Apogee Instruments SI-111 Owner's Manual - Page 14
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Target Temperature Measurement
The detector output from SI-100 series 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:
4
4
T
T
m
T
D
where T
is target temperature [K], T
T
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 (10 C increments
across a -15 C to 45 C range) by plotting measurements of T
then plotted as function of T
determine m and b at any T
2
m
C
2
T
D
2
b
C
2
T
C
D
Where C2, C1, and C0 are the custom calibration coefficients listed on the calibration certificate (shown above)
that comes with each SI-100 series radiometer (there are two sets of polynomial coefficients, one set for m and
one set for b). Note that T
273.15) before m and b are plotted versus T
To make measurements of target temperatures, Eq. (1) is rearranged to solve for T
T
are input, and predicted values of m and b are input:
D
4
T
T
m
T
D
Emissivity Correction
Appropriate correction for surface emissivity is required for accurate surface temperature measurements. The
simple (and commonly made) emissivity correction, dividing measured temperature by surface emissivity, is
incorrect because it does not account for reflected infrared radiation.
The radiation detected by an infrared radiometer includes two components: 1. radiation directly emitted by the
target surface, and 2. reflected radiation from the background. The second component is often neglected. The
magnitude of the two components in the total radiation detected by the radiometer is estimated using the
emissivity (ε) and reflectivity (1 - ε) of the target surface:
E
E
Sensor
T
arg
S
b
(1)
D
is detector temperature [K], S
D
and second order polynomials are fitted to the results to produce equations that
D
:
D
C
1
T
C
0
(2)
D
1
T
C
0
(3)
D
is converted from Kelvin to Celsius (temperature in C equals temperature in K minus
D
.
D
1
S
b
273
.
15
4
D
1
E
et
Background
is the millivolt signal from the detector, m is
D
4
4
– T
versus mV. The derived m and b coefficients are
T
D
(4)
(1)
[C], measured values of S
T
and
D