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.
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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.
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.
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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.
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 coordinates: x, y, and Y. The x and y coordinates are the same as in the CIE xy chromaticity diagram, while the Y coordinate is the same as in the CIE XYZ color space. The CIE xyY color space is useful for specifying colors in terms of their hue, saturation, and brightness.
How to download CIE color matching functions
If you want to download CIE color matching functions data for your own use or analysis, you need to know where to find them, what formats they are available in, and how to download them. Here are some tips and steps to help you with this process.
The sources of CIE color matching functions data
There are several sources that provide CIE color matching functions data online, but not all of them are official or reliable. Some of them may have errors or inconsistencies in their data, or may not follow the latest standards or recommendations from the CIE. Therefore, it is advisable to use only trusted and reputable sources that are affiliated with or endorsed by the CIE.
One of such sources is , which is maintained by Noboru Ohta, a professor emeritus at Rochester Institute of Technology and a former chair of several technical committees of the CIE. The CRG website provides CIE color matching functions data for various standard observers and illuminants, as well as other related data and resources. The data are available in tabular and graphical forms, and can be downloaded as text files or Excel files.
Another source is , which is the official website of the International Commission on Illumination. The CIE website provides CIE color matching functions data as part of its publications, which are the authoritative documents that contain the standards and recommendations of the CIE. The publications are available for purchase or download, depending on the type and date of the publication. Some of the publications that contain CIE color matching functions data are: - CIE 015:2018 Colorimetry, 4th Edition - CIE 170-2:2015 Fundamental Chromaticity Diagram with Physiological Axes - Part 2: Spectral Luminous Efficiency Functions and Chromaticity Diagrams - CIE S 026/E:2018 CIE System for Metrology of Optical Radiation for ipRGC-Influenced Responses to Light - CIE 224:2017 CIE 2017 Colour Fidelity Index for accurate scientific use
The formats and steps of downloading CIE color matching functions data
The formats of CIE color matching functions data may vary depending on the source and the type of data. However, the most common formats are text files (.txt) and Excel files (.xls or .xlsx), which can be easily opened and manipulated by various software applications. The text files usually contain columns of numerical values separated by spaces or commas, while the Excel files usually contain tables or charts of numerical values with labels and headers.
The steps of downloading CIE color matching functions data may also vary depending on the source and the type of data. However, the general steps are as follows: - Go to the source website and navigate to the page that contains the data you want to download. - Select the format and the file name of the data you want to download, and click on the download link or button. - Save the file to your desired location on your computer or device. - Open the file with your preferred software application and check if the data are correct and complete.
The applications and uses of CIE color matching functions data
CIE color matching functions data have many applications and uses in various fields and industries that deal with light and color, such as: - Colorimetry, which is the science of measuring and quantifying colors objectively. - Color management, which is the process of ensuring that colors are displayed or printed as intended across different devices and platforms. - Color science, which is the interdisciplinary field that studies the physical, physiological, psychological, and cultural aspects of color. - Color engineering, which is the application of color science to design and optimize products, systems, and environments that involve color. - Color education, which is the teaching and learning of color theory, principles, and practices.
Some of the specific examples of how CIE color matching functions data can be used are: - To calculate the tristimulus values or chromaticity coordinates of any spectral color or light source, by multiplying the spectral power distribution by the CIE color matching functions. - To convert colors from one color space to another, by using a matrix transformation or a lookup table based on the CIE color matching functions. - To evaluate the color quality or performance of a light source, by comparing its chromaticity coordinates or color rendering index to a reference illuminant or a standard observer. - To create or modify colors in digital images or graphics, by adjusting their tristimulus values or chromaticity coordinates according to a desired effect or preference.
Conclusion
CIE color matching functions are mathematical descriptions of how a typical human observer perceives colors under a given illuminant. They are important because they allow us to measure and describe colors objectively, using numerical values that can be reproduced and communicated across different devices and platforms. They are also essential tools for color management, which is the process of ensuring that colors are displayed or printed as intended across different devices.
CIE color matching functions data can be downloaded from various sources online, but it is advisable to use only trusted and reputable sources that are affiliated with or endorsed by the CIE. The most common formats of CIE color matching functions data are text files and Excel files, which can be easily opened and manipulated by various software applications. The steps of downloading CIE color matching functions data are generally simple and straightforward, but they may vary depending on the source and the type of data.
CIE color matching functions data have many applications and uses in various fields and industries that deal with light and color, such as colorimetry, color management, color science, color engineering, and color education. Some of the specific examples of how CIE color matching functions data can be used are to calculate the tristimulus values or chromaticity coordinates of any spectral color or light source, to convert colors from one color space to another, to evaluate the color quality or performance of a light source, and to create or modify colors in digital images or graphics.
FAQs
Here are some frequently asked questions and answers about CIE color matching functions and their data.
What is the difference between CIE 1931 2-degree standard observer and CIE 1964 10-degree standard observer?
The CIE 1931 2-degree standard observer is based on the experiments that used a small visual field of 2 degrees, which is equivalent to the size of the thumb at arm's length. The CIE 1964 10-degree standard observer is based on the experiments that used a larger visual field of 10 degrees, which is equivalent to the size of the fist at arm's length. The CIE 1964 10-degree standard observer is more representative of the peripheral vision, while the CIE 1931 2-degree standard observer is more representative of the central vision. The CIE 1964 10-degree standard observer also has slightly different color matching functions than the CIE 1931 2-degree standard observer, especially in the short-wavelength region.
What is the difference between CIE XYZ color space and CIE xyY color space?
The CIE XYZ color space and the CIE xyY color space are equivalent, but they use different coordinates to represent colors. The CIE XYZ color space uses 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 CIE xyY color space uses three coordinates: x, y, and Y, where x and y are derived from X and Z by dividing them by the sum of X, Y, and Z, and Y is the same as in the CIE XYZ color space. The x and y coordinates represent the chromaticity of the color, while the Y coordinate represents the luminance of the color.
What is the difference between chromaticity and luminance?
Chromaticity and luminance are two aspects of color perception that are independent of each other. Chromaticity refers to the hue and saturation of a color, which are determined by the wavelength and purity of light. Luminance refers to the brightness or intensity of a color, which is determined by the amount of light. For example, a red apple and a green apple may have the same luminance, but different chromaticities. Similarly, a dim red light and a bright red light may have the same chromaticity, but different luminances.
What is the difference between color gamut and color rendering index?
Color gamut and color rendering index are two measures of color quality or performance of a light source or a device. Color gamut refers to the range or extent of colors that can be reproduced by a light source or a device, compared to a reference or ideal set of colors. Color rendering index refers to the ability of a light source or a device to render or reproduce the colors of objects faithfully, compared to a reference or ideal light source. For example, a monitor may have a large color gamut, but a low color rendering index, meaning that it can display many colors, but not accurately. Conversely, a light bulb may have a small color gamut, but a high color rendering index, meaning that it can only produce a few colors, but very accurately.
How can I use CIE color matching functions data in Excel?
If you have downloaded CIE color matching functions data as Excel files (.xls or .xlsx), you can use them in Excel by following these steps: - Open the Excel file that contains the CIE color matching functions data. - Select the range of cells that contains the data you want to use. - Copy and paste the data into another Excel file or worksheet that you want to work with. - Use Excel formulas or functions to perform calculations or conversions with the data. - Use Excel charts or graphs to visualize or compare the data. 44f88ac181
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