We know that the quantification of color and light is in an abstract sense, so the differences in color and other physical differences are distinct. For example, when we use a measuring stick to measure the length of an object, people often arbitrarily divide it into uniform small segments. Even small lengths that cannot be distinguished by the human eye can be judged by measuring tools. But when people use Colorimeters to measure the color of objects, it is different.

Firstly, people cannot correctly distinguish the amount of color difference, and they cannot use physical instruments to analyze and measure colors because color data has meaningless numerical values. This is also the reason for the emergence of color difference meters, which are precision and complex color detection tools.

In colorimetry, people call the color difference (range of change) that cannot be felt by the human eye the wide capacity of color. The capacity of the color scheme reflects the distance between chromaticity points on the CIE xy chromaticity map. We know that the chromaticity diagram plays a very important role in the development of color difference meters, with each color occupying a unique point on the chromaticity diagram. However, for people’s visual perception, when the color coordinate position changes slightly, the human eye still considers its original color and cannot sense its change.

Therefore, in colorimetry, the amount of color difference within the distance (or range) of visual effect change is visually equivalent.

In 1942, D.L. Macadam, a researcher at the Kodak Institute in the United States, published a paper on human visual capacity, which remains the fundamental work in quantitative calculation and measurement of color differences to this day.

In order to study the visual difference, McAdam selected 25 color chromaticity points at different positions on the CIE xy chromaticity map as standard chromaticity lights, with chromaticity coordinates x and y. Then draw 5~9 straight lines in different directions for the chromaticity points, take the colored lights on the opposite sides to match the color of the standard colored light, and the same observer will allocate the proportion of light to determine the wide capacity of color discrimination. Calculate the standard deviation of the chromaticity coordinates obtained through 50 repeated color matching experiments. Namely:

Standard Deviation Formula

As shown in Figure 1 below, radiating lines are emitted in various directions around the established standard chromaticity point, and it is found that the distance varies in different directions. Around standard chromaticity points, point trajectories with a distance of one standard deviation in different directions are connected to form an approximate ellipse.

At the same time, we can also see from the graph that the ellipses formed by 25 different chromaticity points on the chromaticity map are of different sizes, and their major axis directions are also different. This indicates that in the xy chromaticity diagram, the width capacity of colors in different positions and directions is different.

The same geometric distance on the standard CIE xy chromaticity map corresponds to different visual color differences in different color regions and directions of color change. The wide capacity of each ellipse in Figure 1 is plotted as 10 times the standard deviation of the experimental results.

Figure 1

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