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

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

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

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)

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)

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

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=(T 90 -T ref )(T 90 /T ref )(  / )(1/  3)

Effective wavelength of 650 nm and 906 nm filters since 1994

Reference photocurrent, non-linearity, gain ratios  Reference photocurrent – from fixed point u = ( T 90 2 /c 2 ) (  I Ref / I Ref ): typically ~1e-4 (type A)  Non-linearity – detector and electronics on one gain setting  Non-linearity – inter-gain setting (type B)

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 = ( T 90 2 /c 2 ) (  SSE)

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=(T 90 /T ref ) 2  T drift (1/  3)

Typical reference thermometer uncertainty in scale realisation at 650 nm

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

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)

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

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.

Uncertainties from transfer thermometer - III  Mismatch in wavelength between reference and transfer thermometers mod((( s - t )/c 2 ).T 2 90.(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

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

Worked example

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?

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”

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)