{"defaultlang":"zh","titlegroup":{"articletitle":[{"lang":"zh","data":[{"name":"text","data":"基于振镜的准直光源功率稳定控制器"}]},{"lang":"en","data":[{"name":"text","data":"Power stability controller for collimating-light source based on scanlab Power Stability Controller for Collimating-light Source Based on Scanlab"}]}]},"contribgroup":{"author":[{"name":[{"lang":"zh","surname":"肖","givenname":"岚","namestyle":"eastern","prefix":""},{"lang":"en","surname":"XIAO","givenname":"Lan","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"}],"role":["first-author"],"deceased":false},{"name":[{"lang":"zh","surname":"袁","givenname":"银麟","namestyle":"eastern","prefix":""},{"lang":"en","surname":"YUAN","givenname":"Yinlin","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":["corresp"],"corresp":[{"rid":"cor1","lang":"en","text":"E-mail： ylyuan@aiofm.ac.cn","data":[{"name":"text","data":"E-mail： ylyuan@aiofm.ac.cn"}]}],"email":"ylyuan@aiofm.ac.cn","deceased":false},{"name":[{"lang":"zh","surname":"翁","givenname":"建文","namestyle":"eastern","prefix":""},{"lang":"en","surname":"WENG","givenname":"Jianwen","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"孟","givenname":"凡刚","namestyle":"eastern","prefix":""},{"lang":"en","surname":"MENG","givenname":"Fangang","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"康","givenname":"晴","namestyle":"eastern","prefix":""},{"lang":"en","surname":"KANG","givenname":"Qing","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"李","givenname":"健军","namestyle":"eastern","prefix":""},{"lang":"en","surname":"LI","givenname":"Jianjun","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":[],"deceased":false}],"aff":[{"id":"aff1","intro":[{"lang":"zh","label":"1","text":"中国科学院合肥物质科学研究院 安徽光学精密机械研究所 通用光学定标与表征技术重点实验室，合肥 230031","data":[{"name":"text","data":"中国科学院合肥物质科学研究院 安徽光学精密机械研究所 通用光学定标与表征技术重点实验室，合肥 230031"}]},{"lang":"en","label":"1","text":"Key Laboratory of Optical Calibration and Characterization，Anhui Institute of Optical and Fine Mechanics，Hefei Institutes of Physical Science， Chinese Academy of Sciences，Hefei 230031，China","data":[{"name":"text","data":"Key Laboratory of Optical Calibration and Characterization，Anhui Institute of Optical and Fine Mechanics，Hefei Institutes of Physical Science， Chinese Academy of Sciences，Hefei 230031，China"}]}]},{"id":"aff2","intro":[{"lang":"zh","label":"2","text":"中国科学技术大学，合肥 230026","data":[{"name":"text","data":"中国科学技术大学，合肥 230026"}]},{"lang":"en","label":"2","text":"University of Science and Technology of China，Hefei 230026，China","data":[{"name":"text","data":"University of Science and Technology of China，Hefei 230026，China"}]}]}]},"abstracts":[{"lang":"zh","data":[{"name":"p","data":[{"name":"text","data":"针对特殊准直光源的稳定性控制需求，提出一种基于振镜的激光功率稳定控制方法。将石英片与振镜连接固定，采用入射光角度与透过率的关系作为信号调节原理，当振镜带动石英片旋转时，对石英片透射的光信号大小进行调节。基于菲涅尔定律，开展平板玻璃旋转角度与透过率参数分析，论证旋转角度范围等参数，为实现光源的功率稳定提供输出参数支持。利用监视反馈探测器进行实时数据监测和反馈。通过PID算法，对监视探测器信号与参考调节功率对应电压的误差进行调制，实现对振镜输出角度的准确调节。采用该功率稳定器对He-Ne 632.8 nm激光器进行了稳功率实验，并采用Trap探测器进行功率输出的实验验证。试验结果表明：经过功率稳定控制后的激光器稳定性：其标准离差率"},{"name":"italic","data":[{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"为0.016%（1 800 s），其峰峰起伏"},{"name":"italic","data":[{"name":"text","data":"S"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"为±0.042%（1 800 s）。峰峰起伏"},{"name":"italic","data":[{"name":"text","data":"S"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"降至激光器自由运行时约为1/8.79，标准离差率"},{"name":"italic","data":[{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"改善1/13.76，稳定性得到了较好的改进。"