Color temperature

The CIE 1931 x,y chromaticity space, also showing the chromaticities of black-body light sources of various temperatures (Planckian locus), and lines of constant correlated color temperature.

Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, and other fields. The color temperature of a light source is determined by comparing its chromaticity with that of an ideal black-body radiator. The temperature (usually measured in kelvins (K)) at which the heated black-body radiator matches the color of the light source is that source's color temperature; for a black body source, it is directly related to Planck's law and Wien's displacement law.

Counterintuitively, higher color temperatures (5000 K or more) are "cool" (green–blue) colors, and lower color temperatures (2700–3000 K) "warm" (yellow–red) colors. Cool-colored light is considered better for visual tasks. Warm-colored light is preferred for living spaces because it is considered more flattering to skin tones and clothing. Color temperatures in the 2700–3600 K range are recommended for most general indoor and task lighting.

Categorizing different lighting

Temperature	Source
1700 K	Match flame
1850 K	Candle flame
2700–3300 K	Incandescent light bulb
3350 K	Studio "CP" light
3400 K	Studio lamps, photofloods, etc.
4100 K	Moonlight, xenon arc lamp
5000 K	Horizon daylight
5500–6000 K	Typical daylight, electronic flash
6500 K	Daylight, overcast
9300 K	CRT screen
Note: These temperatures are merely approximations; considerable variation may be present.

Because it is the standard against which other light sources are compared, the color temperature of the thermal radiation from an ideal black body radiator is defined as equal to its surface temperature in kelvin, or alternatively in mired (micro-reciprocal degrees kelvin). For source other than ideal black bodies, the color temperature of the thermal radiation emitted from it may differ from its actual surface temperature. In an incandescent light bulb the light is of thermal origin and is very close to that of an ideal black-body radiator.

However, many other light sources, such as fluorescent lamps, emit light primarily by processes other than raising the temperature of a body. This means the emitted radiation does not follow the form of a black-body spectrum. These sources are assigned what is known as a correlated color temperature (CCT). CCT is the color temperature of a black body radiator which to human color perception most closely matches the light from the lamp. Because such an approximation is not required for incandescent light, the CCT for an incandescent light is simply its unadjusted temperature, derived from the comparison to a black body radiator.

The sun

As the sun crosses the sky, it may appear to be red, orange, yellow or white depending on its position. The changing color of the sun over the course of the day is mainly a result of refraction and, to a lesser extent, scattering of light, and is unrelated to black body radiation. The blue color of the sky is not caused by black-body radiation, but rather to Rayleigh scattering of the sunlight from the atmosphere, which tends to scatter blue light more than red. This phenomenon has nothing to do with the properties of a black body.

Daylight has a spectrum similar to that of a black body. In professions involving color reproduction, such as photography and publishing, daylight is often approximated using standard illuminant D50 or D65, as recommended by the CIE.

Hues of the Planckian locus, in the mired scale.

For colors based on the black body, blue is the "hotter" color, while red is actually the "cooler" color. This is the opposite of the cultural associations that colors have taken on, with "red" as "hot", and "blue" as "cold". The traditional associations come from a variety of sources, such as water and ice appearing blue, while heated metal and fire are of a reddish hue. However, the redness of these heat sources comes precisely from the fact that red is the coolest of the visible colors, the first color emitted as heat increases.

Color temperature applications

"Color temperature" is sometimes used loosely to mean "white balance" or "white point". However, color temperature has only one degree of freedom, essentially the blue–yellow axis, whereas white balance has two, adding the magenta–green axis.

Film photography

Film sometimes appears to exaggerate the color of the light, since it does not adapt to lighting color as our visual perception does. An object that appears to the eye to be white may turn out to look very blue or orange in a photograph. The color balance may need to be corrected while shooting or while printing to achieve a neutral color print.

Film is made for specific light sources (most commonly daylight film and tungsten film), and used properly, will create a neutral color print. Matching the sensitivity of the film to the color temperature of the light source is one way to balance color. If tungsten film is used indoors with incandescent lamps, the yellowish-orange light of the tungsten incandescent bulbs will appear as white (3200 K) in the photograph.

