Author Affiliations
1Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan , China2University of Chinese Academy of Sciences, Beijing 100049, Chinashow less
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 ; (b) sub-aperture after introducing positioning error ; (c) sub-aperture after positioning error compensation ; (d) ; (e)
Fig. 8. Effect of full-aperture stitching compensation. (a) Original sub-aperture stitching surface ; (b) stitching surface after introducing positioning error ; (c) stitching surface after positioning error compensation ; (d) ; (e)
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
Parameter | Value |
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Population scale Np | 200 | Crossover probability Pc | 0.5 | Mutation probability Pm | 0.1 | Iterations G | 200 | Range of , /pixel | [-10,10] | Range of /(°) | [-5,5] |
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Table 1. Key parameters of genetic algorithm
Parameter | Value |
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Equation | | a | 300100 | b | 43.782677 | Center coordinate | x0=299900.003191,y0=1.598171 |
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Table 2. Simulated cylindrical mirror parameters
Evaluation index | Addition of positioning error | Algorithm calculation results | Residuals |
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θadd /(°) | xadd/pixel | yadd /pixel | θc /(°) | xc/pixel | yc /pixel | θe /(°) | xe/pixel | ye /pixel |
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| -5 | 0 | 0 | -4.9969 | 0.0157 | 0.0136 | -0.0031 | -0.0157 | -0.0136 | | -4 | 1 | 1 | -4.0009 | 1.2911 | 0.9062 | 0.0009 | -0.2911 | 0.0938 | | -3 | 2 | 2 | -3.0036 | 2.0384 | 2.0097 | 0.0036 | -0.0384 | -0.0097 | | -2 | 3 | 3 | -2.0023 | 2.8883 | 3.1367 | 0.0023 | 0.1117 | -0.1367 | | -1 | 4 | 4 | -1.0015 | 3.7140 | 3.9763 | 0.0015 | 0.2860 | 0.0237 | | 0 | 5 | 5 | 0.0008 | 5.1053 | 4.9998 | -0.0008 | -0.1053 | 0.0002 | | 1 | 6 | 6 | 0.9999 | 6.1349 | 5.9788 | 0.0001 | -0.1349 | 0.0212 | | 2 | 7 | 7 | 2.0024 | 6.8761 | 6.9162 | -0.0024 | 0.1239 | 0.0838 | | 3 | 8 | 8 | 3.0012 | 7.9279 | 7.9932 | -0.0012 | 0.0721 | 0.0068 | | 4 | 9 | 9 | 3.9998 | 9.1483 | 8.9674 | 0.0002 | -0.1483 | 0.0326 | | 5 | 10 | 10 | 5.0006 | 10.340 | 10.1482 | -0.0006 | -0.3400 | -0.1482 | PV | | | | | | | 0.0067 | 0.6260 | 0.2420 | RMS | | | | | | | 0.0019 | 0.1830 | 0.0732 |
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Table 3. Addition of positioning error and algorithm estimation results
Sub-aperture | θadd /(°) | xadd/pixel | yadd /pixel |
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Sub-aperture 1 | 0 | 0 | 0 | Sub-aperture 2 | 3 | 2 | 2 | Sub-aperture 3 | 2 | 3 | 2 | Sub-aperture 4 | 5 | 3 | 3 | Sub-aperture 5 | 2 | 1 | 3 |
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Table 4. Position error addition of sub-apertures