# Optimal Configurations of Mueller Polarimeter for Gaussian-Poisson Mixed Noise
## 4 Discussion
However, in our method, there will only be one or two (depending on the measurement structure) variables to optimize. However, the cost function proposed by [PERSON] et al. is the Euclidian distance between the columns of the measurement matrix and the columns of the ideal matrix, which means the ideal matrix must be known, or the optimal matrix should be optimized before the configuration optimization. However, only the ideal matrix of four polarization illumination/analysis states is known as Equation (6) shows; therefore, this method cannot optimize the measurement system with more than four polarization illumination/analysis states. By analyzing the Gaussian-Poisson mixed noise, the optimization problem of the instrument matrix can be reduced to two main indicators--a zero row sum and a minimum EWV of the instrument matrix. Then, change the first indicator into a geometric constraint to make it easy to meet the indicator. Furthermore, instead of simply optimizing the instrument matrix, we propose several different measurement systems and optimize configurations of the measurement systems in order to make the optimization results practically meaningful. In the optimization process, we analyze in detail how different measurement systems make geometric simplification to reduce the complexity of the optimization and obtain the optimal instrument matrix. We finally obtained the optimal configurations for a number of different measurement systems represented by RPRQ, FPRHRQ, FPDFVR, and FPDHVR. As can be observed from Tables 1-4, the instrument matrixes optimized by this method have minimal CN and EWV. When performing polarization measurements, if these measurement systems that we have optimized are used, the given measurement configurations can be directly used to make the measurements optimal without complicated optimization of the instrument matrix. Although only a single PSA or PSG is optimized in this paper, the PSA and PSG have the same set of polarization states in illumination and analysis, and they can both be directly used in the best configuration given. When performing polarization measurements, the optimal Stokes measurement can be achieved by using a PSA with this configuration, or the optimal configuration can be applied to both PSA and PSG to make the whole Muller measurement system optimal and effectively restrain noise, improve measurement accuracy, and make the estimation variance caused by Poisson noise independent of the sample. In contrast to instrument matrix optimization methods such as minimizing CN [10] and EWV [11], this method optimizes the actual measurement configuration rather than just the instrument matrix itself, and the method can be applied to measurement systems with different devices. If the measurement system used is not mentioned in this paper, the optimization method can also be used. Thus, we could obtain the optimal measurement configuration with the regular measurement structure and make it possible to use the optimal configuration for measurement. However, this method still has some weaknesses and limitations. First, it can only optimize for the even number of polarization illumination/analysis states. What is more,the sum of the instrument matrix rows must be zero after the geometric constraint, but the geometric constraint is only a special case to make the sum zero. This means that this method cannot be optimized for all cases. However, the optimal instrument matrix is not unique, but there are an infinite number of them (the instrument matrix of more than four polarization illumination/analysis states). The optimal instrument matrix optimized by this method is also not unique. Each time this method is used for optimization, different results may be obtained. This difference may affect the speed of the measurement. For example, the rotating motor rotates at different angles. This is also a potentially optimizable factor.