Influence of laser communication Risley prism system error on pointing accuracy

激光通信旋转双棱镜系统误差对指向精度的影响 Influence of laser communication Risley prism system error on pointing accuracy 1 2 first-author 邱　赛（1997-），男，硕士研究生， 2017年于中国地质大学（武汉）获得学士学位，主要从事激光通信旋转双棱镜光束指向系统方面的研究。 E-mail：qiusai_edu@163.com http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424331&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424329&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424331&type= 24.39500427 34.20204163 邱　赛 （1997-），男，硕士研究生， 2017年于中国地质大学（武汉）获得学士学位，主要从事激光通信旋转双棱镜光束指向系统方面的研究。 E-mail： qiusai_edu@163.com qiusai_edu@163.com 1 corresp E-mail： sljlu@163.com E-mail： sljlu@163.com 盛　磊（1981-），男，博士，副研究员，2014年于中国科学院大学获得博士学位，主要从事光电测控设备软件开发及数据处理的研究。E-mail：sljlu@163.com http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424337&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424335&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424337&type= 25.10000610 31.87300110 盛　磊 （1981-），男，博士，副研究员，2014年于中国科学院大学获得博士学位，主要从事光电测控设备软件开发及数据处理的研究。E-mail： sljlu@163.com sljlu@163.com 1 1 1 中国科学院 长春光学精密机械与物理研究所， 吉林 长春 130033 中国科学院 长春光学精密机械与物理研究所， 吉林 长春 130033 Changchun Institute of Optics， Fine Mechanics and Physics， Chinese Academy of Sciences， Changchun 130033， China Changchun Institute of Optics， Fine Mechanics and Physics， Chinese Academy of Sciences， Changchun 130033， China 中国科学院大学， 北京 100049 中国科学院大学， 北京 100049 University of Chinese Academy of Sciences， Beijing 100049， China University of Chinese Academy of Sciences， Beijing 100049， China 分析了旋转双棱镜系统存在的误差源，根据误差源，采用光线矢量传播方法建立了光束指向模型，基于光束指向模型求旋转双棱镜系统出射光束指向偏差对系统误差的偏导数；在指向区域中，根据各个误差的测量精度分析误差对指向精度的影响。仿真计算结果表明，理论指向偏差最大值为0.362 0°，理论指向偏差均方根为0.047 0°；桌面实验结果表明，在99.54%的指向区域中，实验偏差最大值为0.356 3°，实验偏差均方根为0.023 3°，均小于仿真计算值。这一结果表明，本文对旋转双棱镜系统的误差分析较为准确，对旋转双棱镜平台的设计和补偿修正具有一定的参考价值。 The error source of the Risley prism system is analyzed and used to establish the beam-pointing model by using the light vector propagation method. The beam pointing model is used to calculate the partial derivative of the pointing deviation of the output beam from the Risley prism system to each error in the system. In the pointing area， the influence of errors on pointing accuracy is analyzed according to the accuracy of each error. The simulation calculation results show that the maximum theoretical pointing deviation is 0.362 0°， and the theoretical root mean square deviation is 0.047 0°. The desktop experimental results show that in 99.54% of the pointing area， the maximum experimental deviation is 0.356 3°， and the experimental deviation root mean square of 0.023 3° is less than the calculated simulation value. This result shows that the error analysis of the Risley prism system is accurate and could be used as a reference for the design and compensation of the Risley prism platform. 激光通信 旋转双棱镜 指向模型 误差分析 laser communication Risley prism pointing model error analysis 1 引　言 1 在激光通信指向系统中，通信双方通常采用捕获、跟踪、瞄准（Acquisition， Tracking， Pointing，ATP）技术建立并保持通信链路 ［ 1 1 - 3 3 1-3 ］ 。传统的ATP系统由于使用了万向式指向机构，其体积和质量普遍偏大，不能较好满足空间激光通信需求；旋转双棱镜系统则具有体积小、扫描范围大、对载体振动不敏感、动态性能好等优势，更适用于空间激光通信环境 ［ 4 4 - 8 8 4-8 ］ 。然而，旋转双棱镜系统存在多项误差，这些误差严重影响出射光束的指向精度 ［ 9 9 - 13 13 9-13 ］ 。为分析误差对光束指向的影响，本文展开对旋转双棱镜的误差分析与研究。 目前，旋转双棱镜的研究多针对旋转双棱镜的解算方法和扫描方式展开。周远等人 ［ 6 6 - 7 7 6-7 ］ 采用光束矢量传播方法推导了光束指向模型，但该指向模型未考虑系统存在的误差源。李锦英、Warger等 ［ 8 8 ， 14 14 ］ 研究了旋转双棱镜的扫描方式，旋转双棱镜有多重扫描方式可扫描全视野，不同扫描方式具有不同的扫描优势。Horng等 ［ 15 15 ］ 仅研究了轴承和楔形倾斜对最终指向的影响，其误差研究仅限于几个固定角度，其他角度未分析。ZHANG等 ［ 16 16 ］ 研究了轴承倾斜角随机误差与棱镜倾斜角随机误差对最终指向结果的影响，也仅限于几个固定角度下的误差研究与分析。 本文全面分析了对最终指向有影响的指向偏差，将对指向偏差影响相同的误差源归为一类，一共有4类误差，分别为棱镜楔角误差、入射光误差、棱镜转角误差和棱镜倾斜角误差。采用求偏导法求出出射光束指向偏差与各误差间的变化关系，根据各个误差的测量精度计算出它对出射光束指向偏差的影响。根据误差合成理论计算出射光束的总偏差，并用实验验证本文的误差分析结果，对后续的误差补偿与修正具有一定的参考价值。 2 工作原理与误差源 1 2.1　旋转双棱镜工作原理 2 旋转双棱镜系统中，两块棱镜采用背靠背方式进行排列；两块棱镜耦合可改变光束光程，进而改变光束指向。旋转双棱镜原理如 图1 图1 所示。 2.2　旋转双棱镜误差源 2 旋转双棱镜系统由激光器、两块旋转棱镜、两个电动旋转台和靶面等部分组成。激光器发射激光束至旋转棱镜П 1 ，经旋转棱镜П 1 折射，其出射光束进入旋转棱镜П 2 折射，其出射光束即为旋转双棱镜系统的出射光束。旋转双棱镜光束出射端放置相机作为靶面，相机获取出射光斑位置，经计算得到出射光束偏转角 Φ 和方位角 Θ 。旋转双棱镜的总体构成如 图2 图2 所示。 3 误差指向模型建立 1 首先建立坐标系，以棱镜П 1 的直角面中心为坐标原点 O ，与光轴重合为 Z 轴，以激光源发出的光束传播反方向为正向； Y 轴垂直于水平面，竖直向上为正向； X 轴与 Y 轴和 Z 轴为右手定则关系，其坐标系如 图1 图1 所示。 本文参考非近轴光线建立指向模型的方法，基于折射定律，采用光线矢量传播方法建立光束指向模型，光线矢量传播如 图3 图3 所示。 棱镜П 1 斜面法线矢量为 n 1 li ，棱镜П 1 直角面法线矢量为 n 1 ri ，棱镜П 2 直角面法线矢量为 n 2 li ，棱镜П 2 斜面法线矢量为 n 2 ri ，那么有： <math display="block" id="M1"><mtable><mtr><mtd><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo></mtd></mtr><mtr><mtd><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo></mtd></mtr><mtr><mtd><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424360&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424359&type= 71.54333496 31.41133499 其中： α 1 ， α 2 分别为棱镜П 1 ，П 2 的楔角；由于存在误差，棱镜П 1 光轴对理想光轴存在倾斜角，此倾斜角可用偏转角 B 1 和方位角 L 1 描述；棱镜П 2 光轴对理想光轴存在倾斜角，棱镜П 2 的倾斜角可用偏转角 B 2 和方位角 L 2 描述； θ 1 ， θ 2 分别为棱镜П 1 ，П 2 的转角。 