Fig. 1. Diagram of the detection and correction of the piston error based on far-field interference image clarity

Fig. 2. Curves of J varying with piston errors under different bandwidths of 0 nm, 3.2 nm, 16 nm, 32 nm, and 320 nm

Fig. 3. Curves of J varying with piston errors under bandwidths of 3.2 nm and 16 nm

Fig. 4. Curves of J varying with piston errors under bandwidths of 0 nm and 3.2 nm

Fig. 5. Variation trend of J with piston error under different spectral density distributions

Fig. 6. Iterative curves of J and e when the piston error takes different values

Fig. 7. Influence of Δd. (a) Δd is an integer multiple of half center wavelength; (b) Δd is a non-integer multiple of half-center wavelength

Fig. 8. Far-field interferograms before and after correction. (a) Before correction; (b) after correction

Fig. 9. Comparison of the convergence speed between bilateral and unilateral disturbance method

Fig. 10. Curve of J varying with piston errors under a bandwidth of 32 nm

Fig. 11. Comparison of the two methods. (a) Results of the unilateral disturbance method; (b) result of the bilateral disturbance method; (c) comparison of absolute error

Fig. 12. The impact of noise. (a) Iterative curve of absolute error before and after noise reduction by the threshold method; (b) comparison of absolute error before and after noise reduction by the threshold method

Fig. 13. Sub mirror arrangement and interferograms. (a) Sub mirror arrangement; (b) far-field interferogram before correction; (c) far-field interferogram after correction; (d) ideal far-field interferogram

Fig. 14. Iteration curve of sub mirror errors and absolute errors of Sub mirror after correction. (a) Iteration curve of sub mirror errors; (b) absolute errors of sub mirror after correction