Ranger HRC™ operator´s manual – Theory of thermal imaging
Publ. No. TM G007971 Rev. A1 – ENGLISH (EN) – Sept 09. 2008 241
Figure 17.6 Planckian curves plotted on semi-log scales from 100 K to 1.000 K. The dotted
line represents the locus of maximum radiant exitance at each temperature as described by
Wien’s displacement law. 1: Spectral radiant exitance (W/cm2 (μm)); 2: Wavelength (μm).
17.3.3 Stefan-Boltzmann’s law
By integrating Planck’s formula from l = 0 to l = ∞, we obtain the total
radiant exitance M
e
) of a blackbody:
This is the Stefan-Boltzmann formula after Josef Stefan, 1835–1893,
and Ludwig Boltzmann, 1844–1906), which states that the total emissive
power of a blackbody is proportional to the fourth power of its absolute
temperature. Graphically, M
e
represents the area below the Planck curve
for a particular temperature. It can be shown that the radiant exitance in
the interval l = 0 to l
max
is only 25 % of the total, which represents about
the amount of the sun’s radiation which lies inside the visible light spec-
trum.