根据折射定律，棱镜各界面的折射方程如下： <math display="block" id="M2"><mtable><mtr><mtd><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub><mo stretchy="false">)</mo><mo>,</mo></mtd></mtr><mtr><mtd><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><mn mathvariant="normal">1</mn><mo>=</mo><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><mn mathvariant="normal">2</mn><mo>=</mo><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><mn mathvariant="normal">3</mn><mo>=</mo><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><mn mathvariant="normal">4</mn><mo>=</mo><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msubsup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">[</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi>l</mi><mi>i</mi></mrow></msup><mo>⋅</mo><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">]</mo><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mroot><mrow><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><mn mathvariant="normal">1</mn></mrow><mrow/></mroot><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">[</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">]</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mroot><mrow><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><mn mathvariant="normal">2</mn></mrow><mrow/></mroot><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">[</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">]</mo><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mroot><mrow><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><mn mathvariant="normal">3</mn></mrow><mrow/></mroot><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">[</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">]</mo><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mroot><mrow><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><mn mathvariant="normal">4</mn></mrow><mrow/></mroot><mo>=</mo></mtd></mtr><mtr><mtd><mtext>                                          </mtext><mo stretchy="false">(</mo><mi>K</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>M</mi><mo stretchy="false">)</mo><mo>,</mo><mtext>                           </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424364&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424362&type= 75.60733032 58.41999817 其中： s 1 li 为入射光矢量； s 1 lo ， s 1 ro 分别为光束在棱镜П 1 斜面和直角面折射后的出射光束； s 2 lo ， s 2 ro 分别为光束在棱镜П 2 直角面和斜面折射后的出射光束，即双棱镜系统的出射光束； K ， L ， M 为出射光束的方向余弦。 出射光束偏转角 Φ 与方位角 Θ 分别为： <math display="block" id="M3"><mi>Φ</mi><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><mo>-</mo><mi>M</mi><mo stretchy="false">)</mo><mo>,</mo><mi>Θ</mi><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mi>L</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424370&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424367&type= 59.60533142 3.80999994 . 4 误差分析 1 旋转双棱镜指向模型包含4大误差，分别为棱镜楔角误差、入射光误差、棱镜转角误差和棱镜倾斜角，各自的误差范围可由检测设备获得。在求偏导分析某一误差时，其余误差均取其精度为误差设定值进行误差分析，误差源精度及其设定值如 表1 表1 所示。 名称 符号 精度 设定值 П 1 楔角 α 1 1″ 17.195 8° П 2 楔角 α 2 1″ 17.203 0° 入射倾斜角 B G 1″ 0.030 0° 入射方位角 L G 1″ -0.021 1° П 1 转角 θ 1 0.001 62° 0.001 62° П 2 转角 θ 2 0.001 62° 0.001 62° П 1 倾斜角 B 1 -0.006 6~0.005 4° -0.006 6° П 1 方位角 L 1 -0.000 2~0.004 1° 0.004 1° П 2 倾斜角 B 2 -0.008 2~0.007 4° -0.008 2° П 2 方位角 L 2 -0.006 5~ 0.005° -0.006 5° 4.1　棱镜楔角误差分析 2 旋转双棱镜指向模型中包含出射光束偏转角 Φ ， Θ 与棱镜楔角 α 1 ， α 2 的关系式。根据指向模型分别计算 Φ ， Θ 对 α 1 ， α 2 的偏导数，如 式（4） 式（4） 所示： <math display="block" id="M4"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">5</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">5</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">5</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424384&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424380&type= 64.68533325 22.26733208 ， 其中：（ X As 4 ， Y As 4 ， Z As 4 ），（ X As 5 ， Y As 5 ， Z As 5 ）分别为向量 As 4， As 5的三维坐标，由 式（5） 式（5） 得到； K ， L ， M 为出射光束的方向余弦，由式（2）可知。 <math display="block" id="M5"><mtable columnalign="left"><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">1</mn><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">1</mn><mo>=</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">1</mn><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">1</mn></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">2</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">3</mn><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mi>A</mi><mi>s</mi><mn mathvariant="normal">2</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">3</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">3</mn><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">3</mn><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">2</mn><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">5</mn><mo>=</mo><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>+</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">2</mn><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">5</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">5</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">5</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424388&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424386&type= 128.27000427 68.74933624 . 