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基于等效矢量模型的双光楔逆解算法研究

冯建鑫 王强 王雅雷 胥彪

冯建鑫, 王强, 王雅雷, 胥彪. 基于等效矢量模型的双光楔逆解算法研究[J]. 中国光学. doi: 10.37188/CO.2021-0117
引用本文: 冯建鑫, 王强, 王雅雷, 胥彪. 基于等效矢量模型的双光楔逆解算法研究[J]. 中国光学. doi: 10.37188/CO.2021-0117
FENG Jian-xin, WANG Qiang, WANG Ya-lei, XU Biao. Research on risley-prism inverse algorithm based on equivalent vector model[J]. Chinese Optics. doi: 10.37188/CO.2021-0117
Citation: FENG Jian-xin, WANG Qiang, WANG Ya-lei, XU Biao. Research on risley-prism inverse algorithm based on equivalent vector model[J]. Chinese Optics. doi: 10.37188/CO.2021-0117

基于等效矢量模型的双光楔逆解算法研究

doi: 10.37188/CO.2021-0117
基金项目: 国家自然基金(No. 61603183);南京航空航天大学研究生创新基地(实验室)开放基金(No. Kfjj20201502)
详细信息
    作者简介:

    冯建鑫(1982—),男,江苏沛县人,博士,副教授,硕士生导师,2008年、2012年于哈尔滨工业大学分别获得硕士、博士学位,主要从事运动载荷视轴稳定技术、高精度跟瞄控制技术等方面的研究。E-mail:fengjx774@163.com

    王 强(1995—),男,湖北黄石人,硕士研究生,2018年于南京航空航天大学获得学士学位,主要从事智能控制算法、光楔高精度控制技术等方面的研究。E-mail:wq0227@nuaa.edu.cn

  • 中图分类号: O439; TH703

Research on risley-prism inverse algorithm based on equivalent vector model

Funds: Supported by National Natural Science Foundation of China (No. 61603183); Nanjing University of Aeronautics and Astronautics graduate student innovation base (laboratory) Open Fund Project (No. kfjj20201502)
More Information
  • 摘要: 为了进一步提高双光楔结构中反解算法的计算精度、减少计算时间,为此本文将正演迭代法与光楔等效矢量模型相结合,提出等效矢量迭代法。首先,根据光楔对光线的偏转作用建立光楔等效矢量模型。接着,利用矢量叠加的方法求解双光楔出射光线的矢量坐标。然后,将等效矢量模型代入双光楔两步逆解算法中进行计算,求解双光楔旋转角度的近似值。最后,利用正演迭代、逐步逼近的思想,提出等效矢量迭代逆解算法,并计算得到双光楔的旋转角度。实验结果表明:该算法的计算精度达到10 μm级别,计算时间在0.1 ms以内。该算法能有效提高计算精度、降低计算时间,在高精度光束指向领域具有广泛的应用前景。
  • 图  1  双光楔系统坐标系示意图

    Figure  1.  Schematic diagram of the coordinate system of Risley-prism

    图  2  界面处光线折射光路图

    Figure  2.  Light path diagram of light refraction at the interface

    图  3  旋转单光楔光路

    Figure  3.  Single Rotating Risley-prism optical path

    图  4  旋转双光楔等效矢量模型

    Figure  4.  Equivalent vector model of the single Risley-prism

    图  5  旋转双光楔等效矢量模型

    Figure  5.  Equivalent vector model of the Risley-prism

    图  6  两步逆解法流程图

    Figure  6.  Flow chart of two step inverse method

    图  7  等效矢量迭代法流程图

    Figure  7.  Flow chart of the equivalent vector iteration method

    图  8  两步法(左)目标轨迹、扫描轨迹(右)棱镜转角

    Figure  8.  Two step method (L) target trajectory and scanning trajectory (R) Prism angle

    图  9  等效矢量两步法(左)目标轨迹、扫描轨迹(右)棱镜转角

    Figure  9.  Equivalent vector two-step method (L) target trajectory and scanning trajectory (R) Prism angle

    图  10  正演迭代法(左)目标轨迹、扫描轨迹(右)棱镜转角

    Figure  10.  Forward iterative refinement algorithm (L) target trajectory and scanning trajectory (R) Prism angle

    图  11  等效矢量迭代法(左)目标轨迹、扫描轨迹(右)棱镜转角

    Figure  11.  Equivalent vector iteration method (L) target trajectory and scanning trajectory (R) Prism angle

    图  12  D2的影响(上)正演迭代法;(下)等效矢量迭代法

    Figure  12.  Influence of D2 (U) forward iteration method; (D) equivalent vector iteration method

    图  13  视场角大小产生的影响

    Figure  13.  The influence of Angle of view

    图  14  DSP实验装置图

    Figure  14.  Experimental device

    表  1  四种逆解算法的结果比较

    Table  1.   Comparison of the results of four inverse algorithms

    名称最小误差
    /mm
    最大误差
    /mm
    平均误差
    /mm
    计算
    时间/s
    两步法0.03910.41290.10310.008464
    等效矢量两步算法0.040650.53660.24560.007889
    正演迭代算法2.8114×10?058.5770×10?041.1093×10?040.346347
    等效矢量迭代
    算法
    4.1163×10?071.5946×10?067.3820×10?070.035116
    下载: 导出CSV

    表  2  两种逆解算法的计算结果比较

    Table  2.   Comparison of the results of two inverse algorithms

    名称目标点位置扫描点位置误差 /mm时钟 周期计算时间/ms
    正演迭代算法(3.063254, 2.025168)(3.062726, 2.024727)6.880 $ \times {10^{ - 03}}$5613073.702
    (?0.7943821, 2.657489)(????????0.7942457, 2.656589)9.103 $ \times {10^{ - 04}}$5443413.631
    (1.368747, ????????0.765749)(1.369308, ????????0.766287)7.776 $ \times {10^{ - 04}}$5407863.607
    (?4.084592, ???????????????3.019157)(?4.083504, ???????????????3.018215)1.439 $ \times {10^{ - 03}}$5407863.667
    等效矢量迭代法(3.063254, 2.025168)(3.063266, 2.025181)1.772 $ \times {10^{ - 05}}$133530.08906
    (?0.7943821, 2.657489)(?0.7943828, 2.657509)1.980 $ \times {10^{ - 05}}$133440.08900
    (1.368747, ?0.765749,)(1.368718, ?0.765717)4.258 $ \times {10^{ - 05}}$138170.09216
    (?4.084592, ?3.019157)(?4.084604, ?3.019171)1.875 $ \times {10^{ - 05}}$134310.08906
    下载: 导出CSV
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