}]}]},{"lang":"en","data":[{"name":"p","data":[{"name":"text","data":"Aiming at the technical stability requirement of special collimating light source， a method based on scanlab is proposed. The relation between incident Angle and transmittance is used as the principle of signal regulation. The quartz plate is fixed with the scanlab， and the transmittance of the quartz is adjusted when the scanlab rotates. Real-time data feedback is carried out by monitoring detector. Rotation angle， transmittance parameters of quartz and the range of angle are analyzed based on Fresnel's law， for supportting to realize the power stability of light source. PID algorithm is used to modulate the error of the signal of the monitoring detector and the voltage corresponding to reference power so as to accurately adjust the output of scanlab. The stabilizer is used to control the power of He-Ne 632.8nm laser， and the Trap detector is used to verify the level of power stability. The experiment results of the stability of the laser after modulation is as follows： the standard deviation C"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":" is 0.016% （1800s） and the peak-to-peak fluctuation S"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":" is ±0.042% （1800s）. Compared with the free-running result， S"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":" and C"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":" are improved to 1/8.79 and 1/13.76 respectively， and the power stability of the laser is enhanced."}]}]}],"keyword":[{"lang":"zh","data":[[{"name":"text","data":"激光功率稳定"}],[{"name":"text","data":"振镜"}],[{"name":"text","data":"菲涅尔定律"}],[{"name":"text","data":"反馈控制"}]]},{"lang":"en","data":[[{"name":"text","data":"laser power stability"}],[{"name":"text","data":"scanlab"}],[{"name":"text","data":"fresnel's law"}],[{"name":"text","data":"feedback control"}]]}],"highlights":[],"body":[{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"1 引 言"}],"level":"1","id":"s1"}},{"name":"p","data":[{"name":"text","data":"目前在高精度的光谱辐射测量领域，激光等高稳定性的准直光源对于探测器的光谱响应度等参数的高精度测量具有重要作用"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"1","type":"bibr","rid":"R1","data":[{"name":"text","data":"1"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"3","type":"bibr","rid":"R3","data":[{"name":"text","data":"3"}]}}],"rid":["R1","R2","R3"],"text":"1-3","type":"bibr"}},{"name":"text","data":"］"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"激光光源功率稳定方法主要有两种，分别是控制激光发生过程和采用外部调节装置。前者通过控制激光器电流和温度"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"4","type":"bibr","rid":"R4","data":[{"name":"text","data":"4"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"6","type":"bibr","rid":"R6","data":[{"name":"text","data":"6"}]}}],"rid":["R4","R5","R6"],"text":"4-6","type":"bibr"}},{"name":"text","data":"］"}]},{"name":"text","data":"等方法实现激光输出功率的稳定，但温度和电流的改变会带来输出频率的扰动，造成频率稳定性差。内调制技术无法解决因电源电压过滤不足、谐振器元件的振动、气体激光器中气体放电的不稳定性、染料激光器中液体密度的波动、多模激光器的模式竞争等"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"7","type":"bibr","rid":"R7","data":[{"name":"text","data":"7"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"8","type":"bibr","rid":"R8","data":[{"name":"text","data":"8"}]}}],"rid":["R7","R8"],"text":"7-8","type":"bibr"}},{"name":"text","data":"］"}]},{"name":"text","data":"因素造成激光器功率不稳定问题。外调制通过光调制器直接对输出光束进行调制，既不会引入附加噪声，还具有适用性强、灵活性高等特点；主要采用电光"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"9","type":"bibr","rid":"R9","data":[{"name":"text","data":"9"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"12","type":"bibr","rid":"R12","data":[{"name":"text","data":"12"}]}}],"rid":["R9","R10","R11","R12"],"text":"9-12","type":"bibr"}},{"name":"text","data":"］"}]},{"name":"text","data":"、声光"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"13","type":"bibr","rid":"R13","data":[{"name":"text","data":"13"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"16","type":"bibr","rid":"R16","data":[{"name":"text","data":"16"}]}}],"rid":["R13","R14","R15","R16"],"text":"13-16","type":"bibr"}},{"name":"text","data":"］"}]},{"name":"text","data":"调制原理调节光谱透过率实现激光输出功率的稳定。声光调制是基于声光（AO）效应的功率调节方式，因其较快的响应时间、驱动信号容易获得、成本低，同时较高的衍射效率（可大于90%）使得激光利用率较高"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"17","type":"bibr","rid":"R17","data":[{"name":"text","data":"17"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"，但是衍射效率高的材料并不具有高的光损伤阈值，想要优良的功率控制能力，不仅更大的晶体，还需要更高的驱动功率，同时还会延长开关时间。