# Color temperature

The color temperature is a measure to quantitatively determine the color impression of a light source.

The color temperature is defined as the temperature of a black body , a Planckian radiator. It is the temperature (of such a radiator) that belongs to a certain color of the light emitted by this radiation source. In practice, this is the temperature whose light effect is most similar to the descriptive color with the same brightness and under specified observation conditions.

Characteristic light colors according to DIN EN 12665
Light source Color temperature in Kelvin Color temperature in mired
Warm white below 3300 K over 303 mired
Neutral white 3300-5300K 303-189 Mired
Daylight white (also cold white) over 5300 K under 189 mired

## Definition and unit of measure

Color temperature in Kelvin

The unit of color temperature is Kelvin (K). From this the mired (= 10 6  K −1 ) is derived as a million times the reciprocal of the Kelvin value. In the CIE diagram , each color temperature of a light source has a white point of this type of lighting. The spectral distribution of the light from emitters with the same color temperature can be very different, so-called metameric light sources. As with incandescent lamps, metameric light can have a continuous spectrum or, as with energy-saving lamps and flat screens, be limited to a few narrow spectral bands. The color rendering index indicates the quality of the color rendering when illuminated with a light source.

## Calculation of the color temperature

CIE XYZ color space. The black line corresponds to the color of the black body. The colors of monochromatic radiation with a wavelength of 380 ... 700 nm are on the border .

background

The CIE-XYZ color space is one of the first mathematically defined color spaces, which was created in 1931 by the International Commission on Illumination (Commission Internationale de l'Éclairage). The color space shown in the CIE standard table shows all colors that can be additively mixed from the spectral colors. It concerns all colors that can be achieved in principle. Every perceptible color can be expressed in the three parts x, y and z.

preparation

The red component of the color is plotted on the X-axis of the standard table, whereas the Y-axis shows the green component of the color. Both the green and the red component can be read directly from the standard table. The basic condition x + y + z = 1 means that the z-value can be dispensed with in the CIE diagram, as this can be determined by simply transforming the equation x + y + z = 1 into z = 1 - x - y.

calculation

If you want to calculate the color temperature of a light source, you have to determine its so-called color location. This color location is then compared with the color words of the black body. They are used as a reference for calculating the color temperature of lamps. The color temperature is not determined in the xy color space , but in the uv color space. The uv color space has the advantage that it represents color differences better. The following equations clarify the relationship between the uv color space and the xy color space:

${\ displaystyle u = {\ frac {4x} {- 2x + 12y + 3}} \ quad v = {\ frac {6y} {- 2x + 12y + 3}}}$

## photography

Influence of different color temperature settings in digital photography. See text for an explanation

In photography, it is important to take the color temperature into account so that a subject can be recorded in the colors that (should) correspond to the natural visual impression. The picture on the right shows the color rendering of the same motif when taking a picture with different manually set color temperatures of the light source, given in Kelvin. For example, in order to compensate for the yellowish hue of a halogen lamp (2800 K), i.e. to adapt the colors to the natural visual impression of the human being, the photo is given a blue cast that intensifies the underrepresented blue components. Conversely, with the 10,000 K setting, yellow-orange color tones are intensified in order to display a motif illuminated by blue-tinged light with as neutral a color as possible. If the automatic white balance is used by digital photo and video cameras, the circuit tries independently to determine the appropriate setting - based on the "whitest" image area.

The international standard for medium sunlight is 5500 Kelvin; it is the tone of a sunny day with a clear sky in the morning or afternoon. Daylight films are sensitized in such a way that, at color temperatures around 5500 K, they enable color reproduction that corresponds to reality. Artificial light films correspond to a color temperature of 3100 to 3400 K, depending on the type.

