FLIR Photon Manual Book page 59

According to Kirchhoff's law, for any
material the spectral emissivity and
spectral absorptance of a body are
equal at any specified temperature and
wavelength. That is:
ε = α
λ λ
From this we obtain, for an opaque
material (since α + ρ
λ
ε + ρ = 1
λ λ
For highly polished materials ε
approaches zero, so for a perfectly
reflecting material (for example. a perfect
mirror) we have:
ρ = 1
λ
For a graybody radiator, the Stefan-
Boltzmann formula becomes:
W = εσT [Watt/m ]
4 2
This states that the total emissive power
of a graybody is the same as a blackbody
at the same temperature reduced in
proportion to the value of ε from the
graybody.
Blackbody
Wavelength (µm)
Figure 12. Spectral radiant emittance of three
types of radiators.
History and Theory of Infrared Technology
= 1):
λ
λ
Selective radiator
Graybody
1.0
0.5
0.0
Wavelength
Figure 13. Spectral emissivity of three types of
radiators.
Infrared Semi-transparent Materials
Consider a non-metallic, semi-
transparent body in the form of a thick
flat plate of plastic material. When the
plate is heated, radiation generated
within its volume must work its way
toward the surfaces through the
material in which it is partially absorbed.
Moreover, when it arrives at the surface,
some of it is reflected back into the
interior. The back-reflected radiation is
again partially absorbed, but some of
it arrives at the other surface, through
which most of it escapes, but part of it
is reflected back again. Although the
progressive reflections become weaker
and weaker, they must all be added up
when the total emittance of the plate is
sought. When the resulting geometrical
series is summed, the effective emissivity
of a semi-transparent plate is obtained as:
(1 –ρ ) (1 – τ )
= ______________
ε λ λ
λ 1 – p t
λ λ
When the plate becomes opaque this
formula is reduced to the single formula:
ε = 1 – p
λ λ
Blackbody
Selective
radiator
Graybody
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