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Planckian locus
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Planckian locus
In physics and color science, the Planckian locus or black body locus is the path or locus that the color of an incandescent black body would take in a particular chromaticity space as the blackbody temperature changes. It goes from deep red at low temperatures through orange, yellowish, white, and finally bluish white at very high temperatures.
A color space is a three-dimensional space; that is, a color is specified by a set of three numbers (the CIE coordinates X, Y, and Z, for example, or other values such as hue, colorfulness, and luminance) which specify the perceived attributes of a particular homogeneous visual stimulus. A chromaticity is a color projected into a two-dimensional space that ignores brightness. For example, the standard CIE XYZ color space projects directly to the corresponding chromaticity space specified by the two chromaticity coordinates known as x and y, making the familiar chromaticity diagram shown in the figure. The Planckian locus, the path that the color of a black body takes as the blackbody temperature changes, is often shown in this standard chromaticity space.
In the CIE XYZ color space, the three coordinates defining a color are given by X, Y, and Z:
where M(λ,T) is the spectral radiant exitance of the light being viewed, and X(λ), Y(λ) and Z(λ) are the color matching functions of the CIE standard colorimetric observer, shown in the diagram on the right, and λ is the wavelength. The Planckian locus is determined by substituting into the above equations the black body spectral radiant exitance, which is given by Planck's law:
where:
and
This will give the Planckian locus in CIE XYZ color space. If these coordinates are XT, YT, ZT where T is the temperature, then the CIE chromaticity coordinates will be
Note that in the above formula for Planck's Law, you might as well use c1L = 2hc2 (the first radiation constant for spectral radiance) instead of c1 (the "regular" first radiation constant), in which case the formula would give the spectral radiance L(λ,T) of the black body instead of the spectral radiant exitance M(λ,T). However, this change only affects the absolute values of XT, YT and ZT, not the values relative to each other. Since XT, YT and ZT are usually normalized to YT = 1 (or YT = 100) and are normalized when xT and yT are calculated, the absolute values of XT, YT and ZT do not matter. For practical reasons, c1 might therefore simply be replaced by 1.
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Planckian locus AI simulator
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Planckian locus
In physics and color science, the Planckian locus or black body locus is the path or locus that the color of an incandescent black body would take in a particular chromaticity space as the blackbody temperature changes. It goes from deep red at low temperatures through orange, yellowish, white, and finally bluish white at very high temperatures.
A color space is a three-dimensional space; that is, a color is specified by a set of three numbers (the CIE coordinates X, Y, and Z, for example, or other values such as hue, colorfulness, and luminance) which specify the perceived attributes of a particular homogeneous visual stimulus. A chromaticity is a color projected into a two-dimensional space that ignores brightness. For example, the standard CIE XYZ color space projects directly to the corresponding chromaticity space specified by the two chromaticity coordinates known as x and y, making the familiar chromaticity diagram shown in the figure. The Planckian locus, the path that the color of a black body takes as the blackbody temperature changes, is often shown in this standard chromaticity space.
In the CIE XYZ color space, the three coordinates defining a color are given by X, Y, and Z:
where M(λ,T) is the spectral radiant exitance of the light being viewed, and X(λ), Y(λ) and Z(λ) are the color matching functions of the CIE standard colorimetric observer, shown in the diagram on the right, and λ is the wavelength. The Planckian locus is determined by substituting into the above equations the black body spectral radiant exitance, which is given by Planck's law:
where:
and
This will give the Planckian locus in CIE XYZ color space. If these coordinates are XT, YT, ZT where T is the temperature, then the CIE chromaticity coordinates will be
Note that in the above formula for Planck's Law, you might as well use c1L = 2hc2 (the first radiation constant for spectral radiance) instead of c1 (the "regular" first radiation constant), in which case the formula would give the spectral radiance L(λ,T) of the black body instead of the spectral radiant exitance M(λ,T). However, this change only affects the absolute values of XT, YT and ZT, not the values relative to each other. Since XT, YT and ZT are usually normalized to YT = 1 (or YT = 100) and are normalized when xT and yT are calculated, the absolute values of XT, YT and ZT do not matter. For practical reasons, c1 might therefore simply be replaced by 1.
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