CIE 1931 Color Space

CIE 1931 Color Space – Standard Colorimetric System Defining Color Matching Functions

Overview

The CIE 1931 color space, established by the Commission Internationale de l’Éclairage (CIE) in 1931, is the foundation of modern color science and colorimetry. It provides a standardized, quantitative way to describe every color visible to the average human eye, connecting measurable physical properties of light with human color perception. This system is essential for industries that demand precise color reproduction, such as display manufacturing, paints and coatings, lighting design, digital imaging, textiles, and printing.

The CIE 1931 color space is built on the concept of tristimulus values—X, Y, and Z—derived from a set of color matching functions that model the average human observer’s color sensitivity. It allows for the accurate specification, measurement, and reproduction of color in a device-independent manner and forms the backbone for further colorimetric systems and standards.

Historical Background

Before the 20th century, color was described mainly in subjective or qualitative terms. In the 1920s, experiments by W. D. Wright and J. Guild measured how human observers matched monochromatic lights using mixtures of three primaries. The CIE synthesized this empirical data to define a standard observer and a mathematical color space, ensuring reproducibility and universality.

Key Milestones:

• 1920s: Wright and Guild’s color matching experiments.
• 1931: CIE publishes the CIE 1931 RGB and XYZ color matching functions and establishes the CIE 1931 color space.
• Subsequent decades: Adoption of CIE 1931 as the international foundation for color measurement and communication.

Color Matching Functions (CMFs)

Color Matching Functions (CMFs) describe how much of each of three imaginary primaries is needed to match any given wavelength of visible light, based on average human vision. The most widely used set is the CIE 1931 XYZ color matching functions—x̅(λ), y̅(λ), z̅(λ)—which are tabulated at 1 nm intervals across the visible spectrum (360–830 nm).

• x̅(λ): Related to red sensitivity.
• y̅(λ): Closely matches the human eye’s perception of brightness (luminous efficiency).
• z̅(λ): Related to blue sensitivity.

These functions are the mathematical foundation for all subsequent colorimetric calculations, ensuring that all visible colors can be described using positive values—crucial for practical color measurement.

Tristimulus Values (X, Y, Z)

The tristimulus values (X, Y, Z) numerically specify a color stimulus:

• X: Red-related response.
• Y: Green-related response, also corresponds to luminance (brightness).
• Z: Blue-related response.

They are calculated as follows:

X = k ∫ S(λ) x̅(λ) dλ
Y = k ∫ S(λ) y̅(λ) dλ
Z = k ∫ S(λ) z̅(λ) dλ

where:

• S(λ) is the spectral power distribution of the light source or object.
• k is a normalizing constant.
• x̅(λ), y̅(λ), z̅(λ) are the CIE color matching functions.

Y is particularly important as it represents luminance—directly related to the perceived brightness of the color.

Chromaticity Coordinates (x, y, z)

To describe color independently of brightness, the chromaticity coordinates are derived from XYZ:

• x = X / (X + Y + Z)
• y = Y / (X + Y + Z)
• z = Z / (X + Y + Z) = 1 – x – y

In practice, only x and y are needed, as z is determined by the other two.

The CIE 1931 Chromaticity Diagram

The CIE 1931 (x, y) chromaticity diagram is a two-dimensional plot showing all perceivable hues and saturations for the standard observer. Key features:

• Spectral locus: The curved outer edge, representing monochromatic (single-wavelength) colors.
• Line of purples: The straight edge connecting the extremes of the spectral locus; represents non-spectral purples.
• Interior: All physically realizable colors, including those produced by mixing spectral lights.

The diagram is indispensable in:

• Visualizing the gamut of devices (e.g., the triangle formed by RGB primaries of a display).
• Assessing color differences and relationships.
• Specifying lighting and color standards.

Spectral Locus

The spectral locus traces the chromaticity coordinates of pure spectral colors (from about 380 nm to 700 nm). It defines the boundary of the chromaticity diagram, with the most saturated colors at each wavelength. The straight line of purples connects the ends of the locus (violet and red), enclosing all perceivable chromaticities.

CIE Standard Colorimetric Observer

The CIE 1931 2° standard observer represents the average color-matching abilities of a typical human viewing a 2° field of view (central retina). This is supplemented by the CIE 1964 10° observer, accounting for a wider field.

Both are defined by published tables of XYZ color matching functions and are crucial for standardizing color measurements across industries.

Luminous Efficiency Function V(λ)

V(λ) is the standard photopic (daylight) luminous efficiency curve, peaking at 555 nm (green). The CIE 1931 y̅(λ) function matches V(λ), so the Y tristimulus value corresponds to perceived brightness (luminance), measured in candelas per square meter (cd/m²).