Filters on a camera lens, or color gels over the light source(s) may also be used to correct color balance. When shooting with a bluish light (high color temperature) source such as on an overcast day, in the shade, in window light or if using tungsten film with white or blue light, a yellowish-orange filter will correct this. For shooting with daylight film (calibrated to 5600 K) under warmer (low color temperature) light sources such as sunsets, candle light or tungsten lighting, a bluish (e.g. #80A) filter may be used.

If there is more than one light source with varied color temperatures, one way to balance the color is to use daylight film and place color-correcting gel filters over each light source.

Photographers sometimes use color temperature meters. Color temperature meters are usually designed to read only two regions along the visible spectrum (red and blue); more expensive ones read three regions (red, green, and blue). However, they are ineffective with sources such as fluorescent or discharge lamps, whose light varies in color and may be harder to correct for. Because it is often greenish, a magenta filter may correct it. More sophisticated colorimetry tools can be used where such meters are lacking.

Desktop publishing

In the desktop publishing industry, it is important to know your monitor’s color temperature. Color matching software, such as ColorSync will measure a monitor's color temperature and then adjust its settings accordingly. This enables on-screen color to more closely match printed color. Common monitor color temperatures, along with matching standard illuminants in parentheses, are as follows:

5000 K (D50), 5500 K (D55), 6500 K (D65), 7500 K (D75), 9300 K.

Designations such as D50 are used to classify color temperatures of light tables and viewing booths. When viewing a color slide at a light table, it is important that the light be balanced properly so that the colors are not shifted towards the red or blue.

Digital cameras, web graphics, DVDs, etc. are normally designed for a 6500 K color temperature. The sRGB standard commonly used for images on the internet stipulates (among other things) a 6500 K display whitepoint.

TV, video, and digital still cameras

The NTSC and PAL TV norms call for a compliant TV screen to display an electrically "black-and-white" signal (minimal color saturation) at a color temperature of 6500 K. On many actual sets, however, especially older or lower-quality units, there is a very noticeable deviation from this requirement.

Most video and digital still cameras can adjust for color temperature by zooming into a white or neutral colored object and setting the manual "white balance" (telling the camera that "this object is white"); the camera then shows true white as white and adjusts all the other colors accordingly. White-balancing is necessary especially when indoors under fluorescent lighting and when moving the camera from one lighting situation to another. Most cameras also have an automatic white balance function that attempts to determine the color of the light and correct accordingly. While these settings were once unreliable, they are much improved in today's digital cameras, and will produce the "correct" white balance in a wide variety of lighting situations.

Artistic application via control of color temperature

The house above appears a light cream during the midday, but seems a bluish white here in the dim light before full sunrise. Note the different color temperature of the sunrise in the background.

Experimentation with color temperature is obvious in many Stanley Kubrick films; for instance in Eyes Wide Shut the light coming in from a window was almost always conspicuously blue, whereas the light from lamps on end tables was fairly orange. Indoor lights typically give off a yellow hue; fluorescent and natural lighting tends to be more blue.

Video camera operators can also white-balance objects which aren't white, downplaying the color of the object used for white-balancing. For instance, they can bring more warmth into a picture by white-balancing off something light blue, such as faded blue denim; in this way white-balancing can serve in place of a filter or lighting gel when those aren't available.

Cinematographers do not "white balance" in the same way as video camera operators; they can use techniques such as filters, choice of film stock, pre-flashing, and after shooting, color grading (both by exposure at the labs and also digitally). Cinematographers also work closely with set designers and lighting crews to achieve the desired effects.

For artists, most pigments and papers have a cool or warm cast, as the human eye can detect even a minute amount of saturation. Gray mixed with yellow, orange or red is a "warm gray". Green, blue, or purple, create "cool grays". Note that this sense of temperature is the reverse of that of real temperature; bluer is described as "cooler" even though it corresponds to a higher-temperature blackbody.

WARM GRAY	COOL GRAY
Mixed with 6% yellow.	Mixed with 6% blue.

