frudawski

# planck

The planck function calculates the spectral radiant exitance M of a Planck radiator for a given black body temperature T in K, as in equation 1:

(1) \qquad M(\lambda,T) = \frac{c_1}{\lambda^5}\frac{1}{\exp\left({\frac{c_2}{T\cdot\lambda}}\right)-1}

With:

c_1 = 3.741771852 \cdot 10^{-16}~\mathrm{W}\cdot\textrm{m}^2

c_2 = 1.438776877 \cdot 10^{-2}~\mathrm{m}\cdot\textrm{K}

Note: Since the redefinition of the Boltzmann constant in 2018 the constants c_1 and c_2 are now exact values.

Usage:

[M,x,y,u,v] = planck(T,lam,mode)

Where:

Examples

Spectral radiant exitance for a block body temperature of 5000 K:

M = planck(5000);
plotspec(360:830,M)
ylabel('spectral radiant exitance in W m^{-2} nm^{-1}')

Result:

Spectral radiant exitance for several black body temperatures:

lam = 0:10:1000;
T = 4000:1000:9000;
M = planck(T,lam);
plot(lam,M)
xlabel('\lambda in nm')
ylabel('spectral radiant exitance in W m^{-2} nm^{-1}')
legend('4000 K','5000 K','6000 K','7000 K','8000 K','9000 K')

Result:

Colour coordinates for a planck radiator of 9000 K:

[~,x,y,u,v] = planck(9000)

Result:

x = 0.2869
y = 0.2956
u = 0.1921
v = 0.2969

Reference

Günther Wyszecki, W. S. Stiles: Colour Science - Concepts and Methods, Quantitative Data and Formulae, 2nd Edition. John Wiley & Sons, Inc., 2000, ISBN: 978-0-471-39918-6.

The NIST Reference on Constants, Units and Uncertainty, first radiation constant

The NIST Reference on Constants, Units and Uncertainty, second radiation constant