Potential for improved radiation thermometry measurement uncertainty through implementing a primary scale in an industrial laboratory

The fixed point cells were graphite crucibles, 24 mm in diameter, 40 mm long and had a 3 mm diameter blackbody cavity enclosed in an ingot of metal–carbon alloy at the eutectic composition, with a volume of about 3 cm³. The melting temperature values used were those specified in [10]. NPL had recently been involved in this project to assign thermodynamic temperatures to fixed points and so was in a position to judge the agreement between the cells used in the fixed point temperature assignment and this work. The Pt–C and Co–C cells were equivalent to those on which the published data is available. The Re–C cell used here was specially designed for extreme robustness and was able to survive temperature changes of hundreds of degrees Celsius per minute [9]; however, the cell has comparatively thick walls, and consequently a low emissivity and larger temperature drop across the cavity wall. The influence of these features was found to cause the radiance temperature to be 0.3 °C lower than the conventional design. This difference was applied as a correction to the published value. The values used were 2474.38  ±  0.35 °C for rhenium–carbon, 1738.28  ±  0.18 °C for platinum–carbon and 1324.24  ±  0.13 °C for cobalt–carbon.

Different fixed-point cells were used for the ATK and for the two S1 based devices. Allowance was made for non-reproducibility between cells in the uncertainty budget, the dominant contributions were the result of impurities and differences in thermal conditions between furnaces.

The fixed-point cells were pre-set up at NPL in furnace tubes with suitable insulation. This was to simplify the measurement process, rather than any difficulty in setting up at the LAND laboratory, and such insulation is routinely supplied with HTFP purchased from NPL. Installation was then simply a matter of removing the furnace calibration tube and replacing with the appropriate fixed-point cell assembly, with parts shown in figure 1.

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The calibration laboratory at LAND uses a Thermogauge [11] 25.4 mm dual blackbody calibration source. It operates with an argon purge so does not need any window to protect/seal the graphite within an inert atmosphere. The radiation thermometer is aligned on the fixed point cell cavity by eye and/or by scanning to identify the radiance profile when hot. The fixed point assemblies were heated and cooled at approximately 15–20 °C min⁻¹

LAND's S1 are high quality radiation thermometers, based on standard products [12], and specifically designed as working standards for calibrating other thermometers within the production environment. Their traceability is through NPL, though, as previously described, they are two calibration steps removed from ITS-90. Two radiation thermometers from the S1 range, S1-LII and S1-UoS were developed specifically for use with HTFPs in a LAND-NPL collaborative project around fifteen years ago [13]. The calibration history of these instruments has since been tracked and it was found that the design is remarkably stable, with no significant drift in calibration over the intervening years. Prior to modification of S1-UoS, these two S1 instruments were identical and, therefore, provided an excellent testbed for our study.

2.3.1. Unmodified S1-LII.

2.3.2. Modified S1-UoS.

2.3.3. ATK.

General purpose radiation thermometers have a wide spectral response, required in order to achieve good signal to noise ratios at low temperature. The temperature scale that they carry is through transfer-standards with very narrow responses, which follow Planck's Law with lower uncertainty. This is presently how a primary scale at an NMI is transferred to calibration laboratories.

To set up what will be classed a primary scale for this study after calibration at the fixed points, the results were fitted to an interpolation function based on Planck's law, the Sakuma–Hattori equation [15]

$$\begin{eqnarray}&&{{S}_{\operatorname{int}}}=C{{\left[\exp \left(\frac{{{c}_{2}}}{AT+B}\right)-1\right]}^{-1}}\end{eqnarray} \tag{ 1 }$$

There are three adjustable parameters (A, B, C) and c₂ is the second radiation constant in Planck's law, which has a value of 0.014388 mK. With three fixed point measurements the fitting is exact. To reduce the number of fixed points required, one of the parameters can be calculated. It has been shown [16] that the B parameter, which is related to the width of the bandpass spectral response, has only a weak effect upon S_int. A reasonable value for B can, therefore, be calculated if the spectral response is not too wide. The parameter A is near the central wavelength of the spectral response and the calculated temperature for a given signal is very sensitive to small changes in its value, so again the calculated value cannot be used without extensive further characterisation. Parameter B, however is relatively insensitive: for a narrow interference filter a simple 'by-eye' evaluation of the filter spectral response curve can be sufficient to estimate B with insignificant error [17].

