Page 178 - Mechanical Engineers' Handbook (Volume 2)

5 Optical Methods 167

SRE standard relative error, the root-mean-square of the relative errors at the test
points:
SRE n (T c,i T )/T 2 0, i 1/2 (13)
2
0, i
i 1 n
RMS error root-mean-square error:
RMS 1 n (T T ) 1/2

c, i 0, i 2 (14)
n i 1
Mean error algebraic mean error:
Mean
n
1
(T
c,i T ) (15)
0,i
n i 1
where T calculated temperature (K) at measured resistance R i
c
T observed temperature at measured resistance R i
i
The fourth form is the Steinhart–Hart equation. It seems, from this comparison, that
there is little to choose from between the two cubic fits as far as goodness of fit is concerned,
and since the Steinhart–Hart form requires only three constants, it would be preferred.
A calibration equation such as the Steinhart–Hart equation would be used with a com-
mercial probe only when the highest accuracy is required. In most cases, the manufacturer’s
calibration is sufficiently accurate.
Thermistor probes are sold with resistance–temperature calibration tables accurate
within 0.1 or 0.2 K, depending on the probe grade purchased. These tables are typically
in 1-K increments. For computer interpretation, they should be fit to the Steinhart–Hart form
and the coefficients determined for least error.
For the highest precision in measurement of temperature level, the purchased thermistors
must be calibrated against laboratory-grade temperature standards at enough points to deter-
mine all of the constants in the model equation selected. Good practice would suggest one
redundant calibration point to provide a closure check.
When an application requires more precision than provided by the manufacturer’s tables
but less than the highest achievable, a transfer standard instrument can be used. A strain-
free platinum resistance thermometer or a quartz crystal thermometer can be used as such a
transfer standard. Typically, the comparison is made in a well-stirred, temperature-regulated
oil bath or in a comparison block of nickel or copper in an electrically heated oven.
Values of resistance and resistance divided by resistance at 0 C are listed in Table 9 for
two typical commercial probes as functions of temperature ( C) and 1/T (K).

5 OPTICAL METHODS

Optical temperature measurements have become increasingly reliable and accurate as the
electronic arts have advanced. This is especially true in the range below 600 C. Above 600 C,
radiation methods have long enjoyed a position of trust in the measurements community.
Low-temperature data interpretation and analysis that were once only conceptually possible
can now be routinely handled with on-board computing.
There was a veritable explosion of instruments for optical temperature measurement in
the period between 1980 and 2000. Only a few of the many types of optical temperature-
sensing systems will be discussed here.
Bigelow et al. describe the characteristics of commercial radiation temperature detec-
48
tors for the range 173 to 3750 K and estimate the accuracy as between 0.5 and 1.5% of