[en-GB]ord=omit See ./Images/thesisCoverPage.pdf

#  Traceable thermal imaging in harsh environments

J McMillan

()

###### Contents

  1. 1 Introduction
  2. 2 Thermal Imaging Metrology
    1. 2.1 Introduction
    2. 2.2 Radiation thermometer calibration
      1. 2.2.1 Calibration facilities
      2. 2.2.2 ITS-90 calibration
      3. 2.2.3 Size-of-source effect
      4. 2.2.4 Case study: radiation thermometer
    3. 2.3 Thermal imager calibration
      1. 2.3.1 Introduction to thermal imagers
      2. 2.3.2 Calibration facilities
      3. 2.3.3 Signal transfer function characterisation
        1. 2.3.3.1 Uncooled thermal imagers
        2. 2.3.3.2 Cooled thermal imagers
      4. 2.3.4 Non-uniformity correction
        1. 2.3.4.1 Factory method analysis
        2. 2.3.4.2 Flooded field of view method analysis
        3. 2.3.4.3 Translation-correction method analysis
      5. 2.3.5 Size-of-source and distance effect
      6. 2.3.6 Housing temperature variation
      7. 2.3.7 Additional contributors
      8. 2.3.8 Case study: thermal imager
        1. 2.3.8.1 Signal transfer calibration
        2. 2.3.8.2 Distance results
        3. 2.3.8.3 SSE results
        4. 2.3.8.4 Uncertainty assessment
    4. 2.4 Calibration summary
    5. 2.5 Conclusion
  3. 3 Laboratory Surface Temperature Characterisation
    1. 3.1 Introduction
    2. 3.2 Experimental setup
      1. 3.2.1 Defect definition
      2. 3.2.2 Assembly manufacture
      3. 3.2.3 Assembly setup
    3. 3.3 Assembly assessment
      1. 3.3.1 Surface temperature determination
      2. 3.3.2 Thermal characterisation
        1. 3.3.2.1 Coated plate characterisation
        2. 3.3.2.2 Uncoated plate characterisation
      3. 3.3.3 Surface temperature uncertainty analysis
        1. 3.3.3.1 Thermocouple uncertainty
          1. 3.3.3.1.1 Instrumentation
          2. 3.3.3.1.2 Application
        2. 3.3.3.2 Thermal imager uncertainty
          1. 3.3.3.2.1 Instrumentation
          2. 3.3.3.2.2 Application
        3. 3.3.3.3 Combined uncertainty budget
      4. 3.3.4 Discussion
      5. 3.3.5 Assessment summary
    4. 3.4 Radiance correction methods
      1. 3.4.1 Environment setup
      2. 3.4.2 Uncorrected radiance temperature
      3. 3.4.3 Multiple reflection single wavelength
      4. 3.4.4 Multiple reflection all wavelengths
      5. 3.4.5 Ray tracing
      6. 3.4.6 Environment correction comparison
      7. 3.4.7 Emissivity uncertainty
      8. 3.4.8 Summary
    5. 3.5 Conclusions
  4. 4 Characterisation of Nuclear Storage Containers
    1. 4.1 Introduction
    2. 4.2 Experimental setup
      1. 4.2.1 Laboratory setup
      2. 4.2.2 Store setup
        1. 4.2.2.1 SNM container instrumentation
        2. 4.2.2.2 Store configuration
    3. 4.3 Laboratory container assessment
      1. 4.3.1 Thermal characterisation
      2. 4.3.2 Thermal model
      3. 4.3.3 Uncertainty analysis
      4. 4.3.4 Discussion
      5. 4.3.5 Summary
    4. 4.4 Store container assessment
      1. 4.4.1 Thermal characterisation
        1. 4.4.1.1 Thermocouple evaluation
        2. 4.4.1.2 Radiance temperature evaluation
          1. 4.4.1.2.1 Region of interest evaluation
          2. 4.4.1.2.2 Calibration interpretation of measurements
          3. 4.4.1.2.3 Temperature evaluation
      2. 4.4.2 Uncertainty analysis
        1. 4.4.2.1 Thermocouple uncertainties
          1. 4.4.2.1.1 Instrumentation
          2. 4.4.2.1.2 Application
        2. 4.4.2.2 Radiance temperature uncertainties
          1. 4.4.2.2.1 Instrumentation
          2. 4.4.2.2.2 Application
        3. 4.4.2.3 Compiled uncertainty budgets
      3. 4.4.3 Discussion
        1. 4.4.3.1 Temperature comparisons
        2. 4.4.3.2 Uncertainty component assessment
        3. 4.4.3.3 Key observations
      4. 4.4.4 Summary
    5. 4.5 Conclusions
  5. 5 Concluding Remarks
  6. A Supporting Literature
    1. A.1 Radiation Heat Transfer
      1. A.1.1 Definition of a blackbody radiator
      2. A.1.2 Planck distribution law
      3. A.1.3 Stefan-Boltzmann law
    2. A.2 Surface Photo-thermal Properties
      1. A.2.1 Definition of emissivity
      2. A.2.2 Kirchhoff law
      3. A.2.3 Experimental determination of emissivity
      4. A.2.4 Traceability of emissivity measurement
      5. A.2.5 Applications of emissivity measurement
      6. A.2.6 Summary
  7. B Supporting Measurement Data
    1. B.1 Measurement data

## Abstract

Despite being regarded as a well-established field, temperature measurement
continues to pose significant challenges for many professionals in the
metrology industry. Thermal imagers enable fast, non-contact and a full field
measurement, however there is a lack of metrological development to support
their use. Here, thermal imagers have been examined for the monitoring of
special nuclear material containers; the surface temperature is an important
parameter for store management decisions. Throughout this research: a
selection of thermal imagers were calibrated and made traceable to the
International Temperature Scale of 1990; laboratory observations of a proxy
steel plate were made; initial measurement of nuclear material storage
containers were made; then a deployment to an inactive store was demonstrated.
For this technique to be feasible, uncertainties less than
$10\text{\,}\mathrm{\SIUnitSymbolCelsius}$ would be required.

During the laboratory calibration of an uncooled and cooled thermal imager
against blackbody reference sources, across the measured temperature range of
$10\text{\,}\mathrm{\SIUnitSymbolCelsius}100\text{\,}\mathrm{\SIUnitSymbolCelsius}$
the uncertainties were less than $3.20\text{\,}\mathrm{\SIUnitSymbolCelsius}$
($k=2$) and $0.50\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) respectively.
Here $k$ is the uncertainty coverage factor. When these calibrations were
applied to the plate, regions of steel and higher emissivity coating were
evaluated. These uncoated regions were measured with a thermal imager to
demonstrate temperature differences compared to surface mounted thermocouples
of $8.3\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and uncertainties up to
$30.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$). For the coated regions
this temperature difference was reduced to
$1.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$ with uncertainties up to
$6.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$).

Extending this approach to store containers – each instrumented with internal
heaters and thermocouples – yielded poor comparability between thermocouples
and an external thermal imager. Using a revised container instrumentation,
deployment of two uncooled thermal imagers to an inactive store to observe the
container was completed. From this measurement campaign the surface
temperature determined using a thermal imager for a container ranged from
$4.9\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) to
$20.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$). These results
demonstrate the feasibility of thermal imagers being deployed to nuclear
material stores for the assessment of radioactive material behaviour in
storage containers.

### Declaration of Originality

This thesis and the work to which it refers are the results of my own efforts.
Any ideas, data, images or text resulting from the work of others (whether
published or unpublished) are fully identified as such within the work and
attributed to their originator in the text, bibliography or in footnotes. This
thesis has not been submitted in whole or in part for any other academic
degree or professional qualification. I agree that the University has the
right to submit my work to the plagiarism detection service TurnitinUK for
originality checks. Whether or not drafts have been so-assessed, the
university reserves the right to require an electronic version of the final
document (as submitted) for assessment as above.

Signature |
---|---
Date |

### Acknowledgements

The tangible output from this doctorate pales when compared to the joy and
value from the journey. The countless catch ups and brainstorming with the
people I care about are the most important results from my research.

### Publications

The following instances of external recognitions are detailed in Table 1,
conference presentations shown in Table 2 and posters submitted to conferences
in Table 3.

Table 1: Publications submitted through this research project. Index |  Publication |  Status
---|---|---
1 |  McMillan J L, Hayes M, Hornby R, Korniliou S, Jones C, O’Connor D, Simpson R, Machin G, Bernard R and Gallagher C. Thermal and dimensional evaluation of a test plate for assessing the measurement capability of a thermal imager within nuclear decommissioning storage. Measurement, 202:111903, 2022. |  Accepted
2 |  McMillan J L, Hayes M, Simpson R and Sweeney S. Radiance correction methods and a cross-comparison of applicability. Quantitative InfraRed Thermography Journal. |  Draft
3 |  McMillan J L, Hayes M, Korniliou S, Simpson R, Machin G, Bernard R and Gallagher C. Evaluating nuclear material storage containers using thermal imagers. Nuclear Engineering and Design. |  Draft
Table 2: Conferences attended through this research project. Conference |  Date |  Presentation Title
---|---|---
PostGraduate Institute Conference 2021, Teddington |  October 2021 |  So you think you can measure temperature?
Table 3: Posters submitted to conferences through this research project. Conference |  Date |  Poster Title
---|---|---
PostGraduate Institute Conference 2020, Teddington |  October 2020 |  Towards traceable thermal imaging of nuclear waste containers

##  Chapter 1 Introduction

Temperature measurement has a storied past with many scientists defining their
own realisation of a temperature scale, but with the turn of the 20th century
these were unified through an International Temperature Scale. The most recent
of which, the International Temperature Scale of 1990 is the practical
realisation of temperature achievable using contact thermometers (metal in
glass, thermocouples or resistance thermometers) as well as radiation
thermometers.

Thermal imaging technology development has been growing since the 1940s with
roots in observation and detection. As such the principle requirements of
hardware included temperature sensitivity, linearity, responsivity and low
size, weight and power. Increasing commercial demand has made the technology
more accessible both through cost, instrument footprint and critically through
the omission of liquid nitrogen cooling; this has led to deployment in a
diverse range of applications, more of which now use the absolute temperature
determination capability of the equipment.

In comparison to radiation thermometry, there are many unique characteristics
of thermal imagers that do not facilitate straightforward surface temperature
determination (e.g. focal plane uniformity, pixel cross-talk). On top of this
there are other phenomena they share with radiation thermometers explored in
Chapter 2 which challenge low uncertainty temperature measurement such as
influence on the measurement due to surface emissivity, size-of-source effect,
detector temperature sensitivity.

Existing application of thermal imagers for surface temperature determination
has been demonstrated in each: healthcare [1], ground based satellite testing
[2] and nuclear material storage container assessment [3].

The research presented within this thesis focuses on temperature metrology and
outlines a robust surface temperature measurement methodology using thermal
imagers. Experimental detail in the application to both controlled laboratory
and semi-controlled in-situ measurements is presented, with computational
extrapolation to a wider set of thermal environments. These should provide an
understanding of the current state-of-the-art in temperature metrology and
insight into the largest sources of experimental uncertainty that require
consideration.

The primary narrative through this research comprises the progression from the
surface temperature measurement in a laboratory of a proxy stainless steel
plate in Chapter 3, to a nuclear material container and finally to this
container in an inactive store environment in Chapter 4. This is with the
objective to evaluate the suitability of using a thermal imager for surface
temperature determination in a harsh environment. To demonstrate the
feasibility of thermal imaging in this application, both agreement with a
surface mounted thermometer within their respective uncertainties and
measurement uncertainties below $10\text{\,}\mathrm{\SIUnitSymbolCelsius}$
would be necessary.

Apparent radiance temperature as measured by thermal imagers can be considered
using the Planck distribution law. Through both this relationship between
object temperature, wavelength and spectral radiance, as well as the
understanding of radiation heat transfer, the contribution from surface
emitted radiance and any number of reflected components can be described.
Emissivity of a surface describes the ability of a surface to absorb and emit
electromagnetic radiation, which governs the photo-thermal behaviour of a
surface with regard to its environment. A good understanding of the material
properties and its environment are necessary in order to reliably use thermal
imaging to determine surface temperature. Emissivity corrections are explored
in this work using a range of assumptions and under more general cases. This
experimental detail in a laboratory and extrapolation to a simulated
environment are explored in Chapter 3.

Essential to low uncertainty surface temperature measurement using thermal
imagers is a low uncertainty apparent radiance temperature traceable
calibration to an international temperature scale. Through comprehensive
experience with dissemination of temperature to radiation thermometers, a
range of calibration processes have been explored and discussed for thermal
imaging systems; this includes both uncooled detector packages and cooled
proprietary software systems. In addition to a comparison to an international
temperature scale, further system characteristics including the calibration
fit, detector temperature susceptibility, imager non-uniformity and size-of-
source effect are investigated.

Deployment of the radiance temperature assessment and instrumentation
characterisation techniques to the temperature determination of nuclear
material storage containers has been demonstrated in Chapter 4. A transition
from controlled laboratory experiments using a representative stainless steel
plate to an inactive storage facility permitted a detailed investigation into
the sources of error encountered in surface temperature measurement in an
uncontrolled environment.

##  Chapter 2 Thermal Imaging Metrology

###  2.1 Introduction

Measured temperature is a regular occurrence for most people either through
local thermometer measurements or regional meteorology; accurate temperature
measurement requires careful consideration with respect to the measurement
application. All measurements are required to be traceable in order to be
measuring an internationally recognised value and this can be achieved through
traceable instrument calibration to internationally recognised standards; this
enables both lateral comparison between different instruments as well temporal
comparison using the same instrument over a long period of time. This level of
comparability is not possible for uncalibrated instruments.

Through rigorous examination of the calibration parameters for various
instruments, a robust methodology to instrument characterisation can be
implemented and the results deplyed to real-world applications where
confidence in temperature measurement is critical.

