Fig. 1. Amplitude transmittance of GW-FSMs at different topology charges, and corresponding intensity and phase distributions of diffraction optical fields. (a) Amplitude transmittance of GW-FSMs (upper) at ℓ =3, 4, 5, and corresponding intensity (lower) and phase (inset) distributions of diffraction optical fields at z=1 m; (b) intensity (upper) and phase (lower) distributions of diffraction optical fields at different propagation distances produced by GW-FSM at ℓ =4

Fig. 2. Amplitude transmittance of GW-FSMs at ℓ =4 and corresponding intensity distributions of diffraction optical fields at z=1 m with different ρ₀, d₀, a

Fig. 3. Evolution of vortex interference optical field with propagation distance z for designed GW-FSW

Fig. 4. Measurement principle of dynamic displacement via carrier vortex interferometry. (a) Illustration of generation of one-dimensional temporal signal resulting from vortex interference optical field modulated by rotating chopper; (b) normalized one-dimensional temporal signals corresponding to displacement velocities v=0, 1, -0.5 μm/s when angular velocity of chopper Ω=10π rad/s; (c) spectra of time-domain signal

Fig. 5. Experimental system of carrier vortex interferometry. (a) Optical layout, with inset for photo of lithographic GW-FSM; (b) photo of experimental setup, with inset for photo of chopper blade

Fig. 6. Comparison between simulated results (upper) and experimental results (lower) of vortex beam and vortex interferogram at different propagation distances. (a) Vortex beams; (b) vortex interferograms

Fig. 7. Temporal signals (left) and frequency spectra (right) corresponding to angular velocities of chopper of Ω=10π, 8π, 5π, 4π rad/s when surface is still

Fig. 8. Frequency spectra corresponding to surface displacement velocities v=±0.5, ±1, ±1.5 μm/s under different carrier frequencies. (a) f_c=40 Hz; (b) f_c=32 Hz; (c) f_c=20 Hz; (d) f_c=16 Hz

Fig. 9. Doppler frequency error and surface displacement velocity error under different carrier frequencies. (a) f_c=40 Hz; (b) f_c=32 Hz; (c) f_c=20 Hz; (d) f_c=16 Hz

Fig. 10. Effect of surface tilt on dynamic displacement measurement