There are three processes which can occur that prevent a real object from acting like
a blackbody: a fraction of the incident radiation α may be absorbed, a fraction ρ may
be reflected, and a fraction τ may be transmitted. Since all of these factors are more
or less wavelength dependent, the subscript λ is used to imply the spectral depen-
dence of their definitions. Thus:
■
The spectral absorptance
α
λ
= the ratio of the spectral radiant power absorbed by
an object to that incident upon it.
■
The spectral reflectance
ρ
λ
= the ratio of the spectral radiant power reflected by
an object to that incident upon it.
■
The spectral transmittance
τ
λ
= the ratio of the spectral radiant power transmitted
through an object to that incident upon it.
The sum of these three factors must always add up to the whole at any wavelength,
so we have the relation:
For opaque materials
τ
λ
= 0
and the relation simplifies to:
Another factor, called the emissivity, is required to describe the fraction ε of the radiant
emittance of a blackbody produced by an object at a specific temperature. Thus, we
have the definition:
The spectral emissivity
ε
λ
= the ratio of the spectral radiant power from an object to
that from a blackbody at the same temperature and wavelength.
Expressed mathematically, this can be written as the ratio of the spectral emittance
of the object to that of a blackbody as follows:
Generally speaking, there are three types of radiation source, distinguished by the
ways in which the spectral emittance of each varies with wavelength.
■
A blackbody, for which
ε
λ
= ε = 1
■
A graybody, for which
ε
λ
= ε =
constant less than 1
■
A selective radiator, for which ε varies with wavelength
According to Kirchhoff’s law, for any material the spectral emissivity and spectral ab-
sorptance of a body are equal at any specified temperature and wavelength. That is:
From this we obtain, for an opaque material (since
α
λ
+ ρ
λ
= 1
):
20
Publ. No. 1557966 Rev. a155 – ENGLISH (EN) – February 6, 2006
161
20 – Theory of thermography
Summary of Contents for ThermaCAM P45
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