激光扫描共聚焦光谱系统设计

激光扫描共聚焦光谱系统设计 Design of laser scanning confocal spectroscopy system 1 2 first-author corresp 周旻超（1985-），男，江苏江阴人，硕士，副研究员，2011年于南京理工大学获得硕士学位，主要从事高/超分辨显微成像的研究。E-mail：zhoumc@sibet.ac.cn http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460206&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460215&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460211&type= 22.01332855 32.00403595 周旻超 （1985-），男，江苏江阴人，硕士，副研究员，2011年于南京理工大学获得硕士学位，主要从事高/超分辨显微成像的研究。E-mail： zhoumc@sibet.ac.cn zhoumc@sibet.ac.cn 2 corresp E-mail： wangzy@sibet.ac.cn E-mail： wangzy@sibet.ac.cn 王振亚（1993-），男，江苏镇江人，硕士，助理研究员，2018年于苏州科技大学获得硕士学位，主要从事高/超分辨显微成像的研究。E-mail：wangzy@sibet.ac.cn http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460221&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460230&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460225&type= 22.01332855 32.00381470 王振亚 （1993-），男，江苏镇江人，硕士，助理研究员，2018年于苏州科技大学获得硕士学位，主要从事高/超分辨显微成像的研究。E-mail： wangzy@sibet.ac.cn wangzy@sibet.ac.cn 2 2 2 复旦大学 工程与应用技术研究院，上海 200433 复旦大学 工程与应用技术研究院，上海 200433 Academy for Engineering and Technology， Fudan University， Shanghai 200433， China Academy for Engineering and Technology， Fudan University， Shanghai 200433， China 中国科学院 苏州生物医学工程技术研究所，江苏 苏州 215163 中国科学院 苏州生物医学工程技术研究所，江苏 苏州 215163 Suzhou Institute of Biomedical Engineering and Technology， Chinese Academy of Sciences， Suzhou 215163， China Suzhou Institute of Biomedical Engineering and Technology， Chinese Academy of Sciences， Suzhou 215163， China 为提高激光扫描共聚焦显微镜光谱模块的分光性能，设计了双Amici棱镜光谱结构。根据棱镜色散特性，计算得到Amici棱镜和双Amici棱镜的线性与非线性数学模型，给出直视型棱镜结构参数。比较相同色散条件下Amici和双Amici棱镜结构，得到双Amici棱镜组能提供更好的色散线性度。在光谱波段400~700 nm，中心波长偏向角为 <math id="M1"><msup><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mo>°</mo></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460239&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460234&type= 2.20133328 2.62466669 ，最大色散角为4°，光谱分辨率为5 nm的条件下，利用双Amici棱镜结构设计共光轴直视型分光系统。用双Amici棱镜结构和单棱镜对比，进行了光谱分布实验。实验结果表明，双Amici棱镜组的色散线性度明显优于单棱镜，大大改善了因棱镜非线性分光特性对荧光成像光谱分辨率的影响。同时，将双Amici棱镜结构设计进共聚焦光谱成像模块中，对牛肺动脉内皮细胞切片进行了三通道荧光成像，得到了高质量的多通道荧光图像。 A spectral structure for the double Amici prism was designed to improve the spectroscopic performance of a laser scanning confocal microscope spectroscopy module. Linear and nonlinear mathematical models were formulated for the Amici and double Amici prisms， and the structure parameters of direct-viewing prism were chosen according to the prism dispersion characteristics. The structures of the Amici and double Amici prisms were compared for the same dispersion conditions， and the double Amici prism group was found to provide better dispersion linearity. A common optical axis direct vision spectroscopic system was developed using a double Amici prism for a 400-700 nm spectral range and 5 nm spectral resolution， with central wavelength deviation angle of 0° and maximum dispersion angle of 4°. The experimental results show that the dispersion linearity of this structure is significantly better than that of a single prism. Spectral resolution issues caused by the nonlinear spectroscopic characteristics of prisms are greatly reduced. 激光扫描共聚焦 Amici棱镜 色散线性度 共光轴直视型 laser scanning confocal Amici prism dispersion linearity common optical axis direct vision 1 引　言 1 激光扫描共聚焦显微镜成像光学分辨率介于传统光学显微镜和电子显微镜之间，能够实现高分辨率下的无损三维成像，把光学显微成像技术推向了全新的应用阶段，是国内外从事生物医学和材料科学研究不可或缺的高端科研设备 ［ 1 1 - 2 2 1-2 ］ 。与传统宽场显微镜相比，共聚焦显微镜通过针孔滤波的方式，消除焦平面外杂散光的干扰，可实现光学层切扫描成像。 随着生物医学技术的迅速发展，对被测样品进行多种荧光标记物标记的需求日益增高 ［ 3 3 ］ 。因此，多光谱成像技术得到了较为广泛的应用。为了实现对生物样本不同部位的成像，一般采用不同的荧光染料对样本进行荧光标记，但有些荧光染料激发谱较宽容易和其他荧光染料激发谱重叠。为避免多种荧光成像时的荧光串扰问题，激光扫描共聚焦显微系统引入了多光谱成像技术 ［ 4 4 - 5 5 4-5 ］ 。共聚焦实现光谱成像的主要方式有滤光片式、光栅式以及棱镜式等，其中分光元件是光谱成像的核心部件 ［ 6 6 - 7 7 6-7 ］ 。滤光片式荧光分光组件的应用方便简单，但它是固定的波长组合，很大程度上限制了荧光染料选择的灵活性，很难解决荧光串扰问题。因此，光栅或棱镜分光的方法被更多地应用于多光谱成像技术中。光栅分光具有色分辨率高、色散线性均匀等优点，但也有局限性，如光栅系统在宽谱段分光时，存在谱线叠加问题；制造工艺导致光栅分光的杂散光较多，加工难度较大；光栅是通过衍射分光，能量利用率只能达到总能量的60%~70%左右 ［ 8 8 ］ 。共聚焦成像荧光信号较为微弱，光谱衍射效率是十分重要的指标。棱镜分光原理简单，性能稳定，荧光透射效率高（一般大于90%），十分适合应用于共聚焦显微镜的光谱成像。共聚焦显微镜棱镜式分光一般采用单棱镜，由于棱镜材料本身的性质，光谱分辨率存在非线性问题，短波段的色分辨率高，长波段的色分辨率低，因此不同波段的光谱分辨率也是不同的。除此之外，单棱镜的色散会引起光线在传播方向上的偏折，给光学装调增加了一些难度。 复合棱镜组合在设计方面具有更高的灵活性，在保证较高的能量利用率的同时，通过选择棱镜的材料以及控制各棱镜的角度实现入射和出射光束共轴，以及色散的非线性校正 ［ 9 9 ］ 。共聚焦显微镜的模块化研发需要考虑结构小型化、空间利用率高、装调简单等因素，本文采用双Amici棱镜结构作为色散元件，根据Amici棱镜的光学特性推导其共轴条件，优化材料和棱镜顶角实现了宽光谱、共光轴、直视型光谱分光系统，大大改善了棱镜分光的非线性。 2 系统组成 1 激光扫描共聚焦显微镜主要由扫描模块、显微镜和光谱成像模块等部分组成，如 图1 图1 所示。扫描模块中的激光进入显微镜后被物镜聚焦在被测样本上，激发出的荧光经显微镜进入扫描模块，在二向色镜处透射，再经针孔透镜聚焦后通过针孔进入光谱成像模块。