Non-Blackbody Emitters - FLIR Ex series User Manual

18 Theory of thermography
Using the Stefan-Boltzmann formula to calculate the power radiated by the human body,
at a temperature of 300 K and an external surface area of approx. 2 m
This power loss could not be sustained if it were not for the compensating absorption of ra-
diation from surrounding surfaces, at room temperatures which do not vary too drastically
from the temperature of the body – or, of course, the addition of clothing.

18.3.4 Non-blackbody emitters

So far, only blackbody radiators and blackbody radiation have been discussed. However,
real objects almost never comply with these laws over an extended wavelength region –
although they may approach the blackbody behavior in certain spectral intervals. For ex-
ample, a certain type of white paint may appear perfectly white in the visible light spec-
trum, but becomes distinctly gray at about 2 μm, and beyond 3 μm it is almost black.
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 re-
flected, 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 dependence of their
definitions. Thus:
• The spectral absorptance α
ject to that incident upon it.
• The spectral reflectance ρ
ject to that incident upon it.
• The spectral transmittance τ
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 = 0 and the relation simplifies to:
λ
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 = the ratio of the spectral radiant power from an object to that
λ
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
• A graybody, for which ε = ε = constant less than 1
λ
• A selective radiator, for which ε varies with wavelength
According to Kirchhoff's law, for any material the spectral emissivity and spectral absorp-
tance of a body are equal at any specified temperature and wavelength. That is:
From this we obtain, for an opaque material (since α
#T559828; r. AK/40423/40448; en-US
= the ratio of the spectral radiant power absorbed by an ob-
λ
= the ratio of the spectral radiant power reflected by an ob-
λ
= the ratio of the spectral radiant power transmitted
λ
= ε = 1
+ ρ
λ
2 , we obtain 1 kW.
= 1):
λ
89