本文采用逐层求导获取 X As 4 ， Y As 4 ， Z As 4 的具体计算公式。例如，在求 s 2 ro 对 α 1 的偏导数 As 4时，将 s 2 lo 对 α 1 的偏导数设为 As 3，然后再求 As 3，逐级往下求偏导； An 1为最低一级的求偏导， An 1可直接计算得出，最低一级的公式求偏导均可直接计算得出。求 X As 5 ， Y As 5 ， Z As 5 的过程与 X As 4 ， Y As 4 ， Z As 4 的求解方法相同，均由出射光束 s 2 ro 往入射光束 s 1 li 方向逐级求导。 对指向影响的计算公式如下： <math display="block" id="M6"><mtable columnalign="left"><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>α</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>α</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>α</mi><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>α</mi><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424397&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424392&type= 51.47733307 18.88066673 ， 其中Δ α 1 ，Δ α 2 分别为 α 1 ， α 2 的精度。由 表1 表1 可知，由于中心区域误差较大，因此选定中心3°以内的区域为内指向区域，中心3°以外的区域为外指向区域，分两个区域进行分析。由于外指向区域误差占95%以上，故本文仅分析外指向区域的误差数据。棱镜楔角误差对指向结果的影响如 图4 图4 所示。为便于对比分析，具体误差数据仅在 表2 表2 中阐述分析。 名称 误差/（°） 均方根/（°） 名称 误差/（°） 均方根/（°） PΦ α 1 3.84×10 -10 ~0.006 6 0.001 2 PΦ θ2 0.005 6~0.056 0 0.008 5 PΘ α 1 6.29×10 -11 ~0.003 7 6.40×10 -4 PΘ θ 2 4.96×10-9~0.017 2 0.003 0 PΦ α 2 0.001 5~0.006 6 8.10×10 -4 PΦ B 1 1.81×10-7~0.058 4 0.014 9 PΘ α 2 1.19×10 -11 ~0.003 7 6.77×10 -4 PΘ B 1 1.14×10-8~0.307 1 0.036 6 PΦ BG 2.83×10 -9 ~0.001 1 3.06×10 -4 PΦ L 1 7.78×10-10~0.003 6 0.001 0 PΘ BG 1.13×10 -8 ~0.005 8 7.48×10 -4 PΘ L 1 3.81×10-4~0.001 9 3.65×10 -4 PΦ LG 6.65×10 -11 ~2.57×10 -6 3.20×10 -7 PΦ B 2 0.014 6~0.196 0 0.027 8 PΘ LG 2.92×10 -12 ~2.20×10 -6 2.77×10 -7 PΘ B 2 6.50×10-8~0.257 0 0.028 7 PΦ θ 1 9.44×10 -10 ~0.001 4 4.05×10 -4 PΦ L 2 2.43×10-8~0.005 0 0.001 5 PΘ θ 1 1.48×10 -4 ~7.19×10 -4 1.42×10 -4 PΘ L 2 0.006 1~0.012 7 0.001 7 4.2　入射光误差分析 2 旋转双棱镜指向模型中包含出射光束偏转角 Φ ， Θ 与入射光倾斜角 B G ， L G 的关系式。根据指向模型分别计算 Φ ， Θ 对 B G ， L G 的偏导数，如 式（7） 式（7） 所示： <math display="block" id="M7"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424418&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424415&type= 68.49533844 20.23533440 ， 其中： X As 9 ， Y As 9 ， Z As 9 ， X As 13 ， Y As 13 ， Z As 13 如下： <math display="block" id="M8"><mtable columnalign="left"><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">3</mn><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">6</mn><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mi>A</mi><mi>n</mi><mn mathvariant="normal">2</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo>⋅</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">3</mn><mo stretchy="false">)</mo><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo>⋅</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">3</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">7</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">6</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">6</mn><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">6</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">8</mn><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mi>A</mi><mi>s</mi><mn mathvariant="normal">7</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">7</mn><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">7</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">8</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">8</mn><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">8</mn><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">4</mn><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">10</mn><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mi>A</mi><mi>n</mi><mn mathvariant="normal">4</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">4</mn><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">4</mn><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">11</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">10</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">10</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">10</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">12</mn><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mi>A</mi><mi>s</mi><mn mathvariant="normal">11</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">11</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">11</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">12</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">12</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">12</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424429&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424422&type= 133.85800171 71.54333496 . <math id="M9"><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424438&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424436&type= 5.92666674 3.72533321 ， <math id="M10"><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424444&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424441&type= 