Relationship between performance of stochastic parallel gradient descent algorithm and distribution rule of deformable mirror
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摘要: 对随机并行梯度下降算法（SPGD）性能与不同变形镜排布规律的关系进行了研究。以采用Roddier方法生成的由52项Zernike像差构成的畸变波前为整形对象，对SPGD算法的收敛速率和整形效果与变形镜排布规律（单元数分别为19、21、32、37、45、60、61、77、91）之间的关系进行了仿真研究。结果表明：从整体分析，随着变形镜单元数逐渐增多，SPGD算法的收敛速率和整形效果均逐渐变差；从局部分析，由于变形镜元胞类型变化和边缘占空比的影响，在渐变规律中产生了局部差异。
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关键词:
- 波前整形 /
- 随机并行梯度下降算法 /
- 变形镜
Abstract: The relationship between the performance of stochastic parallel gradient descent(SPGD) algorithm and distribution rule of deformable mirror is studied in this paper. The study object is distortion wave-front including 52 order Zernike aberrations created with Roddier method. The simulation research mainly focuses on relationship between convergence rate, shaping effect of SPGD algorithm and distribution rule of deformable mirrors with 19, 21, 32, 37, 45, 60, 61, 77, and 91 units. The results show that from the general analysis, the convergence and shaping effects of SPGD algorithm gradually become worse with actuator number of deformable mirror increases, but from the partial analysis, this trend create local difference due to different cell type and void ratio in the edge of deformable mirror. -
图 4 利用SPGD算法控制不同单元变形镜得到的性能指标J随迭代次数n变化的收敛过程
Figure 4. Convergence course that performance index J changes as iterative number n with SPGD algorithm by controlling different N-unit deformable mirror
图 5 利用SPGD算法分别控制不同N单元变形镜整形到极限情况下得到的残余波前分布
Figure 5. Residual wave-front distribution obtained with SPGD algorithm by controlling different N-unit deformable mirror under the limiting condition
表 1 Jlim、PVlim、RMSlim与不同变形镜单元数N之间的关系
Table 1. Relationship between Jlim,PVlim,RMSlim and different N-unit deformable mirror
N 91 77 61 60 45 37 32 21 19 Jlim=J5000 0.997 6 0.913 6 0.976 4 0.949 4 0.918 0 0.909 0 0.915 0 0.768 4 0.693 2 PVlim 0.168 9λ 0.818 4λ 0.533 7λ 0.754 0λ 0.803 4λ 0.837 2λ 0.733 9λ 1.343 5λ 1.242 8λ RMSlim 0.007 7λ 0.047 9λ 0.024 6λ 0.036 3λ 0.046 6λ 0.049 2λ 0.047 4λ 0.081 7 0.096 3 
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