Fig. 1. Schematic diagrams: (a) illustration of the rotation angle β; the rotation axis is parallel to the surface of the optical platform; (b) side view showing the wedge angle δ to the internal reflection with a tilt angle θ; (c) top view showing the angle of incidence α. (d) Experimental setup for rotational angle measurement. ISO, optical isolator; ND, neutral density filter; M, mirror; L1, L2, lenses; HWP, half-wave plate; BS, beam splitter; SLM, spatial light modulator; SI, rotatable shear interferometer (a wedged optical flat on an electric rotating machinery); CCD, charge-coupled device.

Fig. 2. Interferometric distributions of OAM with different rotation angles (β) of the wedge optical flat for integer topological charge l = 1 are shown in light field distribution from experiment (a) and theory (b), and for fractional topological charge l = 1.5 are shown in light field distribution from experiment (c) and theory (d).

Fig. 3. Experimental interference distributions with a fine resolution of rotational angle (β) at 0.05° in the first and second rows, and a coarse resolution at 0.5° in the third and fourth rows.

Fig. 4. Accuracies of different neural networks for the rotational angle resolution Δβ = 0.05°.

Fig. 5. Image recognition of rotation angle based on the improved residual convolutional network (ResNeXt50). (a) Building blocks in Conv2; (b) building blocks in Conv3; (c) building blocks in Conv4; (d) building blocks in Conv5. The content in each black box is denoted as the filter size and output channels.

Fig. 6. 3D plots of training performance on angle resolution and epochs. (a) Accuracy curve; (b) loss curve.

Fig. 7. Test accuracies of different angle resolutions Δβ.

Fig. 8. Confusion matrices of (a) l = 1, Δβ = 0.1°, (b) l = 1.5, Δβ = 0.1°, (c) l = 1, Δβ = 0.05°, and (d) l = 1.5, Δβ = 0.05°.