6.26533365 3.72533321 ， <math id="M11"><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">9</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424452&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424449&type= 5.67266655 3.72533321 ， <math id="M12"><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424459&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424455&type= 6.94266701 3.72533321 ， <math id="M13"><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424466&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424463&type= 7.19666624 3.72533321 ， <math id="M14"><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">13</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424479&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424473&type= 6.60400009 3.72533321 的求解方法与 <math id="M15"><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424487&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424483&type= 5.92666674 3.72533321 ， <math id="M16"><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424494&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424491&type= 6.26533365 3.72533321 ， <math id="M17"><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424503&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424499&type= 5.67266655 3.72533321 的相同，均由出射光束 s 2 ro 往入射光束 s 1 li 方向逐级求导。 对指向影响的计算公式如下： <math display="block" id="M18"><mtable columnalign="left"><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>B</mi><mi>G</mi></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>α</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi mathvariant="normal">Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>G</mi></mrow></msub></mtd></mtr><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>L</mi><mi>G</mi></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>L</mi><mi>G</mi></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi mathvariant="normal">Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi></mrow></msub></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424511&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424507&type= 56.72666931 18.79599953 ， 其中Δ B G ，Δ L G 分别为 B G ， L G 的精度，由 表1 表1 可知。入射光倾斜角误差对指向结果的影响如 图5 图5 所示。为便于对比分析，具体误差数据仅在 表2 表2 中阐述分析。 4.3　棱镜转角误差分析 2 旋转双棱镜指向模型中包含出射光束偏转角 Φ ， Θ 与棱镜转角 θ 1 ， θ 2 的关系式。根据指向模型分别计算 Φ ， Θ 对 θ 1 ， θ 2 的偏导数，如 式（10） 式（10） 所示： <math display="block" id="M19"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">17</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">17</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">17</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">18</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">18</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">18</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424530&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424526&type= 66.29399872 20.06599998 ， 其中， X As 17 ， Y As 17 ， Z As 17 ， X As 18 ， Y As 18 ， Z As 18 由 式（11） 式（11） 得到： <math display="block" id="M20"><mtable columnalign="left"><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">5</mn><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">14</mn><mo>=</mo><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">5</mn><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">5</mn><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">5</mn></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">15</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">14</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">14</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">14</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">16</mn><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mi>A</mi><mi>s</mi><mn mathvariant="normal">15</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">15</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">15</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">17</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">16</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">16</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">16</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">17</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">17</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">17</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">6</mn><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">18</mn><mo>=</mo><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">6</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi>r</mi><mi>i</mi></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">6</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">18</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">18</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">18</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424538&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424535&type= 133.77333069 50.46133423 ， X As 17 ， Y As 17 ， Z As 17 ， X As 18 ， Y As 18 ， Z As 18 的求解过程与 X As 4 ， Y As 4 ， Z As 4 的相同，均由出射光束 s 2 ro 往入射光束 s 1 li 方向逐级求导。 