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望远镜前组的物镜组通常只具有较小的视场,因此使用一个3片式柯克摄影物镜代替望远镜物镜作为前组,采用像方远心设计对前组进行优化。后组的光线传播过程为前组的镜向同样采用像方远心设计优化方法,对优化结构进行反向即可得到后组结构。
激光器发射的高斯光束直径为1 mm,将物方入瞳直径设置为1.155 mm,以保证光束以30°倾角入射时不发生遮挡。
为避免相邻两路的前组镜片不发生结构干涉,每一路前组的总扫描角度应小于60°,故设置前组的最大有效入射角度
${\theta _{1\max }}$ =28°。为给转镜预留空间,入瞳距离设置为20 mm。由于探测系统用于海洋环境,对耐潮、耐水、耐候性能具有较高要求,根据成都光明玻璃库的玻璃耐潮、耐水、耐候性能,可选取H-BAK1和H-ZF7LA玻璃作为镜片材料。
若舱体表面采用平板玻璃作为窗口,由于舱内介质折射率
${n_a}$ =1,舱外海水折射率${n_w}$ =1.333,后组发射角度${\theta _2}$ 应大于前组入射角度${\theta _1}$ ,以确保探测光束从每一路的窗口进入水中的最大角度为${\theta ^{'}}_2$ =30°。根据折射定律计算,后组的最大发射角度${\theta _{2\max }}$ 应为41.799°。较大的F数有利于控制像差。因为入瞳直径d已经确定,为了增加F数,应使镜组具有较大的焦距。不考虑畸变的影响,焦距
$f$ 、像高$y$ 、视场角$\theta $ 、入瞳$d$ 、$F$ 数关系如公式(1)、(2)所示:$$f = \frac{y}{{\tan \theta }}$$ (1) $$F = \frac{d}{f}$$ (2) 发射光路实际上是一个低倍的缩束变倍光路,根据公式(1)可得图2中前后组焦距的关系:
$$ \frac{{f}_{1}}{{f}_{2}}=\frac{{y}_{1}\cdot{\rm{tan}}{\theta }_{2}}{{y}_{2}\cdot {\rm{tan}}{\theta }_{1}}$$ (3) 因此,增加像高可以使镜组获得较大的
$F$ 数。预留给系统的舱段高度50 mm,故将镜组的最大直径约束到45 mm以内,并通过DMVA操作数约束前后组的像高均为40 mm。在不考虑畸变的情况下,与像高和入瞳匹配的相应的前组焦距${f_1}$ 为37.615mm,后组焦距${f_2}$ 为22.370 mm。从前组平行入射的光束呈锥状汇聚到像面,为了增大后组$F$ 数,减小后组设计难度,则光束出射的束宽变窄对设计较为有利,因此前组保留较大的后截距,后组保留较小的后截距较为合理。为前组分配90 mm的空间,后组分配60 mm的空间,后组的物方光阑到舱体发射窗口表面预留10 mm空间。前组、后组的初始的结构参数如表1所示。表 1 初始结构参数
Table 1. Parameter of original structure
Former group parameter Value Latter group parameter Value Image height/mm 40 Image height/mm 40 f1/mm 37.615 f2/mm 22.370 Total length/mm ≤90 Total length/mm ≤60 Field/(°) ±28 Field/(°) ±41.799 首先对前组进行优化,并以前组的优化设计作为后组的初始结构,仍用像方远心设计进行优化,优化完成将镜组反向,得到的前、后组结构参数,舱内转移光路如图4所示。
初步优化后的前、后组参数如表2所示。
表 2 初步优化后的参数
Table 2. Parameter after primary optimization
Former group parameter Value Latter group parameter Value Image height/mm 40.000 Image height/mm 40.000 f1/mm 39.669 f2/mm 27.045 Total length/mm 90.000 Total length/mm 60.000 Field/(°) ±28 Field/(°) ±41.799 初步优化后发射系统的最大发射角度
${\theta _{2\max }}$ 达到41.799°,满足出平板窗后覆盖±30°扫描视场的要求。 -
设计中期望
${\theta _1}$ 到${\theta _2}$ 的映射具有线性关系。按光学设计的一般规则,查看0、0.3、0.5、0.7、1等5个相对视场入射光线在前、后组像面的高度。由于系统畸变,初步优化的系统中,二者0°、8.4°、14°、19.6°、28°5个视场角入射的光线在像面高度的分布并不一致,如表3所示。表 3 前、后组像高
Table 3. Image height of former and latter group
${\theta _1}$/(°) Former group image height/mm ${\theta _2}$/(°) Latter group image height/mm 0 0 0 0 8.4 5.826 12.540 5.903 14 9.743 20.900 9.863 19.6 13.729 29.259 13.706 28 19.990 41.799 19.932 利用畸变命令查看光束以0.56°间隔从前组入射,从后组射入空气中的角度分布情况,如图5所示。
理想的发射角与入射角