The spectral response passband of the filter was close to rectangular, as shown in figure 2. Knowledge of this, together with the manufacturer's data sheet, giving the FWHM a nominal value of 88.4 nm, allows the following calculation for this shape of filter [16]

$$\begin{eqnarray}&&{{\sigma}^{2}}=\frac{\text{FWH}{{\text{M}}^{2}}}{12}\end{eqnarray}$$

and from the result, parameter B can be approximated as

$$\begin{eqnarray}&&B=\frac{{{c}_{2}}}{2}{{\left(\frac{\sigma}{{{\lambda}_{0}}}\right)}^{2}}\end{eqnarray}$$

with c₂ = hc/k = 0.014388 with h, c and k the Planck constant, speed of light and the Boltzmann constant respectively and λ₀ the centre wavelength of the filter at nominally 809 nm. The calculated value for this parameter can therefore be inserted directly into (1), meaning that two fixed points would be sufficient for a complete calibration according to the MeP-K. Such generic information is generally available from manufacturers, but is inadequate for an ITS-90 scale realisation where uncertainty in spectral response is often the biggest source of uncertainty in the temperature scale.

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The uncertainties propagate in a fairly complex manner, and at each temperature there is a contribution from both uncertainty in the reference points' temperatures and from the signals from the instrument. Fortunately, the propagation equations for any number of fixed points are known [18]. For the case of three fixed-points the equations become

$$\begin{eqnarray}&&\frac{\partial T}{\partial {{T}_{\text{l}}}}\approx \frac{\left(T-{{T}_{m}}\right)\left(T-{{T}_{n}}\right)}{\left({{T}_{\text{l}}}-{{T}_{m}}\right)\left({{T}_{\text{l}}}-{{T}_{n}}\right)}\end{eqnarray}$$

$$\begin{eqnarray}&&\frac{\partial T}{\partial {{S}_{\text{l}}}}\approx \frac{{{\lambda}_{0}}T_{\text{l}}^{2}}{{{c}_{2}}}\frac{\partial T}{\partial {{T}_{\text{l}}}}\frac{1}{{{S}_{\text{l}}}}\end{eqnarray}$$

with the indices l, m, n referring to the three fixed points The uncertainty at any temperature u_T due to uncertainty in the fixed point temperature (u_Tl,m,n) and uncertainty in the measured signal at that fixed point (u_sl,m,n) is given by

$$\begin{eqnarray}&&{{u}_{\text{T}}}={{\left[\underset{lmn}{\sum}\,{{\left(\frac{\partial T}{\partial {{T}_{lmn}}}{{u}_{\text{T}}}_{lmn}\right)}^{2}}+\underset{lmn}{\sum}\,{{\left(\frac{\partial T}{\partial {{S}_{lmn}}}{{u}_{\text{S}}}_{lmn}\right)}^{2}}\right]}^{1/2}}\end{eqnarray} \tag{ 2 }$$

The fixed-point temperature uncertainty is intrinsic to the fixed point cell itself. It contains components for the knowledge of the pure ingot melting temperature [8], effect of impurities, temperature drop across the fixed point cell cavity wall, the identification of the point at which the fixed point is judged to be at the melting temperature and an allowance for the intrinsic repeatability of the transition [19]. Allowance was also made for possible variation due to different thermal conditions in different furnaces and complications arising from the very fine alloy microstructure with consequent large interfacial energy effects.

Equation (2) therefore gives the uncertainty in the calibration of the instrument. The combination of the propagated uncertainties from the calibration points is then combined with uncertainties associated with the actual use of the instrument: the effect of ambient conditions, size-of-source-effect, current to voltage conversion, stability and non-linearity. This uncertainty is intrinsic to the instrument in a given measurement situation, here it is the calibration comparison conditions at NPL. Using the Wien approximation gives

$$\begin{eqnarray}&&\frac{\partial T}{\partial S}\approx \frac{{{\lambda}_{0}}{{T}^{2}}}{{{c}_{2}}}\frac{1}{S}\end{eqnarray}$$

This leads to an additional component

$$\begin{eqnarray}&&\frac{\partial T}{\partial S}{{u}_{\text{s}}}\end{eqnarray}$$

which is added in quadrature to the other terms in (2).

