Uncertainty Budgets for Calibration of Radiation Thermometers below the Silver Point

Below the freezing point of silver, radiation thermometers are generally calibrated by implementing the multi-point interpolation method using blackbody measurements at three or more calibration points, rather than the ITS-90 extrapolation technique. The interpolation method eliminates the need to measure the spectral responsivity and provides greater accuracy at the longer wavelengths required below the silver point. This article identifies all the sources of uncertainty associated with the interpolation method, in particular, those related to the reference blackbody temperatures (either variable-temperature or fixed-point blackbodies) and to the measured thermometer signals at these points. Estimates are given of the ‘normal’ and ‘best’ uncertainties currently achievable. A model of the thermometer response is used to propagate all the uncertainties at the reference points and provide a total uncertainty at any temperature within the calibration range. The multi-point method has the effect of constraining the total uncertainty over this range, unlike the ITS-90 technique for which the uncertainties propagate as T ². This article is a joint effort of the working group on radiation thermometry of the Consultative Committee for Thermometry (CCT), summarizing the knowledge and experience of all experts in this field.     

Comparison System for the Calibration of Capsule-Type Standard Platinum Resistance Thermometers at NMIJ/AIST

A new comparison system has been constructed using a Gifford- McMahon type cryogenic refrigerator for the calibration of capsule-type standard platinum resistance thermometers (CSPRTs) below 273.16 K at the National Metrology Institute of Japan (NMIJ). The system can compare six CSPRTs at once. A gold-plated comparison block, in which CSPRTs are mounted for calibration, is made from oxygen-free high-conductivity copper. The standard uncertainties related to the temperature control of the system are estimated to be 0.04 mK. The calibrated values for CSPRTs and a rhodium–iron resistance thermometer obtained using the comparison system are in good agreement with those obtained by the direct realization of the low-temperature fixed points of the ITS-90 within the combined standard uncertainty for the calibration using the comparison system.     

Metal–Carbon Eutectics to Extend the Use of the Fixed-Point Technique in Precision IR Thermometry

The high-temperature extension of the fixed-point technique for primary calibration of precision infrared (IR) thermometers was investigated both through mathematical simulations and laboratory investigations. Simulations were performed with Co–C (1,324°C) and Pd–C (1, 492°C) eutectic fixed points, and a precision IR thermometer was calibrated from the In point (156.5985°C) up to the Co–C point. Mathematical simulations suggested the possibility of directly deriving the transition temperature of the Co–C and Pd–C points by extrapolating the calibration derived from fixed-point measurements from In to the Cu point. Both temperatures, as a result of the low uncertainty associated with the In–Cu calibration and the high number of fixed points involved in the calibration process, can be derived with an uncertainty of 0.11°C for Co–C and 0.18°C for Pd–C. A transition temperature of 1,324.3°C for Co–C was determined from the experimental verification, a value higher than, but compatible with, the one proposed by the thermometry community for inclusion as a secondary reference point for ITS-90 dissemination, i.e., 1,324.0°C.     

Toward Carbon Dioxide Vapor-Pressure Thermometer

The Temperature Group Laboratory of the National Metrology Institute of Turkey (TUBITAK UME) has realized the scale in the range from the argon triple point (83.8058 K) to the copper freezing point (1357.77 K) and also constructed the International Temperature Scale of 1990 (ITS-90) defining fixed points (Preston-Thomas, Metrologia 27, 3 (1990)). The scale is realized in the low-temperature sub-range by interpolation between the triple points of water, mercury, and argon. The calibration of thermometers below the temperature of the triple point of mercury requires the realization of the argon triple point. Since calibration laboratories are asking for references down to ?60 °C, a triple point of carbon dioxide (CO₂) gives this opportunity to be used as a secondary fixed point. Another aim of this work is to study the ability of CO₂ vapor pressure to realize a vapor-pressure thermometer for covering the range from 216 K up to room temperature. This realization is intended to provide an approximation of the international temperature scale in this temperature range. The vapor-pressure thermometer is intended to be assessed by using the triple point of carbon dioxide and by measuring the pressure values at the temperatures of the triple points of mercury and water. Realization of the triple-point temperature of carbon dioxide and the development of the vapor-pressure thermometer will be investigated and presented in this article.     

