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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(中英文), 2022, 15(1): 56-64. 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(中英文), 2022, 15(1): 56-64. doi: 10.37188/CO.2021-0117
FENG Jian-xin, WANG Qiang, WANG Ya-lei, XU Biao. Risley-prism inverse algorithm based on equivalent vector model[J]. Chinese Optics, 2022, 15(1): 56-64. doi: 10.37188/CO.2021-0117
Citation: FENG Jian-xin, WANG Qiang, WANG Ya-lei, XU Biao. Risley-prism inverse algorithm based on equivalent vector model[J]. Chinese Optics, 2022, 15(1): 56-64. 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

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,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  旋转单光楔等效矢量模型

    Figure 4.  Equivalent vector model of the rotary single 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(a)目标轨迹、扫描轨迹与(b)棱镜转角

    Figure 8.  (a) Target trajectory and scanning trajectory and (b) rotation angle of prism for two-step method

    图 9  等效矢量两步法(a)目标轨迹、扫描轨迹与(b)棱镜转角

    Figure 9.  (a) Target trajectory and scanning trajectory and (b) rotation angle of prism for equivalent vector two-step method

    图 10  正演迭代法(a)目标轨迹、扫描轨迹与(b)棱镜转角

    Figure 10.  (a) Target trajectory and scanning trajectory and (b) rotation angle of prism for forward iterative refinement algorithm

    图 11  等效矢量迭代法(a)目标轨迹、扫描轨迹与(b)棱镜转角

    Figure 11.  (a) Target trajectory and scanning trajectory and (b) rotation angle of prism for equivalent vector iteration method

    图 12  D2对两种算法的影响。(a)正演迭代法;(b)等效矢量迭代法

    Figure 12.  Influence of D2 on two algorithms. (a) Forward iteration method; (b) equivalent vector iteration method

    图 13  视场角大小对(a)正演迭代算法和(b)等效矢量迭代算法的影响

    Figure 13.  Influence of angle of view on (a) forward interative refinement algorithm and (b) equivalent vector iteration method

    图 14  DSP实验装置图

    Figure 14.  Experimental device

    表  1  4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2.8114×10−58.5770×10−41.1093×10−40.346347
    等效矢量迭代
    算法
    4.1163×10−71.5946×10−67.3820×10−70.035116
    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^{ - 3} }$5613073.702
    (−0.7943821, 2.657489)(−​​​​​​​0.7942457, 2.656589)9.103 $\times {10^{ - 4} }$5443413.631
    (1.368747, −​​​​​​​0.765749)(1.369308, −​​​​​​​0.766287)7.776 $\times {10^{ -4} }$5407863.607
    (−4.084592, −​​​​​​​​​​​​​​3.019157)(−4.083504, −​​​​​​​​​​​​​​3.018215)1.439 $\times {10^{ - 3} }$5407863.667
    等效矢量迭代法(3.063254, 2.025168)(3.063266, 2.025181)1.772 $\times {10^{ - 5} }$133530.08906
    (−0.7943821, 2.657489)(−0.7943828, 2.657509)1.980 $\times {10^{ - 5} }$133440.08900
    (1.368747, −0.765749,)(1.368718, −0.765717)4.258 $\times {10^{ - 5} }$138170.09216
    (−4.084592, −3.019157)(−4.084604, −3.019171)1.875 $\times {10^{ - 5} }$134310.08906
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-29
  • 修回日期:  2021-07-13
  • 网络出版日期:  2021-08-20
  • 刊出日期:  2022-01-19

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