For thermometers this traceability is demonstrated through calibration to the
International Temperature Scale of 1990 (ITS-90) [4]. Rather than the
thermodynamic temperature explored in literature and realised in a laboratory
(e.g. through acoustic thermometry [5] or Johnson noise thermometry [6]),
thermometry using contact thermometers (e.g. thermocouples and resistance
thermometers) or non-contact radiation thermometers is made traceable to a
practical temperature scale comprising a set of fixed temperature points
(analogous to a set of rungs on a ladder). Fixed-points refer to the melting
or freezing temperatures at which a material passes through a phase
transition; at these temperatures the energy heating or cooling the material
is used to break or form structural bonds and so demonstrate a repeatable
known temperature. These fixed points up to the freezing point of silver
($961.78\text{\,}\mathrm{\SIUnitSymbolCelsius}$) define ITS-90 and beyond this
the scale is defined by the radiation emitted by an object using the Planck
distribution law to relate this radiance and temperature.

This chapter will explore the calibration of radiation thermometers and
thermal imagers. Each of these will be substantiated through a case study of
an instrument calibration then comparisons and discrepancies between the two
will be detailed. Textbook literature to support the physics described here is
presented in Section A.1 and Section A.2 where each radiation heat transfer
and the description of emissivity are introduced. The concepts of emissivity
are less pertinent during calibration due to the high emissivity nature of the
reference sources used. However during the subsequent chapters where in-situ
applications are investigated, emissivity plays a greater role.

###  2.2 Radiation thermometer calibration

Radiation thermometers capture infrared radiance to measure the apparent
radiance temperature of an object. Beyond its dependence on the temperature of
the surface and its environment, apparent radiance temperature is also a
function of the surface emissivity defined (detailed in Section A.2), it
comprises a proportion of radiance from the observed surface and that from
reflected contributions (discussed in Section 3.4). Calibration of a radiation
thermometer is carried out using high emissivity (typically greater than
0.999) temperature reference blackbody sources and so throughout this chapter
the reflected component will be omitted. The design of these sources and their
subsequent use for the calibration of a Device Under Test (DUT) is described
in this section.

####  2.2.1 Calibration facilities

For the calibration of an optical instrument that measures thermal radiation,
the use of a blackbody source can be used. It should have the following
properties (in addition to the characteristics outlined in Section A.1.1) [7,
8]:

  1. 1.

High hemispherical total emissivity over the appropriate spectral range and
emission direction

  2. 2.

Sufficiently large aperture size for the DUT optical characteristics

  3. 3.

Low temperature non-uniformity radially; and longitudinally for a cavity

  4. 4.

Have demonstrable traceability to the International Temperature Scale of 1990

These criteria can be achieved for example by using variable temperature heat-
pipe blackbody cavities in the temperature range from
$-60\text{\,}\mathrm{\SIUnitSymbolCelsius}1000\text{\,}\mathrm{\SIUnitSymbolCelsius}$;
a typical design is shown in Figure 2.1. To accommodate this wide temperature
range a series of working fluids are used and these fluids surround the
radiating cavity [9]; these fluids each operate in a specific operating
temperature range: ammonia from
$-60\text{\,}\mathrm{\SIUnitSymbolCelsius}50\text{\,}\mathrm{\SIUnitSymbolCelsius}$;
water from
$50\text{\,}\mathrm{\SIUnitSymbolCelsius}270\text{\,}\mathrm{\SIUnitSymbolCelsius}$;
caesium from
$250\text{\,}\mathrm{\SIUnitSymbolCelsius}650\text{\,}\mathrm{\SIUnitSymbolCelsius}$;
and sodium from
$500\text{\,}\mathrm{\SIUnitSymbolCelsius}1000\text{\,}\mathrm{\SIUnitSymbolCelsius}$
[7]. The high emissivity value of the cavity is achieved through: high cavity
surface emissivity (e.g. 0.9), high temperature uniformity along the cavity
length (below $10\text{\,}\mathrm{\SIUnitSymbolCelsius}$ [10]) and increased
effective cavity emissivity using geometrical enhancement. Typical cavity
surfaces are high emissivity paints where suitable or oxidised surfaces at
higher temperatures. The longitudinal and radial temperature uniformity along
the cavity is managed through the behaviour of the heat-pipe where it
maintains high thermal conductivity along the condenser length. Finally,
cavity emissivity can be enhanced through the use of an elongation of cavity
length with respect to opening aperture diameter (refer to Eq. 2.1 [11]) or
more often through complex cavity structures: pyramids at the cavity rear,
ridges along the cavity length, asymmetric conical cavities, narrower opening
apertures than cavity diameter or spherical cavity recesses between pyramid
bases at the rear wall [12],

Figure 2.1: Typical construction of a heat-pipe cavity for radiance
temperature reference standards. This cavity would be placed in a uniform
thermal environment and the passive heat transfer from the working fluid would
ensure an isothermal radiating cavity.

$\varepsilon_{cavity}=1-\frac{1-\varepsilon_{wall}}{\varepsilon_{wall}}\frac{1}{1+\nicefrac{{l^{2}}}{{r^{2}}}}\mathrm{.}$
(2.1)

Here the geometry of a simple cavity – of length $l$ and radius $r$ – is
enhanced from $\varepsilon_{wall}$ to $\varepsilon_{cavity}$ solely through
the object geometry [7]. The radiance temperature may be traceable to ITS-90
either through direct radiance comparison with a calibrated radiation
thermometer or through a calibrated thermometer in close proximity to the back
wall of the radiating cavity (as depicted in Figure 2.1).

Through each of these design considerations, a blackbody characterisation
source with a measurement uncertainty from
$0.02\text{\,}\mathrm{\SIUnitSymbolCelsius}1.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$
($k=2$) can be achieved [13, 14, 15, 16, 17] and the calibration of radiation
thermometers can be demonstrated to achieve uncertainties from
$0.05\text{\,}\mathrm{\SIUnitSymbolCelsius}0.3\text{\,}\mathrm{\SIUnitSymbolCelsius}$
($k=2$) in the temperature range from
$-60\text{\,}\mathrm{\SIUnitSymbolCelsius}1000\text{\,}\mathrm{\SIUnitSymbolCelsius}$
[18].

####  2.2.2 ITS-90 calibration

Using the facilities detailed in Section 2.2.1, the ITS-90 below the silver
point can be transferred either from an ITS-90 calibrated contact thermometer
or by comparison using an ITS-90 calibrated radiation thermometer. For the
DUT, the instrument is aligned to the reference source at a prescribed
distance, with a temperature-regulated aperture plate placed in front of the
cavity. This aperture plate reduces the reflected environmental radiance, the
radiance from objects in the background (e.g. neighbouring furnace enclosure)
and often to provide a cold aperture radiance signal compared to the hotter
furnace radiance from within the aperture. At each calibration temperature
setpoint, the blackbody temperature and DUT temperature reading are recorded
for an identical duration, either through direct comparison or subsequent
measurement of the radiating cavity.

If the DUT offers an analogue output capability then this response can also be
calibrated against ITS-90. This requires the sensitivity $\delta$ (temperature
response per volt) to either be linear across its operational temperature
range, or to be fully characterised in this range. The sensitivity values can
be calculated from the $i^{th}$ measurement by calculating the localised
sensitivity within nominally $1\text{\,}\mathrm{\SIUnitSymbolCelsius}$, this
is shown in Eq. 2.2,

$\delta_{i}=\left\lvert\frac{T_{i}-T_{i+1}}{V_{i}-V_{i+1}}\right\rvert\mathrm{.}$
(2.2)

Where the measured voltage $V_{i}$ is from the instrument analogue output,
$T_{i}$ is the equivalent ITS-90 measured temperature from the reference
source and $i+1$ corresponds to the next higher temperature setpoint.

####  2.2.3 Size-of-source effect

The Size-of-Source Effect (SSE) arises because the indicated reading of an
instrument is affected by radiation from outside the nominal field of view and
leads to a distorting effect on the measurement [19]. The define measurement
region within the field of view of the thermometer is likely to measure
radiation outside of this area, conversely radiation from within the field of
view may not reach the detector. This effect arises from scattering in the
optical path and for a given optical system when the surface area of an
observed source decreases, the contribution due to this effect increases.

This should be evaluated, for all such instruments being calibrated as an
ongoing monitoring and assessment of the system to identify any gradual
changes to the optical performance. The SSE measurement procedure is often
performed at the highest temperature used in the calibration and becomes more
sensitive to variation as the apparent temperature approaches ambient
temperatures; due to the radiance contributions becoming comparable. The SSE,
$\sigma$, is described by Eq. 2.3 which is determined by the ratio of the
radiances (Eq. A.1) at two aperture diameters,

$\sigma=\frac{e^{\frac{c_{2}}{\lambda
T_{\varphi_{i}}}}-1}{e^{\frac{c_{2}}{\lambda T_{\varphi_{max}}}}-1}\mathrm{.}$
(2.3)

Here $T_{\varphi_{i}}$ is the measured temperature in kelvin at the $i^{th}$
aperture and $T_{\varphi_{max}}$ is the equivalent temperature at the greatest
aperture diameter. $\lambda$ is the instrument effective wavelength and
$c_{2}$ is the second radiation constant. Evaluation of the SSE results is
carried out by determining the smallest aperture with which the DUT provides
an acceptable measurement. An indication of a satisfactory SSE value for a
particular aperture is to be within $2\text{\,}\mathrm{\char 37\relax}$ of the
maximum aperture value (e.g. above 0.98 for temperatures greater than ambient
and below 1.02 for temperatures below ambient) [19].

An SSE profile measured at a particular temperature may not be representative
of the profile at other temperatures if the signal from the blackbody is not
much greater than that from the surrounding field of view. It is possible to
infer a temperature invariant instrument SSE through the method described in
[20]. Through the use of this SSE measurement it is possible to correct for a
measurement at one target size to another; for example if a calibration is
performed at one aperture size, this can be applied to all target sizes within
the tested range of aperture sizes.

####  2.2.4 Case study: radiation thermometer

A Heitronics TRT IV.82 radiation thermometer (S/N: 4182) was calibrated over
the temperature range from
$-30\text{\,}\mathrm{\SIUnitSymbolCelsius}1000\text{\,}\mathrm{\SIUnitSymbolCelsius}$
using National Physical Laboratory (NPL) standard blackbody sources. The
temperatures of the blackbodies were determined through the use of ITS-90
calibrated thermometers (as shown in Figure 2.1). The aperture diameter of
each blackbody was set to nominally $40\text{\,}\mathrm{mm}$ using blackened
apertures. For the calibration points greater than
$50\text{\,}\mathrm{\SIUnitSymbolCelsius}$ the apertures were water-cooled.
The distance from the front of the thermometer lens to the aperture was
nominally $504\text{\,}\mathrm{mm}$. The thermometer was aligned to the centre
of the aperture using the sighting optics.

The calibrated digital voltmeter was connected to the output terminals of the
thermometer. The calibration was performed by recording at each temperature
the output signal of the test thermometer and the temperature of the blackbody
source. The mean of at least 60 readings was used to determine each
calibration point.

Results of both an ITS-90 calibration and SSE assessment of a Heitronics TRT
IV.82 radiation thermometer are described here. These results are shown in
Figure 2.2, the associated SSE results are displayed in Figure 2.3.

02004006008001000020040060080010000.960.981.001.021.041.061.081.101.121.14

Instrument Output / $\text{\,}\mathrm{mV}$

Instrument Sensitivity /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{\,}{\mathrm{mV}}^{-1}$

Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$OutputSensitivity Figure
2.2: Measurement data from the radiation thermometer calibration presented in
Table B.1. Output is presented on the left y-axis and the sensitivity on the
right y-axis. 0.600.650.700.750.800.850.900.951.000102030405060

Size-of-Source Effect / [a.u.]

Aperture Diameter / $\text{\,}\mathrm{mm}$ $98\text{\,}\mathrm{\char
37\relax}$ at $8\text{\,}\mathrm{mm}$ Figure 2.3: Size-of-source effect data
from the radiation thermometer calibration using an aperture set ranging from
$4\text{\,}\mathrm{mm}60\text{\,}\mathrm{mm}$ diameter. The SSE was measured
using a source at $1000\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

The calibration uncertainties are given in Table B.2. The reported expanded
uncertainties are based on standard uncertainties multiplied by the coverage
factor $k$ given in Table B.2, providing a coverage probability of
approximately $95\text{\,}\mathrm{\char 37\relax}$. The expanded uncertainty
comprises the uncertainty associated with the NPL standards and the
uncertainty associated with the instrument under test. Instrument uncertainty
includes components for the resolution and stability of the test instrument,
the alignment on the calibration source and the residual from the transfer
function from the calibration.

Calibration and Measurement Capability (CMC) describes the best achievable
uncertainty result demonstrated through an independent audit that has been
accredited by an organisation such as the United Kingdom Accreditation Service
(UKAS) [21]. Specifically with respect to an NPL calibration of radiation
thermometers these are shown in Figure 2.4 against the measured uncertainties.
These CMCs have been determined through extensive rigour and demonstrated by
international comparisons between accredited laboratories [22].

0.00.20.40.60.81.002004006008001000

Exapanded Uncertainty / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$Instrument
UncertaintyCMCs Figure 2.4: Measurement uncertainties for the Heitronics TRT
IV.82 across the calibration temperature range, normalised to a coverage
factor of $2.0$. The CMCs are representative of the lowest uncertainties that
can be issued by NPL for this type of measurement [18].

The results shown provide context for the achievable apparent radiance
temperature measurement uncertainty for the instrument, here the instrument
approaches these boundaries but does exceed.

###  2.3 Thermal imager calibration

Calibration of radiation thermometers is a mature field within which
metrological instrumentation is used to measure and disseminate the ITS-90.
Similarities between radiation thermometers and thermal imagers enable their
behaviour to be characterised using identical reference sources. Extending the
calibration from the comparatively narrow field of view of the single spot
infrared radiation thermometer to the extended field of view for the thermal
imager introduces particular limitations to the calibration of a thermal
imager and these will be detailed here, alongside unique developments to
calibrate this instrumentation.

This section will explore the history of thermal imagers, nuances to
calibration facilities beyond those used for radiation thermometers, and the
characterisation of each: signal transfer function, non-uniformity, size-of-
source effect, effect from distance and housing temperature effect. These are
explored within a case study for a cooled and uncooled thermal imager and
evaluated with respect to a radiation thermometer.

