Fig. 3. Comparison of sampling efficiency between ordered and disordered designs.

a–c Ordered polarization filter arrangements and the corresponding volume enclosed within the Poincaré sphere. The red box denotes the basic arrangement unit. The coordinate axes represent the last three components of the Stokes-like vector ${\mathit{M}}_{i,j}={\left[m_{i,j}^0,m_{i,j}^1,m_{i,j}^2,m_{i,j}^3\right]}^T$. d $\mu \left(\mathit{\Lambda },\mathit{\Psi }\right)$ on different arrangements. Due to variations in sampling efficiency within each 12 × 12 patch of the designed disordered metasurface array, we randomly select 10,000 patches from our 400 × 400 metasurface array to calculate the sampling efficiency and illustrate these results in the form of density plot for fairness. The inset in (d) is a 12 × 12 patch, serving as an example to illustrate the arrangement of random polarization encoding.