Metamerism

Metamerism occurs when two different spectral power distributions produce the same color sensation to an observer under a specific illuminant. Such pairs are called metamers. While essential for practical color matching (e.g., in printing or textile dyeing), metamerism can cause color matches to fail if the lighting or observer changes—known as metameric failure.

Primary Colors in Colorimetry

In CIE 1931, primaries are mathematical constructs, not physically realizable lights:

• The original RGB primaries (700 nm red, 546.1 nm green, 435.8 nm blue) were used in experiments.
• The XYZ primaries are imaginary but ensure all visible colors can be represented with positive values.

Standard Illuminants

Standard illuminants are reference light sources with known spectral distributions, ensuring consistency in color measurement:

• Illuminant A: Simulates incandescent light (~2856 K).
• Illuminant D65: Represents average daylight (~6504 K).

These are essential for reproducible, meaningful color specifications.

Spectral Power Distribution (SPD)

An SPD describes the intensity of light at each wavelength. It is fundamental for calculating how a light source or object will appear, as the SPD, together with the standard observer functions and standard illuminant, determines the resulting color coordinates.

Additive Color Mixing

Additive mixing (used in displays, projectors, etc.) involves combining light of different wavelengths. The CIE 1931 model is inherently additive, as tristimulus values represent quantities of primaries required to reproduce a color.

Color Space

A color space is a model describing a range of colors (gamut). CIE 1931 XYZ is the reference; other spaces (sRGB, Adobe RGB, CIELAB) are derived from it for specific devices or perceptual uniformity.

Luminance

Luminance is perceived brightness, represented by the Y value in the CIE 1931 space. It’s a key parameter in lighting, display calibration, and visual ergonomics.

Illuminant

An illuminant is any light source characterized by its SPD. Standard illuminants like D65 are used for consistent color evaluation and calibration.

Color Difference Formulas (ΔE*)

ΔE* quantifies the perceptual difference between two colors, most commonly using the CIELAB color space. Corrections (CIE94, CIEDE2000) improve accuracy for non-uniformities in human color vision.

Device Color Gamuts and Gamut Mapping

A device’s color gamut is the subset of colors it can reproduce. On the CIE chromaticity diagram, device gamuts are often shown as triangles (for RGB displays). Gamut mapping ensures colors are consistently reproduced across devices with different gamuts.

Color Rendering Index (CRI) and Correlated Color Temperature (CCT)

• CRI: Measures how faithfully a light source renders colors compared to a reference.
• CCT: Specifies the color appearance of a light source, relating it to a blackbody at a given temperature.

These metrics are calculated using the CIE 1931 system and are crucial for lighting design and specification.

Observer Variability and Metameric Failure

Individual differences in cone sensitivities, eye health, and aging cause variations in color perception. As a result, standard observer-based matches may not be perfect for everyone or under all lighting, leading to observer metamerism and illuminant metamerism.

Transformations to Other Color Spaces

XYZ serves as the universal reference. Device-specific spaces (e.g., sRGB) are matrix transformations of XYZ; perceptually uniform spaces (CIELAB, CIELUV) are non-linear transforms designed for visual uniformity.

Measurement Instruments: Colorimeters and Spectroradiometers

• Colorimeters: Use filters to mimic the standard observer and quickly measure tristimulus values.
• Spectroradiometers: Measure the full SPD for precise, flexible color analysis.

Both are essential for color quality control, display calibration, and lighting specification.

Applications and Impact

The CIE 1931 color space is indispensable in:

• Display calibration: Ensures consistent color reproduction across screens.
• Lighting design: Specifies color temperature, rendering, and brightness.
• Manufacturing: Guarantees color consistency in textiles, plastics, paints, and printing.
• Digital imaging: Underpins color management systems and workflows.
• Research: Provides a common language for color science, vision, and psychophysics.

Summary

The CIE 1931 color space is the international standard for describing, measuring, and communicating color as perceived by humans. Using mathematically defined color matching functions, tristimulus values, and chromaticity coordinates, it enables accurate, reproducible color specification in science, engineering, and industry.

Whether calibrating a display, specifying a light source, or matching paints, the CIE 1931 system is the universal reference for objective, device-independent colorimetric measurement.

Further Reading

• CIE Official Website
• Wikipedia – CIE 1931 color space
• Color and Vision Research Laboratory – CIE Color Matching Functions
• Understanding Color – Bruce Lindbloom

See Also

• Colorimetry
• CIELAB Color Space
• Standard Illuminants
• Metamerism (Color)

Keywords: CIE 1931, color space, chromaticity diagram, color matching functions, tristimulus values, luminance, metamerism, color difference, standard illuminant, color science, photometry, colorimetry, XYZ, color gamut.