Deep learning-based conjugate orbital angular momentum interferometry for in-plane displacement measurement

A deep learning-based phase demodulation algorithm is proposed for measuring in-plane displacements in conjugate orbital angular momentum (OAM) interferometry. The phase demodulation hybrid neural network (PDHNN) is designed to directly demodulate petal-shaped interferograms in a single step. PDHNN employs a custom ResNet-transformer architecture with deformable convolutions and attention mechanisms to extract rotation-sensitive features from petal-shaped interferograms for robust phase demodulation. The algorithm has been validated using both simulated and experimental data. Experimental results show that the demodulation accuracy reaches 91.60% within an error margin of 1°, and within a 0.1° error range, the average displacement error is 0.13 nm, demonstrating high robustness and stability in noisy conditions.