Fig. 1. Conventions for the pupil vector and field vector

Fig. 2. Stellar images for different assembly errors. (a) Without misalignments, and with misalignment in (b) x direction; (c) y direction and (d) x & y direction

Fig. 3. Flow chart of misalignment calculation

Fig. 4. Optical layout of Hilbert optical system

Fig. 5. Distribution of PSF and ellipticity under different misalignment status. (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4

Fig. 6. Distribution of ellipticity (a) e₁, (b) e₂ in ideal status

Fig. 7. Distribution of ellipticity (a) e₁, (b) e₂ in misaligned status

Fig. 8. Distribution of ellipticity parameter (a) e₁ and (b) e₂ in the case of introduced II, distribution of ellipticity parameter (c) e₁ and (d) e₂ in the case of calculated II

Fig. 9. Processes and results in the case of introduced II. (a) Variation of MF value with iteration times; (b) Distribution of particle swarm after the 1st iteration; (c) Distribution of particle swarm after the 15th iteration; (d) Output misalignment

Fig. 10. Misalignment calculation error in different SNR