INRIM–NMC Comparison of Pt/Pd Calibration Above the Ag Point

A comparison of a Pt/Pd calibration above the Ag point between the INRIM and NMC was arranged with the aims of evaluating measurement systems and exploiting the potential of the Pt/Pd thermocouples. Two commercial Pt/Pd thermocouples were used as transfer thermometers. A calibration method using a blackbody cavity as a transfer source and a radiation thermometer as a reference thermometer was adopted in both institutes. The T ₉₀ carried by the radiation thermometers is established by an extrapolation technique for INRIM and by scale realization according to ITS-90 definition for NMC and, therefore, this exercise is also a useful comparison of different approaches to disseminate T ₉₀ above the Ag point. The comparison results are presented and analyzed.     

Monochromator-Based Absolute Calibration of a Standard Radiation Thermometer

Centro Español de Metrología (CEM) is disseminating the International Temperature Scale (ITS-90), at high temperatures, by using the fixed points of Ag and Cu and a standard radiation thermometer. However, the future mise-en-pratique for the definition of the kelvin (MeP-K) will include the dissemination of the kelvin by primary methods and by indirect approximations capable of exceptionally low uncertainties or increased reliability. Primary radiometry is, at present, able to achieve uncertainties competitive with the ITS-90 above the silver point with one of the possible techniques the calibration for radiance responsivity of an imaging radiometer (radiance method). In order to carry out this calibration, IO-CSIC (Spanish Designated Institute for luminous intensity and luminous flux) has collaborated with CEM, allowing traceability to its cryogenic radiometer. A monochromator integrating sphere-based spectral comparator facility has been used to calibrate one of the CEM standard radiation thermometers. The absolute calibrated standard radiation thermometer has been used to determine the temperatures of the fixed points of Cu, Co–C, Pt–C, and Re–C. The results obtained are 1357.80 K, 1597.10 K, 2011.66 K, and 2747.64 K, respectively, with uncertainties ranging from 0.4 K to 1.1 K.     

Calibration of Thermocouples and Infrared Radiation Thermometers by Comparison to Radiation Thermometry

The National Metrology Institute of Spain (CEM) has designed, characterized, and set-up its new system to calibrate thermocouples and infrared radiation thermometers up to 1600 °C by comparison to radiation thermometry. This system is based on a MoSi₂ three-zone furnace with a graphite blackbody comparator. Two interchangeable alumina tubes with different structures are used for thermocouples and radiation thermometer calibrations. The reference temperature of the calibration is determined by a standard radiation thermometer. Normally, this is used at CEM to disseminate the International Temperature Scale of 1990 (ITS-90) in the radiation range, and it refers to the Cu fixed point. Several noble metal thermocouples and infrared radiation thermometers with a central wavelength near 900 nm have been calibrated, and their uncertainty budgets have been obtained.     

Realization of the ITS-90 at IMGC in the range of long stem PRTS

IMGC has established the fixed points required by the International Temperature Scale of 1990 (ITS-90) for long-stem platinum resistance thermometers (PRTs) at the highest accuracy level. The present paper describes the fixed point apparatus and the measuring procedures used at IMGC for the accurate realization of each fixed point, and gives some data on the typical phase transitions thereby obtained. Moreover, since IMGC has developed both traditional and sealed cells for the realization of the freesing or melting points of metals, the different types of cells and the procedure used for their construction and preparation are also supplied. Finally, the reproducibilities of the freezing points of Sn, Zn, Al, and Ag were evaluated by means of several determinatiaons with one standard thermometer.Translated from Izmeritel'naya Tekhnika, No. 12, 58–62, December, 1993.     