电光调制是利用电光（EO）效应对输出光束进行调节，优点是可以对高频率的波动进行调制"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"7","type":"bibr","rid":"R7","data":[{"name":"text","data":"7"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"；具有高损伤阈值的电光晶体，例如磷酸二氢钾、磷酸二氢铵，物理化学性能并不稳定，需要防潮解措施，而且具有较高的半波电压；铌酸锂、钽酸锂等晶体具有低的半波电压，物理化学性能稳定，但其光损伤阈值较低，适用于100 mW以下的激光器"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"18","type":"bibr","rid":"R18","data":[{"name":"text","data":"18"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"19","type":"bibr","rid":"R19","data":[{"name":"text","data":"19"}]}}],"rid":["R18","R19"],"text":"18-19","type":"bibr"}},{"name":"text","data":"］"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"现阶段基于电光和声光元件的激光功率稳定控制器仅存在对单波长激光器的研究和应用。此外这类激光功率稳定控制器都对入射光的偏振状态敏感"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"20","type":"bibr","rid":"R20","data":[{"name":"text","data":"20"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"21","type":"bibr","rid":"R21","data":[{"name":"text","data":"21"}]}}],"rid":["R20","R21"],"text":"20-21","type":"bibr"}},{"name":"text","data":"］"}]},{"name":"text","data":"，偏振方向必须与晶体内部传播方向一致，并且对激光器的功率大小有限制。针对波长可调谐激光光源、超连续白光激光器光源、激光泵浦氙灯等一些特殊准直光源的稳定性控制，例如宽光谱范围、宽动态范围、适应各种偏振特性输入、高损伤阈值等技术要求，开展新工作体制的激光功率稳定控制器研制和应用技术，是非常有必要的。"}]},{"name":"p","data":[{"name":"text","data":"本文提出一种基于菲涅尔定律的激光功率稳定控制方法，采用振镜旋转石英片的方式控制入射光的透射分量，采用PID控制算法对监视探测器的反射光进行闭环控制，从而实现光源的功率输出稳定。这种控制方法具有宽谱带、高损伤阈值的特点，还有驱动功率小，成本低等优点。本文所提到的准直光源功率稳定方法可用于高稳定性定标光源的研制，实现太阳光谱辐照度仪实验室绝对光谱响应定标。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"2 功率稳定控制器的结构组成"}],"level":"1","id":"s2"}},{"name":"p","data":[{"name":"text","data":"光源功率稳定控制器（Scanlab power stability controller，以下简称“SPSC”）主要由石英片、分束器（BS）、探测器（SPD）、跨阻放大器、多功能数据采集卡、控制主机、驱动控制模块和振镜构成。"}]},{"name":"fig","data":{"id":"F1","caption":[{"lang":"zh","label":[{"name":"text","data":"图1"}],"title":[{"name":"text","data":"基于振镜的功率稳定控制系统（SPSC）结构组成"}]},{"lang":"en","label":[{"name":"text","data":"Fig.1"}],"title":[{"name":"text","data":"Structure and composition of SPCS"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381985&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381987&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381986&type=","width":"69.05599976","height":"45.77299881","fontsize":""}]}},{"name":"p","data":[{"name":"text","data":"分束片BS对准直光源的光信号进行分光处理，其中5%的反射光用于对输出光信号的稳定性进行实时监测和反馈；95%的光信号作为稳定后的光信号输出。分束片BS的反射光路设有监视探测器，探测器进行光电转换，转换后的电流信号采用跨阻放大器进行"},{"name":"italic","data":[{"name":"text","data":"I"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"V"}]},{"name":"text","data":"放大，经过多功能数据采集卡进行模拟数字转换。"}]},{"name":"p","data":[{"name":"text","data":"本系统选用增量式PID作为反馈控制算法，增量式PID控制器不仅继承了传统PID控制器原理简单、易于实现、适用面广、控制参数相互独立、参数的选定简单的优点，还克服了传统PID控制器抗干扰能力差、计算繁琐、容易造成误差叠加等缺点"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"14","type":"bibr","rid":"R14","data":[{"name":"text","data":"14"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"。控制主机根据光信号的监测值，采用增量式PID控制算法，反馈调节振镜带动石英片旋转，实现激光光源光信号的精细调节。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"3 SPSC的工作原理及分析"}],"level":"1","id":"s3"}},{"name":"p","data":[{"name":"text","data":"激光功率稳定控制器的工作原理主要基于菲涅尔定律，调节高速振镜带动石英平板，从而改变石英平板与入射光的夹角，实现反射和透射通量的调节。石英平板的反射和透射通量的原理如"},{"name":"xref","data":{"text":"图2","type":"fig","rid":"F2","data":[{"name":"text","data":"图2"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"F2","caption":[{"lang":"zh","label":[{"name":"text","data":"图2"}],"title":[{"name":"text","data":"石英平板的反射和透射光路"}]},{"lang":"en","label":[{"name":"text","data":"Fig.2"}],"title":[{"name":"text","data":"Light reflectance and transmittance of flat glass"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381988&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381990&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381989&type=","width":"76.31475830","height":"49.96147156","fontsize":""}]}},{"name":"p","data":[{"name":"text","data":"根据菲涅尔定律，一束完全非偏振光以角度i入射至一片平板玻璃上，入射光的反射和透射光路见如"},{"name":"xref","data":{"text":"图2","type":"fig","rid":"F2","data":[{"name":"text","data":"图2"}]}},{"name":"text","data":"所示。