Ranger HRC™ operator´s manual – Theory of thermal imaging
Publ. No. TM G007971 Rev. A1 – ENGLISH (EN) – Sept 09. 2008
The sum of these three factors must always add up to the whole at any
wavelength, so we have the relation:
1
=
+
+
λ
λ
λ
τ
ρ
α
For opaque materials
t
l
= 0 and the relation simplifies to:
1
=
+
λ
λ
ρ
α
Another factor, called the emissivity, is required to describe the fraction
ε
of the radiant exitance of a blackbody produced by an object at a specific
temperature. Thus, we have the definition:
The spectral emissivity
ε
l
= the ratio of the spectral radiant power from
an object to that from a blackbody at the same temperature and wave-
length.
Expressed mathematically, this can be written as the ratio of the spectral
exitance of the object to that of a blackbody as follows:
λ
λ
λ
ε
,
,
e
o
M
M
=
Generally speaking, there are three types of radiation source, distinguish-
ed by the ways in which the spectral exitance of each varies with wave-
length.
• A blackbody, for which
ε
l
=
ε
= 1
• A graybody, for which
ε
l
=
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 absorptance of a body are equal at any specified temperature and
wavelength. That is:
λ
λ
α
ε =
From this we obtain, for an opaque material (since
α
l
+
ρ
l
= 1):
1
=
+
λ
λ
ρ
ε
