Millimeter-range nanoscale displacement measurement through diffraction-field encoding and deep-learning decoding

This is the authors' abstract. We don't add key points for this paper.

High-precision displacement sensing is essential for precision positioning systems in manufacturing and metrology processes, but achieving nanoscale measurement over millimeter-scale ranges remains a significant challenge. To solve this challenge, this paper proposes a diffraction-image-based approach for nanoscale displacement sensing by exploiting the sensitivity of diffraction patterns to the position of a diffracting object. A compact optical system consisting of a light source, an aperture plate, and an image sensor is developed, in which displacement information is encoded in the diffraction field and decoded through a deep-learning framework. The Cramér–Rao lower bound is further employed to evaluate the theoretical displacement resolution limit of the proposed method. To enhance regression performance, a multi-scale combined loss function is introduced for network optimization. The approach is validated through online experiments using a Newport translation stage. Experimental results demonstrate that the system achieves approximately 10 nm displacement resolution and 200 nm full-scale measurement accuracy over a 1 mm range, with a repeatability better than 40 nm. These results reveal that displacement information encoded in diffraction-field redistribution can be effectively recovered by deep learning, providing a simple and low-cost solution for high-precision displacement measurement.