由于石英玻璃厚度很薄，材料对光的吸收可忽略不计。光束经过"},{"name":"italic","data":[{"name":"text","data":"N"}]},{"name":"text","data":"次折射后经平板玻璃两面透射输出，出射光是所有透射光束的叠加。"}]},{"name":"p","data":[{"name":"text","data":"设入射光的光强为"},{"name":"italic","data":[{"name":"text","data":"I"}]},{"name":"sub","data":[{"name":"text","data":"in"}]},{"name":"text","data":"，透射光的光强为"},{"name":"italic","data":[{"name":"text","data":"I"}]},{"name":"sub","data":[{"name":"text","data":"T"}]},{"name":"text","data":"，反射光的光强为"},{"name":"italic","data":[{"name":"text","data":"I"}]},{"name":"sub","data":[{"name":"text","data":"R"}]},{"name":"text","data":"，则："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（1）"}],"data":[{"name":"math","data":{"math":"IT=Iin(T2+T2R2+T2R4+T2R6+…)","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381992&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381991&type=","width":"65.70133209","height":"4.65666676","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF1"}},{"name":"dispformula","data":{"label":[],"data":[{"name":"math","data":{"math":"IR=Iin(R+T2R+T2R3+T2R5+T2R7+…)","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381994&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381993&type=","width":"72.89800262","height":"4.65666676","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF2"}},{"name":"p","data":[{"name":"text","data":"（2）"}]},{"name":"p","data":[{"name":"text","data":"其中，"},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"R"}]},{"name":"text","data":"分别为透射和反射系数，上式为等比数列，"},{"name":"italic","data":[{"name":"text","data":"R"},{"name":"sup","data":[{"name":"text","data":"2"}]},{"name":"text","data":"<"}]},{"name":"text","data":"1，"},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"text","data":"=1-"},{"name":"italic","data":[{"name":"text","data":"R"}]},{"name":"text","data":"，假设不考虑玻璃的吸收，有："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（3）"}],"data":[{"name":"math","data":{"math":"IT∥=Iin∥1-R∥1+R∥","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381996&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381995&type=","width":"26.67000008","height":"8.89000034","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF3"}},{"name":"dispformula","data":{"label":[{"name":"text","data":"（4）"}],"data":[{"name":"math","data":{"math":"IR∥=2Iin∥R∥1+R∥","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381998&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381997&type=","width":"22.18266678","height":"8.89000034","fontsize":""}}},{"name":"text","data":"."}],"id":"DF4"}},{"name":"p","data":[{"name":"text","data":"同理，垂直分量："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（5）"}],"data":[{"name":"math","data":{"math":"IT⊥=Iin⊥1-R⊥1+R⊥","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382000&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35381999&type=","width":"27.17799950","height":"8.63599968","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF5"}},{"name":"dispformula","data":{"label":[{"name":"text","data":"（6）"}],"data":[{"name":"math","data":{"math":"IR⊥=2Iin⊥R⊥1+R⊥","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382002&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382001&type=","width":"22.69066620","height":"8.63599968","fontsize":""}}},{"name":"text","data":"."}],"id":"DF6"}},{"name":"p","data":[{"name":"text","data":"透射光和反射光的总强度为："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（7）"}],"data":[{"name":"math","data":{"math":"IT=IT∥+IT⊥=Iin∥1-R∥1+R∥+Iin⊥1-R⊥1+R⊥","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382004&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382003&type=","width":"66.20932770","height":"8.89000034","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF7"}},{"name":"dispformula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nm波段折射率"},{"name":"italic","data":[{"name":"text","data":"n"}]},{"name":"text","data":"为1.445 