# AVT Color Measurement Fundamentals Series: Part 3

## Understanding CIE L*a*b* and ΔE

Part 3 in a 5-part series on color measurement fundamentals

The second article in this series, “Understanding Light and Color Vision”, described how color is detected and processed by the human visual system and how our knowledge of vision was used to create the Standard Observers. It also discussed how light is described in terms of spectral power and the difference between real sources and illuminants. Standard observers, illuminants, and spectral reflectance, discussed in the first article in this series, “Understanding Spectral Reflectance”, are the basic components used to create the CIE L*a*b* color space. CIE L*a*b*, also written CIELAB, is the most commonly used system for modelling how the color of an object is perceived by humans, and for modeling the difference in appearance between the color of two objects. Color difference is described using the metric, ΔE.

### CIE L*a*b*

The color of objects is best quantified in the context of how they are perceived. The word, “perception,” refers to how the brain processes information. The opponent theory of color vision describes how the red, green, and blue signal from the eyes is transformed into red-green, yellow-blue, and light-dark channels. The CIE L*a*b* color space is based on this principle. The L* dimension represent lightness and darkness in the range 0 to 100, where 0 is black and 100 is a perfect reflecting white. The a* dimension represents redness and greenness on the positive and negative axes, respectively. The b* dimension represents yellowness and blueness on the positive and negative axes, respectively. Both a* and b* are boundless, but values generally stay within the range of -150 and 150. The spectral reflectance, illuminant, and standard observer are entered into the CIE L*a*b* model and the outputs are the L*, a*, and b* values, as illustrated in Figure 1. Figure 1. Illustration of CIE L*a*b* color space calculated using an input illuminant, standard observer, and spectral reflectance.

In addition to L*, a*, and b*, the quantities chroma, C*, and hue angle, hab, are also useful. Chroma, calculated using Eq. 1,  refers to how colorful an object appears (“saturation,” a term often confused with chroma, has a slightly different meaning in color science literature). Higher chroma values are more colorful and less neutral.

Eq.1 Hue, in units of degrees, is associated with the name of the color, and calculated using Eq. 2.

Eq.2 A given color can be described using either L*, a*, and b* (Euclidean coordinates), or using L*, C*,and hab (polar coordinates), since one can be transformed to the other without loss of information. The CIE L*, a*, b*, C*, and hab values for four process colors are shown in Figure 2. Taking cyan as an example, the L* value is 51, indicating a mid-range lightness. The a* value is -52 and the b* value is -60, indicating it’s in the green/blue quadrant of the L*a*b* color space. The chroma value, C*, is 80, indicating the patch is quite colorful, and the hue angle, hab, is 229, also indicating the color’s presence in the green/blue quadrant (bounded by 180 and 270 degrees). Figure 2. The CIE L*, a*, b*, C*, and hab values for four process colors.

CIE L*a*b* measurements are often plotted on two-dimensional projections of the color space. The four process colors from Figure 2 are plotted on an a*b* axis and on an L*C* axis in Figure 3. Figure 3. Four process colors from Figure 2 are plotted on an a*b* axis and on an L*C* axis.

A set of process colors printed at different tone values are shown in Figure 4. Tone value refers to the amount of ink on the paper. A solid, 100% patch has the most ink. The color of the patch approaches the color of the paper as the tone value decreases. Figure 4. Cyan, magenta, yellow, and black process color tint ramps plotted on an a*b* axis and on an L*C* axis.

The plots in Figure 4 show several interesting features of process colors. The yellow solid, for example, has a high L* value. Paper also has a high L* values. So, as the tone value decreases, the lightness stays about the same. The yellow solid also has a high C* value. So, while L* changes very little, there is a sharp decrease in C* as the tone value decreases. Black has almost the opposite effect. The black solid is very dark, with a low L*. The decrease in tone value is accompanied by a sharp decrease in L*. The black solid is also very neutral, with a C* near zero. As tone value decreases, C* increases because the paper is more colorful than the black ink.

### Color Difference

The CIE L*a*b* color space is used to quantify how colors are perceived. The next step is to understand how colors are perceived to be different. The million-dollar question is, “How different can two colors be before they are perceived to be different?” The term, Just Noticeable Difference, is often used to describe that threshold. The aim in designing a color difference formula is for a value of 1.0 to indicate the threshold of perceived difference. If the color difference is less than 1.0, then most people would not be able to perceive a difference, and if the color difference is greater than 1.0, then most people would be able to perceive a difference. However, keep in mind throughout this discussion that color difference, like the rest of colorimetry, is based on the experience of an average person and not that of a specific individual, which may be quite different.

The scientists who developed the CIE L*a*b* color space aimed to make it uniform, meaning that the perceived difference between adjacent color spaced evenly around the CIE L*a*b* space would be the same. This assumption, a good starting point, gave rise to the first color difference formula. The general designation of color difference is “ΔE.” The “Δ” refers to a change, or difference, and the “E” refers to the German word, empfindung, meaning sensation. Of course, color is a sensation, so ΔE is the perceived difference in the sensation of color.