When the fixed point measurements were evaluated equation (1) was fitted to the results and the uncertainty budgets were calculated using equation (2). The values used for temperature for the fixed-point cells were the best available thermodynamic melting temperatures. Each thermometer therefore carried what will be, once the expected changes to the MeP-K are incorporated, a primary thermodynamic scale. The three thermometers were compared at NPL from 1000 °C to 2600 °C using a Thermogauge dual blackbody similar to that at used at LAND. In addition, the ATK instrument was compared to the main NPL primary ITS-90 realisation [20]. The scales were compared at the UoS under conditions that would be found in an end-user laboratory; as opposed to the particular conditions of the dedicated and accredited radiation thermometry labs of LAND and NPL. This was, in essence, a robustness test of the S1-UoS instrument's ability to transfer the scale to the end user. Its field of view was translated laterally and longitudinally on a Land Instruments R1200B approximate blackbody furnace [8].

The temperature measurement by all radiation thermometers is affected by the size of the object that they measure. This is due to various issues with the quality of the optical system and is impossible to eliminate entirely. The size-of-source-effect for the S1-UoS was carefully measured using a 140 mm diameter integrating sphere, with a 125 W tungsten halogen lamp and a 50 mm aperture. At the aperture was fixed a 10 mm thick Perspex plate; with a 3 mm diameter, 2.6 mm deep plastic approximate blackbody set into its centre. The thermometer was arranged such that its field of view was entirely filled by the blackbody. Were there to be no sensitivity to radiation outside the thermometer field of view, no signal would be measured and there would be no size-of-source-effect. In practice, radiation is measured from outside the field of view and it can be quantified as a function of source-size by in-turn placing a series of apertures in front of the Perspex plate, in order to simulate an increased source-size.

Tolerance to changes in ambient temperature were measurement by blowing warm air into the S1-UoS through a small hole in its chassis, whilst monitoring an internal thermocouple.

With their own primary scale LAND would be in a position to supply an instrument directly calibrated to it, which would be expected to offer very low uncertainties. In order to demonstrate the benefits to end users, measurements were made at the UoS with all three instruments measuring the temperature of a three-zone furnace.

Typical melt and freeze cycles are shown in figure 3. It can be seen that the output of S1-LII increases as it is heated by the thermal energy radiated from the fixed-point cell at approximately 2500 °C. This is corrected for using the measured instrument internal temperature.

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The calibration results at the three fixed points of cobalt–carbon, platinum–carbon and rhenium–carbon are the input to equation (2) together with the in-use uncertainties determined from the instrument characterisation. The overall uncertainty is shown in figure 4. This is the uncertainty that would arise from the instrument in assigning a temperature to, for example, a calibration blackbody source. A previous comparison between HTFPs and a traditional calibration was previous undertaken [21]. With all the measurement uncertainties evaluated and combined, we find that the ATK, which was specifically designed for low uncertainty under a study of this methodology, was the more accurate.

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The high volume production instrument most similar to the S1 [12] has a measurement uncertainty guaranteed to be lower than 10 °C (0.7% K) k  =  2 whilst measuring a target of 1150 °C. As shown in figure 4, the HTFP calibration methodology improves the measurement uncertainty by a factor of five over this value for commercial thermometers. Whilst the improvement was huge, it should be noted that the datasheet value is the worst case that is expected from a production batch of instruments, where a simplified calibration procedure is used and no attempt is made to account of individual thermometer uncertainties. This approach makes it possible to manufacture thermometers in volume; it is too time consuming to calibrate high volume production instruments using HTFPs. End users can pay for an additional service to have the true uncertainties evaluated for their instrument.