####  2.3.1 Introduction to thermal imagers

Thermal imaging was first developed as a military technology in the early
twentieth century and in the 1950s it was declassified and broader research
began. Initial instruments comprised a mirror mounted on a motor to scan
across a scene and build a thermal image. During the 1960s indium antimonide
based detectors were developed, these were cooled by liquid nitrogen manually
decanted into the detector reservoir [23].

Two infrared radiation detection methods employed within thermal imagers are
photon-based and thermal-based. Photon detection is observed when a photon
interacts with an electron in a material, if the photon energy exceeds the
ionisation energy of the electron an hole-electron pair is generated and this
can be detected by the read-out integrated circuit. Thermal detection refers
to any mechanism through which a change in temperature leads to a measurable
material property change. One example of this is the resistive bolometer, here
the electrical resistance of a film changes when absorbing infrared radiation.
This change in material behaviour is measured by the read-out integrated
circuit [24].

####  2.3.2 Calibration facilities

Similar to radiation thermometer calibration, the use of a blackbody source
(with identical properties as shown in Section 2.2.1) is typical for the
calibration of a thermal imager; the second requisite property, a sufficiently
large aperture size for the DUT field of view introduces a limitation to these
sources for thermal imager calibration. Due to design constraints, it is
challenging to manufacture a sufficiently large heat-pipe cavity that
demonstrates a high thermal stability and rapid temperature changes (due to
its large mass).

Attempts to design large aperture cavity reference have been shown to be
successful at temperatures close to ambient, where heat transfer losses are
less restrictive. These take the form of blackbody cavities submerged within
stirred fluid baths; the greatest source of uncertainty for these reference
sources are the greater impact from convective losses and condensation at
temperatures below the dew point [25].

Alternative radiation sources include: flat-plate radiators and collimating
projection systems [26]. Commercially available flat-plate sources comprise a
thermally-regulated metal plate covered with a high emissivity coating [27,
28]; these systems offer a larger radiating surface in turn for lower source
emissivities, poorer thermal stability and greater radial non-uniformity. A
diagram of a typical flat-plate radiator is shown in Figure 2.5. Achieving
greater radiating source sizes than typical flat-plate calibrators and
offering a collimated beam profile, an infrared collimator can be used for the
calibration of a thermal imager and many other characterisation tests (e.g.
Noise Equivalent Temperature Difference (NETD), Minimum Resolvable Temperature
Difference (MRTD)). A collimator system can comprise a radiating source (often
a flat-plate calibrator) and through the use of a primary collimating mirror,
project a collimated beam of a greater size (displayed in Figure 2.6) [29, 30,
31].

Figure 2.5: Typical construction of a flat-plate radiator for radiance
temperature reference standards. This radiator comprise a thermal insulated
and heated radiating surface with a monitoring thermometer in close proximity.
Figure 2.6: Example construction of a collimator source. The radiation from a
source blackbody (here a flat-plate radiator is shown) is projected onto a
primary collimating mirror to produce a collimated beam of radiation for
calibration.

Detailed in Section 2.2.1, using state-of-the-art reference sources
thermometers are able to demonstrate uncertainties as low as
$0.3\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Given equivalent sources, thermal
imaging systems are able to demonstrate uncertainties between
$0.45\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
$2.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) in the limited temperature
range from
$10\text{\,}\mathrm{\SIUnitSymbolCelsius}120\text{\,}\mathrm{\SIUnitSymbolCelsius}$
[32, 33, 34]. This discrepancy between what is achievable between radiation
thermometers and thermal imagers is large; there are approaches that can be
taken to reduce this variation.

####  2.3.3 Signal transfer function characterisation

In the same manner that the response of the radiation thermometer against
ITS-90 was described and demonstrated in Section 2.2.2 and Section 2.2.4, the
response signal from a thermal imager may be correlated against temperature.
Consideration should be given to the specific instrument and its internal
processing architecture – if the detector response is interrogated – that
intermediary proprietary processing steps are reduced. This access to a raw
signal will vary between instruments but is critical to reduce detrimental
unknown influences on the signal transfer function [24].

Two specific examples are explored here, the use of an uncooled microbolometer
and a cooled photon detector based thermal imager. The microbolometer
instrument response is interrogated from an early stage of the response
processing pipeline. The cooled thermal imager has been calibrated using the
manufacturer proprietary software and calibration process. Both were
calibrated against heat-pipe cavity reference sources.

#####  2.3.3.1 Uncooled thermal imagers

The DUT can be calibrated by positioning against the blackbody cavity
reference sources, then recording both the DUT and ITS-90 measurement at a
number of temperature setpoints.

Consideration of the DUT software and system features enabled to ensure
measurement traceability is maintained from the laboratory environment to
deployment. Specifically for uncooled thermal imagers, the flat-field
correction implementation must be determined. This may be that the shutter is
operated once, a fixed time period prior to measurements or that the shutter
is automatically operated when the system requires this (often from either an
internal temperature drift or regular time period parameter). This shutter
operation has been observed to affect temperature measurement and would be
recommended to be avoided during a calibration measurement setpoint [35].

The temperatures of the blackbodies should be determined in terms of ITS-90
and the measurements carried out in accordance with ISO 17025 [36].

The measurements can be used to generate a DUT transfer function presented in
Eq. 2.4, where digital level $S_{DUT}[\mathrm{DL}]$ and measured Focal Plane
Array (FPA) temperature $T_{FPA}$ are used to calculate $t_{90}$ ITS-90
temperatures alongside the calibration coefficients $a$ through $f$,

$\begin{split}t_{90}\left(S_{DUT},T_{FPA}\right)&=\\\ &\hskip 12.50002pta\cdot
S_{DUT}^{2}+b\cdot S_{DUT}\\\ &+c\cdot S_{DUT}\cdot T_{FPA}\\\ &+d\cdot
T_{FPA}^{2}+e\cdot T_{FPA}\\\ &+f\mathrm{.}\end{split}$ (2.4)

This formula is an empiracal fitting function used to described two co-
dependent second order polynomials.

#####  2.3.3.2 Cooled thermal imagers

An example of a thermal imager calibration using the manufacturer guidance
[37] and heat-pipe cavity blackbodies described in Section 2.2 is described
here. The suggested stages of instrument calibration from the manufacturer are
depicted in Figure 2.7.

Figure 2.7: The calibration procedure for the thermal imager. First the
initial calibration files are prepared and then the non-uniformity and bad
pixel replacement are characterised. These characterisations are then utilised
during the comparison of digital level to ITS-90. Following the primary
calibration stage, the measured ITS-90 and digital level values are input to
the calibration files. These updated calibration files (utilising the measured
calibration) are then validated to ensure suitability.

The first three phases are described in the manufacturer guidance material,
however the dissemination of the International Temperature Scale of 1990 and
final validation are an extension to the prescribed procedure.

The file generation phase generates the cal calibration file that describes
integration mode, integration time, temperature range, framerate, relevant
Non-Uniformity Correction (NUC) and Bad Pixel Replacement (BPR) files and
calibration housing temperature. Integration mode describes the detector
readout method, either integrate while read or integrate then read, the former
was used during this calibration. Integration time defines the period the
detector will be exposed for and is typically defined in microseconds. The
temperature range is limited by the saturation temperatures and noise floor
for the specific integration time. The NUC and BPR files specified within this
file are those measured at the relevant integration time. The housing
temperature of the imager during the calibration is measured from the internal
thermometer and is defined here to ensure the imager in the application
environment is within calibration.

The coe NUC file is created by filling the imager field of view with a
blackbody source and following the factory NUC method (refer to Section
2.3.4). The pix BPR file was created by replacing the lens cap for each
integration time and using the auto BPR function.

To populate the calibrated temperature and digital level response for each of
the integration times, the thermal imager should be aligned to the respective
heat-pipe cavity blackbody at a prescribed distance. At each temperature
setpoint the internal imager temperature was recorded as well as the digital
level response and blackbody temperature, over a period of
$2\text{\,}\mathrm{min}$. Table 2.1 depicts the temperature setpoints measured
using each of the four integration times. The saturation limits were specified
to be below $18\,500\text{\,}\mathrm{DL}$ and above
$28\,500\text{\,}\mathrm{DL}$.

Table 2.1: The temperature setpoints measured using each of the four integration times for the cooled thermal imager. Temperature Setpoint / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ |  $175\text{\,}\mathrm{\SIUnitSymbolMicro s}$ |  $75\text{\,}\mathrm{\SIUnitSymbolMicro s}$ |  $50\text{\,}\mathrm{\SIUnitSymbolMicro s}$
---|---|---|---|---
5 |  $\checkmark$ |  $\checkmark$ |  |
20 |  $\checkmark$ |  $\checkmark$ |  |
40 |  $\checkmark$ |  $\checkmark$ |  $\checkmark$ |
60 |  $\checkmark$ |  $\checkmark$ |  $\checkmark$ |  $\checkmark$
80 |  $\checkmark$ |  $\checkmark$ |  $\checkmark$ |  $\checkmark$
100 |  $\checkmark$ |  $\checkmark$ |  $\checkmark$ |  $\checkmark$
125 |  |  $\checkmark$ |  $\checkmark$ |  $\checkmark$
150 |  |  $\checkmark$ |  $\checkmark$ |  $\checkmark$
175 |  |  |  $\checkmark$ |  $\checkmark$
200 |  |  |  $\checkmark$ |  $\checkmark$
225 |  |  |  |  $\checkmark$

For each blackbody cavity measurement the imager was aligned to be central to
the cavity aperture and perpendicular to its surface and positioned so the
cavity aperture was central to the field of view. The region of interest used
to evaluate the thermal imager measurement was maintained through both the
calibration and validation measurements; this ensured that the same region of
the detector was observed in order to minimise non-uniformity effects. An
example Region Of Interest (ROI) is overlaid a measurement of a cavity in
Figure 2.8.

Figure 2.8a A visible image of the aperture for an ammonia heat-pipe reference
source.

232425262728

Apparent Radiance Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Figure 2.8b A region of interest evaluated for blackbody cavity measurements
is highlighted by the dashed square.

Figure 2.8: This measurement is of a $40\text{\,}\mathrm{mm}$ aperture for the
ammonia heat-pipe blackbody cavity at
$40\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

####  2.3.4 Non-uniformity correction

Image non-uniformity of the apparent radiance temperature measured can
comprise a static offset from the on board flat-field pattern. This component
is intrinsic to the data pipeline and often can not be isolated. If this
component should be isolated then a uniform scene must be projected onto the
imager field of view; the measured radiance will now consist of both this on
board static offset and a dynamic scene offset.

A decision needs to be taken at the beginning of a calibration process whether
to implement a new non-uniformity correction file or not. This will affect the
output of the calibration process and reduce the ease with which a historical
comparison to previous calibration can be completed.

The literature details a range of methods to identify this non-uniformity both
through laboratory evaluation [38, 39] and in-situ scene-based approaches [40,
41] as well as the sources for these non-uniformity contributions [42]. Three
methods to evaluate the on board instrument non-uniformity are detailed here.

#####  2.3.4.1 Factory method analysis

A two-point NUC allows the reduction in fixed pattern noise and non-uniformity
by calculating a gain and offset value for each pixel. This works on the
assumption that the response of each pixel can be modelled as having a
multiplicative gain and additive offset.

The following describes the procedure that can be implemented within the
manufacturer proprietary software.

The coe NUC file is created by filling the imager field of view with a
blackbody source and exposing the detector to a low and high temperature
source. This two-point NUC method requires both a large aperture source and
two disparate temperatures, due to these constraints it is preferable to use a
flat-plate calibrator as opposed to the heat-pipe cavity blackbodies. The
imager may be focused at its calibration distance and then positioned closer
to the calibrator surface to fill the field of view (often this is out of
focus). The dynamic range of the imager will be limited by its noise floor and
saturation point in order to maximise the analogue to digital conversion range
for the readout integrated circuit range. The optimal levels to perform the
two-point NUC is at $25\text{\,}\mathrm{\char 37\relax}$ and
$75\text{\,}\mathrm{\char 37\relax}$ of the dynamic range of the detector. For
each integration time used the two-point NUC can be carried out [37].

#####  2.3.4.2 Flooded field of view method analysis

Another method to measure the effect from non-uniformity is to carry out a
single point non-uniformity measurement. This can be completed using a flat-
plate calibrator and flooding the field of view (as per the factory method)
and directly measuring the response. This requires a sufficiently large
radiating source and is limited by the uncertainty of the radiating source.

An example uniformity of a DUT is shown in Figure 2.9. The spatial standard
deviation across this set of measurements is presented in Table 2.2. It can be
shown that this non-uniformity is minimised towards the centre of the
calibration range where the digital level is furthest from its saturation and
noise floor.

Table 2.2: Results from a non-uniformity assessment using a single point measurement. The spatial standard deviation across the region of interest is reported. t90 / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  DUT Digital Level Measurement / [a.u.] |  DUT Standard Deviation / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---
9.8 |  21275 |  0.99
19.8 |  22379 |  0.74
29.9 |  23643 |  0.80
39.9 |  24913 |  0.57
49.9 |  26224 |  0.64
59.9 |  28115 |  0.75
69.9 |  29475 |  0.90
79.9 |  31550 |  0.96
-1.5-1.0-0.50.00.51.01.5

Temperature Difference / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Figure 2.9: The temperature difference measured across a reference source at
$80\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

An approach often observed is to translate a narrow reference source across
the field of view of a thermal imager and collating these together [25].
Whilst this is possible according to the isotropic requirements outlined in
Section A.1.1 in practice this would introduce large error from the radiance
emitted at angles of observation away from the cavity normal. Although if a
collimated projection was used in this approach these errors would not be
observed.

#####  2.3.4.3 Translation-correction method analysis

The following describes the procedure for the independent user measurement
assessment of NUC, for benchmarking and monitoring.

In order to assess the uniformity of the thermal imager focal plane array, the
method outlined in [43] was employed. This technique exploits the statistical
independence of two fixed patterns of noise observed in a typical thermal
image by translating one across the other (Figure 2.10).

Figure 2.10: The translation approach employed to assess non-uniformity as
described in [43]. The square matrix represents a non-uniform time-invariant
surface and the circle represents the non-uniform imager detector as it passes
across the surface.