对指向影响的计算公式如下： <math display="block" id="M21"><mtable columnalign="left"><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>θ</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>θ</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>θ</mi><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>θ</mi><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424544&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424541&type= 50.54600143 18.71133423 ， 其中Δ θ 1 ，Δ θ 1 分别为 θ 1 ， θ 2 的精度，由 表1 表1 可知。棱镜转角误差对指向偏差的影响如 图6 图6 所示。为便于对比分析，具体误差数据仅在 表2 表2 中阐述分析。 4.4　棱镜倾斜角误差分析 2 旋转双棱镜指向模型中包含出射光束偏转角 Φ ， Θ 与两棱镜倾斜角 B 1 ， L 1 ， B 2 ， L 2 的关系式。根据指向模型分别计算 Φ ， Θ 对 B 1 ， L 1 ， B 2 ， L 2 的偏导数，得到： <math display="block" id="M22"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">22</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">22</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">22</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">26</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">26</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">26</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">28</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">28</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">28</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">30</mn></mrow></msub></mrow><mrow><mroot><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>M</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">30</mn></mrow></msub><mi>K</mi><mo>-</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">30</mn></mrow></msub><mi>L</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424561&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424557&type= 65.19332886 45.46599960 ， 其中 X As 22 ， Y As 22 ， Z As 22 ， X As 26 ， Y As 26 ， Z As 26 ， X As 28 ， Y As 28 ， Z As 28 ， X As 30 ， Y As 30 ， Z As 30 由 式（14） 式（14） ， 式（15） 式（15） 可知。 <math display="block" id="M23"><mtable columnalign="left"><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">7</mn><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">19</mn><mo>=</mo><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">7</mn><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">7</mn><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">7</mn></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424568&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424564&type= 133.60400391 12.19200039 ， <math display="block" id="M24"><mtable columnalign="left"><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">8</mn><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">20</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">19</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">19</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>+</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">8</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">19</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>+</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">8</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">8</mn></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">21</mn><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mi>A</mi><mi>s</mi><mn mathvariant="normal">20</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">20</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mi>A</mi><mi>s</mi><mn mathvariant="normal">20</mn></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">22</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">21</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">21</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">21</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">22</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">22</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">22</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">9</mn><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">23</mn><mo>=</mo><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">9</mn><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">9</mn><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><msubsup><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">9</mn></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">10</mn><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">24</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">23</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">23</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>+</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">10</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">23</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>+</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">10</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>+</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">10</mn></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">25</mn><mo>=</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mi>A</mi><mi>s</mi><mn