${\theta _1}$ 具有线性关系。图中用误差棒给出了${\theta _2}$ 与理想发射角的偏差。因为发射角的偏差,相邻后组发射光束的间隔$\Delta {\theta _2}$ 也并不均匀,从误差棒数据看,最大误差约6%。在出窗经历水下传播后,误差的放大可能对探测造成较大的影响。为了解决深水抗压问题,在后组出瞳后5 mm处,需要增加厚度为5 mm的平板H-BAK1玻璃窗。由于光束并非完全平行,平板玻璃窗两侧介质存在的折射率差异导致水下光束的传播偏差增大。查看同样以0.56°间隔入射的光束出窗后在水下传播的情况,绘制不同入射角度的光束发射角,并给出相邻发射光束夹角,如图6所示。
前组入射的光束角度为0°和28°时,由于像高约束,发射角与0°、30°的偏差几乎为0。但由于畸变的不一致,当进入前组的光线以0°~22.2°入射时,发射角增长的斜率大于理想的斜率,相邻光束间隔偏大;当进入前组的光线以22.2°~28°入射时,发射角增长的斜率小于理想的斜率,相邻光束间隔偏小。在接近28°的大入射角条件下,相邻发射光束的夹角仅0.513°,相对0.6°的参考值的误差达到−14.493%。
引起这一误差的根本原因是,前后组角度的线性对应关系并未在优化中受约束,导致前后组相应视场角在像面的像高并不具有一致性。设计中希望
${\theta _1}$ 、${\theta _2}$ 通过像高建立良好的线性关系,于是提出一种畸变匹配的优化方法。引入
$f - \theta $ 镜头设计中的畸变控制方法[30],Zemax中,$f - \theta $ 畸变量由公式(4)决定:$$ \left\{ \begin{array}{l}{D}_{1}=\dfrac{{y}_{1}-{f}_{1}\cdot {\theta }_{1}}{{f}_{1}\cdot {\theta }_{1}}\\ {D}_{2}=\dfrac{{y}_{2}-{f}_{2}\cdot {\theta }_{2}}{{f}_{2}\cdot {\theta }_{2}}\end{array} \right.$$ (4) 式中:
${D_1}$ 代表前组$f - \theta $ 畸变;${D_2}$ 代表后组$f - \theta $ 畸变;${y_1}$ 、${y_2}$ 分别代表前、后组在像面的像高;${f_1}$ 、${f_2}$ 分别代表前、后组的焦距。由公式(3)可知,当
$f - \theta $ 畸变为0,前、后组像高均正比于入射角。由于像高已经通过DMVA操作数约束一致,只要$f - \theta $ 足够小,就可以满足相邻发射光束间隔均匀的要求。系统中对畸变进行约束的操作数为DIST和DIMX,但二者并不直接对
$f - \theta $ 畸变进行约束,引入Zemax系统标准光学畸变量公式(5):$$ \left\{ \begin{array}{l}{D}_{1s}=\dfrac{{y}_{1}-{f}_{1}\cdot {\rm{tan}}{\theta }_{1}}{{f}_{1}\cdot {\rm{tan}}{\theta }_{1}}\\ {D}_{2s}=\dfrac{{y}_{2}-{f}_{2}\cdot {\rm{tan}}{\theta }_{2}}{{f}_{2}\cdot {\rm{tan}}{\theta }_{2}}\end{array} \right.$$ (5) $\theta $ 较小时,其值与正切值近似相等,标准畸变近似等于$f - \theta $ 畸变;随着角度增大,正切值增长会大于$\theta $ 增长,当$f - \theta $ 畸变取值为0时,标准畸变取得负值。因此,前、后两组均在像面发生桶形畸变,且后组在边缘的畸变百分比绝对值大于前组。保持前组不变,通过公式(4)、(5)得到前组的标准畸变像差
${D_{1s}}$ ,通过匹配前、后两组的$f - \theta $ 畸变,利用前组标准畸变对后组的标准畸变进行计算,可以保证前、后组的$f - \theta $ 畸变近似一致,入射角度和发射角度具有良好的线性匹配关系。计算前组入射角度为最大入射角的0°、8.4°、14°、19.6°、28°时的前组实际像面高度,使用EFFL操作数固定
${f_2}$ ,联立公式(4)、(5),代入后组线性对应的${\theta _2}$ ,计算同一像高时的${D_{2s}}$ 。使用DIMX和DISC操作数控制相应入射角${\theta _2}$ 的畸变参数进行优化,优化后的采用平板窗的整组结构如图7所示。若外壳表面的发射窗口要求匹配载具外形,需将平板窗口替换为柱面外形,若使用平凸的柱面镜,发射的光束将会因圆弧表面在出舱后的弧矢方向聚焦,并在远场发散,导致能量过分分散,对探测造成不利影响。因此基于平板窗角度优化的后组设计将平板窗改为柱面的共形窗口,将内侧平面也设置为可变曲率的柱面,并利用像方远心方法继续优化,优化后的共形窗如图8所示。
共形优化的后组曲率和厚度有微小变化,优化后两种方案的透镜参数见表4和表5。
表 4 平板窗发射系统设计方案
Table 4. Prescription for transmitting system with plane window
