This supplementary material provides detailed information and supporting data for a high-precision two-dimensional (2D) displacement metrology system based on a matrix metasurface. The key components include: 1. **Principle of the 2D Displacement Sensor**: The metasurface's spatially-varying Jones matrix is described using Fourier optics, combining diffraction and polarization analysis. The metasurface's Jones matrix is designed to handle horizontal, vertical, and diagonal polarizations for different diffraction orders. 2. **Optimization of the Metasurface**: The optimization process involves setting up a unit supercell of elliptical nanoantennas and using gradient descent to maximize the powers of three diffraction orders while satisfying constraints on contrast and standard deviation. 3. **Fabrication Process**: A step-by-step diagram illustrates the fabrication process, including substrate preparation, film growth, resist coating, patterning, etching, and resist removal. 4. **Data Acquisition and Processing**: The method for aligning and scanning the metasurface, collecting and processing data, and extracting phase information from the modulated power of polarization components is detailed. 5. **Calibration Process**: The linear relationship between the metasurface's displacement and measured phase is established, and the sensitivity and orientation of the 2D displacement are calculated. 6. **Power Contrast Optimization**: Techniques to enhance the power contrast of the output light by optimizing the energy distribution among the three diffraction orders are discussed. The supplementary material also includes figures and references to support the theoretical and experimental findings, providing a comprehensive understanding of the system's design, implementation, and performance.This supplementary material provides detailed information and supporting data for a high-precision two-dimensional (2D) displacement metrology system based on a matrix metasurface. The key components include: 1. **Principle of the 2D Displacement Sensor**: The metasurface's spatially-varying Jones matrix is described using Fourier optics, combining diffraction and polarization analysis. The metasurface's Jones matrix is designed to handle horizontal, vertical, and diagonal polarizations for different diffraction orders. 2. **Optimization of the Metasurface**: The optimization process involves setting up a unit supercell of elliptical nanoantennas and using gradient descent to maximize the powers of three diffraction orders while satisfying constraints on contrast and standard deviation. 3. **Fabrication Process**: A step-by-step diagram illustrates the fabrication process, including substrate preparation, film growth, resist coating, patterning, etching, and resist removal. 4. **Data Acquisition and Processing**: The method for aligning and scanning the metasurface, collecting and processing data, and extracting phase information from the modulated power of polarization components is detailed. 5. **Calibration Process**: The linear relationship between the metasurface's displacement and measured phase is established, and the sensitivity and orientation of the 2D displacement are calculated. 6. **Power Contrast Optimization**: Techniques to enhance the power contrast of the output light by optimizing the energy distribution among the three diffraction orders are discussed. The supplementary material also includes figures and references to support the theoretical and experimental findings, providing a comprehensive understanding of the system's design, implementation, and performance.