Simulations of optimal light polarization state generators and analyzers configurations realized in one-way double pass Mueller polarimetric system using twisted nematic liquid crystal and liquid crystal variable retarder

The dataset contains the results of optimizing the configurations of light polarization state generators and analyzers that can be implemented in one-way double pass Mueller polarimetric system. The same module is used as a generator (PSG) and analyzer (PSA) of different polarization states of light. In the performed numerical simulations, the PSG/PSA module is constructed from a linear polarizer, twisted nematic liquid crystal (TNLC) and liquid crystal variable retarder (LCVR).PSG/PSA descriptionThe elements of the system are represented by a Mueller matrices. The forms of the used Mueller matrices are included in the file: "Mueller_matrix.pdf". It was assumed that for PSG, TNLC director axis of the first layer is aligned along the x-axis of the coordinate system. However, for PSA, TNLC directors at the input surface of the modulator is rotated by an angle π/2. Due to the configuration, TNLC in the PSG and PSA system introduce the same linear phases. The dependence between the voltage of the TNLC and the induced phase difference is not considered. LCVR is set at the azimuth angle of 45° and introduces linear phase differences from the (0;2π>.Optimization processThe numerical PSG/PSA model were simulated and optimized to find the optimal sets of TNLC’s and LCVR’s linear phase differences for every linear polarizer’s azimuth angle, and thereby the best set of generators and analyzers, leading to the minimum system condition number (CN). Also equally weighted variance (EWV) is calculated. The results of optimization process were generated for:different ranges of possible TNLC’s linear phase difference: (0;2π>, (0;3π>, (0;4π>, (0;5π>,different number of configurations realized by PSG/PSA (n={4:20}),azimuthal orientations of the polarizer from 0°-180° with a step of 0.5°.For each azimuth angle of the polarizer randomly permuted n TNLC’s and LCVR’s linear phases and determination instrumental matrices for PSG (the columns of this matrix correspond to the n Stokes vectors of the PSG) and PSA (the rows of this matrix correspond to the n Stokes vectors of the PSA). CN of the polarimeter system was calculated as product of generator’s CN and analyzer’s CN. These steps have been repeated 10 000 times and the minimum CN value corresponding to a given polarizer azimuth angle was determined. Associated with this determined minimum CN value of the system are EWV value and sets of n TNLC’s and LCVR’S linear phases, leading to n Stokes vectors for PSG and PSA.Used software: MATLAB File information and data formatThe data are saved as text files (.txt) and MAT-files (.mat).The resulting files are grouped according to the assumed maximum linear phase difference introduced by TNLC (PDmax):maximum_linear_phase_difference_2pi.zip -> TNLC’s linear phases are generated from the range (0;2π>maximum_linear_phase_difference_3pi.zip -> TNLC’s linear phases are generated from the range (0;3π>maximum_linear_phase_difference_4pi.zip -> TNLC’s linear phases are generated from the range (0;4π>maximum_linear_phase_difference_5pi.zip -> TNLC’s linear phases are generated from the range (0;5π>.Inside, the folders are grouped according to the different number of configurations (n={4:20}). Names are created in this way: number_of_configurations_n.Each folder contains:CN_PSA_vs_alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the CN values of the PSA instrumental matrix (corresponding to the minimum CN value of the system).CN_PSG_vs_alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the CN values of the PSG instrumental matrix (corresponding to the minimum CN value of the system).CN _vs_alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the minimum CN values of the system.EWV _vs_alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the EWV values of the system (corresponding to the minimum CN value of the system).linear_phase1 _alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the set of n TNLC’s linear phases in radians (corresponding to the minimum CN value of the system).linear_phase2 _alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the set of n LCVR’s linear phases in radians (corresponding to the minimum CN value of the system).PSA_vs_alfaP_PDmax_n.mat -> For each azimuth angle of the polarizer saved matrix formed from the Stokes vectors of the analyzers (corresponding to the minimum CN value of the system). Each column is a new Stokes vector.PSG_vs_alfaP_PDmax_n.mat -> For each azimuth angle of the polarizer saved matrix formed from the Stokes vectors of the generators (corresponding to the minimum CN value of the system). Each column is a new Stokes vector.Cell array indices consistent with polarizer azimuth angle indices.Preferred software for analyzing/interpreting results: MATLAB.

