FLIR Exx series User Manual page 169

33
The measurement formula
2. Reflected emission from ambient sources = (1 – ε)τW
tance of the object. The ambient sources have the temperature T
It has here been assumed that the temperature T
ces within the halfsphere seen from a point on the object surface. This is of course
sometimes a simplification of the true situation. It is, however, a necessary simplifica-
tion in order to derive a workable formula, and T
en a value that represents an efficient temperature of a complex surrounding.
Note also that we have assumed that the emittance for the surroundings = 1. This is
correct in accordance with Kirchhoff's law: All radiation impinging on the surrounding
surfaces will eventually be absorbed by the same surfaces. Thus the emittance = 1.
(Note though that the latest discussion requires the complete sphere around the ob-
ject to be considered.)
3. Emission from the atmosphere = (1 – τ)τW
mosphere. The temperature of the atmosphere is T
The total received radiation power can now be written (Equation 2):
We multiply each term by the constant C of Equation 1 and replace the CW products by
the corresponding U according to the same equation, and get (Equation 3):
Solve Equation 3 for U (Equation 4):
obj
This is the general measurement formula used in all the FLIR Systems thermographic
equipment. The voltages of the formula are:
Table 33.1 Voltages
U
obj
U
tot
U
refl
U
atm
The operator has to supply a number of parameter values for the calculation:
• the object emittance ε,
• the relative humidity,
• T
atm
• object distance (D )
obj
• the (effective) temperature of the object surroundings, or the reflected ambient tem-
perature T , and
refl
• the temperature of the atmosphere T
This task could sometimes be a heavy burden for the operator since there are normally
no easy ways to find accurate values of emittance and atmospheric transmittance for the
actual case. The two temperatures are normally less of a problem provided the surround-
ings do not contain large and intense radiation sources.
A natural question in this connection is: How important is it to know the right values of
these parameters? It could though be of interest to get a feeling for this problem already
here by looking into some different measurement cases and compare the relative
#T559845; r. AJ/37554/37554; en-US
refl
is the same for all emitting surfa-
refl
can – at least theoretically – be giv-
refl
, where (1 – τ) is the emittance of the at-
atm
.
atm
Calculated camera output voltage for a blackbody of temperature
T i.e. a voltage that can be directly converted into true requested
obj
object temperature.
Measured camera output voltage for the actual case.
Theoretical camera output voltage for a blackbody of temperature
T according to the calibration.
refl
Theoretical camera output voltage for a blackbody of temperature
T according to the calibration.
atm
atm
, where (1 – ε) is the reflec-
.
refl
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