A small improvement to measurement uncertainty was achieved by the modifications to the S1. These were in part due to the improved temperature stability of the S1-UoS and also due to the shorter effective wavelength at which the modified instrument measured temperature.

In the second part of the experiment, the thermometers were each taken to NPL in order to compare them with NPL's primary ITS-90 scale. This was carried out using the standard procedures and equipment that would be used for any calibration above 1000 °C up to a maximum of 3000 °C. A calibrated standard is used to assign a temperature to a blackbody calibration source. The uniformity is assessed and accounted for in the uncertainty budget with respect to differences in the viewed areas of the different instruments. The emissivity of the source (>0.995) is accounted for based on differences in wavelength between the instruments. The comparison results are shown in figure 5. It is clear that the three instrument agree within their uncertainties. It is expected that tables of differences between ITS-90 and thermodynamic temperature will be published as part of the mise-en-pratique of the definition, but in this case the differences are small compared to the uncertainties and the scales are functionally equivalent.

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In order to investigate potential advantages of the MeP-K for end users, we assessed the temperature of an approximate blackbody calibration furnace at the UoS. The furnace controller measured the temperatures of internal thermocouples and the measurements were not necessarily representative of the radiance temperature that the radiation thermometers measured.

The furnace was set to 1150 °C for the data presented in figure 6. A fourth measurement is also plotted and this was measured by LAND's commercial solution for laboratory calibration, a UKAS certified C100 [22]. The uncertainty plotted for the C100 in figure 6 was measured in LAND's calibration lab during the certification process. These results demonstrate measurements from a primary scale with reasonable accuracy. There was not time to fully investigate source uniformity and stability, but the difference between the two S1 based instruments is similar to that observed in the scale comparison. The excellent performance of the S1-LII demonstrates the potential for improved uncertainties compared to the commercial version of the S1, with its quoted uncertainty of 10 °C and it also compares well with the C100 that LAND supplies as a standard thermometer to their customer's calibration labs.

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Figure 7 shows the difference between the scales generated for the S1-UoS from fitting to all three fixed-points compared to fitting just to two: either cobalt–carbon and platinum–carbon, cobalt–carbon and rhenium–carbon or platinum–carbon and rhenium carbon. The additional parameter was calculated from the manufacturers published data for spectral response of the filter and detector as described in 2.4 above. When used within the range given by the two fixed-points the difference between scales is at the level of the uncertainties.

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Figure 8 shows that the very small measurement area of the S1-UoS gives good tolerance to misalignment from the centre of a calibration furnace.

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The size-of-source-effect was measured using an integrating sphere in order to provide a more sensitive comparison with the other thermometers. Figure 9 shows that this is an aspect of the design in which we have made the S1 performance slightly worse by the modifications. The reduced performance is very likely due to the 5 mm thick thermal insulation that we added to the heater block that has allowed additional stray light to be reflected from it and onto the optical axis, as compared to the uninsulated S1-LII detector holder.

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The S1-UoS thermometer optical system brought its field stop into best focus at a distance of 500 mm from the front of the instrument. A general purpose transfer standard must be relatively insensitive to distance at which it is positioned from the calibration furnace. We see from figure 10 that the S1-UoS thermometer exhibits reasonable tolerance to defocusing, though there is significant measurement error when taking the thermometer far from its best focus. Having established that the furnace has a relatively uniform radiance across its aperture, as shown in figure 8, and that the thermometer's field of view is filled for all target distances, figure 10 is another measure of the size-of-source-effect. As the target increases in size, a greater proportion of the internal mechanical features can become illuminated, leading to an increase in stray radiation reaching the detector and, in turn, increase in the apparent temperature that is measured.

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One of the goals of this study was to produce a high quality primary standard that would be practicable for an end user to realise; through modification to a commercial instrument, without a prohibitive level of expertise and resource. Central to this theme was the addition of a temperature stabilised detector block within the instrument. The ambient temperature stability is shown in figure 11. The detector heater was set to stabilise at 31 °C and the temperature measurement of the S1-UoS remained very stable below 30 °C, showing that we had achieved our goal of temperature stability using a simple heater, at normal room temperature.

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