## 3 Validation on a Case Study
### Polarimeter Simulations  
Analogue numerical simulations were performed to test the polarimeter model, where the plasma current scales accordingly to the electron density. The geometry is similar to the interferometer one, where the reference beam is not needed. The three lasers emit beams with a wavelength of 20 \(\upmu\)m, and each beam is reflected by a 45\({}^{\circ}\) mirror. Then, they cross a linear polariser (Figure 5) which sets the polarisation of the probing beam (in the numerical simulation, a linear polarisation with 45\({}^{\circ}\) has been used, since this configuration maximizes the accuracy and the amount of information which can be extracted from the polarimeter, as discussed in the literature [36]). The rays then cross the plasma and their polarisation changes accordingly with Equation (17). The effect of the mirror and linear polariser on the polarisation of the ray are considered implementing the Mueller matrix of each component on the numerical simulation. The left plot of Figure 5 shows the ray trajectories, while the colour of the ray represents the local Cotton-Mouton phase shift. Note that the influences of the mirrors are not represented in the figure, in order to highlight the plasma effect, while for the proper calculation of the plasma parameters from the polarimeter, a calculation of the Mueller matrix (or Jones matrix and others) of the optics must be performed to ensure accurate results. For example, the polarimeter of JET performs a polarisation calibration in the absence of plasma before each plasma discharge. In these numerical simulations, the effects of the optics are calibrated with the first numerical simulation, when there is no plasma.  
The graphs on the right-top and right-bottom show, respectively, the Faraday rotation and the Cotton-Mouton phase shift performed on the nine numerical simulations. The Faraday rotation of the line of sight 1 and 2 are both positive, being the magnetic field along the propagation direction concordant with the light propagation direction, while the line of sight 3 has a negative rotation. Moreover, the Faraday increase is parabolic since it is composed like the product of the electron density and poloidal magnetic field. Contrariwise, the Cotton-Mouton phase shift is positive and increases linearly in each line of sight since it is dominated by the \(\Omega_{1}\) term, which is proportional to the electron density and the toroidal field (the poloidal field influence is negligible in this configuration).  
Validation of the Stokes model can be performed by measuring the line integral of the electron density with the Cotton-Mouton phase shift, by using the type 1 approximation shown in Equation (15). Figure 6 shows the results of this comparison, also demonstrating that the polarisation model works properly. Contrariwise, the Faraday rotation also is proportional to the poloidal field (along the propagation direction), making the direct measurement of the electron density difficult. However, being that the Cotton-Mouton and the Faraday rotation are linked by the system of Equation (17), a validation on the Cotton-Mouton directly involves the proper propagation of the Faraday rotation.  
Figure 5: Polarimeter results.