# What is the CIE color model?

The CIE color model is a mathematical model that describes how colors can be represented using numerical values. CIE stands for the International Commission on Illumination (Commission Internationale de l’Eclairage), the organization that developed this model in the 1930s.

## History of the CIE Color Model

In the early 20th century, there was no standardized way to quantify or describe colors. Different color order systems like the Munsell color system and the Ostwald color system were proposed, but there was no consensus on which one to use.

To address this, the CIE was established in 1913 to standardize various aspects of light and color, including units of measurement, methods of measurement, and mathematical tools to describe color. In 1931, the CIE defined the first standardized color space, called CIE 1931 XYZ. This was a monumental accomplishment that allowed colors to be communicated accurately between different disciplines for the first time.

## Tristimulus Values

The CIE XYZ color space is based on the concept of tristimulus values. The tristimulus values represent the amounts of the three primary colors (red, green, and blue) needed to match a desired color. Here are some key points about tristimulus values:

• They are denoted by X, Y, and Z.
• Y is the luminance or brightness component.
• X and Z carry the chromaticity information (hue and saturation).
• A set of X, Y, and Z values precisely defines a color.
• They don’t correspond to actual amounts of physical red, green, and blue light.

By specifying the X, Y, and Z tristimulus values of a color, it can be accurately communicated and reproduced.

## The CIE Standard Observer

A key aspect of the CIE color model is the standardized observer. This represents a model of the human visual system, specifically how an average human perceives color.

The CIE defined the spectral sensitivity curves that represent how much visible light the cones in the human eye respond to at each wavelength. These curves were determined by experiments done on human subjects in the 1920s. The curves were averaged to develop a model called the 2-degree standard observer.

This observer model allows different light sources and objects to be quantified in a standard way. The tristimulus values of a color are calculated by multiplying the spectral power distribution of the light by the standard observer curves.

## Chromaticity and the CIE Chromaticity Diagram

The CIE chromaticity diagram displays the chromaticity of different colors in a 2D graph. Chromaticity refers to the hue and saturation of a color, independent of its brightness.

The chromaticity diagram is a horseshoe-shaped graph defined by these axes:

• x axis = X tristimulus value
• y axis = Y tristimulus value

The x and y chromaticity coordinates are calculated from the tristimulus values as follows:

Here is an example CIE 1931 chromaticity diagram:

• Saturated colors are on the outer curve, while less saturated colors are towards the center.
• Colors get bluer towards the bottom and redder towards the top.
• The x and y coordinates precisely define the chromaticity.
• The Y tristimulus value is not displayed here.

By specifying the x and y chromaticity coordinates and the Y luminance, any color can be accurately reproduced.

## CIE Standard Illuminants

In color science, an illuminant refers to the spectral power distribution of the light source shining on an object. Different standard illuminants are defined by CIE to provide a common reference for light sources.

Here are some important CIE standard illuminants and their characteristics:

Illuminant Description
D65 Representing average daylight with a color temperature of 6500K.
A Representing light from a tungsten filament bulb at 2856K.
F2 Representing a cool white fluorescent lamp at 4230K.
E Equal energy illuminant – has equal power at all wavelengths.

These standard illuminants allow colors to be compared under consistent lighting conditions for critical color matching work.

## Advantages of the CIE Color Model

Here are some key benefits of using the CIE color model:

• Device-independent: The tristimulus values are based on human vision rather than device-specific color spaces like RGB or CMYK. This makes colors portable across different mediums.
• Perceptual uniformity: Distances on the CIE diagrams correlate well with human-perceived color differences. This allows accurate mathematical manipulations.
• Standard observer: The standardized observer model provides a common reference for all color measurements and calculations.
• Flexible: Many additional color spaces like CIELAB and CIELUV are derived from CIE XYZ and optimized for different applications.

## Applications of the CIE Color Model

The CIE color model is widely used for these applications:

• Color management: CIE coordinates are used to translate colors consistently across different devices like cameras, displays, printers, etc.
• Lighting: CIE illuminants are used to evaluate light source spectra and lighting design.
• Color difference evaluation: CIE color difference formulas like CIE76, CIE94, CIEDE2000 are used to quantify small color differences.
• Color formulation: Industries like textiles, plastics, and coatings use CIE colors for recipe formulation and quality control.

Overall, the CIE color model underpins most aspects of today’s color science and engineering applications.

## Limitations of CIE Color Model

Despite its widespread use, the CIE color model has some limitations:

• The standard observer represents average human vision under limited testing conditions. It does not account for individual variations.
• The CIE 1931 color space has non-uniformities in the blue region. Later CIE diagrams like 1976 L*u*v* improve on this.
• The model is purely colorimetric. It does not specify optimal colors for visual appreciation and aesthetics.
• Being device-independent, CIE colors need conversion for display on monitors, printing, etc. This can lead to inaccuracies.

Overall though, the CIE framework offers a powerful tool for color specification even with these limitations.

## Conclusion

The CIE color model has fundamentally transformed color science since its introduction in the 1930s. By providing a standardized, quantitative way to specify colors based on human vision, it enabled color communication and reproduction with unprecedented accuracy.

While newer color models address some of its limitations, CIE remains deeply embedded in all aspects of today’s color technology, from displays to lighting to photography and beyond. The rigor and universality of CIE colorimetry will ensure its relevance for any future advances in color science.