09，根据"},{"name":"xref","data":{"text":"式（8）","type":"disp-formula","rid":"DF8","data":[{"name":"text","data":"式（8）"}]}},{"name":"text","data":"、"},{"name":"xref","data":{"text":"式（9）","type":"disp-formula","rid":"DF9","data":[{"name":"text","data":"式（9）"}]}},{"name":"text","data":"和"},{"name":"xref","data":{"text":"式（10）","type":"disp-formula","rid":"DF10","data":[{"name":"text","data":"式（10）"}]}},{"name":"text","data":"，分别模拟了入射光平行分量/垂直分量（PS%）=95/5（%）、50/50（%）和5/95（%）时，透射光强和反射光强与入射角度关系的模拟结果如图所示："}]},{"name":"p","data":[{"name":"text","data":"从"},{"name":"xref","data":{"text":"图3","type":"fig","rid":"F3","data":[{"name":"text","data":"图3"}]}},{"name":"text","data":"中可以看出，当改变石英玻璃角度时，透射分量光强在不同的偏振态下具有不同的透过率，并且随着垂直分量的增加，透过率和反射率曲线波动减小，单调性变好。不同偏振态的光束可采用不同的PID信号调制算法，本文选用垂直线偏振光验证方法可行性，利用格兰泰勒棱镜对激光器输出光束进行垂直方向起偏，仅允许竖直方向的线偏振光通过功率稳定控制器，透过率与入射角度的关系如"},{"name":"xref","data":{"text":"图4","type":"fig","rid":"F4","data":[{"name":"text","data":"图4"}]}},{"name":"text","data":"所示，相较于"},{"name":"xref","data":{"text":"图3（c）","type":"fig","rid":"F3a3","data":[{"name":"text","data":"图3（c）"}]}},{"name":"text","data":"透过率曲线平滑度更好。"}]},{"name":"figgroup","data":{"id":"F3","caption":[{"lang":"zh","label":[{"name":"text","data":"图3"}],"title":[{"name":"text","data":"不同PS%时石英在633 nm波段透射光强和反射光强与入射角度的关系"}]},{"lang":"en","label":[{"name":"text","data":"Fig.3"}],"title":[{"name":"text","data":"Relationship between transmittance and incident angle of quartz at 633nm witht different value of PS%"}]}],"note":[],"layout":"1;2;3;","grid":[[{"name":"fig","data":{"id":"F3a1","caption":[{"lang":"zh","label":[{"name":"text","data":"(a)"}],"title":[{"name":"text","data":"PS%=95/5（%）"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382013&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382015&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382014&type=","width":"76.70000458","height":"62.47809601","fontsize":""}]}}],[{"name":"fig","data":{"id":"F3a2","caption":[{"lang":"zh","label":[{"name":"text","data":"(b)"}],"title":[{"name":"text","data":"PS%=50/50（%）"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382016&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382018&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382017&type=","width":"76.19152832","height":"62.47753143","fontsize":""}]}}],[{"name":"fig","data":{"id":"F3a3","caption":[{"lang":"zh","label":[{"name":"text","data":"(c)"}],"title":[{"name":"text","data":"PS%=5/95（%）"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382019&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382021&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382020&type=","width":"74.91986084","height":"62.47608948","fontsize":""}]}}]],"alternatives":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382023&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382022&type=","width":"76.90000153","height":"213.18530273","fontsize":""}}},{"name":"fig","data":{"id":"F4","caption":[{"lang":"zh","label":[{"name":"text","data":"图4"}],"title":[{"name":"text","data":"垂直线偏振光入射角度和石英片透过率关系"}]},{"lang":"en","label":[{"name":"text","data":"Fig.4"}],"title":[{"name":"text","data":"Relationship between the incident angle of perpendicular linearly polarized light and the transmittance of quartz"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382024&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382026&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382025&type=","width":"76.99400330","height":"60.06000137","fontsize":""}]}},{"name":"p","data":[{"name":"text","data":"在设计功率稳定控制器的石英片角度改变范围时，不仅要考虑对激光波动进行稳幅，并且能保证激光器具有较大的可调功率范围。为实现稳定性实现高于99.9%，根据奈奎斯采样定理，功率调节分辨率应提升2倍以上，即功率调节分辨率低于0.05%。"}]},{"name":"p","data":[{"name":"text","data":"SPSC根据光源的稳定性初始数值，设置入射光源与石英平板的夹角，以及夹角的调节范围。假设激光光源稳定性为±0.5%时，利用最小二乘法对线偏振光经过石英平板的光谱透过率（633 nm）进行α的5次多项式拟合，其中α为入射光束与石英平板的夹角，如"},{"name":"xref","data":{"text":"式（12）","type":"disp-formula","rid":"DF12","data":[{"name":"text","data":"式（12）"}]}},{"name":"text","data":"所示。"