Since ITS90 was established, the whole temperature range
of practical importance has been covered by the internationally
approved temperature standard’. The standard is
realized by defining fixed points with assigned temperature
values and devices to interpolate between them.
Working thermometers are then calibrated against the
standard thermometers, following various kinds of calibration
procedures. A typical calibration system is composed
of two processes; the hardware and the software procedures.
There are many useful reports on the hardware
procedure2,3. Here the software procedure, including calibration
point temperatures, interpolation functions and fitting
accuracy, is discussed. In particular, this report focuses
on deducing optimum calibration procedures applicable to
any kind of temperature sensor.
Temperature sensors are conventionally characterized by
their sensitivity (or working temperature range), stability
and applicability for special conditions in terms of physical
dimensions, response time, use under magnetic fields or
irradiation, etc. The present authors propose a different
aspect for characterization; ‘calibration efficiency’, which
is a measure of how easy it is to calibrate the sensors using
a small number of calibration points, with small residual
errors.
Until now, fitting functions have been proposed for many
kinds of thermometers. Some of the reports developed a
simple calibration procedure for engineering applications4.“.
Smooth fitting functions have also been proposed for a carbon
glass resistance thermometer6, platinum resistance thermometers
( PRTs)~.*, a rhodium iron resistance thermometer’
and a carbon resistance thermometer”. From the
practical point of view, simple and accurate fitting functions
save the user unnecessary time and effort in terms of extra
calibration points.
All of the above reports assumed a typical set of functions,
such as polynomials, and residual errors were studied
according to the order of the function or the number of
calibration points. However, it is unclear whether the
assumed set of functions is the best one for a typical type
of thermometers, no matter how good the fittings look.
Therefore, the calibration efficiency of the sensor can not
be discussed on the same basis for different types of sensors,
such as carbon glass thermometers and platinum
resistance thermometers.
The procedure proposed here is purely deductive and
gives fitting functions from the calibrated data. Finally it
gives a maximum residual error for a given number of calibration
points. As the result is optimized for any kind of
sensor, one can directly compare the maximum residual
error for one particular sensor with others. Thus, it is
expected to present a common basis for comparison of the
calibration efficiency among different kinds of sensors.
The procedure presented here is important for another
reason also. The sensors for industrial standards can be purchased
with a characteristic table in which an ‘allowance’
is given. The allowance is not always adequate for precise
work. In such situations, additional calibrations need to be
carried out to obtain higher accuracy. However, it is unclear
which temperatures should be selected as the calibration
points. Following the procedure here, one is given the best
allocation of the calibration temperatures according to the
requirements in terms of measurement accuracy.