光谱成像模块由准直透镜、分光棱镜、聚焦透镜、可变狭缝以及光电倍增管（Photomultiplier Tube， PMT）组成，荧光进入光谱成像模块后先由准直透镜准直成平行光，再进入分光棱镜和聚焦透镜，分光棱镜将荧光展开成一定宽度的光谱带，利用可调狭缝进行光谱选择并由PMT采集信号。 根据PMT探测面尺寸，分光谱宽需小于5 mm，考虑狭缝电机的步进精度，同时为了保证色散线性度和模块的紧凑性，聚焦透镜焦距为65 mm，色散角度选择 <math id="M2"><msup><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mo>∘</mo></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460269&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460263&type= 2.53999996 2.96333337 ，则光谱宽度约为4.55 mm，满足技术要求。共聚焦光谱成像模块的工作波长为400~700 nm，要求最优光谱分辨率低于5 nm。针孔尺寸为 <math id="M3"><mn mathvariant="normal">30</mn><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460841&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460840&type= 9.48266602 3.64066648 ，中心波长（ <math id="M4"><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">550</mn><mtext> </mtext><mi mathvariant="normal">n</mi><mi mathvariant="normal">m</mi><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460284&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460280&type= 19.64266586 3.80999994 ）偏向角为0°，出射与入射光轴偏移量为0 mm。 3 Amici结构建模及设计 1 本文从棱镜的光学特性出发，根据光束传输角度、棱镜组顶角和材料折射率推导Amici棱镜组的非线性设计方程，并利用小角度近似推导出的线性方程组计算初始解。在初始解的基础上进行非线性优化，最终找到满足线色散的共轴直视型Amici棱镜组。 3.1　线性和非线性设计方法 2 光学元件的设计主要基于光线追迹，如 图2 图2 所示。其中 <math id="M5"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460637&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460632&type= 3.13266683 3.72533321 和 <math id="M6"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460629&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460626&type= 3.13266683 3.72533321 分别为棱镜的顶角， <math id="M7"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460637&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460632&type= 3.13266683 3.72533321 被垂线分为 <math id="M8"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460326&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460321&type= 3.13266683 4.57200003 和 <math id="M9"><msub><mrow><mi>γ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460335&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460330&type= 3.13266683 4.57200003 ， <math id="M10"><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460345&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460340&type= 2.96333337 3.72533321 为入射角， <math id="M11"><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460355&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460350&type= 2.96333337 3.72533321 和 <math id="M12"><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460360&type= 2.96333337 3.72533321 分别为入射光和出射光与光轴的夹角， <math id="M13"><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460374&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460370&type= 2.96333337 3.97933316 为出射角，本文中所有角度遵循现代符号惯例 ［ 10 10 ］ 。 根据斯涅尔定律和几何关系可以得出光线在棱镜组中各角度关系： jian <math display="block" id="M14"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>-</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></mtd></mtr><mtr><mtd><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>n</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><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></mtd></mtr><mtr><mtd><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>=</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>-</mo><mfrac><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mtd></mtr><mtr><mtd><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfenced></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460401&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460395&type= 35.30599976 54.44067001 . 假设光轴平行于棱镜组基准面，空气折射率为1， <math id="M15"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460409&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460406&type= 19.72733307 7.87400007 ，则系统的偏向角为： <math display="block" id="M16"><mtable columnalign="left"><mtr><mtd><mi>δ</mi><mo>=</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><mfenced open="{" close="" separators="|"><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfenced open="{" close="" separators="|"><mrow><msub><mrow><mi>n</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><mfenced open="{" close="" separators="|"><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfenced open="{" close="" separators="|"><mrow><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mfenced></mrow></mfenced></mrow></mfenced><mo>·</mo></mtd></mtr><mtr><mtd><mfenced open="" close="}" separators="|"><mrow><mfenced