For example, representing the three frames depicted in Figure 2.10 as Gaussian
responses within a background of random noise (refer to Figure 2.11), the
method can be demonstrated. The Gaussian peaks represent the imager non-
uniform response and the background noise depicts the blackbody non-
uniformity; given three images of the blackbody as the imager is translated
across the surface, the misaligned imager non-uniformity can be pictured.

-0.010.000.010.020.030.040.050.060.070.080.09$0$$100$$200$$300$$400$$500$$600$$700$$800$$900$$1000$Frame 1SNR 15.86Frame 2SNR 16.27Frame 3SNR 15.15

Signal / [a.u.]

Variable / [a.u.] Figure 2.11: Three arbitrarily valued signals, each with a
random background noise. Each of these signals represents a frame from Figure
2.10 where the peak is indicative of the imager non-uniformity and the noise
depicts the blackbody uniformity.

By aligning frames one and three onto frame two, summing them and dividing by
three, the signal-to-noise ratio of the imager non-uniformity can be
increased. This is visually demonstrated in Figure 2.12. In this particular
example, the signal-to-noise ratio of the Gaussian peak increased by over
$60\text{\,}\mathrm{\char 37\relax}$.

-0.010.000.010.020.030.040.050.060.070.080.09$250$$300$$350$$400$$450$$500$$550$$600$$650$$700$$750$CombinedSNR 25.33

Signal / [a.u.]

Variable / [a.u.] Figure 2.12: Each of the three frames from Figure 2.11 has
been aligned, summed and normalised. This has increased the signal-to-noise
ratio of the Gaussian response.

The process outlined above has been translated to two-dimensional image
arrays. Below is a description of the mathematical process, and a
visualisation using image data from the InfraTec ImageIR 8300.

A set of thermal images observing a flat plate blackbody source (Fluke 4181
Precision IR Calibrator) is shown in Figure 2.13. This is representative of
the data measured within the non-uniformity assessment and is the measured
visualisation of Figures 2.11 and 2.12. From left to right the imager is being
translated from left to right across the radiating blackbody. The circular
artefact (horizontal arrow) located towards the centre of the frame can be
attributed to the imager non-uniformity and its position remains fixed through
the data set. The dark amorphous region (vertical arrow) towards the top of
the frame is a component of the blackbody and is shown to move across the
frame throughout the series of images.

562056405660568057005720

Digital Level / [a.u.]

Figure 2.13: Thermal image of a large area blackbody source at
$150\text{\,}\mathrm{\SIUnitSymbolCelsius}$ at three positions during a
translation data set. From left to right, the imager is being moved from left
to right across the blackbody. In particular, the circular artefact
(horizontal arrow) towards the centre of the frame is a source of non-
uniformity from the imager. The amorphous region (vertical arrow) located
towards the top of the image can be attributed to the radiating surface.

As detailed in [43], the number of pixels the blackbody artefact was displaced
between each frame of the (nominally thirty image) sequence is described by
$\delta$ [$\text{\,}\mathrm{px}\text{\,}{\mathrm{frame}}^{-1}$]. This
component can be estimated to lie within a particular range through
preliminary assessment of the optical setup.

The spatial resolution of the array $\varphi$
[$\text{\,}\mathrm{m}\text{\,}{\mathrm{px}}^{-1}$] in a given configuration
can be described by Eq. 2.5,

$\varphi=\frac{p\cdot d}{f}\mathrm{.}$ (2.5)

Where $p$ is the detector pitch, $d$ is the distance from the imager to the
surface of measurement and $f$ is the lens focal length. The distance is
defined as the distance from the detector itself, however this can vary
between imager models and even between identical models for different lens
architectures. Due to the true distance being non-trivial to determine, the
distance from the front of the lens will be used throughout this work and the
sensitivity of the algorithm will be assessed to account for this. The number
of pixels translated through by a particular displacement $x$
[$\text{\,}\mathrm{m}\text{\,}{\mathrm{frame}}^{-1}$] can be described by Eq.
2.6,

$\delta=\frac{x}{\varphi}\mathrm{.}$ (2.6)

Given a sequence of images of a blackbody as the imager translates across its
surface, each frame can be aligned onto the central frame of the sequence by
applying an array translation of $\pm k\cdot\delta$ columns, where $k$ is the
integer number of frames from the (central) frame to be aligned to. This
summed array can then be normalised column-by-column, accounting for the
particular number of frames that contributed to each summed column.

-0.2-0.1-0.10.00.00.10.1

Relative Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Figure 2.14a The blackbody non-uniformity calculated by applying the
translation-correction technique described above.

-0.4-0.3-0.2-0.10.00.10.20.30.4

Relative Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Figure 2.14b The imager non-uniformity calculated by applying the translation-
correction technique described above.

Figure 2.14: Non-uniformity measured using the translation-correction method.

This normalised array then depicts the blackbody non-uniformity independent of
the detector non-uniformity and is shown in Figure 2.14a. The translation-
correction approach has statistically increased the signal-to-noise ratio of
the imager components, where the fluctuations of signal from the detector is
considered as background noise.

By subtracting the blackbody non-uniformity (Figure 2.14a) from the central
frame of the data sequence, the imager non-uniformity can be calculated. This
imager non-uniformity is shown in Figure 2.14b.

To identify the minimum number of frames required to build a correction, the
standard deviation of the entire imager non-uniformity matrix was calculated
from three frames up to the complete sequence set. This data is presented in
Figure 2.15. This data shows that as the number of frames used increases, the
standard deviation of the imager non-uniformity decreases. This plateaus at
nominally twenty frames. Therefore, a minimum of twenty measured frames is
recommended to reduce the statistical anomalies incurred by the technique.

0.080.100.120.140.160.180.200.220.2405101520253035

Standard Deviation / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Number of Frames Figure 2.15: The standard deviation across the entire
blackbody non-uniformity evaluated with reducing numbers of sequence sizes.
This employed a different thermal imager but the same blackbody source.
Nominally twenty frames are required to minimise the statistical fluctuations
of the technique.

####  2.3.5 Size-of-source and distance effect

Continuing from Section 2.2.3, thermal imagers demonstrate similar effects due
to imperfect optical behaviour. In comparison to infrared radiation
thermometers that are defined as a single point detector, thermal imagers
comprise an array of individual detectors; here the redefinition of SSE
requires precise definition.

For imaging systems, SSE is equivalent to point spread function definitions,
which have a wealth of literature describing how to evaluate and compensate
for this [44, 45]. Complications arising from the different optical
configuration are that the position in the focal plane array that SSE is
evaluated is a single assessment and does not describe the behaviour at other
locations or how they should be compensated [46]. The definition of SSE does
not detail when evaluating images of increasing aperture diameters whether the
region of interest size should be fixed or scale accordingly with the aperture
size. This is presented in Figure 2.16, the blackbody temperature is at
$65\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and the aperture diameter is
increasing from $9\text{\,}\mathrm{mm}40\text{\,}\mathrm{mm}$. As a figure of
merit, for a square $3\times$$3\text{\,}\mathrm{px}$ region of interest, the
object under interrogation should occupy a $10\times$$10\text{\,}\mathrm{px}$
region [47].

181920212223242526

Apparent Radiance Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Figure 2.16: An assessment of the SSE using a thermal imager. The aperture
from left to right are $9\text{\,}\mathrm{mm}$, $20\text{\,}\mathrm{mm}$ and
$40\text{\,}\mathrm{mm}$.

For the instruments investigated within the case study, they were evaluated as
an extension to a radiation thermometer where the central set of pixels are
defined as a fixed ROI throughout the SSE measurements.

As a corollary to SSE the subtended coverage of the thermal imager detector
also varies with distance from the object in the scene. It is often
challenging to distinguish between the distance effect and the size-of-source
effect from the measurement data alone and either requires a priori
information or measurements of the surrounding scene; refer to Figure 2.16 as
an example, by measuring only the cavity it would not be possible to determine
which effect is taking place. As the distance from an object to thermal imager
increases, the spectral radiance decreases; this sensitivity to distance may
be greater depending on the optical configuration or the transmission media.

In typical laboratory conditions it is not likely the transmission media
contributes a measurable effect but in applications where the object is
greater than $2\text{\,}\mathrm{m}$ from the observer this should be
considered and assessed with respect to the transmissivity.

####  2.3.6 Housing temperature variation

Both detector types are susceptible to variation in output response with
respect to the internal hardware temperature; this behaviour introduces a
particular challenge when deploying the instrument in an uncontrolled
environment. There are common and unique sources to this effect for each
thermal imager type, each are impacted by the change in lens refractive index
with temperature and the incident radiance from the internal housing on the
detector. Both detector types are affected by their responsivity change with
temperature; microbolometers can be particularly sensitive to thermal
perturbations from the shutter during a flat-field correction routine and this
effect varies with the shutter temperature.

This response can be characterised through calibration by modifying the
environment temperature within the expected excursion range, often this is
achieved through using an environmental chamber local to the instrument to
induce this variation [48, 49].

Accounting for this effect can be carried out through either the proprietary
manufacturer calibration software (described in Figure 2.7) or by accounting
for this internal temperature variation in the signal transfer function (as
shown in Eq. 2.4 by the $T_{FPA}$ components).

####  2.3.7 Additional contributors

Further to the sources of error discussed, additional contributors are: warm-
up stabilisation, data pipeline processing, factory default parameters, pixel
gain and bias, read-out integrated circuit, integration time interpolation and
NUC look-up tables.

It is recommended that a measurement instrument such as a thermal imager
should be powered up for an appropriate time period prior to measurement to
ensure the local enclosure reaches a thermal equilibrium (for example due to
stray radiation from the internal housing). This is shown in Figure 2.17 where
a microbolometer thermal imager was observing a
$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ reference target; this data was
collected during a collaborative research project with Ben Kluwe, University
of South Wales [50]. Literature supports this measurement by recommending a
$15\text{\,}\mathrm{min}$ initial stabilisation period for this instrument
[51]. In a laboratory environment this is often trivial to achieve, however
during many applications this is not feasible. When an application cannot
achieve this, the initial stabilisation period should be characterised as it
is likely to be unique to that instrument and environment [1].

262728282829303030

00:00

03:00

06:00

09:00

12:00

15:00

18:00

21:00

24:00

27:00

30:00

33:00

20.521.021.522.022.523.023.524.024.5

Apparent Radiance Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

FPA Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Time / mm:ssMeasured TemperatureFPA Temperature Figure 2.17: Warm-up profile
for an uncooled microbolometer thermal imager. This FLIR Lepton was observing
a $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ target and the recommended
$15\text{\,}\mathrm{min}$ warm-up period recommended by literature is
supported by this data [51].

For low uncertainty and repeatable temperature measurements with a thermal
imager, it is prudent to minimise non-systematic effects on measurement
traceability. Operating software control parameters that are used should be
considered with respect to the repeatability and effect on measurements.

For cooled thermal imagers the signal transfer function is determined for
fixed integration times and then interpolated. The uncertainty contribution
from this interpolation should be considered where possible. For uncooled
thermal imagers a look-up table of digital values is implemented for
temperature measurement and this may comprise a step-wise function, the
uncertainty contribution local to these discontinuities may be large and
understanding of where these step changes occur is critical.

####  2.3.8 Case study: thermal imager

To contrast the evaluation techniques used for radiation thermometers, a case
study for thermal imager calibration is presented for both detector types.
Measurement results from the previously outlined sections are detailed.

#####  2.3.8.1 Signal transfer calibration

Uncooled

The FLIR Boson 20320A050-9CAAX was controlled using the FLIR Boson Application
(version 1.4.4). The DUT was calibrated by: recording the digital level
measured by the detector at a framerate of $9\text{\,}\mathrm{Hz}$ as a tiff
file, using high gain mode, manual flat-field correction, without a
supplementary flat-field correction, averager disabled, spatial pattern and
spatial column noise reduction disabled. A flat-field correction was manually
triggered $30\text{\,}\mathrm{s}$ prior to each measurement setpoint. For the
points at $80\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and below the aperture
size of the blackbody was set to nominally $160\text{\,}\mathrm{mm}$ diameter.
For the points at $90\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and above the
aperture size of the blackbody was set to nominally $40\text{\,}\mathrm{mm}$
diameter using water-cooled blackened aperture plates; no correction for size-
of-source effect was made. The measured distance from the aperture of the
blackbody cavity to the mirror was nominally $75\text{\,}\mathrm{mm}$, the
distance from the mirror to the lens housing of the DUT was nominally
$15\text{\,}\mathrm{mm}$. This mirror assembly is shown in Figure 2.18 and was
used to support the end use case for this instrument and optimise footprint
along the axis of the carriage in its narrow deployment location. The
measurement region was taken as the $$71$\times$71\text{\,}\mathrm{px}$$
region at the centrally-aligned coordinates $(162,125)$; subsequent
coordinates were also centrally-aligned. The DUT was aligned so that the
centre of the field of view was positioned at the centre of the blackbody
cavity and the DUT focused on the aperture plate.

Figure 2.18: An optical carriage to mount a pair of uncooled thermal imagers
during an end use application. The imagers were calibrated using this assembly
by positioning the blackbody cavity perpendicular to the axis of the carriage.

The device under test was calibrated over the temperature range from nominally
$10\text{\,}\mathrm{\SIUnitSymbolCelsius}100\text{\,}\mathrm{\SIUnitSymbolCelsius}$
using blackbody sources with calculated emissivities greater than 0.999. The
temperatures of the blackbodies were determined in terms of ITS-90 and the
measurements were carried out in accordance with ISO 17025 [36].

The calibration was performed by recording at each radiance temperature the
mean digital level of the ROI over the measurement period. The average of
twelve measurements over a period of $2\text{\,}\mathrm{min}$ was used for
each radiance temperature setpoint and the temperature of the blackbody source
during the measurements was also recorded. The results of the calibration are
given in Table 2.3. Digital level $S_{DUT}$ and measured FPA temperature
$T_{FPA}$ refer to the measurements from the DUT at the respective temperature
setpoint. These measurements were then used to determine the calibration
coefficients (from Eq. 2.4) and these are presented in Table 2.4.