mathvariant="normal">24</mn><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">24</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">24</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">26</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">25</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">25</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">25</mn><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">26</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">26</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">26</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">11</mn><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424576&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424572&type= 134.36599731 90.00066376 . <math display="block" id="M25"><mtable columnalign="left"><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">27</mn><mo>=</mo><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">11</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">11</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>+</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">11</mn></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">12</mn><mo>=</mo><mo stretchy="false">(</mo><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">13</mn><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">29</mn><mo>=</mo><mo>-</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">13</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>+</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">13</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><mtext>                 </mtext><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">13</mn></mtd></mtr><mtr><mtd><mi>A</mi><mi>n</mi><mn mathvariant="normal">14</mn><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo><mo>,</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mn mathvariant="normal">30</mn><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mi>A</mi><mi>s</mi><mn mathvariant="normal">29</mn><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">29</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>+</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">14</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>-</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><msup><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">(</mo><mi>A</mi><mi>s</mi><mn mathvariant="normal">29</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo>+</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">14</mn><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo></mtd></mtr><mtr><mtd><mtext>                </mtext><mo stretchy="false">(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi></mrow></msup><mo>⋅</mo><msup><mrow><msub><mrow><mi mathvariant="bold-italic">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi></mrow></msup><mo stretchy="false">)</mo><mo>-</mo><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>A</mi><mi>n</mi><mn mathvariant="normal">14</mn><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">30</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">30</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>A</mi><mi>s</mi><mn mathvariant="normal">30</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424579&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424578&type= 148.08200073 54.01733780 X As 22 ， Y As 22 ， Z As 22 ， X As 26 ， Y As 26 ， Z As 26 ， X As 28 ， Y As 28 ， Z As 28 ， X As 30 ， Y As 30 ， Z As 30 的求解过程与 X As 4 ， Y As 4 ， Z As 4 的，均由出射光束 s 2 ro 往入射光束 s 1 li 方向逐级求导。 对指向影响的计算公式如下： <math display="block" id="M26"><mtable columnalign="left"><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>B</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>B</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo></mtd></mtr><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>L</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>L</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424585&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424581&type= 56.13399887 20.23533440 <math display="block" id="M27"><mtable columnalign="left"><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>B</mi><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>B</mi><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo></mtd></mtr><mtr><mtd><mi>P</mi><msub><mrow><mi>Φ</mi></mrow><mrow><mi>L</mi><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Φ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mi>P</mi><msub><mrow><mi>Θ</mi></mrow><mrow><mi>L</mi><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mo>∂</mo><mi>Θ</mi></mrow><mrow><mo>∂</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">Δ</mi><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424590&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424588&type= 56.13399887 18.71133423 其中Δ B 1 ，Δ L 1 ，Δ B 2 ，Δ L 2 分别为 B 1 ， L 1 ， B 2 ， L 2 的精度，由 表1 表1 可知。 