本数据集包含可用于单向双程穆勒偏振测量系统的光偏振态发生器与分析仪配置的优化结果。同一模块既用作光不同偏振态的发生器（Polarization State Generator, PSG），也用作分析仪（Polarization State Analyzer, PSA）。

在数值模拟中，PSG/PSA模块由线偏振器、扭曲向列型液晶（Twisted Nematic Liquid Crystal, TNLC）及液晶可变延迟器（Liquid Crystal Variable Retarder, LCVR）构成。

### PSG/PSA描述
系统各元件由穆勒矩阵（Mueller Matrix）表示，所用穆勒矩阵形式包含于文件“Mueller_matrix.pdf”中。假设PSG中第一层TNLC的指向矢轴沿坐标系x轴对齐，而PSA中调制器输入表面的TNLC指向矢旋转π/2角。该配置下，PSG与PSA中的TNLC引入相同线性相位，未考虑TNLC电压与诱导相位差的依赖关系。LCVR设置为45°方位角，可引入范围为(0;2π>的线性相位差。

### 优化过程
通过模拟与优化PSG/PSA数值模型，为每个线偏振器方位角寻找TNLC与LCVR线性相位差的最优组合，从而得到使系统条件数（Condition Number, CN）最小化的发生器与分析仪最优配置，同时计算等权方差（Equally Weighted Variance, EWV）。

优化结果针对以下场景生成：
- TNLC线性相位差的不同可能范围：(0;2π>、(0;3π>、(0;4π>、(0;5π>
- PSG/PSA实现的不同配置数量：n={4:20}
- 偏振器方位角以0.5°步长覆盖0°-180°范围

针对每个偏振器方位角，随机排列n组TNLC与LCVR线性相位，确定PSG（矩阵列对应其n个斯托克斯矢量（Stokes Vector））与PSA（矩阵行对应其n个斯托克斯矢量）的仪器矩阵（Instrumental Matrix）。偏振仪系统的CN为发生器CN与分析仪CN的乘积。上述步骤重复10000次，以确定给定偏振器方位角对应的最小CN值。与系统最小CN值相关的是EWV值及n组TNLC与LCVR线性相位，这些相位对应PSG与PSA的n个斯托克斯矢量。

使用软件：MATLAB

### 文件信息与数据格式
数据以文本文件（.txt）和MAT文件（.mat）格式存储。结果文件根据TNLC引入的假设最大线性相位差（PDmax）分组：
- maximum_linear_phase_difference_2pi.zip → TNLC线性相位范围为(0;2π>
- maximum_linear_phase_difference_3pi.zip → TNLC线性相位范围为(0;3π>
- maximum_linear_phase_difference_4pi.zip → TNLC线性相位范围为(0;4π>
- maximum_linear_phase_difference_5pi.zip → TNLC线性相位范围为(0;5π>

每个文件夹内按配置数量n分组（文件夹命名格式：number_of_configurations_n），包含以下文件：
- CN_PSA_vs_alfaP_PDmax_n.txt → 第一行为偏振器方位角（单位：弧度），第二行为PSA仪器矩阵的CN值（对应系统最小CN值）
- CN_PSG_vs_alfaP_PDmax_n.txt → 第一行为偏振器方位角（单位：弧度），第二行为PSG仪器矩阵的CN值（对应系统最小CN值）
- CN_vs_alfaP_PDmax_n.txt → 第一行为偏振器方位角（单位：弧度），第二行为系统最小CN值
- EWV_vs_alfaP_PDmax_n.txt → 第一行为偏振器方位角（单位：弧度），第二行为系统EWV值（对应系统最小CN值）
- linear_phase1_alfaP_PDmax_n.txt → 第一行为偏振器方位角（单位：弧度），第二行为n组TNLC线性相位（单位：弧度，对应系统最小CN值）
- linear_phase2_alfaP_PDmax_n.txt → 第一行为偏振器方位角（单位：弧度），第二行为n组LCVR线性相位（单位：弧度，对应系统最小CN值）
- PSA_vs_alfaP_PDmax_n.mat → 存储每个偏振器方位角对应的分析仪斯托克斯矢量矩阵（对应系统最小CN值），每列代表一个斯托克斯矢量
- PSG_vs_alfaP_PDmax_n.mat → 存储每个偏振器方位角对应的发生器斯托克斯矢量矩阵（对应系统最小CN值），每列代表一个斯托克斯矢量

单元格数组索引与偏振器方位角索引一致。

分析/解释结果的推荐软件：MATLAB。