}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（12）"}],"data":[{"name":"math","data":{"math":"t=-2.53×10-10α5+1.90×10-8α4-1.13×10-6α3+1.38×10-6α2-3.46×10-4α+0.94.","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382028&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382027&type=","width":"63.75400162","height":"12.61533356","fontsize":""}}},{"name":"text","data":" "}],"id":"DF12"}},{"name":"p","data":[{"name":"text","data":"入射光源与石英平板的夹角"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"为39°，光谱透过率变化1%时，入射光源与石英平板的夹角调节范围为37.7°至40.4°，如"},{"name":"xref","data":{"text":"图5","type":"fig","rid":"F5","data":[{"name":"text","data":"图5"}]}},{"name":"text","data":"所示。采用旋转台初步调节入射光源与石英平板的初始夹角为39°，通过振镜快速精确调整石英平板在"},{"name":"italic","data":[{"name":"text","data":"-"}]},{"name":"text","data":"1.3°~1.4°范围变化，实现光谱透过率在0.875~0.885之间变化。"}]},{"name":"figgroup","data":{"id":"F5","caption":[{"lang":"zh","label":[{"name":"text","data":"图5"}],"title":[{"name":"text","data":"不同透过率对应的角度调整区间"}]},{"lang":"en","label":[{"name":"text","data":"Fig.5"}],"title":[{"name":"text","data":"Different transmittance interval and corresponding angle adjustment 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scanning area"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382032&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382034&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382033&type=","width":"76.70000458","height":"57.46426392","fontsize":""}]}}]],"alternatives":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382036&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382035&type=","width":"76.90000153","height":"144.93148804","fontsize":""}}},{"name":"p","data":[{"name":"text","data":"通过调节入射光源与石英平板的夹角，以及夹角的调节范围等参数，可实现不同稳定性的光源功率输出控制。本文选择的振镜具有夹角的调节范围为±20°，可实现功率极值变化17.5%的光源功率稳定性控制。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"4 实验设计与验证"}],"level":"1","id":"s4"}},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"4.1　实验装置"}],"level":"2","id":"s4a"}},{"name":"p","data":[{"name":"text","data":"如"},{"name":"xref","data":{"text":"图6","type":"fig","rid":"F6","data":[{"name":"text","data":"图6"}]}},{"name":"text","data":"所示，在激光器出光口设置了小孔光阑，用于限制光束孔径以及减弱其他发散光斑干扰。调整P1和P2，对激光入射光光束进行起偏和偏振钝化，以及消除激光内衍射带来的干扰，设置P2的偏振方向使出射光束为垂直偏振光。SPCS中，石英平板尺寸为10 mm×10 mm×2 mm（"},{"name":"italic","data":[{"name":"text","data":"X"}]},{"name":"text","data":"×"},{"name":"italic","data":[{"name":"text","data":"Y"}]},{"name":"text","data":"×"},{"name":"italic","data":[{"name":"text","data":"Z"}]},{"name":"text","data":"），分束器尺寸与石英平板尺寸相同，振镜底座连接旋转台，可对初始入射角（振镜驱动电压为0 V状态下）进行机械调整。光束经过SPCS调制后经透射光路输出，SPD2采用高精度陷阱探测器，其不确定度优于0.035%"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"23","type":"bibr","rid":"R23","data":[{"name":"text","data":"23"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"，作为功率稳定性的验证探测器，数据采集器（Agilent 34970A）对放大电路处理后的电信号进行信号采集。"}]},{"name":"fig","data":{"id":"F6","caption":[{"lang":"zh","label":[{"name":"text","data":"图6"}],"title":[{"name":"text","data":"实验装置原理图"}]},{"lang":"en","label":[{"name":"text","data":"Fig. 6"}],"title":[{"name":"text","data":"Schematic diagram of experimental device"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382037&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382039&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382038&type=","width":"150.81300354","height":"60.59000015","fontsize":""}]}},{"name":"p","data":[{"name":"text","data":"实验装置搭建后，通过调节系统参数，包括激光器输出功率，内外路光电探测器放大器增益、振镜控制模块的参数及调整频率，最终观察反馈效果。将数据采集器采集的信号通过Allan方差分析，可得到信号的长期缓慢变化。Allan方差对各类噪声的幂律谱项都收敛，可以反映相邻两个采样段内平均频率差的起伏。通过直接统计相邻电压数据之间的偏差，不受数据平均值间的差异影响，可以有效排除其他噪声对激光功率稳定性的干扰，从而准确评估激光输出功率的长期稳定性"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"24","type":"bibr","rid":"R24","data":[{"name":"text","data":"24"}]}},{"name":"text","data":"-25］"}]},{"name":"text","data":"。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"4.2　实验结果"}],"level":"2","id":"s4b"}},{"name":"p","data":[{"name":"text","data":"利用数据采集器在时域上对激光器自由运行状态下的稳定性和针对高稳定性模拟光源的稳定性要求进行一定时长的测试。