棱镜倾斜角误差对指向结果的影响如 图7 图7 所示。为便于对比分析，具体误差数据仅在 表2 表2 中阐述分析。 1,2; 上述误差的误差均方根与最大误差如 表2 表2 所示。由 表2 表2 可知，对出射光束偏转角 Φ 影响最大的误差因素为入射光偏转角 B G 误差、棱镜П 2 旋转角 θ 2 、偏转角 B 1 、方位角 L 1 、偏转角 B 2 、方位角 L 2 ；对出射光束方位角 Θ 影响最大的误差因素为转角 θ 2 、方位角 L 1 、偏转角 B 2 和方位角 L 2 。在进行设计、安装和标定的过程中，需要特别注意控制入射光偏转角 B G 误差、棱镜П 2 旋转角 θ 2 、棱镜П 1 对理想光轴的倾斜角的偏转角 B 1 和方位角 L 1 、棱镜П 2 与理想光轴倾斜角的偏转角 B 2 和方位角 L 2 。 综上所述，对出射光影响较大的因素为棱镜П 1 与理想光轴的倾斜角（即 B 1 ， L 1 ）、棱镜П 2 与理想光轴的倾斜角（即 B 2 ， L 2 ）、棱镜П 2 转角（即 θ 2 ）。 根据误差合成理论计算光束理论指向总偏差，得到： <math display="block" id="M28"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><mi>E</mi><mi>r</mi><mi>r</mi><mi>S</mi><mi>i</mi><mi>m</mi><mi>u</mi><mo>=</mo><mo stretchy="false">(</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>α</mi><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>α</mi><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>B</mi><mi>G</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>L</mi><mi>G</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>θ</mi><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>θ</mi><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>B</mi><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>L</mi><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>B</mi><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo></mtd></mtr><mtr><mtd><mi>P</mi><msup><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>L</mi><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>α</mi><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>α</mi><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>B</mi><mi>G</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>L</mi><mi>G</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>θ</mi><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>θ</mi><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>B</mi><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>L</mi><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>B</mi><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mi>P</mi><msup><mrow><msub><mrow><mi>Θ</mi></mrow><mrow><mi>L</mi><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></msup><mo>.</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424613&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=17424611&type= 152.99267578 12.19200039 光束理论指向总偏差如 图8 图8 所示。MATLAB仿真表明，理论指向总偏差最大值为0.362 0°，理论指向总偏差均方根为0.0470°。 5 实　验 1 5.1　旋转双棱镜实验平台 2 本实验搭建了旋转双棱镜实验平台，如 图9 图9 所示。该平台主要由激光器、两块旋转棱镜、齿轮系统、步进电机、相机、上位机和系统支架组成。激光器发射激光束，激光束经过两块棱镜耦合偏折后照射在相机靶面，相机与上位机共同处理光斑图像获得光斑位置。上位机控制电机转动，电机通过齿轮系统带动棱镜转动。电机内置编码器，实时检测电机位置。 5.2　指向误差实验分析 2 由于相机视场角不够大，本文采用视野拼接技术获取全部指向范围内的光斑位置，实验测得的指向总偏差如 图10 图10 所示。采用MATLAB分析理论指向总偏差与实际指向总偏差，MATLAB分析结果如 表3 表3 所示。在MATLAB分析结果中，理论指向偏差最大值为0.362 0°，理论指向偏差均方根为0.047 0°。实验表明，在99.54%的指向区域中，实验偏差最大值为0.356 3°，小于理论指向偏差最大值0.362 0°，实验偏差均方根为0.023 3°，小于理论指向偏差均方根0.047 0°，实验结果均小于理论分析结果。由 图10 图10 可知，实验结果没有超出理论分析结果，本实验证明了理论分析的合理性。 指向总偏差 最大值/（°） 均方根/（°） 理　论 0.362 0 0.047 0 实　际 0.356 3 0.023 3 6 结　论 1 本文采用光线矢量传播原理建立旋转双棱镜系统光束指向模型，根据该模型，采用求偏导方法计算出射光束指向偏转角和方位角对各个误差的偏导数，并以各误差源的精度范围为输入计算误差源对指向结果的影响。仿真分析得出，对出射光影响较大的误差源包括棱镜П 1 对理想光轴的倾斜角、棱镜П 2 对理想光轴的倾斜角及棱镜П 2 转角。根据对各误差源的分析与仿真结果，本文采用误差合成理论计算各主要误差源对光束指向的总偏差。仿真计算结果表明，理论指向偏差的最大值为0.362 0°，均方根为0.047 0°。桌面实验结果表明，在99.54%的指向区域中，实验偏差的最大值为0.356 3°，均方根为0.023 3°，均小于仿真计算值。这一结果表明本文对旋转双棱镜系统误差的分析较为准确，对旋转双棱镜平台的设计和补偿修正有一定的参考价值。 参考文献 严希 . 无线激光通信APT系统中的光斑跟踪系统研究 ［D］. 西安 ： 西安理工大学 ， 2019 . 无线激光通信APT系统中的光斑跟踪系统研究 YAN X . Research on Spot Tracking System in APT System of Wireless Laser Communication ［D］. Xi'an ： Xi'an University of Technology ， 2019 . （in Chinese） Research on Spot Tracking System in APT System of Wireless Laser Communication 张建强 . 舰载激光通信视轴稳定控制技术研究 ［D］. 长春 ： 中国科学院长春光学精密机械与物理研究所 ， 2020 . 舰载激光通信视轴稳定控制技术研究 ZHANG J Q . Research on Shipborne Laser Communication Optical Stability Control Technology ［D］. Changchun ： Changchun Institute of Optics ， Fine Mechanics and Physics ， Chinese Academy Sciences， 2020 . （in Chinese） Research on Shipborne Laser Communication Optical Stability Control Technology ZHANG J Q ， LIU Y K ， ZHANG F J ， et al . Digital sliding mode control via a novel reaching law and application in shipborne electro-optical systems ［J］. IEEE Access ， 2019 ， 7 ： 139870 - 139884 . Digital sliding mode control via a novel reaching law and application in shipborne electro-optical systems 范大鹏 ， 周远 ， 鲁亚飞 ， 等 . 旋转双棱镜光束指向控制技术综述 ［J］. 中国光学 ， 2013 ， 6 （ 2 ）： 136 - 150 . 旋转双棱镜光束指向控制技术综述 FAN D P ， ZHOU Y ， LU Y F ， et al . Overview of beam steering technology based on rotational double prisms ［J］. Chinese Optics ， 2013 ， 6 （ 2 ）： 136 - 150 . （in Chinese） Overview of beam steering technology based on rotational double prisms 周书芃 . 