defines the color gamut (range of colors) of displays. Calibration and quality control rely on chromaticity measurements for consistent color reproduction. Professional monitors, projectors, and cameras use chromaticity data to maintain color accuracy.

Signal Lighting and Safety

Traffic lights, aviation beacons, and emergency signals must adhere to strict chromaticity regions, ensuring they are easily and reliably recognized under all conditions. Regulatory standards specify these regions for safety.

Color Rendering and Metamerism

Two light sources can match in chromaticity but differ in how they render object colors if their spectra differ—a phenomenon called metamerism. Chromaticity is thus combined with metrics like Color Rendering Index (CRI) and IES TM-30 for a full assessment of light quality.

Color Quality Metrics

• Correlated Color Temperature (CCT): Quantifies “warmth” or “coolness” of white light, derived from chromaticity.
• Duv: Measures deviation from the ideal white on the Planckian locus.

Evolution of Chromaticity Standards

The ongoing refinement of chromaticity systems reflects deeper understanding of human vision and color perception, leading to more precise and robust color control across industries.

Summary

Chromaticity is a foundational concept for specifying and controlling color quality in science, technology, and industry. By characterizing color in terms of hue and saturation alone, independent of luminance, chromaticity enables accurate color specification, comparison, and reproduction across a vast range of applications—from lighting and displays to manufacturing and safety signaling. The evolution of chromaticity standards has paralleled advances in color science, ensuring that products and environments meet ever-higher standards for color consistency and quality.

Related terms: Colorimeter , Luminance , Color Rendering Index (CRI) , Spectroradiometer , Metamerism