Objective Polarimeters, as powerful tools for characterizing the polarization characteristics of light and various samples, have important applications in low signal-to-noise ratio detection fields such as remote sensing and lithography. Traditional polarimeters excel in accuracy, speed, and compactness in strong light fields. However, their measurement accuracy becomes unreliable in low light fields due to strong background noise and interference from complex systems. Recently, the spatially modulated polarimeter based on the vortex wave plate achieves a single measurement of polarization information with a simple optical path. This method, combined with a specific denoising method, measures the full polarization component at low light fields. However, existing research ignores the influence of the size and spatial variation characteristics of the spatially modulated model parameters, which significantly affects the measurement accuracy of the Stokes parameters. Based on keeping the fast axis angle of the polarizer at a level, we theoretically derive and experimentally verify the influence of the fast axis angle of the quarter-wave plate on the measurement accuracy of the Stokes vector at strong light fields and determine the optimal angle using the instrument matrix condition number optimization method. Our work provides a theoretical and experimental basis for high-accuracy polarization measurement in low light fields. Methods Through simulation and experiment, we compare the measurement accuracy under different fast axis angles of the wave plate and select the angle with the highest accuracy and stability using the instrument matrix condition number optimization method. Firstly, the theoretical model of the spatially modulated polarimeter based on the vortex quarter-wave plate is established, and the influence of the fast axis angle of the wave plate on the modulation parameters in the spatially modulated analyzer is quantitatively deduced. The distribution characteristics of modulation parameters are measured by maximum, minimum, mean, and variance. Meanwhile, the polarization information corresponding to the simulated spatially modulated image is solved using a direct enumeration algorithm. We then equate spatially modulated measurement by multiple time-division measurements under different conditions and establish the corresponding instrument matrix. According to the theory of instrument matrix condition number, the optimal angle is determined. Finally, multiple spatial modulated images are measured under different fast axis angles of the wave plate, and the polarization information is solved from simulation and experiment. To verify stability, three repetitive measurements are performed under different experimental environments by changing the output current of the LED. Results and Discussions The influence of the fast axis angle on the characteristics of the model parameters is measured by the maximum, minimum, mean, and variance. From Fig. 2(a) and (b), it is found that the maximum value of m(01) is stable at 0.5, and the minimum value oscillates sinusoidally between 0 and -0.5. The maximum value of m(02) varies between 0.25 and 0.5, oscillating around 0.5 at most angles, while the minimum value changes between -0.25 and -0.5, showing a compound sinusoidal trend. The maximum and minimum values of m(03) change in a sinusoidal trend with a period of 90 degrees, ranging from 0 to +/- 0.5, reaching the maximum value at 0 degrees, with a mean value of 0. Fig. 2(c) and (d) shows the mean and variance of the model parameters. The mean values of m(01) and m(02) change periodically in a sinusoidal trend, the mean value of m(03) is 0, and the variance of the three parameters changes periodically at 90 degrees. The variance of m(01) and m(02) reaches the maximum at 0 degrees, and the minimum value of m(03) at 0 degrees. After processing the simulation data, it can be seen from Table 1 that the error of the S-3 component reaches its maximum when the azimuth is +/- 45 degrees, corresponding to the characteristics of the model parameters. The error of the S-1 and S-2 components reaches its maximum at the azimuth of +/- 30 degrees, but it is two orders of magnitude less than the maximum error of S-3. Considering the accuracy limitation of the enumeration algorithm, the S-1 and S-2 components show high accuracy under different fast axis azimuths. We find that when the fast axis angle of Q2 is 0 degrees, the minimum condition number of the instrument matrix is 3.6158. From 0 degrees to +/- 45 degrees, it shows an upward trend and reaches infinity at +/- 45 degrees as determined by the instrument matrix optimization method. For the experimental data processing, the model parameters under different fast axis angles are shown (Figs. 3-6). The spatially modulated image corresponding to the horizontally polarized light under different fast axis azimuth angles is shown (Fig. 7). Combining three repetitive tests and processing, the measurement accuracy is highest and the stability is the best when the fast axis azimuth is 0 degrees (Tables 2-4). The simulation and experimental results verify the influence of the fast axis angle on the measurement accuracy, which is consistent with our theoretical derivation and optimization results. Conclusions In spatially modulated polarization measurement, the setting of the fast axis azimuth of the wave plate in the spatially modulated analyzer system affects the measurement accuracy. We determine the optimal angle by optimizing the condition number of the instrument matrix. Through theoretical analysis, it is found that the azimuth angle has the greatest influence on the S-3 component. We conduct simulations and experiments to verify the influence of different azimuth angles on measurement accuracy. The experimental results show that the measurement accuracy and stability are optimal when the azimuth angle is 0 degrees. At 45 degrees, the average error of the S-3 parameter reaches its maximum, which is also consistent with theory. Through theoretical derivation and experimental verification, the influence of different fast axis azimuth angles of wave plates on the accuracy of spatially modulated polarization measurement is quantitatively analyzed, providing a theoretical and experimental basis for high-accuracy polarization measurement at low light fields.