消色差旋转双棱镜光束指向控制技术 ［D］. 成都 ： 中国科学院光电技术研究所 ， 2016 . 消色差旋转双棱镜光束指向控制技术 ZHOU SH P . Beam Pointing Techniques Based on Achromatic Risley Prisms ［D］. Chengdu ： Institute of Optics and Electronics ， Chinese Academy of Sciences ， 2016 . （in Chinese） Beam Pointing Techniques Based on Achromatic Risley Prisms 周远 ， 鲁亚飞 ， 黑沫 ， 等 . 旋转双棱镜光束指向的反向解析解 ［J］. 光学 精密工程 ， 2013 ， 21 （ 7 ）： 1693 - 1700 . 旋转双棱镜光束指向的反向解析解 ZHOU Y ， LU Y F ， HEI M ， et al . Analytical inverse solutions for rotational double prism beam steering ［J］. Opt. Precision Eng. ， 2013 ， 21 （ 7 ）： 1693 - 1700 . （in Chinese） Analytical inverse solutions for rotational double prism beam steering 周远 ， 鲁亚飞 ， 黑沫 ， 等 . 旋转双棱镜光束指向解析解 ［J］. 光学 精密工程 ， 2013 ， 21 （ 6 ）： 1373 - 1379 . 旋转双棱镜光束指向解析解 ZHOU Y ， LU Y F ， HEI M ， et al . Analytic solution of optical beam steering based on rotational double prisms ［J］. Opt. Precision Eng. ， 2013 ， 21 （ 6 ）： 1373 - 1379 . （in Chinese） Analytic solution of optical beam steering based on rotational double prisms 李锦英 ， 陈科 ， 彭起 ， 等 . 旋转双棱镜大范围快速高精度扫描技术 ［J］. 光电技术应用 ， 2020 ， 35 （ 2 ）： 44 - 48 . 旋转双棱镜大范围快速高精度扫描技术 LI J Y ， CHEN K ， PENG Q ， et al . Wide-range， fast and high precision scanning technology based on rotational double prisms ［J］. Electro-Optic Technology Application ， 2020 ， 35 （ 2 ）： 44 - 48 . （in Chinese） Wide-range， fast and high precision scanning technology based on rotational double prisms 曹佃生 ， 高云国 . 高精度无导轨位移平台误差分析 ［J］. 光学 精密工程 ， 2012 ， 20 （ 2 ）： 313 - 320 . 高精度无导轨位移平台误差分析 CAO D SH ， GAO Y G . Error analysis of precise non-guiding displacement platform ［J］. Opt. Precision Eng. ， 2012 ， 20 （ 2 ）： 313 - 320 . （in Chinese） Error analysis of precise non-guiding displacement platform 曹佃生 ， 林冠宇 ， 杨小虎 ， 等 . 紫外双光栅光谱仪结构设计与波长精度分析 ［J］. 中国光学 ， 2018 ， 11 （ 2 ）： 219 - 230 . 紫外双光栅光谱仪结构设计与波长精度分析 CAO D SH ， LIN G Y ， YANG X H ， et al . Structure design and wavelength accuracy analysis of ultraviolet double grating spectrometer ［J］. Chinese Optics ， 2018 ， 11 （ 2 ）： 219 - 230 . （in Chinese） Structure design and wavelength accuracy analysis of ultraviolet double grating spectrometer 徐力智 ， 颜昌翔 ， 李颐 ， 等 . 航空摆扫成像像移计算与误差分配 ［J］. 光学 精密工程 ， 2019 ， 27 （ 10 ）： 2071 - 2079 . 航空摆扫成像像移计算与误差分配 XU L ZH ， YAN CH X ， LI Y ， et al . Image motion calculation and error distribution for aerial whisk-broom imaging ［J］. Opt. Precision Eng. ， 2019 ， 27 （ 10 ）： 2071 - 2079 . （in Chinese） Image motion calculation and error distribution for aerial whisk-broom imaging 万振华 ， 赵开春 ， 褚金奎 . 基于偏振成像的方位测量误差建模与分析 ［J］. 光学 精密工程 ， 2019 ， 27 （ 8 ）： 1688 - 1696 . 基于偏振成像的方位测量误差建模与分析 WAN ZH H ， ZHAO K CH ， CHU J K . Modeling and analysis of orientation measurement error based on polarization imaging ［J］. Opt. Precision Eng. ， 2019 ， 27 （ 8 ）： 1688 - 1696 . （in Chinese） Modeling and analysis of orientation measurement error based on polarization imaging 邱赛 ， 盛磊 ， 高世杰 ， 等 . 旋转双棱镜指向系统转角补偿偏差修正方法 ［J/OL］. 光通信技术 ： 1 - 7 ［ 2020-11-15 ］. http：//kns.cnki.net/kcms/detail/45.1160.TN.20201104.1215.004.html http://kns.cnki.net/kcms/detail/45.1160.TN.20201104.1215.004.html . 旋转双棱镜指向系统转角补偿偏差修正方法 QIU S ， SHENG L ， GAO SH J ， et al . Correction method for angle compensation deviation of rotating biprism pointing system ［J/OL］. Optical Communication Technology ： 1 - 7 ［ 2020-11-15 ］. http：//kns.cnki.net/kcms/detail/45.1160.TN.2020110 4. 1215.004.html. http://kns.cnki.net/kcms/detail/45.1160.TN.20201104.1215.004.html. （in Chinese） Correction method for angle compensation deviation of rotating biprism pointing system WARGER W C ， GUERRERA S A ， EASTMAN Z ， et al . Efficient confocal microscopy with a dual-wedge scanner ［C］. Three-Dimensional and Multidimensional Microscopy ： Image Acquisition and Processing XVI. San Jose ， CA. SPIE ， 2009 7184 ： 71840 M-71840M-11. Efficient confocal microscopy with a dual-wedge scanner HORNG J S ， LI Y . Error sources and their impact on the performance of dual-wedge beam steering systems ［J］. Applied Optics ， 2012 ， 51 （ 18 ）： 4168 - 4175 . Error sources and their impact on the performance of dual-wedge beam steering systems ZHANG H ， YUAN Y ， SU L J ， et al . Beam steering uncertainty analysis for Risley prisms based on Monte Carlo simulation ［J］. Opt. Eng. ， 2017 ， 56 （ 1 ）： 014105 - 014105 - 10 . Beam steering uncertainty analysis for Risley prisms based on Monte Carlo simulation 10.37188/OPE.20212906.1281 TH703 TN929.13 A 1004-924X（2021）06-1281-10 邱赛,盛磊,高世杰等.激光通信旋转双棱镜系统误差对指向精度的影响[J].光学精密工程,2021,29(06):1281-1290. 邱赛,盛磊,高世杰等.激光通信旋转双棱镜系统误差对指向精度的影响[J].光学精密工程,2021,29(06):1281-1290. QIU Sai,SHENG Lei,GAO Shi-jie,et al.Influence of laser communication Risley prism system error on pointing accuracy[J].Optics and Precision Engineering,2021,29(06):1281-1290. QIU Sai,SHENG Lei,GAO Shi-jie,et al.Influence of laser communication Risley prism system error on pointing accuracy[J].Optics and Precision Engineering,2021,29(06):1281-1290. 长光复旦联合基金资助项目（No.Y8O732E） 2020-07-01 2020-09-01 2021-06-15 2021-07-12 光学精密工程 6 29