In contrast to traditional physical measurement methods, machine-learning-based precision measurement is a “data-driven” approach that constitutes a new field of research. We report a machine-learning-based precision measurement of a rotational angle from a vortex-mode shear interferometer, as the two-dimensional optical images at different angles contain the interference patterns that are inherently encoded into the light orbital angular momentum states. Through our evaluation of different convolutional neural networks, we have determined that the ResNeXt50 model excels in detecting minute angle changes across resolutions of 0.05°, 0.1°, 0.5°, 4°, and 10°. This model for the vortex beams achieves over 99.9% accuracy for resolutions of 0.1°, 0.5°, 4°, and 10°, and over 97.0% accuracy for the highest 0.05° resolution. The new results in experiments and modeling demonstrate a robust, accurate, and scalable approach to high-precision rotational angle measurement.

In this Letter, we report an Airy-like beam of magnetostatic surface spin wave (AiBMSSW) supported on the ferromagnetic film, which is transferred from the optical field. The propagation properties of AiBMSSW were verified with micromagnetic simulation. From simulation results, the typical parabolic trajectory of the Airy-type beam was observed with an exciting source encoding 3/2 phase pattern. The simulation results coincide well with design parameters. Furthermore, simulated results showed that the trajectories of the AiBMSSW could be tuned readily with varied external magnetic fields. This work can extend the application scenario of spin waves.