Realization of Low-Temperature Fixed Points of the ITS-90 at NMIJ/AIST

A new model of sealed cells with three thermometer wells for calibration of capsule-type thermometers at low-temperature fixed points of the International Temperature Scale of 1990 has been developed at the National Metrology Institute of Japan (NMIJ). The melting curves of Ar and O₂ obtained using the new cells show very flat plateaux and a linear temperature dependence as a function of the inverse liquid fraction (1/F) over the range 1/F = 1 to 1/F = 20 with a narrow melting curve width of 0.1 mK. The melting curves of Ne obtained with the new cell also show very flat plateaux and approximately linear temperature dependence versus 1/F and a narrow melting curve width of 0.1 mK, though with a slight concave structure at high 1/F. The melting temperatures with the new cells agree with previous NMIJ sealed cells within 10 μK, which is similar to the reproducibility of the realization of the triple points at NMIJ. The source dependence of the triple-point temperature of Ne was investigated by filling two of the new cells from different sources of Ne. The difference in the realized triple point temperatures between the two sources is 0.031 mK, consistent with that estimated from isotope analysis. The uncertainties in the calibration of standard platinum resistance thermometers at the low-temperature fixed points are summarized. The uncertainty of the calibration at the triple point of e-H₂ has been reduced to about one-third of its value without the correction by making the isotopic correction on the basis of the technical annex for the ITS-90 in the mise en pratique for the definition of the kelvin.     

Uncertainty Propagation for Platinum Resistance Thermometers Calibrated According to ITS-90

A new supplement to the GUM outlines uncertainty calculations using matrix algebra for models with more than one output quantity. This technique is applied to the problem of uncertainty propagation for platinum resistance thermometers (PRTs). PRTs are calibrated at specified sets of defining fixed points dependent on the desired temperature range. The problem of uncertainty propagation from the fixed-point calibration results plus the resistance of the PRT in use as input quantities to the coefficients of the deviation function as intermediate results and the temperature as a sole output quantity is discussed. A general solution in matrix form for any temperature range of the ITS-90 defined by PRTs is highlighted. The presented method allows for an easy consideration of the input quantity correlations, which differ with the circumstances of the accomplishment of the fixed-point calibrations and the resistance measurement of the thermometer in use. An example calculation for a specific temperature range based on a simplified model for the input quantity correlations demonstrates this benefit.     

NMIJ Constant-Volume Gas Thermometer for Realization of the ITS-90 and Thermodynamic Temperature Measurement

The constant-volume gas thermometer (CVGT) of the National Metrology Institute of Japan (NMIJ), AIST with ³He as the working gas is used as an interpolating gas thermometer to realize the International Temperature Scale of 1990 (ITS-90) from 3 K to 24.5561 K and as a relative gas thermometer for thermodynamic temperature measurement calibrated at the triple point (TP) of Ne. The standard uncertainties of the realization and measurement are estimated to be 0.58 mK and 0.86 mK at a maximum in the mentioned temperature range, respectively. The maximum difference between both temperatures is about 1 mK. In the calibration of the CVGT, the TP of equilibrium hydrogen (e-H₂) is corrected for isotopic composition as specified in the Technical Annex for the ITS-90. The ambiguity of the TP of Ne due to the variability in isotopic composition is included in the uncertainty. Although the CVGT was also used in 2004 to realize the ITS-90, it was modified for the present experiment to reduce some measurement uncertainty components and the working gas was replaced with a higher-isotopic-purity gas. The results from 2004 were recalculated by correcting for the isotopic composition of e-H₂ and differ insignificantly from the present results, except for a wider scatter.     

The Dutch National Realization of the ITS-90 over the Range 13.8033 K–273.16 K

The facility constructed at NMi VSL to realize the ITS-90 in the capsule standard platinum resistance thermometer range (CSPRT, 13.8033–273.16K) is presented. To demonstrate the performance of our facility, the results of a recent measurement campaign are reported, in which 3 NMi VSL CSPRTs were calibrated in the range 13.8–273.16K at all of the fixed points required by the ITS-90. The uncertainty of the calibration of the CSPRTs at each of the fixed points is evaluated in accordance with the most recent recommendations of the Consultative Committee for Thermometry and its Working Groups 1 and 3.     

