Target Temperature Measurement
The detector output from SIL-111 radiometers follows the fundamental physics of the Stefan-Boltzmann Law,
where radiation transfer is proportional to the fourth power of absolute temperature. A modified form of the
Stefan-Boltzmann equation is used to calibrate sensors, and subsequently, calculate target temperature:
b
S
m
T
T
D
4
D
4
T
+
=
−
(1)
where T
T
is target temperature [K], T
D
is detector temperature [K], S
D
is the millivolt signal from the detector, m is
slope, and b is intercept. The mV signal from the detector is linearly proportional to the energy balance between
the target and detector, analogous to energy emission being linearly proportional to the fourth power of
temperature in the Stefan-Boltzmann Law.
During the calibration process, m and b are determined at each detector temperature set point (15 C increments
across a 10 C to 40 C range) by plotting measurements of T
T
4
–
T
D
4
versus mV. The derived m and b coefficients are
then plotted as function of T
D
and second order polynomials are fitted to the results to produce equations that
determine m and b at any T
D
:
0
C
T
1
C
T
2
C
m
D
2
D
+
+
=
(2)
0
C
T
1
C
T
2
C
b
D
2
D
+
+
=
(3)
Where C2, C1, and C0 are the custom calibration coefficients listed on the calibration certificate (shown above)
that comes with each SIL-111 radiometer (there are two sets of polynomial coefficients, one set for m and one set
for b). Note that T
D
is converted from Kelvin to Celsius (temperature in C equals temperature in K minus 273.15)
before m and b are plotted versus T
D
.
To make measurements of target temperatures, Eq. (1) is rearranged to solve for T
T
[C], measured values of S
D
and
T
D
are input, and predicted values of m and b are input:
(
)
15
.
273
4
1
4
−
+
+
=
b
S
m
T
T
D
D
T
(4)