In order to achieve other color temperatures, conversion filters are placed in front of the lens . In digital photography , a white balance is made (often automatically) . Post-processing of incorrect colors in image processing software is possible within certain limits, but this reduces the quality of the image unless the raw data from the camera sensor is used ( RAW photography). The effect of a conversion filter can be quantified; it is given in the unit mired . Negative values ​​stand for bluish filters, positive values ​​for reddish values. The corrected color temperature is obtained by adding the mired value of the filter to the given color temperature of the light. The sign of the filter must be observed.

There are color temperature meters to determine the color temperature . In the 1950s, the Gossen Sixticolor, a device for amateur photographers, was offered exclusively to measure color temperature. A cheaper option was the Color Finder in various light meters from this company. A color bar was compared with different color fields, the (subjectively) most similar color field indicated the color temperature. Since the 1990s, colorimeters with digital displays have been common, in which the measured value is displayed directly in Kelvin.

## Characteristic color temperatures (exemplary)

Color temperature Light source
1500 K candle
2000 K Sodium vapor lamp (SON-T)
2600 K Incandescent lamp (40 W)
2700 K Incandescent lamp (60 W)
2800 K Incandescent lamp (100 W)
2700-2800K Halogen lamp (230 V, Eco-Halogen, 30–60 W)
3000 K Incandescent lamp (200 W)
3000-3200K Halogen lamp (12 V)
3200 K Photo lamp type B, halogen incandescent lamp
3400 K Photo lamp type A or S, late evening sun just before dawn
3600 K Operating theater lighting
4000 K Fluorescent lamp (neutral white)
4120 K Moonlight
4500-5000K Xenon lamp , electric arc
5000 K Morning / evening sun, D50 lamp ( printer )
5500 K Morning / afternoon sun
5500-5600K Electronic flash unit
5500-5800K Midday sun, clouds
6500-7500K Cloudy sky
7500-8500K Fog , heavy haze
9,000-12,000K Blue (cloudless) sky on the shaded north side. Blue hour
15,000-27,000K Clear blue northern sky light

## Subjective color perception

Blackbody radiation curve in the visible spectrum

The color temperature is determined by the physically defined surface properties of a radiator. The usual division of colors into cold or warm tones is based on a subjective feeling and cannot be described by a temperature. Artificial light sources give color perceptions that differ from daylight. Mixtures of different types of light sources can even disturb the feeling of wellbeing.

In the artistic field, the color temperature is often used differently. For example, using the mired scale gives cold colors a low value and warm colors a higher value. The EU regulation 244/2009, which is relevant for energy-saving lamps, explicitly requires that the color temperature be specified in Kelvin.

## Spectral classes of the stars

Star spectrum of class A0V (effective temperature: 9500 K, blue-filled curve), normalized to 1 at 555 nm

The spectral classes of stars are subdivided according to surface temperature . Their spectrum corresponds approximately to the radiation of a black body and is therefore directly related to the color temperature. The two main stars in the constellation Orion , Betelgeuse and Rigel , which are easy to find , can be distinguished very well in terms of color in the starry sky. Betelgeuse is significantly more reddish and, with a surface temperature of 3,450 K, belongs to the spectral class M, the bluish Rigel is significantly hotter at 10,500 K and belongs to spectral class B. With stars that are hotter than the sun, the effective and color temperatures sometimes differ significantly from each other; a typical star of the class A0V (see Wega ) has an effective temperature of approx. 9500 K, but a color temperature of approx. 15000 K.

The sun has an effective surface temperature of 5778 K. This corresponds roughly to the color temperature of the sun as seen from space, i.e. H. without the filtering effect of the earth's atmosphere. Seen from the earth, the light of the sun appears more or less reddened by scattering and absorption in the air, depending on the position of the sun, the land height and the weather conditions. The standard illuminant D50, which corresponds to the lighting with a color temperature of 5004 K, is reached on clear days in the morning or afternoon when the atmosphere is more subdued. Scattered light from the sky, on the other hand, has a much higher proportion of blue and therefore a higher color temperature than direct sunlight (see table).