Uncertainty Evaluation and Validation of a Comparison Methodology to Perform In-house Calibration of Platinum Resistance Thermometers using a Monte Carlo Method

The uncertainty required by laboratories and industry for temperature measurements based on the practical use of platinum resistance thermometers (PRTs) can commonly be achieved by calibration using temperature reference conditions and comparison methodologies (TCM) instead of the more accurate primary fixed-point (ITS-90) method. TCM is suitable for establishing internal traceability chains, such as connecting reference standards to transfer and working standards. The data resulting from the calibration method can be treated in a similar way to that prescribed for the ITS-90 interpolation procedure, to determine the calibration coefficients. When applying this approach, two major tasks are performed: (i) the evaluation of the uncertainty associated with the estimate of temperature (a requirement shared by the ITS-90 method), based on knowledge of the uncertainties associated with the temperature fixed points and the measured electrical resistances, and (ii) the validation of this practical comparison considering that the reference data are obtained using the ITS-90 method. The conventional approach, using the GUM uncertainty framework, requires approximations with unavoidable loss of accuracy and might not provide adequate uncertainty evaluation for the methods mentioned, because the conditions for its valid use, such as the near-linearity of the mathematical model relating temperature to electrical resistance, and the near-normality of the measurand (temperature), might not apply. Moreover, there can be some difficulty in applying the GUM uncertainty framework relating to the formation of sensitivity coefficients through partial derivatives for a model that, as here, is somewhat complicated and not readily expressible in an explicit form. Alternatively, uncertainty evaluation can be carried out by a Monte Carlo method (MCM), a numerical implementation of the propagation of distributions that is free from such conditions and straightforward to apply. In this paper, (a) the use of MCM to evaluate uncertainties relating to the ITS-90 interpolation procedure, and (b) a validation procedure to perform in-house calibration of PRTs by comparison are discussed. An example illustrating (a) and (b) is presented.     

An Adiabatic Calorimeter for the Realization of the ITS-90 in the Cryogenic Range at the LNE-CNAM

The LNE-CNAM, in cooperation with the IPN, has recently developed a new cryogen-free adiabatic calorimeter, to realize the International Temperature Scale of 1990 (ITS-90) in the temperature range between 6 K and 84 K. The new calorimeter, cooled by a closed-cycle Gifford-McMahon refrigerator, is equipped with three thermal shields and two separate vacuum chambers, to minimize the effect of parasitic heat fluxes. The inner adiabatic chamber can accommodate either a multi-compartment cell??containing the triple points of hydrogen, neon, oxygen, and argon, to realize the ITS-90 between 14 K and 84 K??or a comparison block for thermometers, the calibration of rhodium?Ciron (RhFe) thermometers between 6 K and 24 K. The use of a cryogen-free system and a fully computer-controlled measurement chain allow long lasting experiments and good thermal control, resulting in a substantial reduction of the measurement uncertainties. The new adiabatic calorimeter has been successfully tested at the LNE-CNAM. The overall standard uncertainties in the realization of the ITS-90 have been reduced from 2.08 mK to 0.37 mK at the hydrogen triple point, from 1.40 mK to 0.30 mK at the triple point of neon, and are maintained below 0.26 mK at the triple points of oxygen and argon. In the temperature range between 6 K and 24 K, calibrations of rhodium?Ciron resistance thermometers have been carried out with a standard uncertainty of the order of 0.80 mK.     

Spectral Radiation Drift of LEDs Under Step-Mode Operation and Its Effect on the Measurement of the Non-Linearity of Radiation Thermometers

The non-linearity (NL) of radiation thermometers is critically involved when realizing ITS-90 above the silver point. It has to be corrected for, and its uncertainty should be adequately specified. In this article, results are presented of NL measurements based upon the superposition method and involving light emitting diodes (LEDs) with high radiance output, peaked at a wavelength of 645 nm. To this end, the two LEDs in question have been operated in the pulse mode with a fixed phase shift. Their spectral radiances have been measured by the radiation thermometers to be tested, separately or superimposed by means of a beam splitter. Still the drift in the spectral radiance observed after switching on the LEDs has to be taken into account and corrected for, since this drift, interfering during the superposition procedure, could corrupt the sum rule for the fluxes involved, which is the crux of the superposition method. Therefore, experimental research has been carried out to characterize the drift of LEDs operated in the pulse mode with a fixed phase shift. The result indicated that the drift could be roughly specified in terms of characteristic time intervals: non-linear drift in the first tens of seconds followed by a quasi-linear drift in the subsequent time interval. The crossover time from non-linear to quasi-linear drift could be ascertained by experiment. In the course of the superposition process, switching of the LEDs was done in such a way that only the quasi-linear part of the drift was involved which allowed for the correction of the drift in the NL measurements, as will be reported. Two radiation thermometers were involved in the NL measurements at radiance temperatures between the silver point and 3153 K: an LP-4, with a central wavelength of 650 nm and 10 nm bandwidth, manufactured by KE-Technologie and the primary standard pyrometer PSP, with a central wavelength of 660 nm and 10 nm bandwidth, developed by NIM.     