Table 2.3: The results from the calibration of an uncooled thermal imager as described in Section 2.3.3.1. † denotes repeat measurements. t90 / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  DUT Digital Level Measurement / [a.u.] |  FPA Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---
9.8 |  21200 |  32.1
19.8 |  22300 |  32.4
29.9 |  23500 |  32.9
39.9 |  24800 |  33.2
49.9 |  26400 |  33.6
59.9 |  28000 |  33.8
69.9 |  29400 |  33.8
79.9 |  31500 |  34.5
90.1 |  33900 |  33.6
99.7 |  36300 |  32.6
9.8 † |  21200 |  32.2
9.8 † |  21300 |  31.7
19.9 † |  22400 |  31.7
29.9 † |  23600 |  31.7
49.9 † |  26100 |  33.3
99.9 † |  36200 |  33.1
Table 2.4: The calibration coefficient results for the signal transfer measurement of an uncooled thermal imager using the data in Table 2.3. For use with Eq. 2.4. Coefficient Variable | Coefficient Value
---|---
$a$ | $-$ | $1.874\text{\times}{10}^{-7}$
$b$ |  | $1.832\text{\times}{10}^{-2}$
$c$ | $-$ | $4.906\text{\times}{10}^{-5}$
$d$ | $-$ | $2.479\text{\times}{10}^{-1}$
$e$ |  | $1.767\text{\times}{10}^{1}$
$f$ | $-$ | $5.727\text{\times}{10}^{2}$

Cooled

The InfraTec ImageIR 8300 was controlled using IRBIS 3.1 Professional (version
3.1.90). The DUT was calibrated by recording the digital level measured by the
detector at a framerate of $60\text{\,}\mathrm{Hz}$. The calibration tables:
$500\text{\,}\mathrm{\SIUnitSymbolMicro s}$,
$175\text{\,}\mathrm{\SIUnitSymbolMicro s}$,
$75\text{\,}\mathrm{\SIUnitSymbolMicro s}$ and
$50\text{\,}\mathrm{\SIUnitSymbolMicro s}$, were used with DV units selected
in the software as detailed in Table 2.5. The aperture size of each blackbody
was set to nominally $40\text{\,}\mathrm{mm}$ diameter using blackened
aperture plates. The measured distance from the aperture of the blackbody
cavity to the front of the lens of the DUT was nominally
$450\text{\,}\mathrm{mm}$. The measurement region was taken to be the central
$$92$\times$92\text{\,}\mathrm{px}$$ region at the centre of the field-of-
view. The DUT was aligned so that the centre of the field-of-view was
positioned at the centre of the blackbody cavity and the DUT focused on the
aperture plate. The calibration was performed using a combination of
calibration tables as detailed in the result tables.

The calibration was performed by recording, at each radiance temperature: the
mean digital level of the measurement region over the measurement period. The
average of twelve measurements over a period of $2\text{\,}\mathrm{min}$ was
used for each radiance temperature setpoint.

Table 2.5: The results from calibration using each configuration for the cooled thermal imager, with the Integration Time (IT) defined in each column. † denotes repeat measurements. | DUT Measurement / Digital Level
---|---
Range / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  5 …100 |  5 …150 |  40 …200 |  60 …225
t90 / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ IT / $\text{\,}\mathrm{\SIUnitSymbolMicro s}$ |  500 |  175 |  75 |  50
5.0 |  19293 |  18627 |  - |  -
5.0 † |  19294 |  - |  - |  -
5.1 † |  - |  18637 |  - |  -
20.0 |  19766 |  18787 |  - |  -
40.1 |  20758 |  19123 |  - |  -
59.8 † |  22320 |  19686 |  18842 |  18659
60.0 |  22283 |  19653 |  18840 |  18657
79.8 |  24774 |  20526 |  - |  -
79.9 |  - |  - |  19211 |  18904
99.1 |  28174 |  21716 |  19722 |  19242
124.4 |  - |  24059 |  - |  -
124.5 |  - |  - |  20729 |  19913
150.0 |  - |  27536 |  22218 |  20906
150.0 † |  - |  27500 |  22202 |  20896
174.6 |  - |  - |  24197 |  22229
199.5 |  - |  - |  26926 |  24050
199.6 † |  - |  - |  26892 |  24025
225.3 |  - |  - |  - |  26470

The measurements depicted in Figure 2.19 were used to populate the cal
calibration files of the thermal imager and a validation of this calibration
was then carried out. At each of the temperature setpoints from the
calibration measurements, the instrument apparent radiance temperature was
measured against ITS-90 (presented in Table 2.6). The difference between the
ITS-90 and instrument temperature is shown in Figure 2.20. The error bars
indicate the standard uncertainty multiplied by a coverage factor, providing a
coverage probability of approximately $95\text{\,}\mathrm{\char 37\relax}$.

Table 2.6: Results from the validation using each configuration for the cooled thermal imager, with the integration time defined in each column. | DUT Measurement / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---
Range / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  5 …100 |  5 …150 |  40 …200 |  60 …225
t90 / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ IT / $\text{\,}\mathrm{\SIUnitSymbolMicro s}$ |  500 |  175 |  75 |  50
5.0 |  7.7 |  9.5 |  - |  -
20.0 |  20.2 |  19.9 |  - |  -
40.2 |  40.3 |  40.5 |  43.8 |  -
59.9 |  60.2 |  59.7 |  58.0 |  61.6
79.7 |  79.6 |  79.9 |  79.5 |  78.7
98.9 |  99.1 |  99.3 |  98.9 |  98.5
124.6 |  - |  124.4 |  124.2 |  123.9
150.0 |  - |  149.4 |  149.8 |  149.7
174.8 |  - |  - |  174.6 |  174.6
199.6 |  - |  - |  199.1 |  199.5
225.2 |  - |  - |  - |  225.1
$18000$$19000$$20000$$21000$$22000$$23000$$24000$$25000$$26000$$27000$$28000$$29000$$0$$50$$100$$150$$200$$250$

Digital Level / [a.u.]

Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$$500\text{\,}\mathrm{\SIUnitSymbolMicro
s}$$175\text{\,}\mathrm{\SIUnitSymbolMicro
s}$$75\text{\,}\mathrm{\SIUnitSymbolMicro
s}$$50\text{\,}\mathrm{\SIUnitSymbolMicro s}$ Figure 2.19: Measurements from
the calibration of the cooled thermal imager. The digital level measured using
the prepared calibration files at increasing temperatures of ITS-90.
-0.8-0.6-0.4-0.20.00.20.40.60.81.0$0$$50$$100$$150$$200$$250$

Temperature Difference / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$$500\text{\,}\mathrm{\SIUnitSymbolMicro
s}$$175\text{\,}\mathrm{\SIUnitSymbolMicro
s}$$75\text{\,}\mathrm{\SIUnitSymbolMicro
s}$$50\text{\,}\mathrm{\SIUnitSymbolMicro s}$ Figure 2.20: The validation
measurements of the calibrated thermal imager. These measurements show the
temperature difference between ITS-90 and the apparent radiance temperature
from the thermal imager. The lowest temperature setpoint for each integration
time has been omitted due to a poor calibration fit. The error bars indicate
the expanded uncertainty. The markers have been artificially offset to improve
error bar discernability.

The validation measurements were carried out at each temperature setpoint the
calibration was carried out at. Major offsets up to
$-4.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ at the lowest temperature
setpoint for each integration time were observed, and large offsets for the
second lowest for both the $50\text{\,}\mathrm{\SIUnitSymbolMicro s}$ and
$75\text{\,}\mathrm{\SIUnitSymbolMicro s}$ were also observed. This is likely
due to the lower saturation point of $18\,500\text{\,}\mathrm{DL}$ being too
low and causing an inadequate fit from digital level to ITS-90; this noise
floor was increased to $19\,300\text{\,}\mathrm{DL}$. Because of this the
temperature ranges of each integration time for later measurements were
changed to reflect this. For the majority of the integration times across
their complete temperature range the temperature difference is centred about
$0\text{\,}\mathrm{\SIUnitSymbolCelsius}$ with respect to the uncertainties.

#####  2.3.8.2 Distance results

Uncooled

A measurement was carried out at five distances between the DUT and blackbody
cavity at a temperature of nominally
$99.9\text{\,}\mathrm{\SIUnitSymbolCelsius}$. These measurements are presented
in Table 2.7.

Table 2.7: The results from distance effect assessment for the uncooled thermal imager. The DUT temperature was determined using Eq. 2.4 with the measured coefficients (Table 2.4). Distance / $\text{\,}\mathrm{mm}$ |  DUT Digital Level Measurement / [a.u.] |  FPA Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  DUT Measurement / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---|---
75 |  36800 |  31.4 |  101.5
85 |  36800 |  31.4 |  101.4
95 |  36800 |  31.0 |  101.3
105 |  36800 |  31.1 |  101.2
115 |  36700 |  31.2 |  100.9

The effect of distance variation is nominally
$0.6\text{\,}\mathrm{\SIUnitSymbolCelsius}$ across this range of distances.

Cooled

A measurement was carried out at four distances between the DUT and blackbody
cavity at a temperature of $170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ using
the two appropriate integration times. These measurements are presented in
Table 2.8.

Table 2.8: The results from distance effect assessment for the cooled thermal imager. Distance / $\text{\,}\mathrm{mm}$ | DUT Measurement / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---
|  $50\text{\,}\mathrm{\SIUnitSymbolMicro s}$ |  $75\text{\,}\mathrm{\SIUnitSymbolMicro s}$
450 |  169.40 |  169.46
470 |  169.32 |  169.39
500 |  169.20 |  169.27
520 |  169.11 |  169.19

The results demonstrate good agreement between the two integration times and
that the effect of distance variation is less than
$0.29\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

#####  2.3.8.3 SSE results

Uncooled

An assessment of the size-of-source effect was carried out at
$100\text{\,}\mathrm{\SIUnitSymbolCelsius}$ using apertures from
$9\text{\,}\mathrm{mm}$ to $40\text{\,}\mathrm{mm}$. The measurement region
was taken to be the $$13$\times$13\text{\,}\mathrm{px}$$ region at the
centrally-aligned coordinates $(161,130)$. These measurements are presented in
Table 2.9. The size-of-source effect measurements in Table 2.9 are the mean of
three independent measurement sets and the size-of-source effect value is
calculated as the ratio of indicated radiance measurement compared to the
radiance measurement at the largest aperture.

Table 2.9: The results from the size-of-source effect assessment for the uncooled thermal imager. The DUT Temperature was determined using Eq. 2.4. Aperture / $\text{\,}\mathrm{mm}$ |  DUT Measurement / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  Size-of-Source Effect
---|---|---
9 |  97.8 |  0.9788
12 |  98.5 |  0.9855
15 |  99.0 |  0.9903
20 |  99.5 |  0.9953
25 |  99.7 |  0.9980
30 |  99.9 |  0.9996
40 |  99.9 |  1.0000

Cooled

An assessment of the size-of-source effect was carried out at
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ using apertures from
$9\text{\,}\mathrm{mm}$ to $40\text{\,}\mathrm{mm}$. These measurements are
presented in Table 2.10. The size-of-source effect measurements in Table 2.10
are the mean of three independent measurement sets and the size-of-source
effect value is calculated as the ratio of indicated radiance measurement
compared to the radiance measurement at the largest aperture.

Table 2.10: Results from the size-of-source effect measurements for each integration time from the cooled thermal imager. | $50\text{\,}\mathrm{\SIUnitSymbolMicro s}$ | $75\text{\,}\mathrm{\SIUnitSymbolMicro s}$
---|---|---
Aperture / $\text{\,}\mathrm{mm}$ |  DUT Measurement / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  Size-of-Source Effect |  DUT Measurement / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  Size-of-Source Effect
9 |  168.5 |  0.9805 |  168.4 |  0.9798
12 |  168.7 |  0.9858 |  168.7 |  0.9850
15 |  168.9 |  0.9881 |  168.9 |  0.9885
20 |  169.0 |  0.9908 |  169.0 |  0.9917
25 |  169.2 |  0.9943 |  169.2 |  0.9945
30 |  169.3 |  0.9964 |  169.3 |  0.9955
40 |  169.6 |  1.0015 |  169.5 |  1.0000

#####  2.3.8.4 Uncertainty assessment

Uncooled

The calculated measurement uncertainty for each measurement setpoint is shown
in Table 2.11. The reported expanded uncertainties are based on standard
uncertainties multiplied by the coverage factor, $k$, given in the table,
providing a coverage probability of approximately $95\text{\,}\mathrm{\char
37\relax}$.

The uncertainty values in the table include components for the: calibration of
the reference source, stability of the reference source, stability of the DUT,
size-of-source effect reproducibility, uniformity across the central
$$262$\times$262\text{\,}\mathrm{px}$$, the residual of the calibration fit,
stability over a $30\text{\,}\mathrm{min}$ period, the effect of distance
variation, the alignment to the mirror and the manufacturer stated noise
equivalent temperature difference.

Table 2.11: The measurement uncertainties of the uncooled DUT from the data measured. t90 / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  Uncertainty / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  $k$
---|---|---
10 |  2.50 |  2.0
20 |  2.15 |  2.0
30 |  2.20 |  2.0
40 |  1.85 |  2.1
50 |  1.95 |  2.1
60 |  2.10 |  2.1
70 |  2.30 |  2.0
80 |  2.40 |  2.0
90 |  2.75 |  2.0
100 |  3.20 |  2.0

Cooled

The calculated measurement uncertainty for each measurement setpoint is shown
in Table 2.12. The reported expanded uncertainties are based on standard
uncertainties multiplied by the coverage factor, $k$, given in the table,
providing a coverage probability of approximately $95\text{\,}\mathrm{\char
37\relax}$.

The uncertainty values in the table include components for the: calibration of
the reference source, stability of the reference source, stability of the DUT,
resolution of the DUT, size-of-source effect reproducibility and the
repeatability of the calibration. Effects from distance variation or detector
uniformity have not been accounted for.

Table 2.12: The measurement uncertainties of the cooled DUT from the data measured. Range / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  20…100 |  20…150 |  60…200 |  80…225
---|---|---|---|---
IT / $\text{\,}\mathrm{\SIUnitSymbolMicro s}$ |  500 |  175 |  75 |  50
Uncertainty / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  0.50 |  0.35 |  0.30 |  0.30
$k$ |  2.3 |  2.2 |  2.2 |  2.2

###  2.4 Calibration summary

In comparison between the radiation thermometer and the thermal imagers
evaluated the radiation thermometer is able to achieve the lowest
uncertainties that are the closest to the best achievable CMCs; and between
the two imagers the cooled thermal imager achieved lower uncertainties. A
comparison between the uncertainty components considered for the three
instruments are presented in Table 2.13. These results are displayed in Figure
2.21.