功率稳定控制器将应用于高稳定性定标光源的研制，实现太阳光谱辐照度仪实验室绝对光谱响应定标，定标时间为1 800 s，这就要求定标光源在1 800 s内保持高稳定性。"}]},{"name":"p","data":[{"name":"text","data":"标准离差率C"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":"和峰峰起伏率S"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":"的处理公式"},{"name":"sup","data":[{"name":"text","data":"［26］"}]},{"name":"text","data":"如下："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（13）"}],"data":[{"name":"math","data":{"math":"CV=σDN¯×100%","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382041&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382040&type=","width":"29.63333130","height":"8.63599968","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF13"}},{"name":"dispformula","data":{"label":[{"name":"text","data":"（14）"}],"data":[{"name":"math","data":{"math":"CV=±DNMAX-DNMIN2DN¯×100%","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382043&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382042&type=","width":"52.66266251","height":"8.63599968","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF14"}},{"name":"p","data":[{"name":"text","data":"其中，DN为测量出的信号值，"},{"name":"italic","data":[{"name":"text","data":"σ"}]},{"name":"text","data":"为标准差。"}]},{"name":"p","data":[{"name":"text","data":"右图是激光器自由运行（黑线）和采用本文所述的功率稳定控制方法后（红线）的输出光束的波动起伏。对数据进行归一化处理后，采用（13）和（14）式，分别计算出激光器自由运行时和功率稳定控制后的稳定性参数，激光器自由运行时，其标准离差率"},{"name":"italic","data":[{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"为0.219%（1 800 s），其峰峰起伏"},{"name":"italic","data":[{"name":"text","data":"S"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"为±0.369%（1 800 s）。"}]},{"name":"fig","data":{"id":"F7","caption":[{"lang":"zh","label":[{"name":"text","data":"图7"}],"title":[{"name":"text","data":"激光器自由运行和采用PID调制后信号时域波动图"}]},{"lang":"en","label":[{"name":"text","data":"Fig.7"}],"title":[{"name":"text","data":"Beam power stability fluctuation between free-running and after-modulation"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382044&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382046&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382045&type=","width":"76.90000153","height":"57.48284531","fontsize":""}]}},{"name":"p","data":[{"name":"text","data":"可以观察到电源噪声和激光器自发辐射等因素产生的基本噪声，会造成光束稳定性曲线小范围地上下波动，以及激光器由于放电电流不稳定、器件温度导致性能改变和自然老化等因素造成激光器功率的大范围漂动。"}]},{"name":"fig","data":{"id":"F8","caption":[{"lang":"zh","label":[{"name":"text","data":"图8"}],"title":[{"name":"text","data":"激光器自由运行和采用PID调制后信号Allan方差图"}]},{"lang":"en","label":[{"name":"text","data":"Fig.8"}],"title":[{"name":"text","data":"Allan variance diagram between free-running and after-modulation"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382047&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382049&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382048&type=","width":"76.90000153","height":"60.14908218","fontsize":""}]}},{"name":"p","data":[{"name":"text","data":"采用PID调制功率稳定控制后，其标准离差率C"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":"为0.016%（1 800 s），其峰峰起伏S"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":"为±0.042%（1 800 s）。采用功率稳定后的光束峰峰起伏S"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":"降至激光器自由运行时约1/8.79，标准离差率C"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":"改善至1/13.76。从Allan方差图分析，在自由运行状态下，平均时间为1 s时的稳定度为1.178×10"},{"name":"italic","data":[{"name":"sup","data":[{"name":"text","data":"-"}]}]},{"name":"sup","data":[{"name":"text","data":"7"}]},{"name":"text","data":"，平均时间为4 s时达到最好稳定度5.263×10"},{"name":"italic","data":[{"name":"sup","data":[{"name":"text","data":"-"}]}]},{"name":"sup","data":[{"name":"text","data":"8"}]},{"name":"text","data":"，之后发生较大偏移，平均时间在1 024 s时的稳定度为5.703×10"},{"name":"italic","data":[{"name":"sup","data":[{"name":"text","data":"-"}]}]},{"name":"sup","data":[{"name":"text","data":"5"}]},{"name":"text","data":"，激光器本身受到温度、环境扰动等多种原因影响导致稳定性变差；在经过稳定调制后，平均时间为1 s时的稳定度为4.038×10"},{"name":"italic","data":[{"name":"sup","data":[{"name":"text","data":"-"}]}]},{"name":"sup","data":[{"name":"text","data":"8"}]},{"name":"text","data":"，在平均时间8 s时，达到最好稳定度3.040×10"},{"name":"italic","data":[{"name":"sup","data":[{"name":"text","data":"-"}]}]},{"name":"sup","data":[{"name":"text","data":"8"}]},{"name":"text","data":"，随后稳定度略有上升，长期稳定度处于10"},{"name":"italic","data":[{"name":"sup","data":[{"name":"text","data":"-"}]}]},{"name":"sup","data":[{"name":"text","data":"8"}]},{"name":"text","data":"水平。"