Lighting designers sometimes select filters by color temperature, commonly to match light that is theoretically white. Since fixtures using discharge type lamps produce a light of considerably higher color temperature than tungsten lamps, using the two in conjunction could potentially produce a stark contrast, so sometimes fixtures with HID lamps, commonly producing light of 6000–7000 K, are fitted with 3200 K filters to emulate tungsten light. Fixtures with color mixing features or with multiple colors, (if including 3200 K) are also capable of producing tungsten like light. Color temperature may also be a factor when selecting lamps, since each is likely to have a different color temperature.

Lighting

For lighting buildings, it is often important to take into account the color temperature of the light fittings used. For example, a warmer (i.e., lower color temperature) light is often used in public areas to promote relaxation, while a cooler (higher color temperature) light is used in offices. Because of the heightened awareness of the stress that poor lighting can cause, as well as sick building syndrome, many governmental agencies have certain criteria that lighting must meet.

The international color code is often used to denote the temperature of a lamp's light. This code is a three digit number. The first digit refers to the color rendering index: if it is 8, then the CRI is between 80 and 90, if it is 9, it lies between 90 and 100. The next two numbers are the color temperature (to the nearest hundred) divided by one hundred kelvins, thus if the temperature is 6500 K, the number is 65.

Correlated color temperature

The correlated color temperature (T_cp) is the temperature of the Planckian radiator whose perceived colour most closely resembles that of a given stimulus at the same brightness and under specified viewing conditions

— CIE/IEC 17.4:1987, International Lighting Vocabulary (ISBN 3900734070)

Motivation

Black body radiators are the reference by which the whiteness of light sources is judged. A black body can be described by its color temperature, whose hues are depicted above. By analogy, nearly-Planckian light sources such as certain fluorescent or high-intensity discharge lamps can be judged by their correlated color temperature (CCT); the color temperature of the Planckian radiator that best approximates them. The question is: what is the relationship between the light source's relative spectral power distribution and its correlated color temperature?

Background

Judd's (r,g) diagram. The concentric curves indicate the loci of constant purity.

Judd's Maxwell triangle. Planckian locus in red. Translating from trilinear co-ordinates into Cartesian co-ordinates leads to the next diagram.

Judd's uniform chromaticity space (UCS), with the Planckian locus and the isotherms from 1000 K to 10000 K, perpendicular to the locus. Judd calculated the isotherms in this space before translating them back into the (x,y) chromaticity space, as depicted in the diagram at the top of the article.

Close up of the Planckian locus in the CIE 1960 UCS, with the isotherms in mireds. Note the even spacing of the isotherms when using the reciprocal temperature scale, and compare with the similar figure below. The even spacing of the isotherms on the locus implies that the mired scale is a better measure of perceptual color difference than the temperature scale.

The notion of using Planckian radiators as a yardstick to judge other light sources against is not a new one. In 1923, writing about "grading of illuminants with reference to quality of color…the temperature of the source as an index of the quality of color", Priest essentially described CCT as we understand it today, going so far as to use the term apparent color temperature, and astutely recognized three cases:

• "Those for which the spectral distribution of energy is identical with that given by the Planckian formula."
• "Those for which the spectral distribution of energy is not identical with that given by the Planckian formula, but still is of such a form that the quality of the color evoked is the same as would be evoked by the energy from a Planckian radiator at the given color temperature."
• "Those for which the spectral distribution of energy is such that the color can be matched only approximately by a stimulus of the Planckian form of spectral distribution."

Several important developments occurred in 1931. In chronological order:

1. Davis published a paper on correlated color temperature (his term). Referring to the Planckian locus on the r-g diagram, he defined the CCT as the average of the primary component temperatures (RGB CCTs), using trilinear coordinates.
2. The CIE announced the XYZ color space.
3. Judd published a paper on the nature of "least perceptible differences" with respect to chromatic stimuli. By empirical means he determined that the difference in sensation, which he termed ΔE for a "discriminatory step between colors…Empfindung" (German for sensation) was proportional to the distance of the colors on the chromaticity diagram. Referring to the (r,g) chromaticity diagram depicted aside, he hypothesized that:

$K\Delta E=|c_{1}-c_{2}|=\max(|r_{1}-r_{2}|,|g_{1}-g_{2}|)$

These developments paved the way for the development of new chromaticity spaces that are more suited to the estimation of correlated color temperatures and chromaticity differences. Bridging the concepts of color difference and color temperature, Priest made the observation that the eye is sensitive to constant differences in reciprocal temperature:

A difference of one micro-reciprocal-degree ($\mu rd$) is fairly representative of the doubtfully perceptible difference under the most favorable conditions of observation.