Table 2.13: A comparison between the uncertainty components considered for each of the instruments: radiation thermometer, uncooled thermal imager and a cooled thermal imager. Uncertainty Component |  Radiation Thermometer |  Uncooled Thermal Imager |  Cooled Thermal Imager
---|---|---|---
DUT stability |  $\checkmark$ |  $\checkmark$ |  $\checkmark$
NPL reference sources |  $\checkmark$ |  $\checkmark$ |  $\checkmark$
SSE reproducibility |  $\checkmark$ |  $\checkmark$ |  $\checkmark$
Transfer function residual |  $\checkmark$ |  $\checkmark$ |  $\checkmark$
DUT resolution |  $\checkmark$ |  |  $\checkmark$
Alignment |  $\checkmark$ |  |
Distance effect |  |  $\checkmark$ |
Drift |  |  $\checkmark$ |
Mirror alignment |  |  $\checkmark$ |
NETD |  |  $\checkmark$ |
ROI uniformity |  |  $\checkmark$ |
0.00.51.01.52.02.53.03.5050100150200250

Exapanded Uncertainty / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$ThermometerUncooledCooledCMCs Figure
2.21: The uncertainties detailed in the corresponding case study tables for
the radiation thermometer, uncooled thermal imager and cooled thermal imager
respectively. These have been normalised to a coverage factor of $2.0$ and are
shown against the CMC capability.

The uncooled thermal imager uncertainty budget is the most comprehensive and
considers the greatest number of sources. The radiation thermometer and cooled
thermal imager consider similar sources of uncertainty, where the thermal
imager omits an alignment component.

A large temperature dependence for the uncooled thermal imager measurement
uncertainty is observed and the source of this is the non-uniformity
component. The largest contributors to the larger uncertainties for the
thermal imagers in these case studies compared to the radiation thermometer
are due to: non-uniformity, temporal stability and repeatability. The latter
two can be addressed by improving the thermal stability of the environment
local to the thermal imager, the former can also be addressed through greater
uniformity across the detector but is largely subject to the required field of
view size of the application.

Results from the thermometer and cooled thermal imager are similar and appear
dwarfed by the uncooled imager, but it should be noted that a non-uniformity
was not considered within the cooled thermal imager case study. Specific
consideration to the instrument in use should be made because it is expected
this behaviour varies from instrument to instrument.

###  2.5 Conclusion

Chapter 2 introduced the core concepts supporting radiance temperature
measurement including thermal imager apparent radiance temperature
calibration. For the calibration of radiation thermometers, a reference source
of a known temperature and high emissivity should be used; this source may
achieve this temperature stability and appropriate emissivity through: zoned
furnace design, specialised coatings, narrow cylindrical cavities and heat-
pipe liners. These furnaces are typically scoped to accommodate the
temperature range from
$-60\text{\,}\mathrm{\SIUnitSymbolCelsius}1000\text{\,}\mathrm{\SIUnitSymbolCelsius}$
and can enable calibration uncertainties from
$0.05\text{\,}\mathrm{\SIUnitSymbolCelsius}0.3\text{\,}\mathrm{\SIUnitSymbolCelsius}$
($k=2$). The calibration of a radiation thermometer – a Heitronics TRT IV.82 –
against the available reference sources was completed; the results from an
ITS-90 comparison were presented, alongside the size-of-source effect
assessment and the resultant instrument uncertainties of less than
$1.0\text{\,}\mathrm{\SIUnitSymbolCelsius}$ across this range.

Deploying the reference sources for radiation thermometers to the calibration
of thermal imagers introduces limitations to characterisation. The aperture
diameter to the sources are typically close to $50\text{\,}\mathrm{mm}$ and so
subtend a small fraction of the field of view for thermal imagers under test.
This constrains the scope of the assessment to a local region of the image
array and does not enable a full characterisation of the array uniformity.
Beholden to these constraints, a calibration of both a cooled and uncooled
thermal imager against the respective sources was carried out and best
attempts to measure the uniformity was made. Each imager was successfully
calibrated and each of the assessments made, the uncooled and cooled thermal
imagers demonstrated uncertainties from
$1.85\text{\,}\mathrm{\SIUnitSymbolCelsius}3.20\text{\,}\mathrm{\SIUnitSymbolCelsius}$
($k=2$) and from
$0.35\text{\,}\mathrm{\SIUnitSymbolCelsius}0.50\text{\,}\mathrm{\SIUnitSymbolCelsius}$
($k=2$) respectively in the temperature range from
$10\text{\,}\mathrm{\SIUnitSymbolCelsius}100\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

To apply a calibrated apparent radiance temperature from either a radiation
thermometer or thermal imager to an application, to compare to other surface
thermometry methods, a correction for the non-unity emissivity and thermal
surroundings must be made. Introduced in Chapter 3 a comparison between
different radiance correction methods will highlight the situations in which
each approximation demonstrates an acceptable deviation in accuracy.

The techniques described within this chapter have provided a framework for
approaching and evaluating radiance temperature measurements using a thermal
imager and have introduced the concepts pertinent to low uncertainty
measurement. In Chapter 3, the methods presented will be used to characterise
a plate of stainless steel and in Chapter 4 they will be used to assess a
special nuclear material container in an inactive store. Calibration of the
measured data is pertinent in these applications because the enable
measurements of a single container to be reliably monitored from year to year
to ensure appropriate management decisions can be made.

##  Chapter 3 Laboratory Surface Temperature Characterisation

###  3.1 Introduction

Throughout Chapter 2 calibration methods for thermal imagers were explored and
the use of emissivity to determine radiance temperature introduced. Prior to
deploying a thermal imager to measure the surface temperature of inactive
nuclear material containers the measurement capability within a laboratory
environment was explored. Within the controlled laboratory scenario a
representative surface to the storage containers was designed, manufactured
and characterised. With the assistance of an uncertainty budget analysis the
surface temperature measured by a set of thermocouples and a thermal imager
was made.

The two containers evaluated were the Magnox and THermal Oxide Reprocessing
Plant (THORP) Special Nuclear Material (SNM) containers used by Sellafield
Ltd. Accessibility to SNM containers in stores is limited due to required
control measures but ongoing monitoring and inspection is a necessity to
retain confidence in, plan and manage storage. The non-contact
characterisation of container integrity and activity using instrumentation
translated along an inspection rail to view the container surfaces would
provide Sellafield with critical information to support nuclear material
management decisions. External surface temperature has the ability to provide
insight to the internal temperature that is analogous to the radioactivity of
the contents.

Non-destructive testing methods applied to SNM evaluation include:
radiographic, ultrasound, eddy current, magnetic particle and penetrant
testing. These each have their merits and drawbacks that make them suitable
for their respective inspection activities [52]. In particular eddy current
inspection of nuclear material containers has been demonstrated alongside an
automated maintenance inspection facility [53]. Additional testing methods
include phosphor thermometry, this has been applied to a range of nuclear
material containers [54, 55, 3].

Thermal imaging is an optical instrumentation technique that measures the
apparent surface radiance temperature from objects within its field of view.
The determination of surface temperature can be inferred as well as an
evaluation of surface properties through geometrical characterisation of the
thermal imager.

Deployment of a thermal imager for the maintenance of SNM containers could
enable both a non-destructive technique for surface inspection (either through
passive or active thermal imaging [56]) and the surface temperature
measurement of containers to infer internal radioactivity characteristics [3,
57]. Thermal imaging is beneficial over visual imaging [58] in this
application due to the absence of illumination within the stores that does not
inhibit thermal imaging; to enable optical inspection methods a local
illumination source would be required, introducing further sources of error.

The thermal imager was calibrated up to
$225\text{\,}\mathrm{\SIUnitSymbolCelsius}$ to ensure complete calibration
temperature coverage, however given that the surface emissivity of the plate
was much lower than $1.0$, the highest apparent radiance temperature measured
was $130\text{\,}\mathrm{\SIUnitSymbolCelsius}$. It was anticipated that the
container temperature would have ranged from
$10\text{\,}\mathrm{\SIUnitSymbolCelsius}200\text{\,}\mathrm{\SIUnitSymbolCelsius}$
and its environmental temperature from
$10\text{\,}\mathrm{\SIUnitSymbolCelsius}60\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

A thermal management assembly was designed and manufactured. To support an
adjacent defect detection capability study, a series of surface artefacts were
engineered and dimensionally characterised. Whilst the detection capability
for these artefacts will not be discussed, the comparison between radiance
temperature and thermocouple measured surface temperature will be explored.

A set of radiance correction methods will be cross-examined within the scope
of thermal conditions relevant to this application. Here their suitability in
a variety of thermal environments will be profiled.

###  3.2 Experimental setup

In order to validate the measurement capabilities on a controlled system prior
to nuclear material container assessment, a plate was designed and
characterised; this plate is one component within a larger thermal management
assembly. The plate was designed to simulate the material type used in the
application for storage of special nuclear materials with a range of
considerations to minimise sources of uncertainty. The measurement campaign
comprises a measurement of each face of the designed plate, one of these faces
was coated with higher emissivity targets and the reverse side omitted these.
These faces were defined as coated and uncoated respectively.

Once assembled, this plate was observed with a cooled Medium-Wave InfraRed
(MWIR) thermal imager (the InfraTec ImageIR 8300 described in the Section
2.3.8 case study), the radiance temperature determined was compared with that
temperature measured by sub-surface thermocouples.

####  3.2.1 Defect definition

An independent thread of research within this project was the detection of
surface defects using a thermal imager. The four types of artefact that were
investigated both in the coated and uncoated configurations were: scratches,
dents, thinning and pitting. It was expected that scratches, dents and pitting
would introduce geometrical emissivity enhancement, that would be observable
as an apparent radiance temperature step-change. Internal thinning would
introduce measurable surface temperature perturbations; corrosion and surface
contamination would also lead to a change in the apparent radiance
temperature. The specifications for these defects are described below.

A scratch will be defined as a vee-groove with nominally a
$45\text{\,}\mathrm{\SIUnitSymbolDegree}$ slope gradient. Scratch depth is the
distance between the apex of the groove and the height of the neighbouring
surface. This is shown in Figure 3.1a. The width is the distance between the
two top edges of the vee. The length of the scratch is the end-to-end distance
of the groove. The depth is the vertical distance between the apex and the top
edge of the groove.

Dents are ellipsoidal impressions in a surface, this are shown in Figure 3.1b.
The depth of the impression is the distance between the top edge and the
centre of the base. The diameter is the distance between two top edges where
the impression begins.

Surface thinning is a recess into a surface, this is shown in Figure 3.1c. The
depth of the recess is the distance between the top edge and the base. The
diameter is the distance between the two top edges where the recess begins.

Surface pitting is a random array of cylindrical voids of a specified diameter
and depth, this is shown in Figure 3.1d. The diameter of the void distance
between the two top edges where the void begins. The depth of the voids is
defined and identical. The arrangement of the voids is arbitrary but is
localised to the artefact region.

Each of these defects will introduce a change to the surface emissivity due to
geometrical enhancement, this will be measured by the apparent radiance
temperature images of the surface.

Figure 3.1a Scratch defect.  Figure 3.1b Dent defect.

Figure 3.1c Thinning defect.  Figure 3.1d Pitting defect.

Figure 3.1: The array of surface defects engineered and their geometrical
definition.

####  3.2.2 Assembly manufacture

The primary considerations for low uncertainty surface temperature
determination are: high rate of heat transfer from the heating element to
radiating surface, low and known heat loss mechanisms, sufficient contact
thermometer coverage, and known and low uncertainty photo-thermal properties
for the radiating surface. The assembly components are shown in Figure 3.2.

Figure 3.2a Cross-section of the assembly.

Figure 3.2b Lateral view of the plate.

Figure 3.2: The assembly designed for this investigation. (a) Cross-section of
the assembly, from inside to out: radiating plate, thermal conductor plate,
heater and housing. (b) Lateral view comprising the defect zones and coated
reference targets. From left to right, the thermocouples located in each
channel were 0, 1, 2 and 3 respectively.

The housing, insulator and conductor components have been manufactured by
ProTec Ltd (Leamington Spa) and the heater was manufactured by Hawco Limited
(Godalming). The insulator was machined from a cement based high-temperature
insulation board Sindanyo H91, which has a thermal conductivity of
$0.5\text{\,}\mathrm{W}\text{\,}{\mathrm{m}}^{-1}\text{\,}{\mathrm{K}}^{-1}$
and a wall thickness of $20\text{\,}\mathrm{mm}$. The conductor plate is
$5\text{\,}\mathrm{mm}$ thick aluminium with $4\text{\,}\mathrm{mm}$ by
$2\text{\,}\mathrm{mm}$ profile thermometer channels. The radiating plate is a
$1\text{\,}\mathrm{mm}$ thick piece of stainless steel 316L with a cross-
section size of $200\text{\,}\mathrm{mm}$ by $160\text{\,}\mathrm{mm}$.

The plate defect zones were manufactured by both ProTec Ltd and the Mass
Metrology group within NPL. ProTec used a three-axis Computer Numerical
Control (CNC) machine with a $0.1\text{\,}\mathrm{mm}$ tolerance. The pitting
was manufactured using centre drills, the scratches and thinning were
manufactured using a $12\text{\,}\mathrm{mm}$ carbide slot drill. The dents
were manufactured using a range of ball bearings mounted within an Avery 7110
compression machine that were loaded up to $30\text{\,}\mathrm{kN}$. From left
to right (in Figure 3.2b) the dents were manufactured using a
$10\text{\,}\mathrm{mm}$ ball bearing under $10\text{\,}\mathrm{kN}$,
$20\text{\,}\mathrm{kN}$ and $30\text{\,}\mathrm{kN}$ load, and a
$40\text{\,}\mathrm{mm}$ ball bearing under $10\text{\,}\mathrm{kN}$,
$20\text{\,}\mathrm{kN}$ and $30\text{\,}\mathrm{kN}$ load respectively.
Following the defect manufacturing the $20\text{\,}\mathrm{mm}$ square
reference targets were coated with Senotherm Ofen-spray schwarz 17-1644-702338
in order to ensure a higher emissivity region for surface radiance temperature
measurement. From previous experience and similar coatings, it is anticipated
that the emissivity of this material to be close to 0.85 [59], this was not
measured due to project resource constraints. The completed assembly is shown
in Figure 3.3.

