# Optimal Configurations of Mueller Polarimeter for Gaussian-Poisson Mixed Noise
## 4 Discussion  
Since polarization measurement requires the generation and analysis of polarization states by PSA and PSG, and the polarization state analysis is based on the measurement of different polarization states projections, the selection of the generated polarization states \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**States Number** & **CN** & **EWV** & **Parameters** & **Measurement Configuration** \\ \hline
4 & 1.732 & 10.0000 & \(\theta_{P}\) & 0\({}^{\circ}\) \\  & & & \(\theta_{H1}\) & \(2.433^{{}^{\circ}},42.567^{{}^{\circ}},137.433^{{}^{\circ}},87.567^{{}^{ \circ}}\) \\  & & & \(\theta_{Q}\) & \(22.50^{{}^{\circ}},67.50^{{}^{\circ}},112.50^{{}^{\circ}},157.50^{{}^{\circ}}\) \\ \hline
4 & 1.732 & 10.0000 & \(\theta_{P}\) & \(0^{{}^{\circ}}\) \\  & & & \(\theta_{H}\) & \(47.433^{{}^{\circ}},177.567^{{}^{\circ}},2.433^{{}^{\circ}},42.567^{{}^{ \circ}}\) \\  & & & \(\theta_{Q}\) & \(22.50^{{}^{\circ}},67.50^{{}^{\circ}},112.50^{{}^{\circ}},157.50^{{}^{\circ}}\) \\ \hline
8 & 1.732 & 5.0000 & \(\theta_{P}\) & \(0^{{}^{\circ}}\) \\  & & & \(\theta_{H}\) & \(171.46^{{}^{\circ}},36.46^{{}^{\circ}},0.33^{{}^{\circ}},45.44^{{}^{\circ}}\) \\  & & & & \(129.11^{{}^{\circ}},174.11^{{}^{\circ}},160.58^{{}^{\circ}},25.58^{{}^{\circ}}\) \\  & & & & \(155.71^{{}^{\circ}},155.71^{{}^{\circ}},81.4^{{}^{\circ}},81.4^{{}^{\circ}}\) \\  & & & & \(127.84^{{}^{\circ}},127.84^{{}^{\circ}},36.82^{{}^{\circ}},36.82^{{}^{\circ}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The optimal measurement configurations of FPRHRQ. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**States Number** & **CN** & **EWV** & **Parameters** & **Measurement Configuration** \\ \hline
4 & 1.732 & 10.0000 & \(\theta_{P}\) & 0\({}^{\circ}\) \\  & & & \(\theta_{H1}\) & \(2.433^{{}^{\circ}},42.567^{{}^{\circ}},137.433^{{}^{\circ}},87.567^{{}^{ \circ}}\) \\  & & & \(\theta_{Q}\) & \(22.50^{{}^{\circ}},67.50^{{}^{\circ}},112.50^{{}^{\circ}},157.50^{{}^{\circ}}\) \\ \hline
4 & 1.732 & 10.0000 & \(\theta_{P}\) & \(0^{{}^{\circ}}\) \\  & & & \(\theta_{H}\) & \(47.433^{{}^{\circ}},177.567^{{}^{\circ}},2.433^{{}^{\circ}},42.567^{{}^{ \circ}}\) \\  & & & \(\theta_{Q}\) & \(22.50^{{}^{\circ}},67.50^{{}^{\circ}},112.50^{{}^{\circ}},157.50^{{}^{\circ}}\) \\ \hline
8 & 1.732 & 5.0000 & \(\theta_{P}\) & \(0^{{}^{\circ}}\) \\  & & & \(\theta_{H}\) & \(171.46^{{}^{\circ}},36.46^{{}^{\circ}},0.33^{{}^{\circ}},45.44^{{}^{\circ}}\) \\  & & & & \(129.11^{{}^{\circ}},174.11^{{}^{\circ}},160.58^{{}^{\circ}},25.58^{{}^{\circ}}\) \\  & & & & \(155.71^{{}^{\circ}},155.71^{{}^{\circ}},81.4^{{}^{\circ}},81.4^{{}^{\circ}}\) \\  & & & & \(127.84^{{}^{\circ}},127.84^{{}^{\circ}},36.82^{{}^{\circ}},36.82^{{}^{\circ}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The optimal measurement configurations of FPDFVR. and the projected target polarization states is a very important issue, which greatly affects the accuracy of the measurement system and the noise feature. The optimization of the instrument matrix is usually mostly performed by complex algebraic calculations, which require huge arithmetic power, and the complexity of the optimization grows exponentially with the number of polarization illumination/analysis states. For example, in the work of [PERSON] et al. [16], a cost function is built to account for the Euclidian distance between the columns (in the original paper this is rows, because the definition of the instrument matrix is transposed to each other) of the measurement matrix and the columns of the ideal matrix:  
\[\left(\hat{\theta},\delta\right)_{i}=\text{argmin}\sqrt{\frac{1}{3}\sum_{j=1} ^{3}\left(A_{i,j}(\theta,\delta)-A_{i,j}^{*}\right)^{2}} \tag{26}\]  
Then, minimize the cost function by changing retardance \(\delta\) and azimuth \(\theta\) to approximate the optimal instrument matrix and obtain the optimal configuration. Each polarization state has a \(\delta\) and \(\theta\) needed to be optimal, which means there are eight variables needed to be optimal.