Priest proposed to use "the scale of temperature as a scale for arranging the chromaticities of the several illuminants in a serial order."

Over the next few years, Judd published three more significant papers:

1. The first verified the findings of Priest, Davis, and Judd, with a paper on sensitivity to change in color temperature.
2. The second proposed a new chromaticity space, guided by a principle that has become the holy grail of color spaces: perceptual uniformity (chromaticity distance should be commensurate with perceptual difference). By means of a projective transformation, Judd found a more uniform chromaticity space (UCS) in which to find the CCT. Judd determined the nearest color temperature by simply finding the nearest point on the Planckian locus to the chromaticity of the stimulus on Maxwell's color triangle, depicted aside. The transformation matrix he used to convert X,Y,Z tristimulus values to R,G,B coordinates was:
   ${\begin{bmatrix}R\\G\\B\end{bmatrix}}={\begin{bmatrix}3.1956&2.4478&-0.1434\\-2.5455&7.0492&0.9963\\0.0000&0.0000&1.0000\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}$.
   From this one can find these chromaticities:
   $u={\frac {0.4661x+0.1593y}{y-0.15735x+0.2424}}\quad v={\frac {0.6581y}{y-0.15735x+0.2424}}$
3. The third depicted the locus of the isothermal chromaticities on the CIE 1931 x,y chromaticity diagram. Since the isothermal points formed normals on his UCS diagram, transformation back into the xy plane revealed them still to be lines, but no longer perpendicular to the locus.

MacAdam's "uniform chromaticity scale" diagram; a simplification of Judd's UCS.

Calculation

Judd's idea of determining the nearest point to the Planckian locus on a uniform chromaticity space is current. In 1937, MacAdam suggested a "modified uniform chromaticity scale diagram", based on certain simplifying geometrical considerations:

$u={\frac {4x}{-2x+12y+3}}$

$v={\frac {6y}{-2x+12y+3}}$

This (u,v) chromaticity space became the CIE 1960 color space, which is still used to calculate the CCT (even though MacAdam did not devise it with this purpose in mind). Using other chromaticity spaces, such as u'v', leads to non-standard results that may nevertheless be perceptually meaningful.

Close up of the CIE 1960 UCS. The isotherms are perpendicular to the Planckian locus, and are drawn to indicate the maximum distance from the locus that the CIE considers the correlated color temperature to be meaningful: $\Delta uv=\pm 0.05$

The distance from the locus (i.e., degree of departure from a black body) is traditionally indicated in units of $\Delta uv$; positive for points above the locus. This concept of distance has evolved to become Delta E, which continues to be used today.

Robertson's method

Before the advent of powerful, personal computers, it was common to estimate the correlated color temperature by way of interpolation from look-up tables and charts. The most famous such method is Robertson's, who took advantage of the relatively even spacing of the mired scale (see above) to calculate the CCT T_c using linear interpolation of the isotherm's mired values:

Computation of the CCT T_c corresponding to the chromaticity coordinate $(u_{T},v_{T})$ in the CIE 1960 UCS.

${\frac {1}{T_{c}}}={\frac {1}{T_{i}}}+{\frac {\theta _{1}}{\theta _{1}+\theta _{2}}}\left({\frac {1}{T_{i+1}}}-{\frac {1}{T_{i}}}\right)$

where $T_{i}$ and $T_{i+1}$ are the color temperatures of the look-up isotherms and i is chosen such that $T_{i}<T_{c}<T_{i+1}$. (Furthermore, the test chromaticity lies between the only two adjacent lines for which $d_{i}/d_{i+1}<0$.)

