1.3 Color Temperature


In physics PLANCK'S LAW describes the electromagnetic radiation emitted from a so called BLACK BODY RADIATOR at a given temperature. A blackbody radiator is assumed to have very weak interaction with the surrounding environment and to be in a state of equilibrium. Stars are sufficiently good approximations of blackbody radiators.

$\displaystyle E(\lambda ,T)$ $\displaystyle = \frac{2hc^2}{\lambda ^5}\,\frac1{e^\frac{hc}{\lambda kT}-1}$    
$\displaystyle h$ $\displaystyle := 6.625\times 10^{-27}$ erg-sec ...Planck constant    
$\displaystyle k$ $\displaystyle := 1.38\times 10^{-16}$ erg/K ...Boltzmann constant    
$\displaystyle C$ $\displaystyle := 3\times 10^{10}$cm/sec...speed of light    
$\displaystyle E$ $\displaystyle \dots$emitted energy by unit surface area into a fixed direction    
$\displaystyle \lambda$ $\displaystyle \dots$wavelength$\displaystyle , \quad T \dots$temperature in Kelvin$\displaystyle .$    

Figure: Energy distributions of black body and 3 stars
Image /home/andreas/tex/Books/computer-graphics/img//planck.gif     Image /home/andreas/tex/Books/computer-graphics/img//spic-sun-ant.gif
Figure: Surface temperatures of some stars, see plabpc.csustan.edu.html

Classification Surface Color Familiar
  Temperature   Examples
O 30,000$ ^oK$ electric blue  
B 20,000$ ^oK$ blue Rigel
A 10,000$ ^oK$ white Vega, Sirius
F 7,000$ ^oK$ yellow-white Canopus
G 6,000$ ^oK$ yellow Sun, Alpha Centauri
K 4,000$ ^oK$ orange Arcturus, Aldebaran
M 3,000$ ^oK$ red Betelgeuse, Barnard's Star

Figure: Positions of colors from black body radiator at different temperature

Note that many colors (like green and violet) are not lying on this curve, thus have no associated color temperature. Color temperature plays also an important role in photography. Lower temperature means redder; higher temperature means bluer. Household incandescent lighting has a relatively low color temperature-about 3,000^&cir#circ; K. Open flames-candles, campfires-are still lower. By contrast, direct sunlight has a color temperature of about 5,400^&cir#circ; K. Photographic film can not compensate for the color of ambient light like our visual system does. Usual daylight film reproduces color most accurately at 5,400^&cir#circ; K. If it is used inside (without flashlight) the taken pictures will look orange.

Andreas Kriegl 2003-07-23