Uncertainty considerations for the calibration of transfer standard radiation thermometers

1. Uncertainty considerations for the calibration of transfer standard radiation thermometers Graham Machin, NPL

2. Abstract Three broad areas to consider – when formulating Appendix C entry 1.4 “Standard Radiation Thermometers” • ITS-90 scale realisation (fixed point and reference thermometer) • Uncertainties arising from the radiance source (blackbody) • Uncertainties arising from the transfer radiation thermometer ------------------------------------------------------------------------------- Finally a few remarks about … MRA Appendix C entries

3. Introduction • Concerned only with providing cost effective calibration service – NOT absolute best can do – but near best measurement capability • ITS-90 above the silver point only, according to the formal definition • Measurement equation for scale realisation uncertainties – that given in the ITS-90 text – two general contributions 1) the defining fixed point blackbody 2) the reference thermometer

4. ITS-90 realisation uncertainties – fixed point realisation Following factors to be considered: • Intrinsic repeatability of freezes – type A • Impurities – departures from 100% purity • Departure from emissivity =1 • Temperature drop across cavity bottom – due to energy loss through the aperture a) all type B b) taken together for well designed source <10 mK (k=1)

5. ITS-90 realisation uncertainties – reference radiation thermometer • Spectral characterisation • Non-linearity and gain ratios • Secular effects (drift) • Radiance transfer effects (characterised [for e.g.] by SSE)

6. Spectral characterisation uncertainties - 1 Spectral responsivity – usually monochromator – U generally type B • Monochromator uncertainties - wavelength stability/accuracy - repeatability scan to scan (>3 scans then type A) - resolution+stray light • Reference thermometer uncertainties - secular stability of interference filters (stochastic) - out-of-band transmission - temperature coefficient of filters - alignment

7. Spectral characterisation uncertainties - 2 • Other issues – all type B a) calculation of effective wavelength b) use mean effective wavelength at gold point – what uncertainty does this introduce c) detector responsivity uncertainty over filter pass-band • Wavelength uncertainties characterised by: u=(T90-Tref)(T90/Tref)(/)(1/3)

8. Effective wavelength of 650 nm and 906 nm filters since 1994

9. Reference photocurrent, non-linearity, gain ratios • Reference photocurrent – from fixed point u = (T902 /c2) (IRef/ IRef): typically ~1e-4 (type A) • Non-linearity – detector and electronics on one gain setting • Non-linearity – inter-gain setting (type B)

10. SSE – formal uncertainty estimate • SSE – two approaches, formal or pragmatic • Formal – calculate effective target diameters for reference source and blackbody target, apply SSE correction – combine (quadrature) uncertainties of each SSE estimate the type A uncertainty • u = (T902 /c2) (SSE)

11. SSE – pragmatic uncertainty estimate and inter-calibration drift • Pragmatic (for low SSE systems) – calibrate at diameter X mm use up to target diameter Y mm - SSE=SSE(Y) – SSE(X) • Same equation as previous slide but type B ------------------------------------------------------------------------------------ • Secular drift – stability of reference thermometer (e.g. electronics) - type B – largest component up to 2000 °C – reduced by more frequent fixed pt. calibrations • u=(T90/Tref )2 Tdrift (1/ 3)

12. Typical reference thermometer uncertainty in scale realisation at 650 nm

13. Second level MRA CMC entry 1.4 calibrations • Above described top-level calibration • Below describe some uncertainty considerations for “Standard Radiation Thermometers” – laboratories who do not hold a primary calibrated RT but a transfer thermometer calibrated elsewhere IS their standard RT • Limited to calibration of RT by comparison using a transfer radiance source

14. Uncertainties arising from the radiance source • Assume blackbody or quasi-blackbody (emissivity >0.99) • Factors to be considered: • Stability during test – type A • Uniformity across test area – type B - see later • Wavelength dependence (see later)

15. Uncertainties from transfer thermometer - I • Repeatability of reference thermometer output at test temperature (type A) • Repeatability of transfer thermometer output at test temperature (type A) • Thermometer resolution – type B

16. Uncertainties from transfer thermometer - II • Uncertainties associated with corrections for RH and internal thermometer temperature – type B • Standard uncertainty of any ancillary equipment used – e.g. DVM • Uncertainty arising from SSE – strictly negligible as reference thermometer and transfer thermometer are viewing same aperture - when used as transfer standard due care must be taken to equalise the aperture and uniformity of transfer sources – otherwise large uncertainties can accrue.

17. Uncertainties from transfer thermometer - III • Mismatch in wavelength between reference and transfer thermometers mod(((s - t)/c2).T290.(1-).(1/3)) – type B (assume ~1) • Mismatch in target sizes – type B (zero for uniform source) - otherwise (T/d).s.(1/3) i.e. radiance gradient x nominal target size – (arbitrary >98% of signal taken to be target size s) • Short term repeatability (alignment) – type A if low order fit used - type B if repeat point differences used

18. Summary of uncertainty analysis To arrive at the uncertainty in the calibration of a transfer thermometer requires clear knowledge of: • Scale realisation uncertainty – top level 1.4 cmc entry • Transfer source uncertainty plus…. • that associated with both the calibration of and intrinsic to the transfer thermometer – secondary level 1.4 cmc entry

19. Worked example

20. Appendix C of MRA - I • What values are to be put in the Appendix C? • Primary scale realisation (reference thermometer) uncertainties? • Transfer thermometer calibration uncertainties?

21. Appendix C of MRA - II • Technical supplement T7 states “The calibration and measurement capabilities … are those ordinarily available to the customers of an institute through its calibration and measurement services; they are sometimes referred to as best measurement capabilities” • Similar statement in the MRA Glossary – Calibration and measurement capability “the highest level of calibration or measurement normally offered to clients, expressed in terms of a confidence level of 95%, sometimes referred to as best measurement capability”

22. Appendix C of MRA – conclusions • From these statements it is reasonable to conclude that: • Appendix C entry not intended to be the best we can attain in near ideal circumstances • Nor is it to include one-off special calibrations - rather: routine calibrations readily achievable following set procedures - calibrations of good (near-ideal) but real instruments - calibrations for which we would issue a certificate (see T7)