If the isotherms are tight enough, one can assume $\theta _{1}/\theta _{2}\approx \sin \theta _{1}/\sin \theta _{2}$, leading to

${\frac {1}{T_{c}}}={\frac {1}{T_{i}}}+{\frac {d_{i}}{d_{i}-d_{i+1}}}\left({\frac {1}{T_{i+1}}}-{\frac {1}{T_{i}}}\right)$

The distance of the test point to the i'th isotherm is given by

$d_{i}={\frac {(v_{T}-v_{i})-m_{i}(u_{T}-u_{i})}{\sqrt {1+m_{i}^{2}}}}$

where $(u_{i},v_{i})$ is the chromaticity coordinate of the i'th isotherm on the Planckian locus and m_i is the isotherm's slope. Since it is perpendicular to the locus, it follows that $m_{i}=-1/l_{i}$ where l_i is the slope of the locus at $(u_{i},v_{i})$.

Precautions

Although the CCT can be calculated for any chromaticity coordinate, the result is meaningful only if the light sources are nearly white. The CIE recommends that "The concept of correlated color temperature should not be used if the chromaticity of the test source differs more than [$\Delta _{uv}=5\times 10^{-2}$] from the Planckian radiator." Beyond a certain value of $\Delta uv$, a chromaticity co-ordinate may be equidistant to two points on the locus, causing ambiguity in the CCT.

Approximation

If a narrow range of color temperatures is considered—those encapsulating daylight being the most practical case—one can approximate the Planckian locus in order to calculate the CCT in terms of chromaticity coordinates. Following Kelly's observation that the isotherms intersect in the purple region near $(x=0.325,y=0.154)$, McCamy proposed this cubic approximation:

$CCT(x,y)=-449n^{3}+3525n^{2}-6823.3n+5520.33$

where $n=(x-x_{e})/(y-y_{e})$ is the inverse slope line and $(x_{e}=0.3320,y_{e}=0.1858)$ is the "epicenter"; quite close to the intersection point mentioned by Kelly. The maximum absolute error for color temperatures ranging from 2856 (illuminant A) to 6504 (D65) is under 2 K.

A more recent proposal, using exponential terms, considerably extends the applicable range by adding a second epicenter for high color temperatures:

$CCT(x,y)=A_{0}+A_{1}\exp(-n/t_{1})+A_{2}\exp(-n/t_{2})+A_{3}\exp(-n/t_{3})$

where n is as before and the other constants are defined below:

	3–50 kK	50–800 kK
xe	0.3366	0.3356
ye	0.1735	0.1691
A0	-949.86315	36284.48953
A1	6253.80338	0.00228
t1	0.92159	0.07861
A2	28.70599	5.4535×10-36
t2	0.20039	0.01543
A3	0.00004
t3	0.07125

Color rendering index

The CIE color rendering index (CRI) is a method to determine how well a light source's illumination of eight sample patches compares to the illumination provided by a reference source. Cited together, the CRI and CCT give a numerical estimate of what reference (ideal) light source best approximates a particular artificial light, and what the difference is.

Spectral power distribution

File:SPD.png

Here is an example of just how different an incandescent lamp's SPD graph is from that of a fluorescent lamp.

Light sources and illuminants may be characterized by their spectral power distribution (SPD). The relative SPD curves provided by many manufacturers may have been produced using 10-nanometre (nm) increments or more on their spectroradiometer. The result is what would seem to be a smoother ("fuller spectrum") power distribution than the lamp actually has. Owing to their spiky distribution, much finer increments are advisable for taking measurements of fluorescent lights, and this requires more expensive equipment.

See also

• Luminous efficacy
• Over-illumination
• Brightness temperature
• Effective temperature

Further reading

• Stroebel, Leslie (2000). Basic Photographic Materials and Processes (2E ed.). Boston: Focal Press. ISBN 0-240-80405-8. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Wyszecki, Günter (1982). "3.11: Distribution Temperature, Color Temperature, and Correlated Color Temperature". Color Science: Concept and Methods, Quantitative Data and Formulæ. New York: Wiley. pp. 224–229. ISBN 0-471-02106-7. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

External links

• Charity, Mitchell. What color is a blackbody? sRGB values corresponding to blackbodies of varying temperature.
• Lindbloom, Bruce. ANSI C implementation of Robertson's method to calculate the correlated color temperature of a color in XYZ.