open="" close="]" separators="|"><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfenced open="[" close="" separators="|"><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfrac><mrow><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">0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>-</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></mrow></mfenced></mrow></mfenced><mfenced open="" close="}" separators="|"><mrow><mfenced open="" close="}" separators="|"><mrow><mo>-</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfenced></mrow></mfenced><mfenced open="" close="}" separators="|"><mrow><mo>-</mo><mfrac><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></mfenced><mo>.</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460420&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460415&type= 65.36266327 25.39999962 由于棱镜的折射率随波长变化，偏向角也随之变化。传输光束中长波和短波的偏向角之差为色散角 <math id="M17"><mi>Δ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460429&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460426&type= 2.45533323 2.79399991 ，则有： <math display="block" id="M18"><mi>Δ</mi><mo>=</mo><mi>δ</mi><mo stretchy="false">(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">)</mo><mo>-</mo><mi>δ</mi><mo stretchy="false">(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460439&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460434&type= 33.27399826 4.48733330 . 因此，棱镜系统的色散是关于材料折射率、棱镜顶角以及入射光线角度的非线性函数。在经典光学设计中，通常使用中心波长作为主光线进行优化设计，这里设中心波长为 <math id="M19"><mover><mrow><mi>λ</mi></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460449&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460444&type= 1.77800000 3.47133350 。为了根据色散函数得到合适的设计变量，假设棱镜顶角 <math id="M20"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460460&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460455&type= 1.94733346 2.79399991 和入射光线与光轴夹角 <math id="M21"><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460469&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460465&type= 2.96333337 3.72533321 无限小，利用小角度近似系统的偏向角，可得： <math display="block" id="M22"><mtable><mtr><mtd><mi>δ</mi><mo>=</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>=</mo></mtd></mtr><mtr><mtd><mo stretchy="false">(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mi>g</mi><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><mo stretchy="false">(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mi>g</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=24460480&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460474&type= 51.47733307 10.24466610 . 假设波长和折射率近似呈线性关系，中心波长的色散可以写成： <math display="block" id="M23"><mi>Δ</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mover><mrow><mi>λ</mi></mrow><mo>¯</mo></mover><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mover><mrow><mi>λ</mi></mrow><mo>¯</mo></mover><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460489&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460483&type= 32.59666443 9.48266602 ， 其中： <math id="M24"><msub><mrow><mi>δ</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460500&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460493&type= 2.70933342 3.72533321 和 <math id="M25"><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460508&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460503&type= 3.80999994 3.80999994 分别表示单个棱镜的偏向角和阿贝数， <math id="M26"><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mrow><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo></mrow><mo>/</mo><mrow><mo stretchy="false">(</mo><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">F</mi></mrow></msub><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460517&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460512&type= 36.23733139 4.48733330 。取 <math id="M27"><mi>δ</mi><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460526&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460522&type= 8.63599968 2.79399991 ，代入 式（4） 式（4） 和 式（5） 式（5） 可得： <math display="block" id="M28"><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mover><mrow><mi>λ</mi></mrow><mo>¯</mo></mover><mo stretchy="false">)</mo><mo>=</mo><mo>-</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mover><mrow><mi>λ</mi></mrow><mo>¯</mo></mover><mo stretchy="false">)</mo><mo>=</mo><mo>-</mo><mi>Δ</mi><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac></mrow></mfenced></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460536&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460531&type= 60.19800186 10.66800022 . 