Non-Blackbody Emitters - FLIR T460 User Manual

34
Theory of thermography
Figure 34.7 Josef Stefan (1835–1893), and Ludwig Boltzmann (1844–1906)
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
radiation from surrounding surfaces, at room temperatures which do not vary too drasti-
cally from the temperature of the body – or, of course, the addition of clothing.

34.3.4 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
object 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
• A graybody, for which ε
λ
#T559879; r. AH/23788/24627; en-US
= the ratio of the spectral radiant power absorbed by an
λ
= the ratio of the spectral radiant power reflected by an ob-
λ
= the ratio of the spectral radiant power transmitted
λ
= ε = 1
λ
= ε = constant less than 1
2 , we obtain 1 kW.
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