Double-subdivision vortex beam interferometer enhanced by DenseNet for precision displacement measurement

This paper proposes a double-subdivision conjugate vortex beam interferometer integrated with a DenseNet-based deep learning framework for high-precision micro-displacement measurement. The system exploits the linear relationship between the rotation of conjugate vortex beam interference fringes and displacement, achieving doubled sensitivity through polarization modulation and a compact double-reflection optical configuration. The double-subdivision optical path introduces two reflections on the target surface, resulting in a doubled fringe rotation angle compared with a conventional interferometer and producing high-contrast displacement feature maps. DenseNet-169 is further introduced as a robust demodulation backend to replace traditional geometric algorithms and shallow convolutional analysis methods. By leveraging dense feature reuse and stable gradient propagation, the network preserves subtle rotational features and mitigates inherent system-level optical perturbations, thereby improving displacement decoding accuracy. Experimental results demonstrate an average absolute error of 0.33 nm within a 0-1 μm range, maintaining sub-nanometer precision over a wide measurement range. The synergistic integration of double-subdivision optical amplification and DenseNet-based demodulation provides a promising non-contact solution for precision metrology and optical sensing.