## 2 Materials and Methods  
### Fibers and Data Acquisition  
Fiber-optic sensors offer particular characteristics that are of interest in the application of measuring temperature and pressure in radiation environments. The fiber-optic sensor employed in our experiments was a Fiber Bragg Grating (FBG) fabricated by imprinting a discrete optical pattern into the core of the fiber. A FBG is an interferometric device constructed of a series of periodic variations of the refractory index in the core of the fiber. In the simplest case, when a broadband light is coupled into the core of the fiber, the FBG reflects a unique wavelength of light (Figure 1). This characteristic wavelength (or the Bragg wavelength (\(\lambda_{\text{B}}\))) is determined by the effective refractive index (n) of the core and the pitch (\(\Lambda\)) of the refractive index modulation in the core. The sensitivity of a FBG to applied strain and temperature depends on (i) the elastic, thermo-elastic, elasto-optic and thermo-optic properties of the fiber, (ii) the nature of the strain field (e.g., the strain is mainly along the fiber axis or perpendicular to the fiber) and (iii) the temperature field. The relative shift in the Bragg wavelength (\(\Delta\lambda_{\text{B}}\)/\(\lambda_{\text{B}}\)) due to an applied homogeneous and isotropic strain (\(\Delta\varepsilon\)) and a change in temperature (\(\Delta\)T) can be written as [14]  
\[\triangle\lambda_{B}/\lambda_{B}=(1-p_{e})\times\triangle\varepsilon+(\alpha+ \zeta)\times\triangle T \tag{1}\]  
where  
* \(\lambda_{\text{B}}\) is the Bragg wavelength of the FBG when datum strain and temperature is applied to the FBG,
* \(\Delta\lambda_{\text{B}}\) is the change in \(\lambda\)B associated with a change in strain or temperature,
* \(p_{e}\) is the effective strain-optic constant,
* \(\Delta\varepsilon\) is the change in strain experienced over the length of the FBG
* \(\alpha\) is the coefficient of thermal expansion of the fiber (i.e.,)
* \(\zeta\) is the thermo-optic coefficient (i.e.,\(\zeta=\frac{1}{n}\big{(}\frac{\partial n}{\partial T}\big{)}\)), and
* \(\Delta T\) is a change in temperature of the FBG.  
The effective strain-optic constant \(p_{e}\) is given by  
\[p_{e}=\frac{n^{2}}{2}[p_{12}-v(p_{11}+p_{12})]\]  
where \(p_{11}\) and \(p_{12}\) are components of the strain-optic tensor and \(v\) is the Poisson ratio.  
Equation (1) shows that in order to measure changes in strain with a FBG it is necessary to account for the FBG's temperature cross-sensitivity. In this work, two physically separated FBG sensors are used where the first FBG is subjected to both strain and temperature changes and the second FBG is only subjected to temperature changes. By mathematically comparing these two signals, we can infer the temperature-isolated change of strain measurement.  
Three different categories of FBGs were employed in the experiments. Their classification differs depending on their FBG inscription technique and fiber design. We also note that in order to improve accuracy in the wavelength measurements, the FBGs under consideration were \(\pi\)-phase-shifted FBGs which have a very narrow passband feature in their transmission/reflection spectra [15]. In the following text, the \(\pi\)-phase-shifted FBGs will be referred to simply as \"FBGs\", for brevity. The three categories of FBGs are described below with subheadings defining the category name and shorthand in parenthesis.