A Deviation Function Used for the Secondary Realization of the ITS-90 in the Subrange from 83.8033 K to 273.16 K

This article proposes a correlation relation between the resistance ratios of the triple points of argon and mercury. By this relation, the resistance ratio of the triple point of argon can be extrapolated from that of mercury, and a deviation function which is defined in the range from 83.8058 K to 273.16 K can be determined from only the calibration values at the triple points of water and mercury. It is a close approximation to the ITS-90 deviation function in the subrange. Using it, the calibration at the triple point of argon can be saved. Twenty-five standard platinum resistance thermometers are used to check the function. The errors are less than 5 mK. It is sufficient for secondary measurements.     

Calibration by Comparison of Platinum Resistance Thermometers Using Slow Resistance Bridges

Platinum resistance thermometers (PRTs) are calibrated at the highest level in fixed points, as specified in the International Temperature Scale of 1990 (ITS-90). However, in order to reduce cost and time, platinum resistance thermometers can also be calibrated by comparison. In the temperature range from ?100 °C to 300 °C, it is possible to achieve uncertainties as small as 5 mK. A PRT is calibrated by comparison by comparing its resistance reading with the temperature reading of a reference thermometer, placed at the same temperature inside the temperature-controlled calibration medium. The reference thermometer is commonly also a resistance thermometer, so the intrinsic measurement problem is the simultaneous measurement of two resistances. Four methods that perform this measurement are presented in this article. A special emphasis is given to the measurement with slow bridges. Slow bridges are not able to produce a stable resistance reading within 20 s after the connection of the PRT, so they are often considered to be unsuitable for calibration by comparison of PRTs. To overcome this problem, a special method that directly measures the ratio between the reference PRT and PRT under calibration is presented and analyzed. The analysis and measurement results proved that this method and consequently the slow resistance bridges are capable of performing calibration by comparison of PRTs at least at the same level as the conventional methods.     

Stability of Standard Platinum Resistance Thermometers and Rhodium Iron Resistance Thermometers for the Past Decade in NMIJ/AIST

In this study, the stability of four capsule-type standard platinum resistance thermometers (CSPRTs) has been checked by evaluating behavior of the calibrated values at each cryogenic fixed point of the International Temperature Scale of 1990 (ITS-90) below 273.16 K since around 2005. Performance of three capsule-type RhFe resistance thermometers (RIRTs) has been also observed at the triple points of Ne and \(e\hbox {-}\hbox {H}_{2}\). It is confirmed that CSPRTs and RIRTs are stable within the uncertainty of calibration at each low-temperature fixed point for a past decade except for one CSPRT. The resistance of the CSPRT was clearly affected by the accidental mechanical shock at TPW, although the variation of its calibration values was unclear at the triple points of Ar, \(\hbox {O}_{2}\) and Ne and was still within the uncertainty at the triple points of Hg and \(e\hbox {-}\hbox {H}_{2}\). And the CSPRT shows stable behavior after re-calibration again.     

Practical Calibration of Platinum Resistance Thermometers in the Range ?190?��C to 0?��C

The results obtained in the characterization of a low-temperature comparator and its performance in relation to the calibration of metal and borosilicate sheathed standard platinum resistance thermometers (SPRTs) calibrated at the International Temperature Scale of 1990 (ITS-90) fixed points, are presented and discussed. The principal influence quantities are addressed and the estimation of measurement uncertainty supporting the calibration and measurement capability (CMC) accredited by Entidad Nacional de Acreditación (ENAC), the Spanish Accreditation Body, are presented and discussed.     

用锌凝固点和水沸点检定二等标准铂电阻温度计的扩展不确定度评定

按时规范,ＪＪＦ１０５９－１９９９,对二等标准铂电阻温度计在锌凝固点及水沸点检定的不确定度进行了评定,通过建立测量数学模型确定各标准各不确定度分量,并按不确定度传播公式给出固定点间各温度点的扩展不确定度及包含因子。