根据棱镜材料的平均折射率可计算各元素的顶角： <math display="block" id="M29"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msub><mrow><mover accent="true"><mi>n</mi><mo>¯</mo></mover></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfrac><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac></mrow></mfenced></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460546&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460541&type= 41.06333542 10.66800022 ， <math display="block" id="M30"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msub><mrow><mover accent="true"><mi>n</mi><mo>¯</mo></mover></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfrac><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac></mrow></mfenced></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460555&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460551&type= 41.06333542 10.66800022 . 实际上，大多数棱镜不能完美满足小角度近似，因此在设计过程中一般使用线性方程得到初始解，然后利用光学设计软件进行最终的非线性优化。直视系统中目标值 <math id="M31"><msup><mrow><mi>δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460566&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460560&type= 9.82133293 3.04800010 ， <math id="M32"><msup><mrow><mi>Δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460575&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460570&type= 10.07533360 3.04800010 °，光谱波段为400~700 nm。假设系统材料分别为BK7和SF6，在满足目标值的条件下，棱镜顶角的线性和非线性表示如 图3 图3 所示。 从 图3 图3 中看出，在选定玻璃材料后，线性方程在满足目标值时： <math id="M33"><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn mathvariant="normal">85</mn><mo>°</mo><mo>,</mo><mo>-</mo><mn mathvariant="normal">57</mn><mo>°</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460601&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460596&type= 34.71333313 4.48733330 ，非线性方程的最优解为： <math id="M34"><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn mathvariant="normal">88</mn><mo>°</mo><mo>,</mo><mo>-</mo><mn mathvariant="normal">69</mn><mo>°</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460613&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460606&type= 34.71333313 4.48733330 。 <math id="M35"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460621&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460616&type= 3.13266683 3.72533321 在两种计算方式中较为接近， <math id="M36"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460629&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460626&type= 3.13266683 3.72533321 之间存在一定范围。因此，线性方程为非线性的精确设计提供了较好的起点，在优化时可以暂时确定线性解 <math id="M37"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460637&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460632&type= 3.13266683 3.72533321 不变，将 <math id="M38"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460645&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460641&type= 3.13266683 3.72533321 作为变量进行优化。 3.2　玻璃材料选择 2 棱镜系统的光谱色散非线性是不可避免的，只能在优化函数中加入约束条件使色散非线性最小。由 式（1） 式（1） 可知，偏向角是关于波长的函数，对 <math id="M39"><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460655&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460649&type= 1.77800000 2.79399991 求导可得到角色散率 <math id="M40"><mrow><mrow><mi mathvariant="normal">d</mi><mi>δ</mi></mrow><mo>/</mo><mrow><mi mathvariant="normal">d</mi><mi>λ</mi></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460662&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460658&type= 8.55133343 3.30200005 ，其二阶导数所对应的面积可用来度量光谱色散的非线性度，定义为： <math display="block" id="M41"><mi>N</mi><mi>L</mi><mo>=</mo><mo>∫</mo><mfenced open="|" close="|" separators="|"><mrow><mfrac><mrow><msup><mrow><mi mathvariant="normal">d</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>δ</mi></mrow><mrow><mi mathvariant="normal">d</mi><msup><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mrow></mfenced><mi mathvariant="normal">d</mi><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460671&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460668&type= 25.31533241 9.65200043 . 另一种表示光谱色散线性度的方法是取色散梯度的最大值和最小值之比，即光谱采样率（Spectral Sampling Ratio， SSR），SSR表示光谱波段非线性色散偏差的最大量。若SSR=2，最短波长对应的光谱宽度为1 nm，则最长波长对应的光谱宽度为2 nm。 <math display="block" id="M42"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">S</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi><mfenced open="{" close="}" separators="|"><mrow><mfenced open="|" close="|" separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">d</mi><mi>δ</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi>λ</mi></mrow></mfrac></mrow></mfenced></mrow></mfenced></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfenced open="{" close="}" separators="|"><mrow><mfenced open="|" close="|" separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">d</mi><mi>δ</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi>λ</mi></mrow></mfrac></mrow></mfenced></mrow></mfenced></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460678&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460676&type= 29.46400070 21.33600044 . 由上文2.1中色散公式可以看出，满足直视型的Amici棱镜由一块低折射率、高阿贝数的棱镜和一块高折射率、低阿贝数的棱镜组成。根据折射率和阿贝数的范围，通过Matlab软件在商业光学设计软件ZEMAX玻璃目录中读取所有符合的材料。为了提高计算速度，只在使用较为广泛的Schott玻璃目录下进行搜索。根据读取的玻璃组合，给定目标值 <math id="M43"><msup><mrow><mi>δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460684&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460681&type= 9.82133293 3.04800010 °， <math id="M44"><msup><mrow><mi>Δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460808&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460807&type= 10.07533360 3.04800010 °，并将NL和SSR作为约束条件，在所有的玻璃中优化出线性度较好且满足目标值的玻璃组合。选取SSR≤7，其他参数见 表1 表1 。 Notes： Spectral range is 400-700 nm；incident angle <math id="M49"><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460828&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460827&type= 8.29733276 3.21733332 °； <math id="M50"><msup><mrow><mi>δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460830&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460829&type= 8.38199997 2.62466669 °； <math id="M51"><msup><mrow><mi>Δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460747&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460743&type= 8.63599968 2.62466669 °. Glass1 Glass2 <math id="M45"><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460810&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460809&type= 2.70933342 3.21733332 /（°） <math id="M46"><msub><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460812&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460811&type= 2.70933342 3.21733332 /（°） <math id="M47"><msup><mrow><mi>δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460815&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460813&type= 2.70933342 2.62466669 /（°） <math id="M48"><msup><mrow><mi>Δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460720&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460717&type= 2.87866688 2.62466669 /（°） NL SSR N-PK51 N-BASF2 -104.55 124.14 0.00 4.00 2.182 5.99 N-BAF4 N-KZFS2 -144.72 104.49 0.00 4.00 2.193 6.26 N-BAF52 N-KF9 -144.61 112.39 0.00 4.00 2.195 6.49 N-KZFS8 N-BAF52 110.73 -112.78 0.00 4.00 2.205 6.53 N-KZFS11 N-BAF4 99.32 -108.82 0.00 4.00 2.223 6.74 通过 表1 表1 可以看出，在满足线性度较好的条件下，两个棱镜材料的折射率和阿贝数越接近，系统的色散线性度越好。在目标值 <math id="M52"><msup><mrow><mi>Δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460808&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460807&type= 10.07533360 3.04800010 °的条件下，Amici棱镜两个顶角明显增大，在满足光线传输的情况下，会增加分光结构的尺寸。 3.3　双Amici棱镜 2 双Amici棱镜由3个棱镜元素组成，结构完全对称，如 图4 图4 所示。第一个棱镜和第三个棱镜完全一样，具有相同的材料和顶角 ［ 11 11 - 12 12 11-12 ］ 。 双Amici棱镜的对称性表示其线性方程和Amici棱镜组的线性方程几乎相同，在第一个元素的表达式前乘以系数2得到 ［ 13 13 ］ ： <math display="block" id="M53"><mtable><mtr><mtd><mi>δ</mi><mo>=</mo><mn mathvariant="normal">2</mn><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>=</mo></mtd></mtr><mtr><mtd><mn mathvariant="normal">2</mn><mo stretchy="false">(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo>·</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><mo stretchy="false">(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo>·</mo><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=24460770&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460767&type= 51.56200027 9.82133293 ， <math display="block" id="M54"><mi>Δ</mi><mo>=</mo><mn mathvariant="normal">2</mn><mfrac><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mover><mrow><mi>λ</mi></mrow><mo>¯</mo></mover><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><mover><mrow><mi>λ</mi></mrow><mo>¯</mo></mover><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460777&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460772&type= 35.05199814 9.48266602 . 