CIE color matching functions download: A guide to the data sets and their applications
What are CIE color matching functions and why are they important?
Color is a subjective perception that depends on the physical properties of light, the characteristics of the human eye, and the interpretation of the brain. Different people may perceive the same light source or object differently, depending on their individual differences in color vision. To overcome this problem, scientists have developed standardized methods to measure and describe colors objectively, using numerical values that can be reproduced and communicated across different devices and platforms.
One of the most widely used methods is based on the CIE color matching functions, which are the mathematical descriptions of how a typical human observer perceives colors under a given illuminant. The CIE stands for the International Commission on Illumination, which is an organization that sets standards and recommendations for various aspects of light and color. The CIE color matching functions were first defined in 1931, and have been revised and updated several times since then.
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The CIE color matching functions are important because they allow us to convert any spectral distribution of light into three-dimensional color space, where each color can be represented by a unique set of coordinates. This enables us to compare, classify, and manipulate colors in a consistent and accurate way, regardless of the original light source or object. The CIE color matching functions are also essential tools for color management, which is the process of ensuring that colors are displayed or printed as intended across different devices, such as monitors, cameras, scanners, printers, etc.
How CIE color matching functions work
The CIE color matching functions are based on two key concepts: tristimulus values and standard observers. Let's see what they mean and how they relate to each other.
The concept of tristimulus values and standard observers
Tristimulus values are the three numbers that describe the amount of three primary colors (usually red, green, and blue) that are needed to match a given color. For example, if we have a yellow light source, we can match it by mixing some red and green light in certain proportions. The tristimulus values of the yellow light are then equal to the amounts of red and green light that we used, while the blue value is zero.
However, tristimulus values are not absolute, but relative to the choice of primary colors and the characteristics of the observer. Different primary colors may result in different tristimulus values for the same color, and different observers may have different sensitivities to different wavelengths of light. Therefore, we need to define a set of standard primary colors and a standard observer that can be used as a reference for all color measurements.
A standard observer is a hypothetical person who has an average color vision that represents the majority of human population. The CIE has defined several standard observers over the years, based on experimental data from real human subjects. The most commonly used ones are the CIE 1931 2-degree standard observer and the CIE 1964 10-degree standard observer. The numbers 2-degree and 10-degree refer to the size of the visual field that was used in the experiments.
The CIE 1931 color space and the CIE XYZ color space
The CIE 1931 color space is one of the first defined quantitative links between physical wavelengths of light and perceived colors in human vision. It was created by combining the experimental results from two studies by William David Wright and John Guild, who measured the tristimulus values of various spectral colors using different sets of primary colors.
The CIE 1931 color space defines three primary colors that are imaginary, meaning that they do not correspond to any real or physically possible light sources. They are called X, Y, and Z, and they have the advantage of being mathematically independent and covering the entire range of visible colors. The CIE 1931 color space also defines the CIE color matching functions, which are the functions that describe how much of each primary color is needed to match any spectral color. The CIE color matching functions are denoted by x̅(λ), y̅(λ), and z̅(λ), where λ is the wavelength of light in nanometers.
The CIE 1931 color space can be transformed into another color space, called the CIE XYZ color space, by using a simple linear transformation. The CIE XYZ color space is more convenient for calculations and conversions, as it has a more uniform distribution of colors and a clear separation of luminance and chromaticity. The CIE XYZ color space defines three coordinates: X, Y, and Z, which are the tristimulus values of any color with respect to the X, Y, and Z primary colors. The Y coordinate also represents the luminance or brightness of the color, while the X and Z coordinates represent the chromaticity or hue and saturation of the color.
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The CIE xy chromaticity diagram and the CIE xyY color space
The CIE XYZ color space can be further simplified by projecting it onto a two-dimensional plane, called the CIE xy chromaticity diagram. The CIE xy chromaticity diagram is obtained by dividing the X and Z coordinates by the sum of X, Y, and Z coordinates, resulting in two new coordinates: x and y. The x and y coordinates represent the chromaticity of the color, while the luminance is ignored. The CIE xy chromaticity diagram is useful for visualizing and comparing colors, as it shows the hue and saturation of colors as a function of their wavelength.
The CIE xy chromaticity diagram has several important features, such as: - The chromaticity locus, which is the curved boundary of the diagram that corresponds to the spectral colors (single-wavelength colors) and the purple line that connects the ends of the spectrum. - The white point, which is the point on the diagram that corresponds to a neutral or achromatic color (white, gray, or black). The white point depends on the illuminant or light source that is used to view the colors. For example, the white point for daylight is different from the white point for incandescent light. - The color gamut, which is the area on the diagram that represents all the colors that can be reproduced by a given device or system, such as a monitor, a printer, or a camera. The color gamut is usually smaller than the chromaticity locus, meaning that some colors cannot be reproduced accurately by the device or system.
The CIE xy chromaticity diagram can be combined with the luminance coordinate Y to form another color space, called the CIE xyY color space. The CIE xyY color space is equivalent to the CIE XYZ color space, but it uses different co