}]},{"name":"fig","data":{"id":"F9","caption":[{"lang":"zh","label":[{"name":"text","data":"图9"}],"title":[{"name":"text","data":"SPD2输出电压的时域波动图"}]},{"lang":"en","label":[{"name":"text","data":"Fig.9"}],"title":[{"name":"text","data":"Time-domain plot of output voltage of SPD2"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382050&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382052&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382051&type=","width":"76.72899628","height":"59.00199890","fontsize":""}]}},{"name":"p","data":[{"name":"text","data":"分束片将透射光分成95：5两部分，95%的光经过薄石英片后进入SPD1中，5%的光经过薄石英片后进入SPD2中。上图是以0.16 s时间间隔采集得到的SPD2数据。SPD2处在内环反馈中，其电压是实时反馈测量光路的电压，与参考电压进行比较并且根据误差进行调节，电压平均值为1.500 V，与参考电压严格一致，噪声的平均值为零。"}]},{"name":"fig","data":{"id":"F10","caption":[{"lang":"zh","label":[{"name":"text","data":"图10"}],"title":[{"name":"text","data":"SPD2输出电压的Allan方差图"}]},{"lang":"en","label":[{"name":"text","data":"Fig.10"}],"title":[{"name":"text","data":"Allan variance diagram of output voltage of SPD2"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382053&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382055&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=35382054&type=","width":"76.19999695","height":"61.11899948","fontsize":""}]}},{"name":"p","data":[{"name":"text","data":"SPD2的电压值的长期稳定性应与SPD1保持一致。在Allan方差图中，SPD2输出电压的所有噪声中高斯白噪声占主导，在平均时间4 s时，稳定度达到3.844×10"},{"name":"italic","data":[{"name":"sup","data":[{"name":"text","data":"-"}]}]},{"name":"sup","data":[{"name":"text","data":"8"}]},{"name":"text","data":"，在平均时间614 s时，中长期稳定度可达到3.208×10"},{"name":"italic","data":[{"name":"sup","data":[{"name":"text","data":"-"}]}]},{"name":"sup","data":[{"name":"text","data":"12"}]},{"name":"text","data":"。但稳定度与SPD1并不相同，SPD2明显更为稳定。"}]},{"name":"p","data":[{"name":"text","data":"内环本身就存在不稳定性波动，环境误差和探测器测量误差共同作用在外环的激光功率稳定性上。提高反馈路的调制稳定性，减小环境误差，提高探测器的测量精度是改善外环激光功率稳定性的有效办法。"}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"5 结 论"}],"level":"1","id":"s5"}},{"name":"p","data":[{"name":"text","data":"在光辐射定标领域，激光器的稳定性具有重要的作用，具有高稳定性的激光光源可用作超光谱遥感类、生物医学类光电探测系统、太阳绝对光谱辐照度仪的定标光源和性能比对光源。"}]},{"name":"p","data":[{"name":"text","data":"采用振镜转动玻璃片改变透过率的方法，可以对He-Ne激光器进行功率稳定控制。经过功率稳定控制后的激光器稳定性参数为：标准离差率C"},{"name":"sub","data":[{"name":"text","data":"V"}]},{"name":"text","data":"为0.016%（1800s），其峰峰起伏"},{"name":"italic","data":[{"name":"text","data":"S"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"为±0.042%（3 600 s）。峰峰起伏"},{"name":"italic","data":[{"name":"text","data":"S"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"降至激光器自由运行时的1/8.79，标准离差率"},{"name":"italic","data":[{"name":"text","data":"C"},{"name":"sub","data":[{"name":"text","data":"V"}]}]},{"name":"text","data":"改善至1/13.76。此方法对He-Ne激光器的功率稳定性有较好的改进，可以满足高稳定性模拟光源的稳定性要求。"}]},{"name":"p","data":[{"name":"text","data":"石英片对430 n~2 500 nm波长的光都具有高且稳定的透过率，从原理上来说，通过更换石英平板玻璃和监视反馈探测器，基于振镜的功率稳定控制器具有宽动态范围（微光至强光）、宽光谱范围（紫外至中远红外）、高损伤阈值的功率控制稳定功能，可适应激光器、超连续白光激光器等自然光及各种偏振态的准直连续光源的稳定性控制。目前本文仅对稳定性控制进行试验验证，下一步将对动态范围、宽光谱范围的功率控制稳定特性进行理论分析和试验验证，并开展基于振镜的功率稳定控制器典型应用示范研究。"}]}]}],"footnote":[],"reflist":{"title":[{"name":"text","data":"参考文献"}],"data":[{"id":"R1","label":"1","citation":[{"lang":"zh","text":[{"name":"text","data":"吴俊"},{"name":"text","data":"， "},{"name":"text","data":"舒岳阶"},{"name":"text","data":"， "},{"name":"text","data":"曹师宝"},{"name":"text","data":"， "},{"name":"text","data":"等"},{"name":"text","data":". 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