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=(T90-Tref)(T90/Tref)(/)(1/3)

Effective wavelength of 650 nm and 906 nm filters since 1994

Effective wavelength at 650 nm

650.60

650.70

650.80

650.90

651.00

651.10

651.20

651.30

651.40

0 2000 4000

Radiance temperature /K

Eff

ecti

ve w

avel

eng

th /n

m

1994

1997

1999

Effective wavelength at 906 nm

906.10

906.20

906.30

906.40

906.50

906.60

906.70

906.80

906.90

907.00

907.10

0 2000 4000

Radiance temperature /KE

ffec

tive

wav

elen

gth

/nm

1994

1997

1999

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)

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)

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)

Typical reference thermometer uncertainty in scale realisation at 650 nm

Reference thermometer uncertainty

0.00.10.20.30.40.50.60.7

1000 1500 2000 2500 3000Radiance temperature/°C

Un

cert

ain

ties

/°C

wvlgth

ref

N/L

SSE

drift

u(k=1)

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)/c2).T2

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

Source of uncertainty Value Distrib-ution

Divisor Conversion factor

u/°C Comments T=2200 °C

Reference thermometer 0.10 N 1 1 0.10 Transfer thermometer 0.20 N 1 1 0.20 Thermometer resolution 0.10 R 1.73 1 0.06 Scale realisation 0.30 R 1 1 0.30 Corrections for RH 0.00 R 1.73 1 0.00 Corrections for ambient 0.00 R 1.73 1 0.00 DVM uncertainty 0.00 R 1.73 0.001 0.00 Units V: u=0.6V Uncertainty due to SSE 0.00 R 1.73 425.11 0.00 (same target) Wavelength mismatch 0.15 R 1.73 1 0.09 650 nm, 1000 nm,

=0.999 Target size mis-match 0.10 R 1.73 3 0.17 3 mm target for TT Short term repeatability 0.20 N 1 1 0.20 Low order fit Combined U /°C 0.47 Expanded U /°C k=2 0.94

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)