与 式（5） 式（5） 相同，利用线性方程推导出棱镜的顶角表达式为： <math display="block" id="M55"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msub><mrow><mover accent="true"><mi>n</mi><mo>¯</mo></mover></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfrac><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac></mrow></mfenced></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460781&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460779&type= 41.06333542 10.66800022 ， <math display="block" id="M56"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msub><mrow><mover accent="true"><mi>n</mi><mo>¯</mo></mover></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfrac><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac></mrow></mfenced></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460788&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460786&type= 41.06333542 10.66800022 . 其线性方程组如下： <math display="block" id="M57"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>-</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></mtd></mtr><mtr><mtd><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></mtd></mtr><mtr><mtd><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><msub><mrow><mi>n</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><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext></mtd></mtr><mtr><mtd><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>=</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>-</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460790&type= 35.72933197 70.01933289 ， 其中： <math id="M58"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><mfrac><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460799&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460796&type= 19.72733307 7.87400007 ， <math id="M59"><mi>δ</mi><mo>=</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460803&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460800&type= 17.52599907 3.72533321 。尽管双Amici棱镜组的元素有所增加，但由于其完全对称，所以在设计优化过程中没有增加额外的自由度。因此，在设定目标值 <math id="M60"><msup><mrow><mi>δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460806&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460804&type= 9.82133293 3.04800010 °， <math id="M61"><msup><mrow><mi>Δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460808&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460807&type= 10.07533360 3.04800010 °后按照Amici棱镜的设计方式在玻璃库中进行搜索，组合结果如 表2 表2 所示。 Notes： Spectral range is 400-700 nm；incident angle <math id="M66"><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460828&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460827&type= 8.29733276 3.21733332 °； <math id="M67"><msup><mrow><mi>δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460830&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460829&type= 8.38199997 2.62466669 °； <math id="M68"><msup><mrow><mi>Δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460834&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460832&type= 8.63599968 2.62466669 °. Glass1 Glass2 <math id="M62"><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460810&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460809&type= 2.70933342 3.21733332 /（°） <math id="M63"><msub><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460812&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460811&type= 2.70933342 3.21733332 /（°） <math id="M64"><msup><mrow><mi>δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460815&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460813&type= 2.70933342 2.62466669 /（°） <math id="M65"><msup><mrow><mi>Δ</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460819&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460818&type= 2.87866688 2.62466669 /（°） NL SSR CAF2 N-LAK33A -95.04 94.37 0.00 4.00 1.770 5.74 CAF2 N-LAF34 -92.05 90.50 0.00 4.00 1.814 5.97 CAF2 N-LAF35 -92.08 93.38 0.00 4.00 1.830 6.03 CAF2 N-LAF21 -89.48 87.24 0.00 4.00 1.859 6.13 CAF2 N-LASF44 -88.17 84.78 0.00 4.00 1.860 6.21 表2 表2 中按线性度从高到低排列且SSR < 7的双Amici棱镜组合。 图5 图5 为单棱镜、 表1 表1 和 表2 表2 中线性度最优棱镜组合的色散曲线，结合数据表和色散曲线图可以得出：双Amici棱镜组的线性度明显优于单棱镜和Amici棱镜。与Amici结构不同，双Amici结构在棱镜组合外层选择低色散材料，内层为高色散材料（一般为镧系玻璃）。内外层材料的折射率越接近，系统的线性度越好。另外，双Amici棱镜组具备光束零位移的特性，即 <math id="M69"><mi mathvariant="normal">Δ</mi><mi>y</mi><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460836&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460835&type= 11.00666618 3.72533321 ，这有利于后续的光机设计和装调。 4 光学系统仿真 1 综上分析，激光扫描共聚焦光谱分光模块选择双Amici棱镜。共聚焦显微镜成像中，激光激发样本中的荧光信息，沿着物镜、管镜、扫描透镜以及聚焦透镜通过针孔滤波后，再利用准直透镜和棱镜进行光谱分光。