Fig. 1. Principle of the position measurement system based on phase grating

Fig. 2. Schematic diagram of EmG and E−mG when the grating is asymmetric structure

Fig. 3. Structure of the asymmetric grating

Fig. 4. Structure of the decomposed grating. (a) Grating G1; (b) grating G2; (c) grating G3; (d) grating G4

Fig. 5. Structure of the asymmetric grating

Fig. 6. Schematic diagram of E_m and E_－m when h＝(2n－1)λ/4

Fig. 7. Schematic diagram of E_m and E_－m when sin(mπf＋2πΔh/λ)＝0

Fig. 8. Effect of Δh on V and Δx and the corrected Δx when h is certain. (a) Change curve of V with Δh；(b) change curve of Δx with Δh; (c) change curve of Δx with Δh after correction (top tilt)

Fig. 9. Effect of h on V and Δx and the corrected Δx when Δh is certain. (a) Change curve of V with h；(b) change curve of Δx with h; (c) change curve of Δx with h after correction (top tilt)

Fig. 10. Structure of the bottom tilted asymmetric grating

Fig. 11. Schematic diagram of E_m and E_－m when h－Δh/2＝(2n－1)λ/4

Fig. 12. Effect of Δh on V and Δx and the corrected Δx when h is certain. (a) Change curve of V with Δh；(b) change curve of Δx with Δh; (c) change curve of Δx with Δh after correction (bottom tilt)

Fig. 13. Effect of h on V and Δx and the corrected Δx when Δh is certain. (a) Change curve of V with h；(b) change curve of Δx with h; (c) change curve of Δx with h after correction (bottom tilt)

Fig. 14. Structure of the sidewall tilted asymmetric grating

Fig. 15. Schematic diagram of E_m and E_－m when mf＝n－1/2 and n is a positive even value

Fig. 16. Effect of Δf on V and Δx and the corrected Δx when f is certain. (a) Change curve of V with Δf；(b) change curve of Δx with Δf; (c) change curve of Δx with Δf after correction (sidewall tilt)

Fig. 17. Effect of f on V and Δx and the corrected Δx when Δf is certain. (a) Change curve of V with f；(b) change curve of Δx with f; (c) change curve of Δx with f after correction (sidewall tilt)

Fig. 18. Structure of the multiple asymmetric phase grating

Fig. 19. Contrast V changes with f₆ and h₄. (a) m＝1; (b) m＝3; (c) m＝5; (d) m＝7; (e) m＝9

Fig. 20. Position error Δx changes with f₆ and h₄. (a) m＝1; (b) m＝3；(c) m＝5; (d) m＝7; (e) m＝9; (f) after correction

Fig. 21. Calculation results of scalar diffraction theory and RCWA method