Fig. 1. Schematic diagram of sub-aperture stitching. (a) Stitching of adjacent sub-apertures; (b) sub-aperture mechanical positioning error

Fig. 2. Flow chart of the algorithm

Fig. 3. Simulated cylindrical mirror and sub-apertures. (a) Fitting surface of cylindrical mirror; (b) simulated sub-apertures

Fig. 4. Sub-aperture compensation effect. (a)-(d) Residuals between sub-aperture surface and original fitting sub-aperture surface when adding -5°, -2°, 2°, 5° angle errors; (e)-(h) residuals between original fitting sub-aperture surface and sub-aperture surface after angle error compensation

Fig. 5. Simulation of stitching compensation. (a) Original simulation surface; (b) stitching surface after introducing positioning error; (c) stitching surface after positioning error compensation; (d) residuals between original simulation surface and stitching surface after introducing positioning error; (e) residuals between original simulation surface and stitching surface after positioning error compensation

Fig. 6. Measuring device and tested mirror. (a) 6 inch interferometer; (b) elliptic cylindrical mirror

Fig. 7. Effect of single sub-aperture compensation. (a) Original sub-aperture $S_{\mathrm{2}}$; (b) sub-aperture after introducing positioning error $S_{\mathrm{2}}^{\mathrm{\text{'}}}$; (c) sub-aperture after positioning error compensation $N_{\mathrm{2}}$; (d) $S_{\mathrm{2}}-S_{\mathrm{2}}^{\mathrm{\text{'}}}$; (e) $S_{\mathrm{2}}-N_{\mathrm{2}}$

Fig. 8. Effect of full-aperture stitching compensation. (a) Original sub-aperture stitching surface $T_{\mathrm{1}}$; (b) stitching surface after introducing positioning error $T_{\mathrm{2}}$; (c) stitching surface after positioning error compensation $T_{\mathrm{3}}$; (d) $T_{\mathrm{1}}-T_{\mathrm{2}}$; (e) $T_{\mathrm{1}}-T_{\mathrm{3}}$

Fig. 9. Stitching surface and long trace profiler measurement results. (a) Stitching surface before positioning error compensation; (b) stitching surface after positioning error compensation; (c) center line measured by long trace profiler; (d) residuals between long trace profiler surface and stitching surface before error compensation; (e) residuals between long trace profiler surface and stitching surface after error compensation

Table 1. Key parameters of genetic algorithm

Table 2. Simulated cylindrical mirror parameters

Table 3. Addition of positioning error and algorithm estimation results

Table 4. Position error addition of sub-apertures