Figure 3.3: The manufactured assembly comprising from left to right the:
insulator, conductor, plate and heater element. The blue marking indicates the
regions prior to dent manufacturing.

####  3.2.3 Assembly setup

The plate was setup according to the schematic in Figure 3.2, one control
thermocouple was mounted to the heater surface (refer to Figure 3.3). Four
monitoring thermocouples were located within the thermometer channels, one per
channel, from left to right the thermocouples in each channel were 0, 1, 2 and
3 respectively. The monitoring thermocouples were connected to a Fluke 1586A
Super-DAQ Precision Temperature Scanner (S/N: 44000054). Each channel was
configured as a type K thermocouple and using the same internal reference
point. The plate and thermocouple locations are shown in 3.4. The thermal
imager was mounted $20\text{\,}\mathrm{\SIUnitSymbolDegree}$ from the surface
normal of the plate and at a distance of $480\text{\,}\mathrm{mm}$ from
nominally the plate to the front of the lens, this is presented in Figure 3.5.
This angle of observation ensures a reflection component from the plate is
located at the shroud and not from the cooled detector of the thermal imager
itself. At this angle, the distance from centre of the lens to both the far
and near edges on the plate varied from
$490\text{\,}\mathrm{mm}450\text{\,}\mathrm{mm}$.

To improve conductive heat transfer from the heater through to the plate, a
pair of clamps were used with anodised aluminium blocks to apply pressure to
the top of the plate. During the measurements a shroud was placed over the
imager and assembly to reduce background reflection variations and natural
convection.

For the uncoated surface measurements, the same setup was used, albeit the
plate was reversed such that the pitting defects remained the farthest defect
from the thermal imager, then the blocks were replaced.

Figure 3.4: The finished plate is shown, the thermocouple locations are
indicated by crosses. Figure 3.5: Schematic of the MWIR thermal imager
observing the plate. The imager is $20\text{\,}\mathrm{\SIUnitSymbolDegree}$
from the surface normal and $480\text{\,}\mathrm{mm}$ from nominally the plate
to the front of the lens and at its closest point the imager was
$450\text{\,}\mathrm{mm}$ from the plate.

###  3.3 Assembly assessment

The assembly was configured as described in Section 3.2, a description of the
system temperature characteristics will be presented in the characterisation
section followed by the uncertainty budget and a discussion. During the
campaign the measurements were captured over $2\text{\,}\mathrm{min}$ periods
for each integration time at each heater setpoint using the cooled thermal
imager calibration detailed in Section 2.3.8. The apparent radiance
temperature measurements will be corrected using the method detailed in
Section 3.3.1 and subsequently explored in detail in Section 3.4.3.

####  3.3.1 Surface temperature determination

For this apparent radiance temperature correction method, first the apparent
spectral radiance must be considered with respect to the local environment.
Radiance from a surface $L_{\lambda,b}$ is defined by the Planck distribution
law as detailed in Section A.1.2 as

$L_{\lambda,b}(\lambda,T_{b})=\frac{c_{1}}{\lambda^{5}}\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{b}}}}-1}\mathrm{.}$ (3.1)

Here $c_{1}$ and $c_{2}$ are the first and second radiation constant,
$\lambda$ is the wavelength of radiation and $T_{b}$ is the surface
temperature.

Using the Kirchhoff law, an equivalence between the apparent radiance
$L_{app}$, emissivity and shroud radiance $L_{\lambda,b}^{shroud}$
(anticipated reflective component detailed in Section 3.2.3 and corresponding
temperature measured by a nearby hygrometer) is given by

$L_{app}=\varepsilon
L_{\lambda,b}+\left(1-\varepsilon\right)L_{\lambda,b}^{shroud}\mathrm{.}$
(3.2)

This approximation assumes that the reflections are all in the specular
direction and there are no diffuse contributions. Solving Eq. 3.2 for the
surface temperature under this approximation gives

$T_{b}=\frac{c_{2}}{\lambda}\ln\left[\varepsilon\left[\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1}-\frac{\left(1-\varepsilon\right)}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{shroud}}}}-1}\right]^{-1}+1\right]^{-1}\mathrm{.}$ (3.3)

This correction can be used to determine the surface temperature using the
measured temperatures, the estimated spectral mid-point and estimated
emissivity of surfaces under inspection. It should be noted that usage of this
approximation does not consider: potential impact from further reflections,
how to assess the spectral dependency (integrate over the specific spectral
range of the system and optics used), the type of emissivity value used or a
transmission greater than 0. In particular, a single hemispherical total
emissivity value for a surface may be used, however the effect from
directional and spectral emissivity dependence is not accounted for.

####  3.3.2 Thermal characterisation

The plate and its temperature characteristics have been profiled during the
measurements at increasing heater temperature setpoints. The results from this
thermal validation are detailed in the following sections.

#####  3.3.2.1 Coated plate characterisation

Figure 3.6 shows the location and corresponding temperature from the thermal
imager and thermocouples during the $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$
and $170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ coated plate measurements. The
four measurements at the bottom correspond to the respective thermocouples.
The nine central values denote the emissivity corrected radiance temperatures
of the adjacent coated regions, assuming an emissivity of 0.85.

Figure 3.6a Temperature distribution at the
$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ temperature setpoint.

Figure 3.6b Temperature distribution at the
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ temperature setpoint.

Figure 3.6: The measured temperature distribution of the plate during coated
artefact measurements at (a) $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
(b) $170\text{\,}\mathrm{\SIUnitSymbolCelsius}$. The four measurements at the
bottom correspond to the respective thermocouples indicated by the crosses.
The nine central values denote the radiance temperatures of the adjacent
coated regions.

These measurements show that agreement between the radiance temperature and
the mean thermocouple temperature above the
$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ measurement is not demonstrated
when considering the respective measurement uncertainties (refer to Section
3.3.3).

The temperature distribution measured by the thermocouples indicates cooler
temperatures towards the edges of the plate which is anticipated due to the
higher heat transfer from the edges of the heater to the surrounding
insulator. However, this behaviour was not observed from the radiance
temperature measurements, the regions closer to the edge were hotter than at
the centre by up to $8\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

#####  3.3.2.2 Uncoated plate characterisation

For the uncoated plate measurements, the surface emissivity was estimated
using the apparent radiance temperature of the uncoated regions during the
coated plate measurements and comparing to the coated regions. The emissivity
of the stainless steel was estimated to be nominally 0.20. This value is
supported by existing literature reporting the hemispherical total emissivity
of polished stainless steel 316L to be nominally 0.26 at
$200\text{\,}\mathrm{\SIUnitSymbolCelsius}$ [60].

Figure 3.7a Temperature distribution at the
$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ temperature setpoint.

Figure 3.7b Temperature distribution at the
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ temperature setpoint.

Figure 3.7: The measured temperature distribution of the plate during uncoated
measurements at (a) $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and (b)
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$. The four measurements at the
bottom correspond to the respective thermocouples indicated by the crosses.
The nine central values denote the radiance temperatures of the adjacent
coated regions. Note that the defects are shown for context but both coated
regions and artefacts were present on the rear surface from view.

Compared to the coated plate measurements, there is much closer agreement
between the mean thermocouple temperature and radiance temperature. Similarly,
for the $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ measurement setpoint, the
respective temperature distributions between the thermocouple and radiance
temperatures are depicted in Figure 3.7. The surface artefacts are presented
in this image for context, the same regions of interest interrogated from the
surface radiance temperature images were applied to the uniform and smooth
surface at the rear of the target plate. The plate was flipped along its short
edge such that from the imager perspective the defects remain in the same
vertical order.

These measurements demonstrate identical thermocouple distribution to the
coated plate measurements at the conductor plane. The radiance temperature
range is also comparable at $10\text{\,}\mathrm{\SIUnitSymbolCelsius}$ to the
coated region measurements. However there is much closer agreement between the
mean thermocouple temperature and mean radiance temperature; the difference
between the mean temperatures during the coated measurement was
$16\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and here the mean difference is
$2\text{\,}\mathrm{\SIUnitSymbolCelsius}$. This may be due to the estimated
emissivity of 0.20 used. But this may also be a result of a variation in the
thermal conduction between the conductor and target plate due to a different
force applied from the clamped aluminium blocks.

####  3.3.3 Surface temperature uncertainty analysis

Each individual thermocouple and thermal imager uncertainty components have
been evaluated with respect to their uncertainty value, probability
distribution and sensitivity to the measurand. The standard uncertainty is
then combined in quadrature to determine a combined uncertainty. The
uncertainty budgets have been considered according to the Guide to Uncertainty
in Measurement [61].

Each component has been attributed to the respective instrumentation source
and further discretised into an intrinsic instrumentation uncertainty and an
extrinsic application uncertainty.

#####  3.3.3.1 Thermocouple uncertainty

Thermocouple uncertainty components are detailed here.

###### 3.3.3.1.1 Instrumentation

Standard tolerance

BS EN 60584-1:2013 Thermocouples describes the standard tolerance of a type K
thermocouple to be $1.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ or $0.004\cdot
T$ (where $T$ is the measured temperature in Celsius), whichever is larger
[62]. Given that the measurements in this application consider temperatures
below $375\text{\,}\mathrm{\SIUnitSymbolCelsius}$ this component is
consistently a rectangular distribution throughout each budget.

Thermometer bridge accuracy

The manufacturer stated accuracy for temperature measurement using
thermocouples is $0.2\text{\,}\mathrm{\SIUnitSymbolCelsius}$. This is applied
as a normal distribution component in each budget.

###### 3.3.3.1.2 Application

Measurement stability

The mean standard deviation of the four thermocouples over the measurement at
each temperature setpoint was calculated. This corresponds to the temporal
stability of the complete thermocouple assembly but does not consider the
spatial uniformity measured by the thermocouple arrays. The respective values
were applied as a normal distribution component in each budget.

#####  3.3.3.2 Thermal imager uncertainty

Thermal imager uncertainty components are detailed here. The application in
this case is the set of thermal response components responsible for
temperature determination.

###### 3.3.3.2.1 Instrumentation

Calibration

The calibration of the thermal imager is detailed in Section 2.3.8. This
includes components for: the calibration of the reference source, stability of
the reference source, stability of the imager, resolution of the imager, drift
of the reference source and the residual of the calibration fit. This varied
between the four integration times but was below
$0.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2.3$) and the appropriate
values were applied as a normal distribution to each budget.

Housing temperature stability

During each measurement, the housing temperature of the thermal imager was
recorded and the standard deviation during each respective dataset was applied
to the budgets as a normal distribution. The relationship between measured
temperature and the housing temperature is not one-to-one and is assumed to
have less of an effect than this and so this an over estimation of this
component. This effect however does not account for the variation of the
housing temperature in the laboratory from that during calibration.

Size-of-source effect

The size-of-source effect was evaluated as described in Section 2.3.8.3, the
repeatability of $0.18\text{\,}\mathrm{\SIUnitSymbolCelsius}$ was scaled from
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ to the respective temperatures
measured throughout each measurement. These values were applied as a
rectangular distribution component in each budget.

Distance effect

The distance effect was evaluated as described in Section 2.3.8.2 , the
repeatability of $0.29\text{\,}\mathrm{\SIUnitSymbolCelsius}$ was scaled from
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ to the respective temperatures
measured throughout each measurement. These values were applied as a
rectangular distribution component in each budget.

###### 3.3.3.2.2 Application

Region of interest uniformity

During each measurement set, the mean spatial standard deviation of apparent
radiance temperature measured by the thermal imager at the Regions Of Interest
(ROIs) was evaluated. This was considered as a normal distribution component
in each budget. The sensitivity function for this component is described by
Eq. 3.4. Where $T_{b}$ is the surface temperature, $T_{app}$ is the apparent
radiance temperature, $T_{amb}$ the ambient room temperature, $\varepsilon$
the hemispherical total emissivity, $\lambda$ the measurement wavelength and
$c_{2}$ the second radiation constant [63]. This sensitivity was derived from
Eq. 3.3,

$\displaystyle\begin{aligned} \frac{\partial T_{b}}{\partial
T_{app}}=&\left[\frac{c_{2}}{\lambda T_{app}}\right]^{2}\left[\varepsilon
e^{\nicefrac{{c_{2}}}{{\lambda T_{app}}}}\left(e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}-1\right)^{2}\right]\cdot\\\ &\left[\varepsilon
e^{\frac{c_{2}}{\lambda}\left(\frac{1}{T_{app}}+\frac{1}{T_{amb}}\right)}+\left(\varepsilon-1\right)e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}+e^{\nicefrac{{c_{2}}}{{\lambda T_{app}}}}\right]^{-1}\cdot\\\
&\left[\varepsilon\left(e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1\right)-e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}+e^{\nicefrac{{c_{2}}}{{\lambda T_{amb}}}}\right]^{-1}\cdot\\\
\ln&\left[1+\frac{\varepsilon}{\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1}+\frac{\varepsilon-1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}-1}}\right]^{-2}\mathrm{.}\end{aligned}$ (3.4)

Emissivity measurement

For the coated regions on the surface, the emissivity value of 0.85 was
approximated from the reference measurement [59]. This value was measured
using instrumentation with an uncertainty reported to be $0.04$ (no confidence
factor was reported, so was assumed to be 1). This value was applied as a
normal distribution to each measurement set. The sensitivity function for this
component is described by Eq. 3.5. The same uncertainty was used for both
coated and uncoated regions. This sensitivity was derived from Eq. 3.3,

$\displaystyle\begin{aligned} \frac{\partial
T_{b}}{\partial\varepsilon}=&\left[\frac{c_{2}}{\lambda}\right]\left[\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}-1}-\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1}\right]\cdot\\\ &\left[\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1}+\frac{\varepsilon-1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}-1}\right]^{-1}\cdot\\\
&\left[\varepsilon+\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1}+\frac{\varepsilon-1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}-1}\right]^{-1}\cdot\\\
\ln&\left[1+\frac{\varepsilon}{\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1}+\frac{\varepsilon-1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}-1}}\right]^{-2}\mathrm{.}\end{aligned}$ (3.5)

Emissivity interpretation

For the coated regions on the surface, the emissivity value of 0.85 was
approximated from the reference measurement [59]. This approximation was
evaluated based on emissivity data at three different temperatures and over
the spectral range from $2.7\text{\,}\mathrm{\SIUnitSymbolMicro
m}5.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The uncertainty incurred from
estimating from this data is $0.05$. This value was applied as a normal
distribution to each measurement set. The sensitivity function for this
component is described by Eq. 3.5. The same uncertainty was used for both
coated and uncoated regions.

Ambient temperature measurement

Due to the non-unity emissivity of the surfaces measured, the uncertainty of
the ambient temperature has an influence on the calculated surface
temperature. The measurement uncertainty of the calibrated hygrometer is
$0.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=1$) across the appropriate
temperature range and the variation of room temperature during each
measurement dataset remained below this value. This value was applied as a
normal distribution throughout each dataset using the sensitivity function
described by Eq. 3.6. This sensitivity was derived from Eq. 3.3,

$\displaystyle\begin{aligned} \frac{\partial T_{b}}{\partial
T_{amb}}=&\left[\frac{c_{2}}{\lambda
T_{amb}}\right]^{2}\left[\varepsilon\left(\varepsilon-1\right)e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}\left(e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1\right)^{2}\right]\cdot\\\ &\left[\varepsilon
e^{\frac{c_{2}}{\lambda}\left(\frac{1}{T_{app}}+\frac{1}{T_{amb}}\right)}+\left(\varepsilon-1\right)e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}+e^{\nicefrac{{c_{2}}}{{\lambda T_{app}}}}\right]^{-1}\cdot\\\
&\left[\varepsilon\left(e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1\right)-e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}+e^{\nicefrac{{c_{2}}}{{\lambda T_{amb}}}}\right]^{-1}\cdot\\\
\ln&\left[1+\frac{\varepsilon}{\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1}+\frac{\varepsilon-1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{amb}}}}-1}}\right]^{-2}\mathrm{.}\end{aligned}$ (3.6)

#####  3.3.3.3 Combined uncertainty budget

Considering the components introduced in Section 3.3.3.1 and Section 3.3.3.2,
an example complete budget is detailed for the temperature determination
methods used: thermocouple and thermal imager.

Table 3.1: An example complete uncertainty budget for temperature determination at the $170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ setpoint with the coated plate and $50\text{\,}\mathrm{\SIUnitSymbolMicro s}$ integration time. Each component is attributed to the respective instrument (thermocouple or thermal imager). The uncertainty, $u$, is reported in degrees Celsius except for the emissivity components, the necessary divisor, sensitivity, and the standard uncertainty, $U$, are presented. These were then combined in quadrature and multiplied by the coverage factor. Source |  $u$ |  Divisor |  Sensitivity |  $U$ / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---|---|---
Thermocouple
Tolerance |  1.50 |  1.73 |  1.00 |  0.87
Thermometry bridge accuracy |  0.20 |  1.00 |  1.00 |  0.20
Stability |  0.03 |  1.00 |  1.00 |  0.03
Expanded uncertainty ($k=2$) |  1.8
Thermal Imager
Calibration |  0.30 |  2.20 |  1.00 |  0.14
Housing temperature |  0.03 |  1.00 |  1.00 |  0.03
Size-of-source |  0.18 |  1.73 |  1.00 |  0.10
Distance |  0.29 |  1.73 |  1.00 |  0.17
ROI non-uniformity |  1.06 |  1.00 |  1.04 |  1.10
Emissivity measurement |  0.04 |  1.00 |  50.03 |  2.00
Emissivity interpretation |  0.05 |  1.00 |  50.03 |  2.50
Ambient temperature |  0.10 |  1.00 |  0.01 |  0.00
Expanded uncertainty ($k=2$) |  6.8

Table 3.1 describes the complete budget describing the measurements at the
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ temperature setpoint for the
coated plate using the $50\text{\,}\mathrm{\SIUnitSymbolMicro s}$ integration
time. Each component is attributed to the instrument it originates from and
either an intrinsic instrumentation uncertainty or extrinsic application
uncertainty. The uncertainty value $u$ is reported as degrees Celsius unless
otherwise stated (for the emissivity components). The divisor describes the
probability distribution of the component, either a normal or rectangular
distribution. The sensitivity is 1.00 for surface temperature components but
requires conversion for other units to a standard uncertainty in degrees
Celsius. For each instrumentation and application, the respective component
standard uncertainties were combined in quadrature. The combined uncertainty
includes both instrumentation and application uncertainty components and
multiplies by $2$ for a $95\text{\,}\mathrm{\char 37\relax}$ confidence
interval.

A reduced summary of the measurement uncertainty at each coated region of
interest temperature setpoint is presented in Table 3.2, the equivalent values
for the uncoated measurements are presented in Table 3.3. These describe the
greatest uncertainty between the relevant integration times for each
temperature setpoint.

Table 3.2: A summary of the instrumentation, application and combined measurement uncertainties for each temperature setpoint during the coated plate measurements. These values correspond to the respective uncertainty budgets (refer to Table 3.1) constructed for each measurement. The greatest of the appropriate integration time uncertainties at each setpoint is reported. | Thermocouple Uncertainty / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ | Thermal Imager Uncertainty / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---
Temperature Setpoint / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  Instrument |  Application |  Expanded ($k=2$) |  Instrument |  Application |  Expanded ($k=2$)
30 |  0.9 |  0.0 |  1.8 |  0.2 |  0.5 |  1.0
70 |  0.9 |  0.0 |  1.8 |  0.2 |  1.7 |  3.4
110 |  0.9 |  0.1 |  1.8 |  0.3 |  2.4 |  4.8
130 |  0.9 |  0.1 |  1.8 |  0.3 |  2.8 |  5.5
150 |  0.9 |  0.0 |  1.8 |  0.2 |  3.1 |  6.2
170 |  0.9 |  0.0 |  1.8 |  0.2 |  3.4 |  6.8
Table 3.3: A summary of the instrumentation, application and combined measurement uncertainties for each temperature setpoint during the uncoated plate measurements. These values correspond to the respective uncertainty budgets (refer to Table 3.1) constructed for each measurement. The greatest of the appropriate integration time uncertainties at each setpoint is reported. | Thermocouple Uncertainty / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ | Thermal Imager Uncertainty / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---
Temperature Setpoint / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  Instrument |  Application |  Expanded ($k=2$) |  Instrument |  Application |  Expanded ($k=2$)
30 |  0.9 |  0.0 |  1.8 |  0.2 |  2.1 |  4.2
70 |  0.9 |  0.0 |  1.8 |  0.2 |  8.1 |  16.2
110 |  0.9 |  0.0 |  1.8 |  0.3 |  11.1 |  22.1
130 |  0.9 |  0.0 |  1.8 |  0.3 |  12.4 |  24.7
150 |  0.9 |  0.0 |  1.8 |  0.3 |  13.6 |  27.3
170 |  0.9 |  0.1 |  1.8 |  0.3 |  15.1 |  30.1

These show that thermocouple measurement is dominated by the standard
manufacturer tolerance component; addressing this would require calibrated
thermometers with a traceable calibration. The application components
contribute the most to the thermal imager temperature measurement, in
particular the largest of which are the emissivity and measured spatial non-
uniformity. It is unclear whether the ROI uniformity is a result of the
thermal imager detector non-uniformity, variation in coating emissivity (due
to application method) or a surface temperature variation.

The uncertainty of the emissivity measurement is an assumed value and so does
not correspond to a value reported through a calibration certificate. Despite
this, the sensitivity function (Eq. 3.5) indicates that the magnitude of this
component is primarily a result of the apparent and ambient temperature
difference, and non-unity emissivity.

####  3.3.4 Discussion

Evaluation of the plate measurements in both coated and uncoated
configurations was presented in the preceding sections. The dimensional
characterisation results are discussed in detail in the published manuscript
[64]. Section 3.3.2 broadly summarised the contact thermocouple and surface
radiance temperatures; an excerpt of the surface temperature distributions is
presented. The primary route of heat loss from the system was conduction
through the base of the insulator and from convection at the surface was
identified. The uncertainty analysis is detailed in Section 3.3.3, the
individual components for each system are introduced, an example budget is
stated and the combined uncertainties are presented for the different
measurement conditions.

Determination of radiance temperature from apparent radiance temperature
requires a good knowledge of the surface emissivity for accurate measurements.
In a simple case that assumes only one instance of reflection, and that both
the object surface and ambient environment possess spectrally independent and
Lambertian emissivity, the surface temperature can be solved through Planck’s
law [63].

When comparing the temperatures for the coated plate: thermocouple and surface
radiance temperatures shown in Figure 3.6 there is poor broad agreement, up to
$1.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$ at the
$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ setpoint and
$16\text{\,}\mathrm{\SIUnitSymbolCelsius}$ at the
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ setpoint. For these measurements a
comparison between the nine ROIs shown in Figure 3.7 (numbered in reading
order), the radiance temperature and the surface temperature evaluated from
the thermocouples are presented in Figure 3.8.

Through the $70\text{\,}\mathrm{\SIUnitSymbolCelsius}$,
$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
$130\text{\,}\mathrm{\SIUnitSymbolCelsius}$ temperature setpoints there is a
stratification of thermocouple values where each of the three central ROIs
measured greater temperatures than radiance temperature measurements. This is
caused by the large non-uniformity between thermometer channels (refer to
Figure 3.4) and is not observed by the thermal imager data. This may be a
result of an air gap between the plate and conductor plate growing in size due
to thermal expansion and heat transfer reducing. Visual inspection of images
captured during testing indicate the flexibility of the target plate has
resulted in some bowing for the central region of the plate. At
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$, the ROIs with the poorest
agreement to contact thermocouples are those along the top row and the central
column.

Additional sources of disparity between thermocouple and surface radiance
temperature measurement may be from variation in contact pressure between the
plate and conductor plate due to inconsistent clamp force. A comparison
between the mean thermocouple temperature measured at identical heater
temperature setpoints during the coated (Figure 3.6) and uncoated (Figure 3.7)
measurements demonstrate less than $1\text{\,}\mathrm{\SIUnitSymbolCelsius}$
difference ($2\text{\,}\mathrm{\SIUnitSymbolCelsius}$ at the
$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ setpoint) and so this is
considered to be negligible in this case with respect to the thermocouple
measurements.

For the uncoated plate measurements a comparison between the nine ROIs shown
in Figure 3.6, the radiance temperature and an approximation of the surface
temperature evaluated from the thermocouples is presented in Figure 3.9.

Due to the increased sensitivity for the emissivity components for the thermal
imager temperature determination, the error bars are the dominant feature in
this comparison. Compared to the coated measurements, there is better
agreement between the methods up to
$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$. This suggests that the assumed
emissivity value for stainless steel is more appropriate than that used for
the Senotherm coating. It is clear from these results the importance for low
uncertainty emissivity measurement when using radiance temperature techniques,
which is especially critical when measuring reflective surfaces.

25.026.027.028.029.030.031.0$1$$2$$3$$4$$5$$6$$7$$8$$9$525456586062646668$1$$2$$3$$4$$5$$6$$7$$8$$9$7580859095100105$1$$2$$3$$4$$5$$6$$7$$8$$9$859095100105110115120$1$$2$$3$$4$$5$$6$$7$$8$$9$100105110115120125130135140$1$$2$$3$$4$$5$$6$$7$$8$$9$115120125130135140145150155160$1$$2$$3$$4$$5$$6$$7$$8$$9$

Surface Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ SetpointThermal
ImagerThermocouple$70\text{\,}\mathrm{\SIUnitSymbolCelsius}$
Setpoint$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint

\makebox(0.0,0.0)[]{{} }

$130\text{\,}\mathrm{\SIUnitSymbolCelsius}$ SetpointROI
Identifier$150\text{\,}\mathrm{\SIUnitSymbolCelsius}$
Setpoint$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint Figure 3.8: A
comparison between the surface temperature determinations from the thermal
imager and thermocouples with their equivalent uncertainties ($k=2$) at each
temperature setpoint. The ROI identifier corresponds to the nine coated
regions as shown in Figure 3.6 numbered in reading order.
2224262830323436$1$$2$$3$$4$$5$$6$$7$$8$$9$45505560657075808590$1$$2$$3$$4$$5$$6$$7$$8$$9$708090100110120130$1$$2$$3$$4$$5$$6$$7$$8$$9$8090100110120130140150$1$$2$$3$$4$$5$$6$$7$$8$$9$100110120130140150160170$1$$2$$3$$4$$5$$6$$7$$8$$9$110120130140150160170180190$1$$2$$3$$4$$5$$6$$7$$8$$9$

Surface Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ SetpointThermal
ImagerThermocouple$70\text{\,}\mathrm{\SIUnitSymbolCelsius}$
Setpoint$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint

\makebox(0.0,0.0)[]{{} }

$130\text{\,}\mathrm{\SIUnitSymbolCelsius}$ SetpointROI
Identifier$150\text{\,}\mathrm{\SIUnitSymbolCelsius}$
Setpoint$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint Figure 3.9: A
comparison between the surface temperature determinations from the thermal
imager and thermocouples with their equivalent uncertainties ($k=2$) at each
temperature setpoint. The ROIs were observing the uncoated regions at
identical positions to the coated regions.

A deeper analysis into the correspondence between thermocouple and radiance
temperature can demonstrate a clear conclusion to the plate measurements. As
discussed previously, it is understood that as the plate distorts and due to
the fixed anchor points, the plate may have flexed in the centre.
Investigation into this distortion suggests this may have been up to
$0.1\text{\,}\mathrm{mm}$ at the highest temperatures. A revised design was
not implemented due to the project time constraints. For a more robust
comparison between thermometry techniques, this leads to an omission of the
central column of regions of interest (ROI 2, ROI 5 and ROI 8) for the
analysis. Additionally the thermocouples were spatially located (as shown in
Figure 3.4) along the centre of the channels and so only those radiance
temperature ROIs were considered: i.e. ROI 4 and ROI 6. A reduced comparison