Fig. 1. Diagram of rotation angle

Fig. 2. Precision displacement measurement system based on vortex beam conjugate interference

Fig. 3. Schematic diagram of interferogram data processing for sub-nanometer displacement measurement

Fig. 4. Schematic diagram of interferogram data processing for large measuring range displacement measurement

Fig. 5. Results for optical system design. (a) System structure; (b) imaging result

Fig. 6. Design scheme for experimental system

Fig. 7. Experimental setup for precision displacement measurement system. (a) Before packaging; (b) after packaging

Fig. 8. Collected interference patterns. (a) Before displacement; (b) after displacement

Fig. 9. Relative intensity distribution corresponding to data markers on ring

Fig. 10. Experimental results of sub-nanometer measurement scheme

Fig. 11. Relative intensity varying with time

Fig. 12. Experimental results. (a) Displacement measurement results; (b) error distribution

Fig. 13. Vortex beam interference correction scheme based on global optimization algorithm

Fig. 14. Displacement measurement schemes before and after DE algorithm correction. (a) Distorted vortex beam conjugate interferograms before and after displacement; (b) corrected vortex beam conjugate interferograms before and after displacement; (c) relative intensity distribution on ring before correction; (d) relative intensity distribution on ring after correction