仿真模型参数如下：光谱波段为400~700 nm，物镜选择Zebasek_007.zmx，其NA为1.4，放大倍率为100，针孔大小为 <math id="M70"><mn mathvariant="normal">30</mn><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460841&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460840&type= 9.48266602 3.64066648 ，聚焦和准直透镜均为三胶合透镜。选择数据 表2 表2 中线性度最好的玻璃组合，确定棱镜材料属性后，利用双Amici线性方程组先计算出各棱镜顶角的初始值。在棱镜每个面前设置坐标断点，并将倾斜量设为变量。仿真优化结果如 图6 图6 所示。 1,2; 根据 图6 图6 （a）可知，光束在像面上的色散距离为4.5 mm左右，即棱镜的角色散为4°，色散线性程度与理论计算结果基本一致。 5 实　验 1 激光扫描共聚焦光谱成像系统中光束透过针孔后经过准直透镜准直，进入分光棱镜，分光棱镜将荧光进行光谱展开并经过透镜聚焦形成一条分离的光谱带。在聚焦像面处设有两个可联动的狭缝片，通过移动单个狭缝改变狭缝宽度，另一个狭缝带动整个狭缝宽度进行光谱选择，狭缝电机最小步进为2.5 <math id="M71"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460856&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460855&type= 4.99533367 3.64066648 。选通的光谱进入PMT转换成电流信号。 实验利用可变狭缝和单轴精密位移台模拟电机移动，白光通过光纤进入准直透镜后经过棱镜分光，再由透镜将光谱带聚焦在狭缝面。这里选择顶角为60°的等边色散单棱镜和由3个等边棱镜胶合成的双Amici棱镜进行实验。其中，双Amici结构在棱镜组合外层选择低色散材料，内层为高色散材料。因此，在有限范围内外层选择F2材料（ V d =36.37），内层选择N-SF11材料（ V d =24.76）。实验测试平台如 图7 图7 所示。 利用影像仪将可变狭缝调至40 <math id="M72"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460856&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24460855&type= 4.99533367 3.64066648 ，并固定在精密位移台上。光谱仪探测光纤固定在狭缝后，通过移动精密位移台进行波长的选取，记录移动距离和光谱中心波长，拟合位置-波长曲线。读取ZEMAX仿真结果中的数据，将仿真结果和实验数据进行对比，如 图8 图8 所示。双Amici棱镜在色散线性度上优于单棱镜，实验测得的数据基本与理论值相同。在满足色散要求的情况下，双Amici棱镜可以在一定程度上优化系统的色散非线性度，提高激光扫描共聚焦系统光谱成像结果的准确性。 该双Amici棱镜结构经过实验验证后，放置到激光扫描共聚焦显微镜的光谱成像模块中进行光谱成像实验。 图9 图9 （a）是激光扫描共聚焦显微镜， 图9 图9 （b）是共聚焦产品的光谱成像模块。 1;2; 采用光谱成像技术对牛肺动脉内皮细胞切片进行了多通道荧光成像。该切片采购自赛默飞世尔科技公司，用DAPI、Alexa Fluor 488和MitoTracker Red 3种染料分别对牛肺动脉内皮细胞的细胞核、肌动蛋白和线粒体进行荧光标记。采用405，488和561 nm激光同时去激发样本荧光，按照尽量避免荧光串色的原则设置3种荧光通道的带宽，DAPI激发的荧光光谱设置为［460 nm，490 nm］，Alexa Fluor 488激发的荧光光谱设置为［520 nm， 540 nm］，MitoTracker Red激发的荧光光谱设置为［600 nm，630 nm］。三通道同时采集荧光图像，成像时间约为5 s，图像分辨率是2 048×2 048。 图10 图10 是三通道荧光成像图片。从 图10 图10 可以看出，不同荧光通道得到的图像形态完全不同，说明不同荧光标记的细胞结构都能够很好地呈现出来，几乎不存在荧光串色问题。 6 结　论 1 高分辨显微成像近年来发展迅速，激光扫描共聚焦相比于生物荧光显微镜具有高分辨率和宽光谱成像的优势。目前，市面上共聚焦光谱模块多选择单棱镜或光栅作为分光元件。光栅虽然能实现更高的光谱分辨率下，但其荧光传输效率较低；单棱镜一般选恒偏向角棱镜，其分光具有较严重的色散不均匀性且光路需要通过反射镜转折。本文针对直视型共轴分光棱镜展开研究，提出Amici棱镜和双Amici棱镜组的初始结构计算方法，并利用优化算法给出了线性度较好的棱镜组结构参数。最终选择双Amici棱镜作为光谱模块的分光元件，通过光学仿真实现了目标色散和中心波长零偏转，整个光学模块结构简单、紧凑。实验结果表明：双Amici棱镜结构相比单棱镜具有更好的光谱线性度，可以提高光谱成像时光谱选择的准确性。 参考文献 陈丽妃 ， 黄慧 ， 陈琦 ， 等 . 活体共聚焦显微镜检测糖尿病患者角膜病变的研究进展 ［J］. 中国临床新医学 ， 2021 ， 14 （ 8 ）： 836 - 839 . doi: 10.3969/j.issn.1674-3806.2021.08.24 http://dx.doi.org/10.3969/j.issn.1674-3806.2021.08.24 活体共聚焦显微镜检测糖尿病患者角膜病变的研究进展 CHEN L F ， HUANG H ， CHEN Q ， et al . Research progress of in - vivo confocal microscopy in detecting corneal lesions in diabetic patients ［J］. Chinese Journal of New Clinical Medicine ， 2021 ， 14 （ 8 ）： 836 - 839 . （in Chinese） . doi: 10.3969/j.issn.1674-3806.2021.08.24 http://dx.doi.org/10.3969/j.issn.1674-3806.2021.08.24 Research progress of in-vivo confocal microscopy in detecting corneal lesions in diabetic patients 石伟 ， 张凯林 ， 侯晓东 . 边缘凸起式超显微硬度压痕的共聚焦测量 ［J］. 光学 精密工程 ， 2021 ， 29 （ 5 ）： 1014 - 1023 . doi: 10.37188/OPE.20212905.1014 http://dx.doi.org/10.37188/OPE.20212905.1014 边缘凸起式超显微硬度压痕的共聚焦测量 SHI W ， ZHANG K L ， HOU X D . Confocal microscopic measurement of ultramicro hardness considering indentation pile-up ［J］. Opt. Precision Eng. ， 2021 ， 29 （ 5 ）： 1014 - 1023 . （in Chinese） . doi: 10.37188/OPE.20212905.1014 http://dx.doi.org/10.37188/OPE.20212905.1014 Confocal microscopic measurement of ultramicro hardness considering indentation pile-up 马军山 ， 侯琳琳 ， 付东翔 ， 等 . 双荧光标记生物芯片激光共聚焦检测系统 ［J］. 光学 精密工程 ， 2005 ， 13 （ 6 ）： 727 - 734 . doi: 10.3321/j.issn:1004-924X.2005.06.018 http://dx.doi.org/10.3321/j.issn:1004-924X.2005.06.018 双荧光标记生物芯片激光共聚焦检测系统 MA J SH ， HOU L L ， FU D X ， et al . Two-laser scanning confocal system for microarray analysis ［J］. Opt. Precision Eng. ， 2005 ， 13 （ 6 ）： 727 - 734 . （in Chinese） . doi: 10.3321/j.issn:1004-924X.2005.06.018 http://dx.doi.org/10.3321/j.issn:1004-924X.2005.06.018 Two-laser scanning confocal system for microarray analysis 张运海 ， 杨皓旻 ， 孔晨晖 . 激光扫描共聚焦光谱成像系统 ［J］. 光学 精密工程 ， 2014 ， 22 （ 6 ）： 1446 - 1453 . doi: 10.3788/ope.20142206.1446 http://dx.doi.org/10.3788/ope.20142206.1446 激光扫描共聚焦光谱成像系统 ZHANG Y H ， YANG H M ， KONG CH H . Spectral imaging system on laser scanning confocal microscopy ［J］. Opt. Precision Eng. ， 2014 ， 22 （ 6 ）： 1446 - 1453 . （in Chinese） . doi: 10.3788/ope.20142206.1446 http://dx.doi.org/10.3788/ope.20142206.1446 Spectral imaging system on laser scanning confocal microscopy LI W Z ， YUAN X ， XU B ， et al . Applications of multiplexed immunohistochemistry/immunofluorescence and multispectral imaging technology in the field of tumor immunotherapy ［J］. Journal of Chinese Pharmaceutical Sciences ， 2020 ， 29 （ 10 ）： 734 - 747 . doi: 10.5246/jcps.2020.10.069 http://dx.doi.org/10.5246/jcps.2020.10.069 Applications of multiplexed immunohistochemistry/immunofluorescence and multispectral imaging technology in the field of tumor immunotherapy 孙慈 ， 杨晋 ， 朱继伟 ， 等 . 