All color differences begin with the calculation of differences between the L*a*b* components, shown in Eq. 3. In most industrial cases a sample color is compared to a reference color to determine how far production is from an aim point. The original color difference formula proposed with the introduction of the CIE L*a*b* color space in 1976, and referred to as ΔE*ab, or ΔE76­, is the simple Euclidean distance between sample and reference L*a*b* point. In the years following the introduction of CIE L*a*b* and ΔE*ab, further experiments found that the CIE L*a*b* color space was not as uniform as originally expected. A pair of colors some distance apart in one part of the color space may be perceived as different, while another pair of colors the same distance apart would not be perceived as different. Unfortunately, new color spaces designed to mold the CIE L*a*b* into a perceptually uniform space never took off because CIE L*a*b* quickly became entrenched in industry. Therefore, rather than fix CIE L*a*b*, new color difference formulas, increasing in both accuracy and complexity over the years, have been proposed. The identifier of ΔE continues to be used, but with different subscripts to refer to different formulas. The most recent (and complex) formula to be crowned the “best” formula and gain worldwide acceptance, is ΔE00, adopted in 2002. While tweaks to ΔE00 are still being proposed, the industry has pretty much concluded that ΔE00 is good enough and focused their energy on other ventures within the color science universe. Other formulas of note that are used frequently in the printing industry are ΔE94 and ΔEcmc (2:1). Some formulas, such as ΔEcmc, often have additional configurable parameters (the 2:1, for example) used to fine-tune lightness and chroma tolerance.

While it isn’t necessary to understand the equations or the exact meaning of these different formulas, it’s important to understand that they exist and what they are trying to accomplish. The illustration in Figure 5 shows two yellow points, A and B, plotted on an a*b* axis. Samples A and B are not perceptibly different. Around Point A is a red circle indicating a ΔE*ab of 1.0. Point B is well outside the red circle, which suggests Point A and Point B look different. However, we know that the CIE L*a*b* color space is not uniform. Rather than a circle, the color tolerance around Point A is better drawn as an elongated ellipse, such as that in ΔE00. The ΔE00 for Points A and B is 0.90, which suggests Points A and B are not perceptibly different. Figure 5. Two points that are not perceptibly different. Point A is surrounded by a ΔE*ab tolerance ellipse (solid red) and an elliptical tolerance ellipse, such as that in ΔE00 (the dotted ellipse).

An example of color differences calculated for two orange points is shown in Figure 6. The sample point is compared to the target. The L*a*b* values are provided for each point, along with the differences between each L*a*b* dimension and the color differences calculated using three different formulas. The differences between the color difference formulas is illustrated by differences between the three ΔE values. ΔE*ab has a value of 3.48, while ΔEcmc and ΔE00 have values of 1.37 and 2.05. In the context of printing, if the tolerance was set at 2 ΔE, it’s clear how the choice of color difference formula factors into the success or failure of a production run. It’s important for printers to understand what formula they are required to use and how that choice affects their ability to match targets within the specified tolerance. Figure 6. L*a*b* values for a real sample and target orange, with the L*a*b* differences and color differences from three formulas

Inline color measurements produce a lot of data about the production of individual colors during a job. L*a*b* plots of these measurements can be useful in identifying outlying measurements and whether there were any systematic errors in color during production. Inline color measurement points are shown for cyan and violet patches in Figure 7. Underlying the measurement points are ΔE00 tolerance ellipses. Points within inner ellipse are within 1.0 ΔE00, points within the second ellipse are within 2.0 ΔE00, and points within the third ellipse are within 3.0 ΔE00. Most color measurement points were within 1.0 ΔE00 for both colors, indicating the process was well controlled. Figure 7. L*a*b* plots of cyan and violet inline color measurement data. ΔE00 tolerances ellipses underlie the measurement data.

#### Summary

The CIE L*a*b* color space is a model of how the average person views color patches under average lighting conditions in specific fields of view. It’s a standard model used throughout the world in color management for graphic arts and industrial color applications. Color difference, described using the ΔE metric, is use globally to compare pairs of color patches. However, while the CIE L*a*b* color space is now ubiquitous, the proper method for using it is not well understood. In addition, ΔE, another ubiquitous metric, is mistakenly understood by many to be a single number that represents whether two colors are or are not different. However, in actuality, each ΔE formula estimates the likelihood that the average observer will be able to differentiate between two colors. The values can vary depending on the formula and weightings used. One of its greatest utilities is as a quality control tool. ΔE removes the bias of visual matching from industrial color production and color management, and allows companies around the world to communicate quality using the same language.

Further learning:

This is the third article in a series of five articles covering color measurement fundamentals. The next article, “Understanding Density,” will explain how density measurements are used in graphic arts applications and how to interpret the density data you encounter in the printing process. It also discusses how density is used as a color management and process control tool.

AVT Color Measurement Fundamentals Series: