of the data in Figure 3.8 and Figure 3.9 is shown in Figure 3.10 and Figure
3.11.

25.526.026.527.027.528.028.529.029.530.030.546565758596061626364468284868890929446100102104106108110112461141161181201221241261281304613013213413613814014214414646

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 3.10: A
reduced comparison between the surface temperature determinations from the
thermal imager and thermocouples at each temperature setpoint. This data is
from the coated region plate measurements shown in Figure 3.8.
22232425262728293031324650556065707580854675808590951001051101151201254690100110120130140150461001101201301401501601704612013014015016017018019046

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 3.11: A
reduced comparison between the surface temperature determinations from the
thermal imager and thermocouples at each temperature setpoint. This data is
from the uncoated region plate measurements shown in Figure 3.9.

Here it is shown for the coated measurements that there is good agreement
between the thermocouple and thermal imager at all temperatures within the
prescribed uncertainty. Aside from the
$70\text{\,}\mathrm{\SIUnitSymbolCelsius}$ setpoint, the data suggests the
radiance temperature is too low; therefore the emissivity correction applied
is not sufficient and a lower emissivity of 0.80 may be more suitable. For the
uncoated regions the thermocouple and radiance measurements are in agreement
at all temperature setpoints. In this case the radiance temperature is
typically greater than the contact measurement; therefore a greater emissivity
of 0.25 may be more appropriate. Both of these reduced dataset comparisons
support a moderate reduction in the measurement uncertainty of each
instrument, assuming the agreement with a thermal model can be demonstrated.

A tabular representation of the difference between radiance and thermocouple
temperature is presented in Table 3.4 and Table 3.5 for the coated and
uncoated measurements respectively. The corresponding differences for
respective emissivity values of 0.80 and 0.25 are also presented.

Table 3.4: Comparison between the temperature difference between the thermocouple and radiance temperature during the coated measurements. The original emissivity corresponds to 0.85 and this data is shown in Figure 3.10, and the revised emissivity is 0.80. Temperature Setpoint / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ | Original Temperature Error / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ | Revised Temperature Error / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---
|  ROI 4 |  ROI 6 |  ROI 4 |  ROI 6
30 |  1.5 |  1.4 |  1.2 |  1.0
70 |  0.4 |  -0.3 |  -1.0 |  -1.7
110 |  1.8 |  0.3 |  -0.1 |  -1.6
130 |  1.8 |  -0.2 |  -0.4 |  -2.4
150 |  2.2 |  4.1 |  -0.3 |  1.7
170 |  2.9 |  4.7 |  0.2 |  2.0
Mean Error |  1.8 |  1.7 |  -0.1 |  -0.2
Table 3.5: Comparison between the temperature difference between the thermocouple and radiance temperature during the uncoated measurements. The original emissivity corresponds to 0.20 and this data is shown in Figure 3.11, and the revised emissivity is 0.25. Temperature Setpoint / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ | Original Temperature Error / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ | Revised Temperature Error / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---
|  ROI 4 |  ROI 6 |  ROI 4 |  ROI 6
30 |  1.4 |  1.1 |  2.4 |  2.1
70 |  -8.0 |  -7.7 |  -2.5 |  -2.2
110 |  -9.2 |  -8.7 |  -1.6 |  -1.1
130 |  -10.1 |  -9.4 |  -1.6 |  -1.0
150 |  -11.5 |  -10.5 |  -2.1 |  -1.1
170 |  -12.5 |  -10.8 |  -2.2 |  -0.4
Mean Error |  -8.3 |  -7.7 |  -1.2 |  -0.6

These tables show that currently the largest offset for the surface
temperature measurement is for the
$-12.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ at
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ during the uncoated measurements.
Following an evaluation of the applied emissivity correction, the greatest
offset is reduced to $-2.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ at
$70\text{\,}\mathrm{\SIUnitSymbolCelsius}$ during the uncoated measurements.
Furthermore the mean error is greatly reduced for both regions of interest
during both coated and uncoated measurements. To determine this error, the
greatest magnitude of error at either setpoint was recorded in order to
identify an appropriate emissivity value. A visualisation of this emissivity
revision is shown in Figure 3.12 where the same uncertainties are presented
alongside revised surface temperature calculations for the thermal imager.

25.026.027.028.029.030.031.032.04656575859606162636465468486889092949646102104106108110112114461161181201221241261281301324613213413613814014214414614846

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 3.12:
Following the revised emissivity for the coated region measurements in Table
3.4, a comparison in the same form as Figure 3.10 is presented.

The uncertainty budgets for the surface temperature determination of high
emissivity regions detail the measurement uncertainty reaching
$6.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) at
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$. The intrinsic thermal imager
uncertainty is nominally consistent at
$0.3\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) across this temperature
range and as presented in Table 3.1, the greatest source of uncertainty for
temperature determination is from the emissivity measurement. The estimation
for emissivity uncertainty of approximately 0.05 is close to national
measurement institute grade measurement (as good as 0.01 ($k=1$) depending on
material) and so this particular component would reduce to a standard
uncertainty of $0.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Reduction of this
component further requires reducing the sensitivity component (Eq. 3.5) which
is dominated by the disparity between apparent and ambient temperatures as
opposed to the emissivity itself (refer to Figure 3.13).

$0$$10$$20$$30$$40$$50$$60$$70$$20$$40$$60$$80$$100$$120$$140$$160$$180$$200$

Emissivity Uncertainty Sensitivity / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Surface Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$$\varepsilon=\quad$0.85$\varepsilon=\quad$0.95$\varepsilon=\quad$0.9995
Figure 3.13: Functional form of the emissivity sensitivity (Eq. 3.5) for
increasing temperature at a number of emissivities. Note that this sensitivity
is largely dominated by the difference between apparent and ambient
temperatures and that the emissivity itself has a smaller effect.

It should be noted that these equations are dependent on the spectral response
of the instrument in use. Throughout these calculations a value of
$3.85\text{\,}\mathrm{\SIUnitSymbolMicro m}$ has been used, but if a long-wave
infrared instrument would be considered then that would result in greater
sensitivity coefficients throughout.

From these observations it is shown that the measurement of surface
temperature is a challenging task. It is affected by both differing materials
and varying surface properties, applying this to an application will require
careful consideration to each of these aspects.

####  3.3.5 Assessment summary

An aspect of surface (and by inference, internal) temperature measurement
using an external thermal imager was evaluated. The challenges introduced by
emissivity on radiance temperature measurement were explained in detail, with
the largest contributor to uncertainty being the absence of traceable
emissivity measurement. Verification of the surface radiance measurements
against the contact thermocouple temperatures indicated that there exist
discrepancies above $70\text{\,}\mathrm{\SIUnitSymbolCelsius}$ during the
coated region measurements and above
$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ during the uncoated region
measurements. These may be a result of the value of emissivity used throughout
the calculations or varying contact pressure across the plate. The systematic
offset observed during the coated measurements suggest the emissivity value
may be inappropriate, and this was supported by the different emissivity
results presented in Table 3.4 and Table 3.5. However the poor agreement
between two experimental temperature measurements would be supported if the
presence of a thermal gradient from thermometer channel to radiating surface
was present. An estimation of the surface emissivity was demonstrated and the
recalculation of temperature error between thermocouple and radiance
temperature, using this emissivity, enabled a reduction of error to
$1.2\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

###  3.4 Radiance correction methods

For radiance temperature measurement methods (e.g. radiation thermometers or
thermal imagers) to be deployed outside of a controlled laboratory environment
with approximated blackbody sources, the effect from emissivity on radiance
temperature must be considered. A selection of radiance correction methods
will be introduced and explored; specifically they will be compared with
respect to an existing thermal environment for the SNM containers. This study
should be considered independent from the laboratory assessment in Section
3.3, although there are conclusions to be made with implications there and in
the following chapter. Following the correction method comparison,
environments where the respective correction methods incur sufficiently low
uncertainty contributions will be presented.

Within the literature, the principles of radiance summation are detailed in
[63] and from this any series of radiance contributions to an observation
could be described. Summation of radiance contributions that are truncated to
that emitted from the surface and that reflected from the surface is typical
and often encountered [65, 66]. This presupposes that the radiance observed
from the surroundings originates from a blackbody source and not another
object with a non-unity emissivity; whilst this assumption can be made for
many environments this should be stated when used. Considering multiple
reflections as proposed in both [67, 68] provide robust methodologies for
considering all radiance contribution sources.

Consideration of the geometry within a thermal environment is considered in
[69, 70] where the view factor from an object to a target surface is
considered to ascertain its radiance contribution component in the emissivity
correction.

Alternative emissivity compensation techniques include: dual-wavelength
pyrometers, Fourier-transform infrared spectrometry or polarisation pyrometry
[71].

To evaluate the radiance correction methods the corrected radiance temperature
(representative of surface temperature) will be compared to the surface
temperature. For each of the correction methods under investigation ambient
environment and apparent radiance temperatures will be provided. A
representative spectral range for instrument response will be defined and a
set of traceable directional spectral emissivity data provided. To calculate
this apparent radiance temperature a known representative value of a complex
scenario must be known; this value may either be measured in a well defined
environment or simulated computationally. Under this comparison the baseline
that each correction method will be compared against will be the ray tracing
method introduced in Section 3.4.5, this method will be used to generate the
apparent radiance temperature interpreted by each correction method when
calculating surface temperature.

####  3.4.1 Environment setup

As introduced in Section 3.1, the thermal system being explored in this
chapter comprises the properties outlined in Table 3.6. The case study will
extend beyond the shrouded blackbody background by introducing a container
reflection.

Table 3.6: Constraints to the thermal system under investigation here are detailed, this includes the: instrument spectral range; surface and ambient temperature ranges; and the surface emissivity. The reflection container temperature is the initial reflection component in position one. Characteristic |  Description
---|---
Instrument spectral range |  $7.5\text{\,}\mathrm{\SIUnitSymbolMicro m}14.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$
Surface temperature range |  $10\text{\,}\mathrm{\SIUnitSymbolCelsius}200\text{\,}\mathrm{\SIUnitSymbolCelsius}$
Ambient temperature range |  $10\text{\,}\mathrm{\SIUnitSymbolCelsius}60\text{\,}\mathrm{\SIUnitSymbolCelsius}$
Reflection container temperature |  $50\text{\,}\mathrm{\SIUnitSymbolCelsius}$
Target container hemispherical total emissivity |  $0.06$ to $0.94$

Specifically the environment will comprise a pair of SNM containers within an
enclosure being observed from two positions, one where the reflection
component will include the second container and a second position where the
reflection component observes the enclosure wall. This enclosure arrangement
is shown in Figure 3.14, these images are rendered within pbrt-v3 (unmodified)
[72] and represent the relative radiance observed from each of the two
observation positions. Each of the parameters detailed in Table 3.6 will be
explored through a parametric study.

Figure 3.14a Position one.

Figure 3.14b Position two.

Figure 3.14: Construction of the radiance correction comparison environment.
The two containers are displayed and the two observation positions are either
side of the lower container. At position one the reflection container is in
the specular direction, at position two the walls are in the specular
direction.

Figure 3.14 describes the geometry of the test environment to be considered. A
pair of containers were positioned within a spherical environment at the
ambient temperature, the surface temperature of the observation container (the
lower container in 3.14) was set to the surface temperature variable. Two
positions were evaluated, position one will arrange the reflection container
(the higher container in 3.14) in the specular direction from the observation
surface position two arranges the walls in the specular direction from the
observation surface. Between test cases, the emissivity of the entire
observation container was described by the surface emissivity parameter.
Throughout all tests the reflection container was maintained at a temperature
of $50\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and demonstrate the medium
emissivity material. The walls were maintained at the ambient temperature and
will demonstrate an emissivity of a blackbody.

The three emissivity materials used – low, medium and high – correspond to
silica coated aluminium, stainless steel and a Nextel coating respectively.
Measurements for these materials are shown in Figure 3.15, low and medium
materials were acquired through commercial projects (and permitted for
dissemination) [2, 73, 74] and the high emissivity was reported by PTB [75].
The temperatures these were evaluated at were
$100\text{\,}\mathrm{\SIUnitSymbolCelsius}$,
$15\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
$120\text{\,}\mathrm{\SIUnitSymbolCelsius}$, respectively.

0.000.050.100.150.200.250.300.350.400.450.140.160.180.200.220.240.260.280.300.910.920.930.940.950.960.970.98891011121314

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

$10\text{\,}\mathrm{\SIUnitSymbolDegree}$$30\text{\,}\mathrm{\SIUnitSymbolDegree}$$50\text{\,}\mathrm{\SIUnitSymbolDegree}$$70\text{\,}\mathrm{\SIUnitSymbolDegree}$
Silica Coated Aluminium $\varepsilon=0.06$

Directional Spectral Emissivity / [a.u.]

Stainless Steel $\varepsilon=0.21$

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

Wavelength / $\text{\,}\mathrm{\SIUnitSymbolMicro m}$ Nextel
$\varepsilon=0.94$ Figure 3.15: Measured directional spectral emissivity data
used to describe the surfaces in the radiance correction comparison
environment. Each angle corresponds to the zenith angle the emissivity was
measured at, where $0\text{\,}\mathrm{\SIUnitSymbolDegree}$ denotes the
surface normal. The indicated value in each plot is the hemispherical total
emissivity used during one of the correction methods.

Silica coated aluminium is largely spectrally and angularly independent aside
from the region at $8\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The reflective
region is principally a result of the aluminium interaction with radiation as
detailed in literature [76]. Reflectivity of steel decreases as wavelength
increases and becomes more reflective at greater angles of incidence; the
Nextel is spectrally and angularly independent within its measurement
uncertainty.

####  3.4.2 Uncorrected radiance temperature

The scale of the realised error from omitting a correction for emissivity
depends entirely on the disparity between surface and ambient temperature and
the emissivity itself. In the event of surface temperature and ambient
temperature reaching equilibrium then regardless of the emissivity, apparent
radiance temperature will represent the surface temperature. Should there be a
difference between surface temperature and ambient temperature then the
emissivity will have a direct impact on the magnitude of incurred error. For
this scenario the radiance temperature $T_{b}^{unc}$ is given by Eq. 3.7,

$T_{b}^{unc}=T_{app}\mathrm{.}$ (3.7)

####  3.4.3 Multiple reflection single wavelength

For the Multiple Reflection Single Wavelength (MRSW) correction method, in
order to correct radiance temperature first the apparent spectral radiance
must be considered with respect to the local environment. This derivation
follows on from that in Section 3.3.1 and extends it to an additional
reflection instance. Radiance from a surface $L_{\lambda,b}$ is defined by the
Planck distribution law as detailed in Section A.1.2 as

$L_{\lambda,b}(\lambda,T_{b})=\frac{c_{1}}{\lambda^{5}}\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{b}}}}-1}\mathrm{.}$ (3.8)

Using the Kirchhoff law, an equivalence between the apparent radiance
$L_{app}$, target container emissivity, target container radiance
$L_{\lambda,b}^{target}$, reflection container emissivity, reflection
container radiance $L_{\lambda,b}^{reflection}$ and ambient radiance
$L_{\lambda,b}^{wall}$ under the assumption of two surface reflections is
given by

$L_{app}=\varepsilon^{target}L_{\lambda,b}^{target}+\left[1-\varepsilon^{target}\right]\left[\varepsilon^{reflection}L_{\lambda,b}^{reflection}+\left(1-\varepsilon^{reflection}\right)L_{\lambda,b}^{wall}\right]\mathrm{.}$
(3.9)

This approximation assumes that the reflections are all in the specular
direction and there are no diffuse contributions. Solving Eq. 3.9 for the
surface temperature under this approximation gives

$T_{b}^{mrsw}=\frac{c_{2}}{\lambda}\ln\left[\varepsilon^{target}\left[\frac{1}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{app}}}}-1}-\frac{\left(1-\varepsilon^{target}\right)}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{reflection}}}}-1}\right]^{-1}+1\right]^{-1}\mathrm{.}$ (3.10)

Equation 3.10 is valid for a single reflection instance where the reflection
container emissivity equals one. When an additional reflection is considered
such as the case in this radiance comparison the reflection container
temperature can be described by

$T_{reflection}=\frac{c_{2}}{\lambda}\left[\ln\left(1+\left(\frac{\varepsilon^{reflection}}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{\lambda,b}^{\prime
reflection}}}}-1}+\frac{1-\varepsilon^{reflection}}{e^{\nicefrac{{c_{2}}}{{\lambda
T_{\lambda,b}^{wall}}}}-1}\right)^{-1}\right)\right]^{-1}\mathrm{.}$ (3.11)

Where $T_{\lambda,b}^{\prime reflection}$ is the reflection container
temperature under this additional reflection condition. 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.

####  3.4.4 Multiple reflection all wavelengths

To develop from Section 3.4.3 for the Multiple Reflection All Wavelengths
(MRAW) method, the spectral response of the system can be introduced in the
approximation by integrating the spectral radiance over $\mathrm{d}\lambda$ to
determine the radiance. This will in turn require an extension beyond the
hemispherical total emissivity to the hemispherical spectral emissivity. Under
this approximation the spectral response of the imager, $r(\lambda)$, can be
introduced if known,

$L_{b}(T)=\int\limits_{\lambda}L_{\lambda,b}(\lambda,T)\cdot
r(\lambda)\mathrm{d}\lambda\mathrm{.}$ (3.12)

Using the same reflection assumption from Eq. 3.9, the surface temperature
using this approximation, $T_{b}^{mraw}$, can be computed. Contrary to Eq.
3.10, an analytical solution cannot be solved and instead this must be
approached numerically. Further to this the sensitivity coefficients can only
be understood through computation of their magnitude under different
environments.

The calculations for this method were made using software provided by Michael
Hayes, National Physical Laboratory. The software approximates the
calculations shown in Eq. 3.12 using the stated input parameters [73].

####  3.4.5 Ray tracing

An alternative to discrete descriptions of the system under the approximations
given above is to evaluate the complete system using ray tracing. One of the
core principles of ray tracing methods is to be physically based, which means
that the units and algorithms used are based on and constrained by the theory
of electromagnetism. Ray tracing is based on geomtrical optics rather than
wave optics and so does not consider interference or polarisation effects. For
the correction methods presented above they will each be compared using the
measurements simulated with this technique.

Reflectivity measurements have been used by graphical rendering groups within
the fields of video games and cinematography; however it has broader
applications for metrology in land and sea surface temperature measurements as
well as in the visualisation of painted materials, advertisements and product
descriptions. The lack of attention to physically-based models has limited its
use within research areas where robust physical descriptions are critical,
such as in architecture or the lighting industry.

A measured reflectivity databases (such as the Mitsubishi Electric Research
Laboratories database [77] can be processed within Monte Carlo rendering
engines such as: Hyperion by Disney [78], Arnold by Sony [79], the RTX
platform by NVIDIA, Filament by Google, pbrt originating from Stanford
university [72] and the Mitsuba renderer by Jakob [80]. It is through the use
of these rendering systems that the complete architecture from radiation
emission, to surface behaviour and radiation detection, can be evaluated and
an image generated.

The radiation transport equation employed by these rendering systems, which
describes the exitant radiance $L_{\lambda,o}(p;\theta_{r},\varphi_{r})$
incident on an image pixel from point $p$ on a surface in the scene is shown
in Eq. 3.13 [72],

$L_{\lambda,o}(p;\theta_{r},\varphi_{r})=L_{\lambda,em}(p;\theta_{r},\varphi_{r})+\int\limits_{0}^{2\pi}\int\limits_{0}^{\nicefrac{{\pi}}{{2}}}\rho(p;\lambda;\theta_{i},\varphi_{i};\theta_{r},\varphi_{r};T)L_{\lambda,i}(p;\theta_{i},\varphi_{i})\lvert\cos\theta_{i}\rvert\mathrm{d}\theta_{i}\mathrm{d}\varphi_{i}\mathrm{.}$
(3.13)

Where $L_{\lambda,em}(p;\theta_{r},\varphi_{r})$ is the emitted radiance;
$\rho(p;\lambda;\theta_{i},\varphi_{i};\theta_{r},\varphi_{r};T)$ is the Bi-
directional Reflectivity Distribution Function (BRDF) at point $p$; and
$L_{\lambda,i}(p;\theta_{i},\varphi_{i})$ is the incident radiance on the
surface. This BRDF is a principle component in the complete description of a
synthesised scene.

Using this ray tracing method alongside both known geometry of the system
including all sources of infrared radiation and their respective directional
spectral emissivities, an accurate estimation of the apparent radiance
temperature can be realised. The silica coated aluminium and stainless steel
materials were defined to be entirely specular, whilst the Nextel coating was
diffuse. It should be noted that whilst this method accounts for the behaviour
of multiple reflections, it is not a fully realised thermal model that
simulates the three heat transfer modes (i.e. increased radiative heat
transfer from container to container at higher surface emissivities).

Apparent radiance temperatures calculated using this method was parsed by the
two respective correction methods in Section 3.4.3 and Section 3.4.4. The
calculations for this method were made using software provided by Michael
Hayes, National Physical Laboratory. This software is based on a heavily
modified version of pbrt-v2 that appropriately handles the Planck distribution
radiometrically, input from directional spectral emissivity data and
atmospheric absorption [73].

####  3.4.6 Environment correction comparison

As described in Section 3.4.1, during this radiance correction comparison, the
parameter space to be explored is defined by Table 3.6. Within this space, for
the two observation positions described in Figure 3.14 and for the three
observation container surface emissivities, the temperature difference between
corrected and defined surface temperature will be presented through an
intensity plot; this difference is described by Eq. 3.14 where
$T_{b}^{\prime}$ is the corrected surface temperature for the respective
methods (e.g. $T_{b}^{unc}$, $T_{b}^{mrsw}$ or $T_{b}^{mraw}$),

$\Delta T=T_{b}^{\prime}-T_{b}\mathrm{.}$ (3.14)

Any unique approaches taken by either of the correction methods are described
in the corresponding sections above. These results are shown in Figure 3.16
through Figure 3.21; where the value is close to zero, the method correction
error is minimal. To facilitate interpretation of the plots and their varied
colour bar scales, a green highlighted region is overlaid; this denotes the
region about zero (corresponding to zero correction error) and spans a single
standard deviation from the respective results array. The magnitude of these
low correction error regions are detailed in the figure captions; this region
can be used to identify comparable low uncertainty regions between the plots.

20406080100120140160180200102030405060102030405060102030405060

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

-160-100-4020Uncorrected

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

Ambient Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$04812Temperature
Difference / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$MRSW

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

-200-120-4040MRAW Figure 3.16: Position one, emissivity 0.06. The standard deviation of the datasets indicating the highlighted ranges are: $51.4\text{\,}\mathrm{\SIUnitSymbolCelsius}$, $3.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and $30.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$. 204060801001201401601802001020304050602040608010012014016018020010203040506020406080100120140160180200102030405060

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

-150-100-500Uncorrected

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

Ambient Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$024681012Temperature Difference /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$MRSW

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

-95-55-152565MRAW Figure 3.17: Position two, emissivity 0.06. The standard deviation of the datasets indicating the highlighted ranges are: $52.0\text{\,}\mathrm{\SIUnitSymbolCelsius}$, $3.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and $30.0\text{\,}\mathrm{\SIUnitSymbolCelsius}$. 204060801001201401601802001020304050602040608010012014016018020010203040506020406080100120140160180200102030405060

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

-120-80-40040Uncorrected

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

Ambient Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$0246810Temperature Difference /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$MRSW

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

-3-2-101234MRAW Figure 3.18: Position one, emissivity 0.21. The standard deviation of the datasets indicating the highlighted ranges are: $39.9\text{\,}\mathrm{\SIUnitSymbolCelsius}$, $2.3\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and $1.2\text{\,}\mathrm{\SIUnitSymbolCelsius}$. 204060801001201401601802001020304050602040608010012014016018020010203040506020406080100120140160180200102030405060

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

-125-80-3510Uncorrected

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

Ambient Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$0246810MRSW

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

-2-10123Temperature Difference / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$MRAW Figure 3.19: Position two, emissivity 0.21. The standard deviation of the datasets indicating the highlighted ranges are: $40.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$, $2.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and $1.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$. 204060801001201401601802001020304050602040608010012014016018020010203040506020406080100120140160180200102030405060

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

-4-3-2-1012Uncorrected

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

Ambient Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$-2-101234Temperature Difference /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$MRSW

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

-1.0-0.7-0.4-0.10.20.5MRAW Figure 3.20: Position one, emissivity 0.94. The standard deviation of the datasets indicating the highlighted ranges are: $1.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$, $1.3\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and $0.2\text{\,}\mathrm{\SIUnitSymbolCelsius}$. 204060801001201401601802001020304050602040608010012014016018020010203040506020406080100120140160180200102030405060

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

-4-3-2-1012Uncorrected

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

Ambient Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$-2-101234Temperature Difference /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$MRSW

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

-0.7-0.5-0.3-0.10.10.3MRAW Figure 3.21: Position two, emissivity 0.94. The standard deviation of the datasets indicating the highlighted ranges are: $1.4\text{\,}\mathrm{\SIUnitSymbolCelsius}$, $1.3\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and $0.2\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

Throughout these comparisons it can be observed that for all methods, as the
emissivity increases, the magnitude of error decreases; nominally the error
decreases from
$217\text{\,}\mathrm{\SIUnitSymbolCelsius}1\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

For an uncorrected radiance temperature the largest underestimation occurs in
the upper-left region and the low error region is consistently where
$T_{b}\approx T_{amb}$. Under the high emissivity container the range in error
across the parameter space is reduced to
$7\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

For the MRSW correction the range of error decreases from
$14.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$, through
$10.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ to
$5.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$ as the emissivity increases. For
the wall reflection environment (position two) the parameter space is linear
from the upper-left to lower-right region, where the largest correction error
is when the surface temperature is high whilst ambient temperature is low. For
large regions of the parameter space, the MRSW correction is close to zero and
does not incur a large error (demonstrated by the wide highlighted bands).

At lower observation container emissivities where the radiance contribution
from the reflection container (position one environment) becomes greater, a
local minima of error is shown about the reflection container temperature. For
the medium emissivity environment a minor deformation of the highlighted
region from position two to position one is shown that increases the
correction error at regions further from the reflection container temperature
(in both planes). For the low emissivity environment this deformation is
greater due to the larger contribution to apparent radiance temperature from
the walls.

During the plate measurements in Section 3.3 the MRSW correction was applied.
Across this narrow parameter space (surface temperatures from
$20\text{\,}\mathrm{\SIUnitSymbolCelsius}80\text{\,}\mathrm{\SIUnitSymbolCelsius}$
and ambient temperatures from
$21\text{\,}\mathrm{\SIUnitSymbolCelsius}23\text{\,}\mathrm{\SIUnitSymbolCelsius}$)
that could be represented by position two with the wall in the specular
direction from the uncoated stainless steel, the incurred temperature error
from this correction method was from
$-0.3\text{\,}\mathrm{\SIUnitSymbolCelsius}0.4\text{\,}\mathrm{\SIUnitSymbolCelsius}$.
Therefore the correction used was suitable in this application.

For the MRAW correction the range of error decreases from
$303\text{\,}\mathrm{\SIUnitSymbolCelsius}$, through
$6.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ to
$1.0\text{\,}\mathrm{\SIUnitSymbolCelsius}$ as the emissivity increases. This
large reduction of error suggests the MRAW method is too sensitive to
uncertainty in the input parameters as a result from the low emissivity. For
the medium and high emissivity comparisons the MRAW correction demonstrates
the lowest correction error across each of the parameter spaces. The region of
lowest error occurs when $T_{b}\approx T_{amb}$, this is demonstrated in
Figure 3.23 when the apparent radiance temperature passes through the stated
ambient temperature and is because the contributions from all sources for the
apparent radiance are comparable. A local region of large correction error
occurs when the surface temperature is low and ambient temperature is high
(lower-right region).

Between positions one and two, the difference in correction error is more
apparent at lower emissivities because the radiance contribution from the
reflection on the observation container increases. This shows that the
approximations made by each method are applicable for most background
environments in the specular direction, but care must be taken when the
difference between the reflection container and wall surface temperatures is
great (for example when outside of the shaded green region). This may be
likely in a case study of the SNM store where a hot container is in the
specular direction but was suitable for the laboratory investigation detailed
in this chapter.

####  3.4.7 Emissivity uncertainty

When accounting for the effect on surface temperature measurement from
emissivity uncertainty, this can be evaluated depending on the correction
method used. The multiple reflection single wavelength method from Section
3.4.3 was used in the representative test case in this chapter (refer to
Section 3.3), this analytical solution enables a direct sensitivity analysis
for each parameter to be calculated. By evaluating the partial differential of
surface temperature with respect to emissivity, this sensitivity can be
identified (refer to Eq. 3.5).

A comparison between the magnitude of this emissivity uncertainty component
with respect to the temperature parameters defined in Table 3.6 is shown in
Figure 3.22. For the estimated material properties, the emissivity uncertainty
is $0.2$ ($k=1$); for the three measured emissivity values the estimated
emissivity uncertainty was $0.008$ ($k=1$), $0.024$ ($k=1$) and $0.006$
($k=1$) respectively.

0102030405060$20$$60$$100$$140$$180$050100150200250300$20$$60$$100$$140$$180$01002003004005006007008009001000$20$$60$$100$$140$$180$0.00.20.40.60.81.01.21.41.61.8$20$$60$$100$$140$$180$0.00.51.01.52.02.53.03.5$20$$60$$100$$140$$180$0510152025303540$20$$60$$100$$140$$180$

Expanded Emissivity Uncertainty Component /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$

Estimated Nextel

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

$10\text{\,}\mathrm{\SIUnitSymbolCelsius}$$60\text{\,}\mathrm{\SIUnitSymbolCelsius}$Estimated
Steel

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

Estimated Si-Al

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

Measured NextelSurface Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$Measured SteelMeasured Si-Al Figure
3.22: The emissivity uncertainty component for a potential surface temperature
measurement budget in both a $10\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
$60\text{\,}\mathrm{\SIUnitSymbolCelsius}$ environment. Estimated materials
have a $0.2$ $\left(k=1\right)$ uncertainty and measured materials are $0.006$
$\left(k=1\right)$, $0.024$ $\left(k=1\right)$ and $0.008$ $\left(k=1\right)$
respectively. The emissivity values are $0.94$, $0.21$ and $0.06$ for Nextel,
steel and silica coated aluminium respectively.

From these results it is clear that for most materials when the ambient
temperature is greater, the corresponding uncertainty component is minimised
due to the reduced difference between ambient and surface temperatures. For
the lower emissivity measured material, this reaches close to
$50\text{\,}\mathrm{\SIUnitSymbolCelsius}$ in the most extreme case, but this
remains much lower than the estimated material impact that approaches
$1000\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

The sensitivity of surface temperature determination is shown in Figure 3.13
with a $20\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ambient background
temperature, for three different emissivity values, the difference between
apparent radiance temperature and calculated surface temperature at increasing
surface temperatures is shown in Figure 3.23. For a surface of 0.85
emissivity, a measured apparent radiance temperature of
$200\text{\,}\mathrm{\SIUnitSymbolCelsius}$ will be nominally
$10\text{\,}\mathrm{\SIUnitSymbolCelsius}$ below the surface temperature;
additionally the difference in temperature error at this temperature between
an emissivity of 0.85 and 0.99 is $9\text{\,}\mathrm{\SIUnitSymbolCelsius}$.
Further, the equivalent difference in error between emissivity values of 0.26
and 0.40 is $35\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Therefore the
importance of low uncertainty emissivity measurement (traceable and
metrologically determined) for surface temperature determination using a
thermal imager is clear. The gradient of the error increases for materials of
lower emissivities and so the scope for higher uncertainties increases when
measuring surfaces with lower emissivity. The effect of this is presented in
Table 3.3 where the contribution from emissivity – with similar emissivity
uncertainty – has a greater effect on the standard uncertainty.

-40-30-20-1001020304050607020406080100120140160180200

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

Apparent Radiance Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$$\varepsilon=0.40$$\varepsilon=0.85$$\varepsilon=0.99$
Figure 3.23: The difference between the apparent radiance and surface
temperature for three materials with a
$20\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ambient temperature and using an
instrument with the same spectral response as used in the measurements from
this chapter.

####  3.4.8 Summary

Throughout the subsequent laboratory and in-situ measurements, a
simplification of the MRSW radiance correction method has been implemented.
This could be described by using Eq. 3.10 and assuming the reflection surface
is a blackbody, this was equivalent to the scenario in position two. To
ascertain the suitability of this method an investigation into its behaviour
across a range of surface and ambient temperatures, a set of measured
emissivities and a pair of background reflection profiles. This was baselined
against an uncorrected measurement and another correction method that
considered both the spectral response of emissivity and thermal imager
response.

It was shown that the magnitude of correction error increases for lower
emissivity materials due to the disparity between surface and apparent
radiance temperatures. The MRSW correction method was largely appropriate
across each of the six environments but incurred the largest errors when the
surface temperature was much greater than the ambient temperature. The region
of lowest error typically occurred when the surface temperature was
approximately equal to the ambient temperature; this was deviated from during
the MRSW measurements with the reflection container in the specular direction
(position one). Contrary to expectations, the MRAW method was not able to
successfully correct the radiance temperature under all conditions and
demonstrated large errors during the low emissivity computations.

###  3.5 Conclusions

The primary objectives of this study were to investigate and evaluate the
feasibility of using a thermal imager to measure container surface
temperature, in order to monitor container activity for ongoing container
monitoring and management.

The primary activities undertaken in this investigation were:

  1. 1.

Design and manufacture of a thermal management assembly

  2. 2.

Thermal evaluation of the target plate

  3. 3.

Assessment of measurement capability through an uncertainty budget review

  4. 4.

Definition of radiance correction methods

  5. 5.

Quantitative comparison of correction methods

Both surface and internal temperatures were evaluated using the plate and
there was reasonable agreement between the experimental measurements in most
instances. Utilisation of a cooled thermal imager in laboratory conditions
demonstrated the state-of-the-art with regard to instrumentation and
controlled environment measurement; deployment to an active store will
necessitate a reduction in hardware form factor and specifications to uncooled
microbolometers (due to the instrument size) to accommodate the store
assessment port size. Employing a microbolometer will marginally increase
instrumentation uncertainty but this component is not anticipated to
significantly affect the overall uncertainty budget, with the largest
uncertainty still remaining as the surface emissivity uncertainty. The reduced
operational stand-off poses a more challenging optical configuration using
wide field of view lenses where image distortion is greater, this will be
further investigated in the following in-situ deployment experiment in Chapter
4.

During the plate measurements, unanticipated assembly spatial non-uniformity
increased the measurement uncertainty achieved by the thermal imager and
reduced the confidence in surface temperature determination for a number of
regions of interests. Additional measures to improve this uniformity have been
identified to be deployed for future studies using the plate. This would also
be supplemented with further reduced uncertainty contact thermometers.
Following a detailed investigation into the experienced non-uniformity –
principally plate distortion – the agreement between the thermal imager
radiance and thermocouple temperature was within the measurement uncertainties
and close to anticipated levels. There was moderate agreement between the
experimental surface temperature measurements during the plate campaign, for
the high emissivity coated regions the mean temperature difference across all
temperature setpoints was $1.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$; for the
lower emissivity uncoated regions this difference increased to
$8.3\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Outstanding discrepancies between
these methods are believed to be caused by an incomplete description of the
thermal pathways present in the laboratory system. In all cases the lack of
robust emissivity data was the dominant component in temperature determination
uncertainty budgets, leading to an expanded temperature measurement
uncertainty up to $6.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$). The
absence of this data becomes more prevalent when measuring surface of high
reflectivity because it scales non-linearly with temperature and the
uncertainty reached $30.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$).

During the laboratory measurements the insight and progress made towards
successful deployment of a thermal imager to an active container store was
significant. The design and manufacture of the plate, as well as the
supporting measurement data and future improvements have produced an effective
tool in the characterisation of a thermal imager for artefact detection
through the appropriate range of temperatures. Instrumentation of the plate
enabled good thermal management and robust thermometry, as well as providing
insight into the thermal distribution that may be present in active
containers.

During the radiance correction comparison the magnitude of correction error
increased at lower emissivities from
$5.8\text{\,}\mathrm{\SIUnitSymbolCelsius}14.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$
(for the MRSW method) as a result of the increased difference between surface
and apparent temperatures. The correction method used through the plate
measurements was demonstrated to be suitable across the majority of the
parameter space and had a low incurred error spanning
$0.7\text{\,}\mathrm{\SIUnitSymbolCelsius}$ within the region of these
measurements.

The laboratory assessment observations here are specific to these materials:
stainless steel 316L and a Senotherm coating on this steel; when investigating
real world surfaces, the effect from changing surface properties (e.g. surface
wear, corrosion or powder deposition) should be evaluated. As discussed in
Section 3.3.3 the sensitivity of uncertainty components evaluated were
dependent on each of the input parameters and radiance correction method
employed. As a rule of thumb the sensitivity – and by inference – temperature
uncertainty increases both as the surface emissivity decreases and when the
apparent radiance temperature differs greatly from the ambient temperature.

The temperature measurement uncertainty budgets support the quality of the
thermal imager calibration carried out and the hardware used; across the
temperature range investigated the intrinsic components of the thermal imager
remained well below the manufacturer stated accuracy and within a reasonable
bounds of surface temperature determination applications. Given traceable
emissivity measurement, the confidence in surface temperature measurement will
improve greatly.

The principle conclusions to be drawn from this study are:

  1. 1.

Surface temperature measurement of containers with thermal imaging is feasible

  2. 2.

Temperature determination agreed to contact thermometers within the estimated
measurement uncertainties

  3. 3.

The proposed radiance correction method is appropriate within the application
parameter space

##  Chapter 4 Characterisation of Nuclear Storage Containers

###  4.1 Introduction

Chapter 3 explored a set of radiance correction methods and deployed one of
these to a laboratory environment and manufactured test plate. This deployment
was investigated further within this chapter through the use of instrumented
containers used in both a laboratory and a store environment. The two
containers evaluated are the THermal Oxide Reprocessing Plant (THORP) and
Magnox containers.

This chapter discusses the development of thermal mapping technology for in-
situ, periodic container monitoring. This thermal mapping was evaluated
through direct surface temperature comparisons between surface mounted
thermocouples and emissivity corrected radiance temperature measurements from
a thermal imaging system.

For each experimental setup, the suitability of a thermal imager for the
determination of surface temperature was evaluated. This comparison was drawn
against surface mounted thermocouples on the containers and considered beside
the respective uncertainty budgets and radiance correction methods. By doing
so, the viability of deploying a thermal imager to an active container store
was determined.

During the laboratory measurements a medium wave cooled thermal imager was
used to observe the instrumented containers. These containers had internal
thermocouples and heaters positioned, the external surface remained unchanged.

For the in-situ measurements a pair of long wave uncooled thermal imagers were
positioned perpendicularly to the surface, whilst a pair of off-axis mirrors
were used to direct the surface radiation from the container to the imagers.
For these measurements the internal instrumentation of the container was
nominally identical to the laboratory measurements; however the external
surface was instrumented with thermocouples, a high emissivity coating and a
series of both scratch and pitting artefact regions. This setup was then
placed within a test store at the James Fisher Nuclear Limited (JFNL) facility
to replicate an active warehouse setup.

This work used test Magnox and THORP containers instrumented to provide
equivalent temperatures to those containers held in store (i.e.
$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ to
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$), located in a replica test store
with an inspection system mounted on a rail below to provide equivalent set up
and access challenges to those posed by active stores.

Prior to deployment within the test store, the instrumented containers were
setup in a laboratory environment using the same instrumentation as the plate
in Chapter 3. During these measurements it was not possible to make a direct
comparison between temperature determination methods and instead a
computational model correction was introduced to the thermocouple analysis.
Despite this correction, the two methods did not compare favourably across the
entire temperature range.

Changes were made when moving to the test store environment and externally
mounted thermocouples were introduced. During this campaign instrumentation
challenges were encountered with the thermal stabilisation of the thermal
imagers. It was demonstrated that this stabilisation error could be mitigated
through rigorous procedure control and when this was omitted, the two
temperature determination methods compared favourably across a range of
temperatures and optical configurations.

A successful measurement campaign will progress the testing, assessment, and
uncertainty analysis for test containers in a replica store and provide
evidence for the suitability of this technique for further deployment.

###  4.2 Experimental setup

For both the laboratory and store measurements, a thermal imaging system was
positioned to observe the external surface of both THORP and Magnox containers
whilst surface mounted thermocouples evaluated surface temperatures.

For the two measurement campaigns two different thermal imaging systems were
used. In the laboratory a single cooled Medium-Wave InfraRed (MWIR) thermal
imager was used and during store measurements a pair of uncooled Long-Wave
InfraRed (LWIR) thermal imagers setup perpendicularly to the inspection
surface with corresponding off-axis mirrors. The specifications for each of
these three imagers are given in Table 4.1 as well as their mean Focal Plane
Array (FPA) temperatures during calibration. The thermal imager naming
conventions correspond to Wide Field Of View (WFOV) and Narrow Field Of View
(NFOV).

Table 4.1: The specifications of the thermal imagers used throughout the measurements. The MWIR imager was used during the laboratory measurements in Section 4.3. The two LWIR imagers were used during the store assessments in Section 4.4. Characteristic |  MWIR Imager |  WFOV LWIR Imager |  NFOV LWIR Imager
---|---|---|---
Manufacturer |  InfraTec |  FLIR |  FLIR
Model |  ImageIR 8300hp |  Boson |  Boson
Product code |  - |  20320H092-9PAAX |  20320A050-9CAAX
Serial number |  8312592 |  S0055574 |  S0032888
Detector |  Indium antimonide |  Vanadium oxide |  Vanadium oxide
Pitch |  $15\text{\,}\mathrm{\SIUnitSymbolMicro m}$ |  $12\text{\,}\mathrm{\SIUnitSymbolMicro m}$ |  $12\text{\,}\mathrm{\SIUnitSymbolMicro m}$
Resolution |  $640\times 512$$\text{\,}\mathrm{px}$ |  $320\times 256$$\text{\,}\mathrm{px}$ |  $320\times 256$$\text{\,}\mathrm{px}$
Spectral response |  $2.0\text{\,}\mathrm{\SIUnitSymbolMicro m}5.7\text{\,}\mathrm{\SIUnitSymbolMicro m}$ |  $7.5\text{\,}\mathrm{\SIUnitSymbolMicro m}14.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$ |  $7.5\text{\,}\mathrm{\SIUnitSymbolMicro m}14.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$
Noise equivalent temperature difference |  $<$$20\text{\,}\mathrm{mK}$ |  $<$$50\text{\,}\mathrm{mK}$ |  $<$$60\text{\,}\mathrm{mK}$
Lens horizontal field of view |  $22\text{\,}\mathrm{\SIUnitSymbolDegree}$ |  $92\text{\,}\mathrm{\SIUnitSymbolDegree}$ |  $50\text{\,}\mathrm{\SIUnitSymbolDegree}$
Lens focal length |  $25.0\text{\,}\mathrm{mm}$ |  $2.3\text{\,}\mathrm{mm}$ |  $4.3\text{\,}\mathrm{mm}$
Software |  IRBIS 3 (version 3.1.90) |  FLIR Boson Application (version 1.4.4) |  FLIR Boson Application (version 1.4.4)
Calibration FPA temperature |  $24.7\pm 2.7$$\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  $34.8\pm 0.3$$\text{\,}\mathrm{\SIUnitSymbolCelsius}$ |  $33.1\pm 0.5$$\text{\,}\mathrm{\SIUnitSymbolCelsius}$

####  4.2.1 Laboratory setup

Special Nuclear Material (SNM) is defined to be: plutonium, uranium-233 or
uranium-235 [81], these are usually stored in stainless steel 316 containers.
SNM containers will corrode over time and therefore it is important that
degradation is effectively monitored. Inspection of active SNM containers
requires high quality quantitative data to demonstrate that they will reach
their design lifetime. The detection of defects on the external surface of
containers is a technical challenge due to the harsh environment, reduced
access and requirement for non-contact inspection. Special nuclear materials
emit gamma rays and neutron radiation that may result in the production of
heat which can be measured by surface thermometry techniques.

The two container types provided by Sellafield, comprising both Magnox and
THORP designs (summarised in Figure 4.1), were inspected using a calibrated
cooled MWIR thermal imager (calibration described in Section 2.3.8 [32]). The
Magnox containers as provided did not have an intact Low-Density PolyEthylene
(LDPE) layer due to their previous heat treatment, instead the remnants of
this layer were observed on the appropriate surfaces. The two Magnox
containers each comprised the anticipated outer container, but the internal
container was the THORP filter-less internal container. The two THORP
containers each comprised one outer, one intermediate and one internal
container.

Figure 4.1: Two container types provided by Sellafield and their schematic
construction. The containers were measured from their longer edge.

For the Magnox measurements a typical Magnox stainless steel outer container
was used with the THORP inner container. For the THORP measurements the
appropriate outer, intermediate and inner containers were used together.

The internal container was instrumented with ten type K monitoring
thermocouples and two heater mats, these are shown in Figure 4.2. A schematic
of these thermocouple locations are shown in Figure 4.3.

Figure 4.2a Internal container with monitoring thermocouples affixed.

Figure 4.2b Internal container with heaters mounted above the monitoring
thermocouples.

Figure 4.2: The thermocouple and heater instrumentation of the inner
container. One thermocouple is attached to the far end side and one other to
the inside of the lid (not in view), three radially spaced
$65\text{\,}\mathrm{mm}$ from the far end, two radially spaced towards the
longitudinal centre ($130\text{\,}\mathrm{mm}$ from far end) and three
radially spaced $195\text{\,}\mathrm{mm}$ from the far end. The heater mats
were pressed against the inside wall and the affixed thermocouples facing the
centre. Figure 4.3: A schematic of the internal container instrumentation. The
dashed lines represent the heaters and the crosses indicate the location of
the ten thermocouples and their respective identification numbers. The
container is presented in its profile perspective and the end view corresponds
to the images in Figure 4.2.

The two heater mats were slightly mis-aligned with the central axis of the
container such that thermocouples 1, 4 and 6 were in closer contact with the
heater. The thermocouples were arranged to be equally distributed across the
length of the container and radially distributed around its circumference. A
pair of thermocouples were affixed to the bottom face and the lid at the
radial origin. The internal container was filled with the steel shot
originally packaged within the container (as a nuclear material proxy) and the
instrumentation cables directed through the appropriate lids.

Figure 4.4: The loaded internal container with the provided steel shot.

For the Magnox container measurements, the internal container was sealed shut
with the threaded lid. This was then placed within the outer container D33-5,
the outer container lid was sealed using high-temperature adhesive tape.

Figure 4.5: The internal container within the Magnox outer. The
instrumentation cables were passed through openings on both container lids and
the outer lid was held in place using high-temperature adhesive tape.

Following the Magnox container measurements, the internal container was
removed and placed within the intermediate THORP container. This was sealed
with high-temperature adhesive tape, placed within the THORP outer container
which was also sealed.

Figure 4.6: The internal container within the THORP intermediate, sealed and
then placed within the THORP outer container. The instrumentation cables were
passed through openings on each container lid, the intermediate and outer lids
were held in place using high-temperature adhesive tape. The bar code serves
as identification for the container whilst in storage.

During the measurements, the heater mats and two control thermocouples affixed
to each heater surface were controlled using bespoke Eurotherm controllers.
The ten monitoring thermocouples were located as shown in Figure 4.3, each was
monitored by the Fluke 1586A Super-DAQ Precision Temperature Scanner. The
thermal imager was mounted $18\text{\,}\mathrm{\SIUnitSymbolDegree}$ to the
normal from the base plane and at a distance of $450\text{\,}\mathrm{mm}$ and
$470\text{\,}\mathrm{mm}$ from the front of the lens, to the Magnox and THORP
containers respectively. This is sown in Figure 4.7.

During the measurements a shroud was placed over the imager and container to
reduce background reflection variations and natural convection.

Figure 4.7a Magnox configuration.

Figure 4.7b THORP configuration.

Figure 4.7c Perspective of configuration.

Figure 4.7: Schematic of the thermal imager observing the both the Magnox and
THORP container. The imager is $18\text{\,}\mathrm{\SIUnitSymbolDegree}$ from
the plane normal in both cases. There is a $450\text{\,}\mathrm{mm}$
separation to the Magnox container and $470\text{\,}\mathrm{mm}$ between the
imager and THORP container. The image shows the Magnox container prior to
inspection.

####  4.2.2 Store setup

The following section details the necessary preparatory activities and
experimental set up for the store measurements. Namely: thermal imager
calibration; instrumented container set up; and set up for store measurements
at the JFNL test store. The thermal imager calibration is described in Section
2.3, this calibration included the mirror setup so the calibrated apparent
radiance temperature accounted for the non-unity reflectivity of the mirrors.

#####  4.2.2.1 SNM container instrumentation

The two special nuclear material container types provided by Sellafield
comprising of both Magnox and THORP designs (summarised in Figure 4.1) were
each inspected using the pair of thermal imagers (one of which was detailed in
the uncooled thermal imager case study in Section 2.3.8).

For the THORP measurements, the appropriate inner, intermediate and outer
containers were used together. For the Magnox measurements, the Magnox outer,
THORP intermediate and THORP inner containers were used together; note that
this configuration differs from the laboratory configuration described in
Section 4.2.1.

The internal container was instrumented with nine monitoring thermocouples
(type K) and two heater mats, these are shown in Figure 4.8. A schematic of
these thermocouple locations is shown in Figure 4.9. The thermocouples were
directly fixed to the surface using adhesive tape.

Figure 4.8a Internal container with monitoring thermocouples affixed.

Figure 4.8b Internal container with heaters mounted above the monitoring
thermocouples.

Figure 4.8: The thermocouple and heater instrumentation of the inner
container. Seven thermocouples were located close together both radially and
longitudinally distributed to correlate with the outer container
configuration. A further two thermocouples were located opposite to the prior
thermocouples to accommodate thermal model comparisons. The heater mats were
pressed against the inside wall and the monitoring thermocouples facing the
centre.

Figure 4.9: A schematic of the internal container instrumentation. The dashed
lines represent the heaters and the crosses indicate the location of the nine
thermocouples and their respective identification numbers. The container is
shown in its profile perspective and the end view corresponds to the images in
Figure 4.8.

The two heater mats were slightly mis-aligned with the central axis of the
container such that thermocouples 1 through 7 were in closer contact with the
heater. A Laird Technologies Tflex HR620 thermal gap pad was used
($0.5\text{\,}\mathrm{mm}$ thick), this was cut to the size of the heater mat
and placed between the heater mat and internal container surface. To minimise
steel shot moving between the heater mat and container surface, the edges of
the heater mat were sealed with Kapton adhesive tape. The internal container
was then filled with the steel shot and sand mixture originally packaged
within the unit and the instrumentation cables directed through the
appropriate lids (completed shown in Figure 4.10).

Figure 4.10: The internal container within the THORP intermediate and outer.
The instrumentation cables were passed through openings on both container lids
and the outer lid was held in place using high-temperature adhesive tape. The
external surface was coated with high emissivity paint and thermocouples
positioned across the surface.

Following the THORP container measurements, the intermediate container was
removed and placed within the outer Magnox container. This was sealed with
high-temperature adhesive tape, then placed on the inspection rail.

A schematic of the external surface and the respective thermocouple and region
of interest identifiers is shown in Figure 4.11. A set of artefacts are
denoted by the zones A through D as shown in Figure 4.11 and labelled by the
rounded-hatched boxes. Zone A consist of ten pits, whilst zone C comprises
twenty pits. Two sets of scratches were manufactured on the surface in zones B
and D, each containing two scratches.

Figure 4.11: A schematic of the external container instrumentation. The dark
regions represent the coating, the crosses indicate the location of the
thermocouples and squares represent the thermal imager regions of interest,
both with their respective identification numbers.

Prior to assembly the two outer containers were sent to Goldburn Finishers Ltd
(Lindford, Hampshire) and a coating of Nextel velvet 811-21 was applied to the
containers according to the diagram in Figure 4.11 [75]. The coating was
stated to be $80\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick and the widths
of the strips were $20\text{\,}\mathrm{mm}$, the finished coating is shown in
Figure 4.10.

#####  4.2.2.2 Store configuration

The James Fisher Nuclear Limited test store is a to scale mock up (rails,
access ports) of the active store facility that allows inactive facility
testing of new condition monitoring and inspection technologies. Whilst a
number of different container channels were available, a single channel was
used for testing the viability and feasibility of thermal imaging.

On the inspection channel a number of non-instrumented containers were placed,
these containers operated as additional observation containers with no thermal
management or content; the inspection container under test was placed toward
the front of the channel. During the measurement capture the facility was used
in a closed state, the surrounding housing was closed up similar to the
laboratory work with an equivalent – albeit larger – shroud to that in the
laboratory work.

The instrumented container for inspection was orientated on the rail to
provide a view of the regions of interest. The thermal imaging inspection
trolley (refer to Figure 4.12a) was mounted to view from directly under the
instrumented container and able to translate along the inspection rail
underneath the container (refer to Figure 4.12b).

Figure 4.12a The optical carriage to mount a pair of uncooled thermal imagers
during the store measurements.

Figure 4.12b Image of the THORP container installed on the inspection channel,
viewed from the inspection side with the thermal imaging inspection trolley
underneath. Imager on the left is the WFOV (S/N: S0055574) and on the right is
the NFOV (S/N: S0032888).

Figure 4.12: Both a) the inspection carriage and b) the carriage in-situ below
a container.

For each measurement temperature setpoint the thermal imaging inspection
trolley was manually translated along the rail underneath the instrumented
container from the front to the back at fixed capture positions along the
length of the container. For each capture position along the
$30\text{\,}\mathrm{mm}$ step, images were recorded at $10\text{\,}\mathrm{s}$
intervals for $1\text{\,}\mathrm{min}$ from each imager using the same
software used in the thermal imager calibration.

###  4.3 Laboratory container assessment

The containers were assembled as described in Section 4.2.1, within this
section a description of the system temperature characteristics will be
presented; the results from the thermal measurements will be summarised;
followed by the uncertainty budget and a discussion.

The objectives of this activity were:

  * •

To set up and validate the thermal operation of each container

  * •

To determine the radiance temperature of each container as a function of
heater power

  * •

To calculate the estimated surface temperature measurement uncertainty for a
given thermal imager

The thermocouples used during this assessment were not calibrated and were
used with manufacturer tolerances, this was noted accordingly in the
uncertainty budget.

####  4.3.1 Thermal characterisation

The containers and their temperature characteristics have been profiled during
the container measurements at increasing heater temperature setpoints; the
results from this validation are presented in the following section. The
Region Of Interest (ROI) placement was arbitrary but attempted to provide a
distributed coverage across the surface within the field of view of the
thermal imaging system whilst minimising surface emissivity perturbations.
Radiance temperature is the apparent radiance temperature with an emissivity
correction applied for the respective room conditions and assumed emissivity
value (as introduced in Section 2.2). The container surface emissivity value
was evaluated from the data presented in [60]. It is clear that this is likely
an inadequate estimate due to the large emissivity variation caused by
different surface finishes. Despite the clear emissivity difference between
the barcode region of the THORP container compared to the surrounding surface,
the same emissivity correction will be applied to the apparent radiance
temperature. It is not simple to estimate the increase in emissivity
introduced by this barcode, however it will be demonstrably clear from the
results the effect from the emissivity increase. The ROI and estimated
thermocouple location for both containers are shown in Figure 4.13.

Figure 4.13: A comparison between thermal (left) and visual (right) images for
the Magnox (top) and THORP (bottom) containers. Locations of the contact
thermocouples below the surface in the internal container are denoted by
crosses. The square regions of interest are shown beside these thermocouple
locations.

A visualisation of the thermocouple measurements at the
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ heater setpoint is shown in Figure
4.14 for both containers. Here the thermocouples measure greater temperatures
in the Magnox container, it was observed that the open end thermocouples
measure relatively cooler than the corresponding thermocouples for the THORP
container.

Figure 4.14a Magnox container.

Figure 4.14b THORP container.

Figure 4.14: The thermocouple measurements at the
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ heater setpoint for the a) Magnox,
and b) THORP containers. The open face of the containers is positioned to the
left.

A visual comparison between the Magnox and THORP container, radiance
temperature and thermocouple measurement at both
$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ is shown in Figure 4.15. The
radiance temperature measurements (square boxes) assume a surface emissivity
of 0.30 and were measured from the indicated regions of interest. Thermocouple
measurements (rounded boxes) from within the internal container and are
corrected for by the offset calculated from the thermal model (detailed in
Section 4.3.2).

Figure 4.15: Comparison between the Magnox (top) and THORP (bottom) container
measurements at $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ (left) and
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ (right). The radiance temperature
measurements assume an emissivity of 0.30 and are denoted by the square boxes.
The thermocouple temperature is the model-corrected thermocouple measurement
introduced in Section 4.3.2 and is indicative of the surface temperature,
these are denoted by the rounded boxes.

The ThermoCouple (TC) measurements from both container measurements indicated
the temperature non-uniformity across both the radial and longitudinal axes of
the containers.

Both containers demonstrated cooler edges (TC 0 and 9) at each temperature
setpoint, so for both cases there were greater thermal losses (due to
conductive and convective heat transfer) at the end faces. At
$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$, the end faces were
$1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ warmer for the THORP container.
These observations can be attributed to each setpoint measurement (albeit with
increasing differences) and suggest that there was more uniform thermal losses
from the THORP container as opposed to the Magnox container that is more non-
uniform in temperature distribution.

For both containers at each temperature, the mean temperature of TC 1, 4 and 6
that were affixed to the top edge were greater than that of the remaining
circumference-mounted thermocouples. This indicates that the effects from
internal convection heating the higher edges and the thermal conductive path
through the rails each container rests on were non-negligible effects,
resulting in nominally $10\text{\,}\mathrm{\SIUnitSymbolCelsius}$ differences.

####  4.3.2 Thermal model

A thermal model was developed to support the assessment of the measurement
data using COMSOL Multiphysics. It was not possible to compare temperatures
measured internally with the thermocouples and externally with the thermal
imager due to the thermal gradients throughout the containers. Therefore to
compare the contact and non-contact temperatures measured during the
laboratory container measurements, the contact thermometer measurements will
introduce a correction based on the model calculations.

The model used the geometry of the containers and their respective
environments, known material properties and computationally solved conductive,
convective and radiative heat transfer interactions at each temperature
setpoint.

Using the developed thermal model, the surface temperature at both the
external region of interest location (refer to Figure 4.13) and equivalent
thermocouple in close proximity was evaluated and difference calculated. For
each container and region of interest, this correction was calculated and
applied to the thermocouple measurements in the laboratory container
measurements.

This computational model was conceptualised and developed by Sofia Korniliou,
National Physical Laboratory [82, 83].

####  4.3.3 Uncertainty analysis

As carried out with the plate measurements in Section 3.3.3, the same
components have been considered for the surface temperature measurement
uncertainty budgets during this assessment. An additional component was
included to account for the Model correction error introduced to the
thermocouple measurement. This was calculated from the difference between the
model surface temperature and thermocouple model-corrected surface
temperature, it was considered a rectangular distribution so a $2\sqrt{3}$
divisor was used and the largest difference from the three ROIs was selected.
An example complete budget is detailed in Table 4.2 and Table 4.3 for each
container and the two temperature determination methods used: thermocouple and
thermal imager.

Table 4.2: An example complete uncertainty budget for temperature determination at the $170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ setpoint with the Magnox container and $175\text{\,}\mathrm{\SIUnitSymbolMicro s}$ integration time. 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
Model correction error |  33.03 |  3.46 |  1.00 |  9.54
Stability |  0.03 |  1.00 |  1.00 |  0.03
Expanded uncertainty ($k=2$) |  19.3
Thermal Imager
Calibration |  0.30 |  2.20 |  1.00 |  0.14
Housing temperature |  0.00 |  1.00 |  1.00 |  0.00
Size-of-source effect |  0.18 |  1.73 |  1.00 |  0.10
Distance effect |  0.29 |  1.73 |  1.00 |  0.17
ROI non-uniformity |  0.50 |  1.00 |  1.69 |  0.85
Emissivity interpretation |  0.08 |  1.00 |  82.68 |  6.61
Ambient temperature |  0.10 |  1.00 |  0.60 |  0.06
Expanded uncertainty ($k=2$) |  13.3
Table 4.3: An example complete uncertainty budget for temperature determination at the $170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ setpoint with the THORP container and $500\text{\,}\mathrm{\SIUnitSymbolMicro s}$ integration time. Source |  $u$ |  Divisor |  Sensitivity |  $U$ / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---|---|---
Tolerance |  1.50 |  1.73 |  1.00 |  0.87
Thermometry bridge accuracy |  0.20 |  1.00 |  1.00 |  0.20
Model correction error |  35.38 |  3.46 |  1.00 |  10.21
Stability |  0.03 |  1.00 |  1.00 |  0.03
Expanded uncertainty ($k=2$) |  20.5
Thermal Imager
Calibration |  0.50 |  2.30 |  1.00 |  0.22
Housing temperature |  0.04 |  1.00 |  1.00 |  0.04
Size-of-source effect |  0.18 |  1.73 |  1.00 |  0.10
Distance effect |  0.29 |  1.73 |  1.00 |  0.17
ROI non-uniformity |  1.46 |  1.00 |  1.53 |  2.24
Emissivity interpretation |  0.08 |  1.00 |  98.72 |  7.90
Ambient temperature |  0.10 |  1.00 |  0.41 |  0.04
Expanded uncertainty ($k=2$) |  16.4

A summary of the measurement uncertainty at each Magnox temperature setpoint
is presented in Table 4.4, the equivalent values for the THORP measurements
are presented in Table 4.5. These describe the greatest uncertainty between
the relevant integration times for each temperature setpoint.

Table 4.4: A summary of the instrumentation, application and combined measurement uncertainties for each temperature setpoint during the Magnox container measurements. | 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 |  0.8 |  2.3 |  0.2 |  1.1 |  2.2
70 |  0.9 |  4.1 |  8.3 |  0.2 |  3.0 |  6.1
110 |  0.9 |  6.8 |  13.7 |  0.3 |  4.7 |  9.4
130 |  0.9 |  7.6 |  15.3 |  0.3 |  5.4 |  10.9
150 |  0.9 |  8.6 |  17.3 |  0.3 |  6.1 |  12.1
170 |  0.9 |  9.5 |  19.2 |  0.2 |  6.7 |  13.3
Table 4.5: A summary of the instrumentation, application and combined measurement uncertainties for each temperature setpoint during the THORP container measurements. | 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 |  0.5 |  2.1 |  0.2 |  1.8 |  3.7
70 |  0.9 |  3.3 |  6.8 |  0.2 |  4.4 |  8.8
110 |  0.9 |  5.7 |  11.5 |  0.2 |  6.3 |  12.5
130 |  0.9 |  7.2 |  14.6 |  0.3 |  6.9 |  13.9
150 |  0.9 |  8.7 |  17.6 |  0.2 |  7.6 |  15.3
170 |  0.9 |  10.2 |  20.5 |  0.3 |  8.2 |  16.4

In comparison to the plate measurements (refer to Section 3.3), the
thermocouple uncertainties were nominally equivalent, but there is a clear
variation in thermal imager application uncertainty. The principle component
contributing to this variation is the sensitivity of the emissivity
uncertainty. Because this sensitivity function (refer to Eq. 3.5) is sensitive
to emissivity it is shown that for the lowest emissivity measurements
(polished steel from uncoated plate measurements) this component is the
greatest, whilst being the least for the Senotherm coated regions on the
plate, and in between for the containers. The variation between the containers
themselves is due to the both the spatial uniformity and emissivity
sensitivity being greater for the THORP container.

####  4.3.4 Discussion

Evaluation of the laboratory container measurements was presented in the
preceding sections. Section 4.3.1 broadly summarised the contact thermocouple
and surface radiance temperatures; an excerpt of the surface temperature
distributions is presented. The uncertainty analysis is detailed in Section
4.3.3, the individual components for each system were identical to those from
the plate budgets; an example budget is stated and the combined temperature
measurement uncertainties are presented for the two container types.

As with the plate a direct comparison between the two temperature
determination methods at three regions of interest in Figure 4.13 has been
carried out. As shown through both the measurement temperatures in Section
4.3.1 there is a large variation from the thermocouple locations to the
radiating surface temperature. To facilitate this comparison between methods,
a correction to the thermocouple measurements based on the calculated
temperature differences using a thermal model was applied. The thermocouples
used for ROI 1 through ROI 3 were TC 6, TC 4 and TC 1 respectively. This
correction incurs a component of uncertainty from any discrepancy between the
computational and experimental thermal descriptions and was appropriately
considered. The comparison plots for the Magnox and THORP containers are shown
in Figure 4.16 and Figure 4.17 respectively.

Magnox1718192021222324252627$1$$2$$3$1015202530354045$1$$2$$3$0102030405060$1$$2$$3$10203040506070$1$$2$$3$1020304050607080$1$$2$$3$102030405060708090$1$$2$$3$

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

$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint

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

Thermal ImagerThermocouple $70\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint

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

$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint
$130\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint ROI Identifier
$150\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint Figure 4.16: 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 correspond to those in Figure 4.13 during the Magnox
container measurements. Note that the thermocouple measurements include a
correction based on the temperature difference described by the thermal model
in Section 4.3.2.

THORP182022242628303234$1$$2$$3$15202530354045505560$1$$2$$3$1020304050607080$1$$2$$3$102030405060708090$1$$2$$3$0102030405060708090100$1$$2$$3$020406080100120$1$$2$$3$

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

$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint

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

Thermal ImagerThermocouple $70\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint

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

$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint
$130\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint ROI Identifier
$150\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Setpoint Figure 4.17: 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 correspond to those in Figure 4.13 during the THORP
container measurements. Note that the thermocouple measurements include a
correction based on the temperature difference described by the thermal model
in Section 4.3.2.

The three Magnox ROIs used were distributed both longitudinally and radially;
one through three were positioned from the lid side to the base end. At
$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ both radiance and thermocouple
values were in good agreement. However the thermocouple measurements became
increasingly disparate from the remaining measurements. It was observed from
the excerpt of thermocouple measurements in Figure 4.14 that the distribution
shown is consistent with Figure 4.16: that the container is cooler at the
edges but with greater coolth towards the base end. The model correction
applied is nominally longitudinally invariant, but this data suggests that the
correction applied is too great at ROIs 1 and 3.

As hypothesised in Section 4.3.1, during the THORP container measurements the
emissivity correction applied to ROI 2 was too great; this is shown by the
radiance temperature being consistently higher than the other ROIs. And so the
emissivity of the barcode region is measurably greater than the surrounding
surface. As with the Magnox container the thermocouple measurements were not
suitably comparable to the radiance temperatures. In this configuration the
correction applied to the thermocouple measurements does vary along the
longitudinal axis. Therefore, there is likely greater disparity, compared to
the Magnox container, between the experimental and model thermal descriptions,
which is not sufficiently described by this model.

The difference in configuration from the Magnox to THORP container, where
there was increased heat transfer to the radiating surface due to larger
diameter, s shown through the temperature measurements. Compared to the plate
measurements where there is nominally $3\text{\,}\mathrm{mm}$ between the base
of the thermometer channel and radiating surface, for the Magnox container
there is at most a $30\text{\,}\mathrm{mm}$ separation through varying sizes
of air spaces. The mean thermocouple temperature is lower due to more heat
transfer to the external environment, the increased temperature range shows
greater variation across the internal container. Additionally, the surface
radiance temperature is higher because the thermal conduction is greater in
this configuration.

####  4.3.5 Summary

From the temperature measurements of the container, it is apparent that there
is a clear distinction between the thermal properties measured for the two
container configurations. It should be noted that the Magnox configuration is
not representative of typical in store Magnox containers and would typically
use a low-density polyethylene container surrounding an aluminium inner
container of a different geometry. This arose from the containers available.
Despite this the laboratory measurements indicated a cooler temperature at the
edges of the Magnox container as opposed to a linear increase towards the base
of the THORP containers. In the experimental setup used, the inner container
was hotter during the Magnox measurements due to reduced thermal losses,
whilst the THORP outer container surface was hotter than the Magnox container.
The laser etched material in the barcode region demonstrated a measurably
greater temperature than the surrounding surface.

In general the radiance and thermocouple temperatures could not be
sufficiently compared due to the thermal model correction implemented.

###  4.4 Store container assessment

During the previous section, the thermal characteristics of two special
nuclear material containers were evaluated using a thermal imager under
laboratory conditions. The next phase of work was to carry out a modified test
campaign using the James Fisher Nuclear Ltd replica test store to assess
containers in an environment equivalent to an active store. The two containers
evaluated within this trial were the Magnox and THORP SNM test containers as
described during the setup in Section 4.2.2.

The objectives of this test campaign were:

  * •

Demonstrate suitability of an uncooled microbolometer in an inactive store

  * •

Implement surface temperature determination in a mock store environment

  * •

To assess whether the difference between radiance temperature and externally
mounted thermocouples is less than the estimated measurement uncertainty at a
confidence level of $95\text{\,}\mathrm{\char 37\relax}$ at each setpoint
temperature

The thermal imagers were successfully calibrated, deployed within JFNL test
store, and an evaluation of surface temperatures and comparison to contact
thermometers has been completed. The results are given in this section. The
following section details the JFNL test store measurement campaign results for
the thermal characterisation of the Magnox and THORP instrumented containers.

The measurement data capture during this trial was carried out by Sofia
Korniliou and Rob Simpson, National Physical Laboratory.

####  4.4.1 Thermal characterisation

The following section details the measurement campaign results for the thermal
characterisation of the Magnox and THORP instrumented containers.

#####  4.4.1.1 Thermocouple evaluation

Prior to use the thermocouples had been calibrated over the range from
$5\text{\,}\mathrm{\SIUnitSymbolCelsius}200\text{\,}\mathrm{\SIUnitSymbolCelsius}$
and the deviation from the International Temperature Scale of 1990 reported.
For each thermocouple a calibration correction to the measured temperature was
applied either through a polynomial fit or fixed offset, depending on the
function of deviation with temperature [84, 85].

For each surface temperature region of interest (shown in Figure 4.11) the
adjacent thermocouples used as the comparator were sampled. The regions of
interest and respective thermocouples are presented in Table 4.6 and visually
overlaid on the thermal image data in Figure 4.18.

Table 4.6: The regions of interest (refer to Figure 4.11) and the respective thermocouples used to assess the reference surface temperature measurement. The size of the ROI is shown for each imager. ROI |  Thermocouple Comparators |  NFOV ROI Size / $\text{\,}\mathrm{px}$ |  WFOV ROI Size / $\text{\,}\mathrm{px}$
---|---|---|---
1 |  12 |  15 |  30
2 |  13 |  15 |  30
3 |  14 |  15 |  30
4 |  15 |  15 |  30
5 |  12, 13 |  15 |  30
6 |  13, 14 |  15 |  30
7 |  14, 15 |  15 |  30
8 |  10 |  15 |  30
9 |  11 |  15 |  30
10 |  10 |  50 |  120
11 |  10, 11, 13, 14 |  15 |  30
12 |  11 |  50 |  120
Figure 4.18: Collated qualitative representation from the THORP
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ NFOV distortion-corrected
measurements. The indicated thermocouples and regions of interest are those
denoted in Figure 4.11.

#####  4.4.1.2 Radiance temperature evaluation

Using the calibration data from the respective thermal imager calibrations, a
calibrated apparent radiance temperature was calculated from the Digital Level
(DL) measurement and mean FPA temperature during each measurement set.

###### 4.4.1.2.1 Region of interest evaluation

For each measurement set, the surface ROIs were identified for each respective
stopping position with respect to the regions shown in Figure 4.11. Due to the
geometry of the storage rail and distance between imager and container, it was
not possible to observe the full ROI set proposed in the campaign
preparations. Notably ROI one through to four were not observable and so ROI
eleven was added to represent an uncoated region. Due to the large area of the
FOV at ROI eight and nine, an additional pair of ROIs were added (ten and
twelve) with a larger ROI size. This enabled the evaluation of the effect from
ROI size on temperature determination, especially due to larger spatial
temperature distribution.

The raw tiff thermal imaging files were evaluated using GNU Octave (version
5.2.0) and the digital level values from each ROI were exported to individual
csv files. The respective ROI files were assessed for each data set, reporting
the mean, temporal standard deviation (standard deviation of each mean from
each extracted ROI) and spatial standard deviation (mean of the standard
deviations from each extracted ROI). This exercise was repeated for each
thermal imager and temperature setpoint for all observable regions of
interest.

###### 4.4.1.2.2 Calibration interpretation of measurements

A challenge encountered at this stage was the disparity between FPA
temperature during the calibration and during each measurement set within the
test store facility. Due to the sensitivity of the signal transfer function
shown in Eq. 2.4, changes to the FPA temperature beyond that experienced
during the calibration process would have a large impact on temperature
measurement accuracy. To illustrate this, the mean FPA temperatures at each
set are detailed in Table 4.7 alongside the mean value the calibration fit was
based on.

Table 4.7: FPA temperatures during each of the measurements sets compared to those used to build the calibration transfer function (Eq. 2.4). Note measurements were not carried out at $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for the Magnox container. Container | Setpoint Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$ | Imager |  Mean FPA Temperature / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---|---
| Calibration | NFOV |  32.9
| WFOV |  34.9
THORP | 30 | NFOV |  26.0
WFOV |  27.8
110 | NFOV |  29.5
WFOV |  31.2
170 | NFOV |  31.7
WFOV |  33.5
Magnox | 30 | NFOV |  -
WFOV |  -
110 | NFOV |  30.2
WFOV |  32.4
170 | NFOV |  32.0
WFOV |  33.1

What can be noted from this data is that there was a discrepancy between the
imager temperature during calibration (when the transfer function was defined
in Eq. 2.4) and when deployed to the store. The entries in the table are
presented chronologically and so what is shown is each imager gradually
warming from set to set.

The effect this discrepancy had on apparent temperature determination varied
between the two imagers, but the WFOV system was more sensitive to this
variation. As a result, a correction from this FPA temperature offset was
applied; the magnitude of this correction was calculated by applying the
results from an independent calibration of a similar instrument (FLIR Boson
20640A050-9PAAX). The data from that calibration was used to define a plane
(two-dimensional function) of the same form used to build the deployed thermal
imager calibration function (shown in Figure 4.19). The digital level
correction was calculated using this plane at the respective FPA temperature
and corrected thermocouple measurement. An exemption to this correction is for
the THORP measurements using the WFOV imager at
$30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$; here this correction was not
sufficient to account for the FPA temperature offset and so an additional
correction of $10\,150\text{\,}\mathrm{DL}$ and $1900\text{\,}\mathrm{DL}$ was
added to the functional correction.

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

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

$0$$10$$20$$30$$40$$50$$60$$70$$16$$18$$20$$22$$24$$26$$28$$30$$32$$34$$23000$$25000$$27000$$29000$

Digital Level / $\text{\,}\mathrm{DL}$

Figure 4.19: A separate calibration of a different FLIR Boson (model:
20640A050-9PAAX) that was calibrated within an environmental chamber. The
plane describes the function relating digital level, blackbody temperature and
FPA temperature. This was used to correct the store measurements of the
thermal imagers.

Using the measured digital level, calculated FPA correction and FPA
temperature, the apparent radiance temperature was calculated. This function
is detailed in [33, 34].

###### 4.4.1.2.3 Temperature evaluation

An emissivity corrected surface radiance temperature for each measurement set
was determined using the multiple reflection single wavelength method
described in Section 3.4.3. Requirements for this calculation are: apparent
radiance temperature (from the calibrated thermal imager), reflected
background radiance temperature (from the calibrated hygrometer remotely
positioned by the workstation), wavelength of the instrument and hemispherical
total emissivity of the surface. It was assumed that the reflected component
evaluated by the hygrometer originated from a blackbody surrounding the
measured surface.

Due to the complexity in determining the particular directional emissivity in
each thermal image, instead the hemispherical total emissivity was used; this
assumption should be considered an under-estimation of the emissivity due to
the angle of measurement (greater than
$10\text{\,}\mathrm{\SIUnitSymbolDegree}$ from the surface plane). The absence
of spectrally considered radiance calculation (e.g. multiple reflection all
wavelength radiance correction) should also be considered carefully if there
are large emissivity variations within the spectral range being considered.
The hemispherical total emissivity for the Nextel coating used was assumed to
be $0.9381\pm 0.0056$ ($k=1$) [75] and the uncoated region was estimated to
have an emissivity of $0.45\pm 0.08$ ($k=1$) [60, 86]. The spectral response
of the thermal imagers is from $7.5\text{\,}\mathrm{\SIUnitSymbolMicro
m}14.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and the value used for lambda
was $10.75\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in these calculations.

The surface temperature determinations from thermal imaging and thermocouples
for each respective region of interest, temperature setpoint and imager is
shown for the Magnox container in Figure 4.20. The corresponding THORP
measurements are shown in Figure 4.21. The error bars shown represent the
$k=2$ uncertainty of each measurement, where the uncertainty budgets are
detailed in Section 4.4.2. These error bars do not include the FPA components
as discussed in Section 4.4.1.2.2, these could be mitigated with a carefully
deployed test campaign and would have effected a large influence on the error
bars that diminishes the behaviour of other uncertainty components.

020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170020406080100110170

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

Thermal ImagerThermocouple NFOV ROI 5

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

WFOV ROI 5

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

NFOV ROI 6

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

WFOV ROI 6

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

NFOV ROI 7

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

WFOV ROI 7

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

NFOV ROI 8

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

WFOV ROI 8 NFOV ROI 9 WFOV ROI 9 NFOV ROI 10 WFOV ROI 10 NFOV ROI 11 Lower
emissivity WFOV ROI 11 Lower emissivity Container Setpoint Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$ NFOV ROI 12 WFOV ROI 12 Figure 4.20:
Magnox surface temperature determined using the thermal imager and
thermocouple. ROIs are at high emissivity coating locations unless specified.
103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170103050709030110170

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

Thermal ImagerThermocouple NFOV ROI 5

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

WFOV ROI 5

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

NFOV ROI 6

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

WFOV ROI 6

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

NFOV ROI 7

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

WFOV ROI 7

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

NFOV ROI 8

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

WFOV ROI 8 NFOV ROI 9 WFOV ROI 9 NFOV ROI 10 WFOV ROI 10 NFOV ROI 11 Lower
emissivity WFOV ROI 11 Lower emissivity Container Setpoint Temperature /
$\text{\,}\mathrm{\SIUnitSymbolCelsius}$ NFOV ROI 12 WFOV ROI 12 Figure 4.21:
THORP surface temperature determined using the thermal imager and
thermocouple. ROIs are at high emissivity coating locations unless specified.

####  4.4.2 Uncertainty analysis

The following section details the uncertainties and estimated combined
uncertainties for the thermal characterisation of the Magnox and THORP
instrumented containers.

#####  4.4.2.1 Thermocouple uncertainties

Thermocouple uncertainty components are detailed here. The thermocouples
associated with each region of interest are detailed in Table 4.6.

###### 4.4.2.1.1 Instrumentation

Calibration uncertainty

This is reported in the respective calibration certificates as a normal
distribution and a coverage factor of 2.0 [84, 85]. From
$5\text{\,}\mathrm{\SIUnitSymbolCelsius}65\text{\,}\mathrm{\SIUnitSymbolCelsius}$
this is $0.05\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) and from
$65\text{\,}\mathrm{\SIUnitSymbolCelsius}200\text{\,}\mathrm{\SIUnitSymbolCelsius}$
this is $0.75\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$).

Calibration fit error

Using the correction data from the certificates for each thermocouple either a
polynomial fit or mean offset was used to describe the respective corrections.
This was dependent on the characteristic of the correction across the full
temperature range (i.e. did the data suitably fit a second-order polynomial).
For the polynomial based corrections, this component is the root mean squared
from the fit; for the mean offset corrections this is the standard deviation
of the corrections reported at each temperature, both have a normal
distribution.

###### 4.4.2.1.2 Application

Measurement stability error

The standard deviation of the thermometer over the measurement period was
recorded and in the instances of multiple thermometers defining the ROI, the
mean of these respective deviations was reported. This was evaluated as a
normal distribution.

Measurement sampling error

For single thermometer ROIs, this component was zero, otherwise this value was
evaluated as the mean of the respective thermometer standard deviation
measurements. This represents the spatial temperature differences measured by
the thermometers and is a normal distribution.

#####  4.4.2.2 Radiance temperature uncertainties

These values are each converted from their respective units (e.g. apparent
radiance temperature, FPA temperature, emissivity and room temperature) to
radiance temperature using sensitivity coefficients. These are described in
Section 3.3.3.2 and the FPA component sensitivities are described in their
respective sections.

###### 4.4.2.2.1 Instrumentation

Calibration

This component collates all of the reported sub-components assessed within the
laboratory characterisation of the instruments. This includes calibration of
the reference source, stability of the reference source, stability of the
instrument, size-of-source effect reproducibility, uniformity across the
centrally assessed pixels, the residual of the calibration fit, stability over
a $30\text{\,}\mathrm{min}$ period, the effect of distance variation and the
alignment to the mirror [33, 34]. This was evaluated as a normal distribution
with a coverage factor as indicated by the calibration.

###### 4.4.2.2.2 Application

Measurement stability error

From each respective set of images for an ROI in a measurement set, the
standard deviation of the mean was evaluated. This typically represented the
temporal variation of the measurement data. However in this instance where the
ROI was manually positioned across the field of view this also represents the
repeatability of ROI placement and temperature variation across the detector
field of view. This is assessed as a normal distribution.

Measurement spatial error

Conversely to the above, the standard deviation across each ROI during the
measurement was recorded, describing the temperature variation across the
surface. The mean standard deviation across the appropriate ROI assessments
was evaluated as a normal distribution.

FPA stability

During the measurements there was a variation of FPA temperature and this
standard deviation was evaluated. The sensitivity of radiance temperature,
$t_{90}$, to FPA temperature, $T_{FPA}$, was derived from Eq. 2.4 and assessed
using,

$\frac{\partial t_{90}}{\partial
T_{FPA}}=c\cdot\left(S_{DUT}+S_{Correction}\right)+2d\cdot
T_{FPA}+e\mathrm{.}$ (4.1)

Where $S_{DUT}$ is the digital level measured, $S_{Correction}$ is the applied
digital level correction and the coefficients $c,d$ and $e$ are from those
described in the respective calibration certificates. This was evaluated as a
normal distribution.

FPA correction applied

The plane correction and additional surplus correction applied to any
measurement sets was accounted for by this component. The magnitude of the
correction was considered as a rectangular distribution and so a $2\sqrt{3}$
divisor was applied. The sensitivity of this component was derived from Eq.
2.4 and evaluated using,

$\frac{\partial t_{90}}{\partial
S}=2a\cdot\left(S_{DUT}+S_{Correction}\right)+b+c\cdot T_{FPA}\mathrm{.}$
(4.2)

Where the coefficients $a,b$ and $c$ are from those described in the
respective calibration certificates. This was evaluated as a normal
distribution.

Emissivity

The coated and uncoated regions had values and uncertainties defined in
Section 4.4.1.2. The corresponding sensitivity for each region of interest was
calculated and this was assessed as a normal distribution.

Room temperature uncertainty

Corresponds to the instrumentation uncertainty of the hygrometer used. From
the calibration certificate, this is
$0.2\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$). This was assessed as a
normal distribution and the appropriate sensitivity calculated.

Variation in room temperature

Where the standard deviation in room temperature exceeded the instrumentation
uncertainty, this value was also considered for its effect on radiance
temperature determination. This was evaluated as a normal distribution with
the appropriate sensitivity calculated.

#####  4.4.2.3 Compiled uncertainty budgets

An excerpt of the uncertainty budgets (total of 80) are presented in Table 4.9
and Table 4.8. Due to the nature of the measurement, there were too many fine
details to demonstrate in this subset of data. Below are the budgets for a
coated ROI from the $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ THORP
measurements and an uncoated ROI from the
$170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Magnox measurements respectively.
These budgets are the largest uncertainty budgets for each container.

Table 4.8: Uncertainty budget from the $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ THORP measurements using the WFOV imager at the coated ROI 5. Source |  $u$ |  Divisor |  Sensitivity |  $U$ / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---|---|---
Thermocouple
Calibration uncertainty |  0.05 |  2.00 |  1.00 |  0.03
Calibration fit error |  0.08 |  1.00 |  1.00 |  0.08
Measurement stability error |  0.12 |  1.00 |  1.00 |  0.12
Measurement sampling error |  0.94 |  1.00 |  1.00 |  0.94
Expanded uncertainty ($k=2$) |  1.9
Thermal Imager
Calibration |  2.10 |  2.10 |  1.04 |  1.04
Measurement stability error |  0.18 |  1.00 |  1.04 |  0.19
Measurement spatial error |  0.19 |  1.00 |  1.04 |  0.19
FPA stability |  0.57 |  1.00 |  22.65 |  12.82
FPA correction applied |  5466 |  1.73 |  0.01 |  17
Emissivity |  0.01 |  1.00 |  4.42 |  0.03
Room temperature uncertainty |  0.10 |  1.00 |  0.06 |  0.01
Variation in room temperature |  0.42 |  1.00 |  0.06 |  0.03
Expanded uncertainty ($k=2$) |  42.7
Table 4.9: Uncertainty budget from the $170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ Magnox measurements using the NFOV imager at the uncoated ROI 11. Source |  $u$ |  Divisor |  Sensitivity |  $U$ / $\text{\,}\mathrm{\SIUnitSymbolCelsius}$
---|---|---|---|---
Thermocouple
Calibration uncertainty |  0.05 |  2.00 |  1.00 |  0.03
Calibration fit error |  0.28 |  1.00 |  1.00 |  0.27
Measurement stability error |  0.69 |  1.00 |  1.00 |  0.69
Measurement sampling error |  11.43 |  1.00 |  1.00 |  11.43
Expanded uncertainty ($k=2$) |  22.9
Thermal Imager
Calibration |  2.25 |  2.00 |  1.92 |  2.16
Measurement stability error |  0.57 |  1.00 |  1.92 |  1.10
Measurement spatial error |  1.17 |  1.00 |  1.92 |  2.24
FPA stability |  0.42 |  1.00 |  0.61 |  0.26
FPA correction applied |  64.1 |  1.73 |  0.01 |  0.30
Emissivity |  0.08 |  1.00 |  69.16 |  5.53
Room temperature uncertainty |  0.10 |  1.00 |  0.91 |  0.09
Variation in room temperature |  0.28 |  1.00 |  0.91 |  0.26
Expanded uncertainty ($k=2$) |  12.9

The uncertainty bars presented in Figure 4.20 and Figure 4.21 omit the two FPA
thermal imager components. The two instrument calibration components are
detailed in the respective certificates. Thermocouple fit error does not vary
much between ROI and measurement set. Thermocouple measurement stability is at
an acceptably low level.

The first comparison to draw is the difference between the two thermocouple
measurement sampling errors. ROI 5 is the mean between two thermocouples and
this component is small. For the ROI 11 measurement the large temperature
variation between thermocouple locations leads to a large incurred
uncertainty.

For these budgets the thermal imager measurement error components do not
demonstrate anything unexpected, they are of an acceptable magnitude and the
spatial component is greater than the stability component. There are many
budgets where the stability component is greater than the spatial component
(e.g. THORP $170\text{\,}\mathrm{\SIUnitSymbolCelsius}$ NFOV ROI 9), this is
an example of either the imager uniformity or ROI placement incurring an error
beyond the expected magnitude of the stability component.

A comparison between the two FPA stability components highlights the variation
in sensitivity between the two imager calibration functions and their
respective sensitivity to this variation. The magnitude of the uncertainty is
comparable, however the effect this had on one imager is greater than that on
the other. The FPA correction accounts for how far the FPA temperature was in-
situ from the laboratory evaluation. Where this component is greater in the
first set (first dataset captured on the campaign) compared to the last set of
the campaign, the impact on the budget is considerable. If this was to be
better managed, through strict protocol deployment in-situ, these components
would have only a minor impact on the surface temperature determination.

As anticipated, the emissivity component had a greater effect for the uncoated
region, and this is exacerbated by the increased sensitivity when observing
lower emissivity surfaces. For comparison, if the uncoated region (with the
estimated uncertainty) was to have a comparable uncertainty to the coated
region, the corresponding standard uncertainty in this example would be
$0.4\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and not a dominant component of
the budget.

There is not much variation in the estimated uncertainty for the two room
temperature components throughout the measurement campaign. What can be
observed is the difference in sensitivity between the two regimes (coated and
uncoated); this difference is caused by the emissivity values used for the two
surfaces.

In comparison to the uncertainties presented in Section 4.3 where the
instrument was a medium wave infrared thermal imager, the greater wavelength
sensitivity of these long wavelength instruments had a detrimental effect on
the uncertainty analysis. Note the wavelength component in the sensitivity
coefficients (e.g. Eq. 3.5) causes a greater value in this instance.

Throughout these measurements, the thermal imager determined surface
temperature was measured with an uncertainty from
$1.9\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) to
$7.2\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) for known emissivity
regions (excluding the FPA temperature components). Similarly, for regions of
an estimated emissivity, surface temperature was determined to be within an
uncertainty from $4.9\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) to
$20.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$). These demonstrate that
the uncertainty can be managed with confidence if the predominant components
are clearly understood.

####  4.4.3 Discussion

The observations from the store container measurements are discussed here. The
comparison between surface temperature determination methods, the uncertainty
analysis and key observations are detailed.

#####  4.4.3.1 Temperature comparisons

Each of these comparisons detail the surface temperature determined
independently by the thermal imagers and thermocouples respectively. A broad
observation that the external surface temperature increases as the internal
heater temperature increase can be made. The rate of increase at the setpoints
is spatially dependent as shown by the ROI variation.

From detailed comparison between the two methods at each of the respective
regions of interest and using each imager, a finer set of conclusions can be
observed. The corrected NFOV thermal imager measurements are significantly
higher than the thermocouple measurements at
$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and above outside of the combined
estimated uncertainties. Whilst higher, the thermal imager measurements were
not outside of the combined estimated uncertainties for ROIs 5, 6, 7 and 11
because the corresponding thermocouple uncertainties were large at those
points. This observed offset between thermal imager measurements and
thermocouple measurements for the NFOV is understood to be from the difference
between calibration and in-situ FPA temperatures. Additional uncertainty may
also be present due to the actual surface location difference between the
defined ROI and thermocouple location, leading to a thermal gradient not
accounted for in the uncertainties. The region closer to the rail should be
cooler due to higher conductive heat transfer from the container through to
the support rail and this holds given their respective locations. This thermal
gradient effect (due to heat transfer to the support rail) can be observed in
each of the ROI 8, 9, 10 and 12 measurements. These ROIs are at either end and
away from the central strip. This overestimation from the thermal imager may
be due to that ROI location having a greater temperature than the associated
thermocouple location.

The thermocouple uncertainty at ROIs 5 and 11 are discernibly greater than at
other measurement locations. ROI 5 is impacted by the large (up to
$15\text{\,}\mathrm{\SIUnitSymbolCelsius}$) difference between thermocouples
12 and 13. This follows to ROI 11, the differences are up to
$13\text{\,}\mathrm{\SIUnitSymbolCelsius}$ but principally due to thermocouple
10 being much cooler than the other three thermocouples.

Given the additional FPA temperature correction applied to the THORP WFOV
measurements at $30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
$110\text{\,}\mathrm{\SIUnitSymbolCelsius}$ there does not appear to be a
clear systematic offset at these measurements that had not been accounted for.
Note that this correction is a result of the calibration function being
defined from the calibration data demonstrating a large gradient in the plane
of FPA temperature beyond the laboratory conditions. This could be better
managed through either greater stabilisation time of both instrument and
environment ahead of the measurement, as shown in the subsequent THORP and
Magnox measurements, or by a complete sensitivity calibration of the thermal
imager (shown in Figure 4.19).

Results from the Magnox measurements, as with the THORP data ROIs 5, 6 and 7
thermal imager and thermocouple results are in agreement within the
uncertainties. This is primarily due to the larger uncertainty coverage
facilitating this and that the thermal imager measurement was hotter than the
thermocouple during NFOV measurements, there is varying agreement for the WFOV
data. There is agreement between the ROI 8 and 10 (and ROI 9 and 12)
measurements suggesting the size of the ROI does not influence the measurement
capability negatively.

Uncoated region measurements were in agreement between the thermal imager and
thermocouple and the larger estimated uncertainty due to uncertainty in
surface emissivity value is clearly observed.

Improvements to the thermal imager measurement in-situ could be achieved
through a broader thermal imager calibration to incorporate FPA temperature
assessment (such as that shown in Figure 4.19). Additionally, using a thermal
model to identify regions of lower thermal gradients where ROI and
thermocouple locations could have been located to minimise spatial uncertainty
issues would have enabled lower uncertainty comparisons.

#####  4.4.3.2 Uncertainty component assessment

The larger uncertainty components can be approached systematically. For ROI 5,
its two largest components are thermal imager calibration (due to FPA
temperature) and spatial components and so the calibration component may be
addressed as discussed above. ROI 6 and 7 (centre of the strip) had an even
larger spatial component but also a large temporal component that suggests the
ROI locations were not well placed between imager positions.

Additional sources of uncertainty are: hygrometer location, inter-reflections
and thermal imager distance variation. During these measurements the radiance
correction was applied using the ambient conditions measured by the hygrometer
located external to the measurement site. Ideally this ambient component would
represent the surface temperature in the specular direction from observation.
If this measurement underestimates the in-situ reflected radiance component,
and it would actually be hotter, then the emissivity compensation will be too
great and the presented radiance temperatures should be increased.

The assumption made for the radiance correction, that there is only one
reflection component, is a simplification and ignores any influence multiple
surface reflections would have on the correction radiance temperature. In an
instance where the measured apparent radiance temperature comprises, for
example, a reflection from a support rail – as demonstrated by position two in
the radiance correction case study (Section 3.4) – then the corresponding
radiance temperature would differ to that currently estimated. Approaching
complex radiance scenarios such as the one presented can be challenging and
prone to misinterpretation; deployment of 3D thermal imaging (ray tracing
based correction) may enable improved results [2, 74].

During the calibration of the thermal imagers, the effect from distance
variation between the mirror and reference source was investigated from
$75\text{\,}\mathrm{mm}115\text{\,}\mathrm{mm}$. If the container surface
measured was outside of this range then there would be a linear correction to
be applied. Determining this at each pixel requires the implementation of the
geometrical correction and rendering of the surface point cloud. This can be
expressed by comparison of the ROIs respective positions in the imager field
of view. ROIs 5, 6 and 7 were further from the imager and would have measured
slightly lower apparent radiance temperatures than if they were closer.
Compared to ROIs 8 through 12, the apparent radiance temperature will be
slightly greater than if they were positioned further from the imager.

#####  4.4.3.3 Key observations

Deployment of the laboratory calibrated thermal imagers to a thermally active
environment given the FPA temperature sensitivity was considered a large error
source. Whilst this was addressed through the deployment of additional
corrective measures and the subsequent uncertainties; when highlighting the
measurement sets that occurred when the system was thermally stable (i.e.
Magnox and THORP at $170\text{\,}\mathrm{\SIUnitSymbolCelsius}$) then it can
be demonsrated that these uncertainty components become negligible. When
including these FPA components, the measurement data is identical to that
presented in Section 4.4.3.1 however the uncertainties represented by the
error bars included the two FPA temperature components. The error bars
presented are considerably larger here for some sets but for those indicated
above, they are equivalent to those in the presented data.

The discrepancy between the anticipated field of view (depicted by the ROI
placement in Figure 4.11) and the in-situ measurement (visualised in Figure
4.18) is both due to the variation in distance between laboratory estimates
and the rail deployment, but primarily due to the observation angle. If the
observation trolley was perpendicular to the container surface then a greater
container surface coverage would be achieved.

Due to the scope of the project, the mirrors used for off-axis observation
were practical but not optimised for the application. Alignment between the
imager field of view and their size led to regions of the thermal imager field
of view being unusable for measurement. Whilst the reflectivity of the mirror
was not independently measured (beyond the manufacturer specification), the
entire system (thermal imager and mirror) calibration accounted for this
characteristic; however the effect from non-perfect reflectivity of the mirror
on temperature measurement was not fully explored. This may have led to
apparent radiance temperatures that were lower than that measured by a perfect
reflector. Despite these concerns, the measurement data did not indicate any
large systematic error that would have originated from the use of the mirrors
and so any further development with bespoke off-axis thermally-regulated
observation apparatus would not be adversely affected through this method.

####  4.4.4 Summary

Calibration of the two thermal imaging systems was carried out, this included
definition of the signal to temperature function and evaluated a range of
system characteristics that could have led to systematic error in application.
As discussed in Section 4.4.1.2.2, the coverage of the calibration in both the
blackbody reference temperature and FPA temperature space was not sufficient
for the application; this resulted in additional corrections to be implemented
for interpretation of the results. Further deployment of these systems to a
store should ensure suitable calibration ahead of the measurements to
accommodate the anticipated environmental temperature range through
environmental chamber calibration.

Suitability of the uncooled microbolometer to the inactive store was shown to
be successful when the instrument and environment thermal stability was
mitigated, shown in the uncertainty budget for the uncoated measurement of the
Magnox container (refer to Table 4.2). Impact from the FPA temperature
components here was minimal and the remaining largest uncertainty components
were: emissivity effect, ROI spatial contribution and the instrument
calibration. The latter two components are intrinsic to the measurement
application and so cannot be actively reduced. As highlighted in Section 4.3,
the use of traceable low uncertainty emissivity measurement in radiance
temperature determination activities would enable an order of magnitude
improvement for the resulting expanded uncertainty. The example given in
Section 4.4.2.3 suggested that for that budget the expanded uncertainty could
be reduced to $6.8\text{\,}\mathrm{\SIUnitSymbolCelsius}$ through the
employment of improved emissivity data. A summary of the surface temperature
measurements of each container using the two thermal imagers are shown in
Figure 4.22. This is the undistorted data for the NFOV whilst this is the
uncorrected WFOV data, due to the inability to apply a geometrical correction.

Figure 4.22: Summary of the surface temperature measurements overlaid on
qualitative representations of the thermal imager data. The respective ROI
positions correspond to those shown in Figure 4.11. Measurement uncertainty
reported is the expanded combined uncertainty with a coverage factor of 2.0
and does not include the FPA components.

Demonstrated in Section 4.4.1.2, the two methods of temperature determination
(thermal imager and thermocouple) were successfully employed to evaluate the
behaviour of the two containers within the store environment. Broadly across
the two containers, two thermal imagers and eight regions of interest, there
was concurrence between the methods. The objective for this aspect of the
investigation was agreement between the thermocouple and radiance temperature
within the measurements uncertainty at all points. This was not achieved,
however there were regions of interest that were consistently susceptible to
error. These ROIs (8, 9, 10 and 12) were observed to be in error due to
surface temperature gradients incurring measurable temperature variation from
ROI and thermocouple location.

###  4.5 Conclusions

To extend beyond the laboratory assessment of the test plate in Chapter 3,
surface temperature determination methods were deployed to a pair of
instrumented containers. This was explored in both an identical laboratory
environment with a cooled MWIR thermal imager, and a test store representative
of an active store environment using a pair of lower cost uncooled LWIR
thermal imagers.

The containers during the laboratory measurements were limited in experimental
design to internal thermocouples. This incurred an additional challenge to
compare surface temperature methods (between thermocouples and thermal imager)
because a computational model correction was required. The surface temperature
comparison was then subject to the uncertainty of the model. It was shown that
at cooler temperatures the methods were in agreement, but above
$130\text{\,}\mathrm{\SIUnitSymbolCelsius}$ the methods did not agree within
their respective uncertainties. This comparison could have been improved
through the use of either: externally mounted thermocouples to enable a direct
comparison; by refining the model to reduce the incurred thermocouple
correction error; or by using a traceable emissivity measurement.

Completion of the in-situ store measurements at the JFNL site enabled
demonstration of two independent thermal imaging systems to observe a
perpendicularly positioned instrumented container. This investigation explored
multiple challenging aspects including: use of off-axis mirror, FPA
temperature dependent calibration, coated and uncoated surface temperature
measurement.

The use of the mirror did not inhibit the use of the instrumentation, the
calibration included the reflectivity properties of the mirror and so there
were no complications when deploying this to the in-situ measurements.
Additionally the use of these mirrors – as shown in Figure 4.12b – enabled
reduced profile inspection trolley designs that could facilitate further
applications (e.g. cross-channel observation).

Despite the limitation imposed by the calibration with reduced environmental
chamber characterisation, this alongside additional data enabled the
successful deployment of the imagers for apparent radiance determination.
These FPA temperature components ranged from
$0.2\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=1$) to
$17.4\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=1$). Emissivity correction to
the apparent radiance temperature was more successful than the laboratory
measurements as demonstrated by the similarity in temperature response between
the coated and uncoated regions.

As detailed in Chapter 3, emissivity was the greatest contributor to the
uncertainty budget. Shown through the two uncertainty budgets presented, in
the case where emissivity uncertainty was low, the respective component was
negligible compared to other larger sources. The effects from these emissivity
components ranged from $0.02\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=1$)
for a coated region to $8.1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=1$) for
an uncoated region. This further supports the necessity to deploy high
confidence emissivity data in a radiance temperature measurement campaign.

A summary of the surface temperature measurements is presented in Figure 4.22.
Throughout these measurements, the thermal imager determined surface
temperature was measured with an uncertainty from
$1.9\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) to
$7.2\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) for known emissivity
regions (excluding the FPA temperature components). Similarly for regions of
an estimated emissivity, surface temperature was determined to be within an
uncertainty from $4.9\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$) to
$20.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($k=2$). The outlined target