超宽谱段高分辨率中阶梯光栅光谱仪的光学设计 ［J］. 光学 精密工程 ， 2021 ， 29 （ 1 ）： 45 - 53 . doi: 10.37188/OPE.20212901.0045 http://dx.doi.org/10.37188/OPE.20212901.0045 超宽谱段高分辨率中阶梯光栅光谱仪的光学设计 SUN C ， YANG J ， ZHU J W ， et al . Optical design of echelle spectrometer with ultra-wide wavelength range and high resolution ［J］. Opt. Precision Eng. ， 2021 ， 29 （ 1 ）： 45 - 53 . （in Chinese） . doi: 10.37188/OPE.20212901.0045 http://dx.doi.org/10.37188/OPE.20212901.0045 Optical design of echelle spectrometer with ultra-wide wavelength range and high resolution 曾朝斌 ， 刘宾 ， 夏正德 ， 等 . 棱镜-光栅组合分光结构参数的优化方法研究 ［J］. 光学学报 ， 2020 ， 40 （ 21 ）： 7 - 15 . doi: 10.3788/aos202040.2105001 http://dx.doi.org/10.3788/aos202040.2105001 棱镜-光栅组合分光结构参数的优化方法研究 ZENG CH B ， LIU B ， XIA ZH D ， et al . Optimal design of spectroscopic structure based on prism-grating combination ［J］. Acta Optica Sinica ， 2020 ， 40 （ 21 ）： 7 - 15 . （in Chinese） . doi: 10.3788/aos202040.2105001 http://dx.doi.org/10.3788/aos202040.2105001 Optimal design of spectroscopic structure based on prism-grating combination 吴从均 ， 颜昌翔 ， 刘伟 ， 等 . 方形孔径棱镜式成像光谱仪光学设计 ［J］. 光学学报 ， 2013 ， 33 （ 12 ）： 228 - 234 . doi: http://ir.ciomp.ac.cn/handle/181722/38963 http://dx.doi.org/http://ir.ciomp.ac.cn/handle/181722/38963 方形孔径棱镜式成像光谱仪光学设计 WU C J ， YAN CH X ， LIU W ， et al . Prism hyperspectral imaging optical system design with rectangular aperture ［J］. Acta Optica Sinica ， 2013 ， 33 （ 12 ）： 228 - 234 . （in Chinese） . doi: http://ir.ciomp.ac.cn/handle/181722/38963 http://dx.doi.org/http://ir.ciomp.ac.cn/handle/181722/38963 Prism hyperspectral imaging optical system design with rectangular aperture 刘兵 ， 刘英 ， 张晓龙 ， 等 . 宽谱段共光轴线色散成像光谱仪三棱镜分光系统设计 ［J］. 光谱学与光谱分析 ， 2016 ， 36 （ 5 ）： 1543 - 1548 . doi: 10.3964/j.issn.1000-0593(2016)05-1543-06 http://dx.doi.org/10.3964/j.issn.1000-0593(2016)05-1543-06 宽谱段共光轴线色散成像光谱仪三棱镜分光系统设计 LIU B ， LIU Y ， ZHANG X L ， et al . Study on coaxial linear dispersion triplet prisms of wide spectral imaging spectrometer ［J］. Spectroscopy and Spectral Analysis ， 2016 ， 36 （ 5 ）： 1543 - 1548 . （in Chinese） . doi: 10.3964/j.issn.1000-0593(2016)05-1543-06 http://dx.doi.org/10.3964/j.issn.1000-0593(2016)05-1543-06 Study on coaxial linear dispersion triplet prisms of wide spectral imaging spectrometer GREIVENKAMP J E . Field Guide to Geometrical Optics ［M］. SPIE Press ， 2004 . doi: 10.1117/3.547461 http://dx.doi.org/10.1117/3.547461 Field Guide to Geometrical Optics EBIZUKA N ， YOKOTA H ， KAJINO F ， et al . Novel direct vision prism and Wollaston prism assembly for diffraction limit applications ［C］. SPIE Astronomical Telescopes + Instrumentation. Proc SPIE 7018， Advanced Optical and Mechanical Technologies in Telescopes and Instrumentation ， Marseille， France . 2008 ， 7018 ： 1601 - 1606 . doi: 10.1117/12.788528 http://dx.doi.org/10.1117/12.788528 Novel direct vision prism and Wollaston prism assembly for diffraction limit applications BLECHINGER F ， HARNISCH B ， KUNKEL B P . Optical concepts for high-resolution imaging spectrometers ［C］. SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics. Proc SPIE 2480 ， Imaging Spectrometry， Orlando， FL， USA . 1995 ， 2480 ： 165 - 179 . doi: 10.1117/12.210871 http://dx.doi.org/10.1117/12.210871 Optical concepts for high-resolution imaging spectrometers HAGEN N ， TKACZYK T S . Compound prism design principles， I ［J］. Applied Optics ， 2011 ， 50 （ 25 ）： 4998 . doi: 10.1364/ao.50.004998 http://dx.doi.org/10.1364/ao.50.004998 Compound prism design principles， I 10.37188/OPE.20223003.0237 TH744.1 A 1004-924X（2022）03-0237-09 周旻超,王振亚,王弼陡等.激光扫描共聚焦光谱系统设计[J].光学精密工程,2022,30(03):237-245. 周旻超,王振亚,王弼陡等.激光扫描共聚焦光谱系统设计[J].光学精密工程,2022,30(03):237-245. ZHOU Minchao,WANG Zhenya,WANG Bidou,et al.Design of laser scanning confocal spectroscopy system[J].Optics and Precision Engineering,2022,30(03):237-245. ZHOU Minchao,WANG Zhenya,WANG Bidou,et al.Design of laser scanning confocal spectroscopy system[J].Optics and Precision Engineering,2022,30(03):237-245. 中国科学院科研仪器设备研制项目（No.Y822141202） 2021-10-12 2021-11-10 2022-02-15 2022-02-17 光学精密工程 3 30