Cross-Scale Positioning of Three Degree-of-Freedom Planar Motions With Subnanometer Resolution Using an Encoded Pattern

High-precision and multiple degree-of-freedom (DOF) position sensing plays a central role in advanced mechatronic systems across a wide variety of applications, including fabrication, manipulation, and surface scanning. However, it remains a challenge to implement high-precision positioning over a large scale due to the inherent contradiction between measurement resolution and range. Here, we propose a visual sensing-based approach for accurate and cross-scale position measurement using an encoded pattern. In this method, the pattern is attached to the moving target, and three-DOF planar positioning (X, Y, and $\theta _{Z}$ ) is realized by analyzing the Fourier spectrum of continuously captured 2-D periodic images. Lateral displacements (X and Y) and rotation angle $\theta _{Z}$ are independently extracted from the phase and amplitude spectra, respectively, ensuring decoupled measurements along all three axes. Real-time trajectory tracking experiments were carried out over a $90\times 90$ mm2 area. The results demonstrate that the system achieves measurement standard deviations (STDs) of 0.81 nm, 0.77 nm, and $2.19~\mu $ rad in the X-, Y-, and $\theta _{Z}$ -axes, respectively. The corresponding expanded uncertainties at a 95% confidence level are ±1.76 nm, ±1.70 nm, and $\pm 4.82~\mu $ rad. The proposed approach provides a practical and scalable solution for trajectory planning and precision control in mechatronic systems that require both cross-scale range and high-precision positioning.