Lens Surface Surface type Radius/mm Thickness/mm Material Semi-diameter/mm Stop Standard Infinity 20.000 Air 0.577 L1 1 Standard −64.875 7.999 H-BAK1 10.736 2 Standard 245.825 4.563 Air 14.397 L2 3 Standard −62.429 5.870 H-ZF7LA 15.940 4 Standard −28.195 1.844 Air 17.045 L3 5 Standard 83.148 8.000 H-BAK1 20.280 6 Standard −65.614 41.725 Air 20.513 Focus plane Standard Infinity 16.725 Air 20.000 L4 7 Standard 72.584 6.308 H-BAK1 20.196 8 Standard −178.896 1.000 Air 19.981 L5 9 Standard 35.081 7.426 H-ZF7LA 18.457 10 Standard 83.958 15.541 Air 16.967 L6 11 Standard 13.985 8.000 H-BAK1 8.067 12 Standard 22.229 10.000 Air 4.536 L7 13 Standard Infinity 5.000 H-BAK1 4.816 14 Standard Infinity 20000.000 Water 7.233 Image Standard Infinity 0.000 Water 11552.561 表 5 共形窗发射系统设计方案
Table 5. Prescription for transmitting system with conformal window
Lens Surface Surface type Radius/mm Thickness/mm Material Semi-diameter/mm Stop Standard Infinity 20.000 Air 0.577 L1 1 Standard −64.875 7.999 H-BAK1 10.736 2 Standard 245.825 4.563 Air 14.397 L2 3 Standard −62.429 5.870 H-ZF7LA 15.940 4 Standard −28.195 1.844 Air 17.045 L3 5 Standard 83.148 8.000 H-BAK1 20.280 6 Standard −65.614 41.725 Air 20.513 Focus plane Standard Infinity 15.812 Air 20.000 L4 7 Standard 76.049 6.190 H-BAK1 20.184 8 Standard −172.721 1.000 Air 19.982 L5 9 Standard 35.089 8.000 H-ZF7LA 18.487 10 Standard 76.462 16.200 Air 16.750 L6 11 Standard 12.782 7.798 H-BAK1 7.894 12 Standard 20.508 10.000 Air 4.523 L7 13 Toroidal −235.145 5.000 H-BAK1 4.710 14 Toroidal −160.000 20000.000 Water 7.117 Image Standard Infinity 0.0000 Water 11552.735 除窗口玻璃外,所有镜片均为球面设计,仅共形窗为双面柱透镜,具有良好的可加工性。由于前、后组共焦面设计,故第2、5、6片为弯月镜,减少了前、后组的场曲,
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通过畸变数据文件,查看光束分别经过平板窗设计和共形窗设计两种转移发射旋转基点的发射系统,光束从窗口发射进入水中的角度偏差。平板窗设计的偏差如图9所示,共形窗设计的偏差如图10所示。
两种设计发射角度偏差均不超过0.4%,以0.6°间隔发射时,相邻光束对0.6°的偏差不超过2%。当探测距离为20 m时,相邻光束中心理论间隔为209.3 mm,该系统发射光束的间隔与理论间隔的绝对差值小于4 mm。
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由于假想探测目标直径为300 mm,为了使光斑直径在20 m的探测距离上不大于目标直径1/3,经过发射系统后,激光的发散角应不大于5 mrad。利用Zemax物理光学传播仿真模拟了分别以0°、8.4°、14°、19.6°、28°入射,初始半径为0.5 mm,初始发散角为1 mrad的高斯光束,经过发射系统调整,在水下传播20 m后的光束半径和发散角。平板窗设计的发射结果如表6所示,共形窗设计的发射结果如表7所示。
表 6 平板窗设计光束发散角
Table 6. Plane window design beam divergence
${\theta _1}$/(°) X beam size/mm X divergence/mrad Y beam size/mm Y divergence/mrad 0 30.618 1.513 30.618 1.513 8.4 26.931 1.313 27.227 1.311 14 20.746 0.986 22.333 1.026 19.6 12.784 0.584 18.375 0.786 28 10.098 0.446 27.975 1.034 表 7 共形窗设计光束发散角
Table 7. Conformal window design beam divergence
${\theta _1}$/(°) X beam size/mm X divergence/mrad Y beam size/mm Y divergence/mrad 0 26.402 1.303 31.576 1.561 8.4 22.553 1.097 27.943 1.346 14 16.208 0.768 22.732 1.044 19.6 9.028 0.413 18.611 0.797 28 14.700 0.649 29.755 1.101 平板窗方案的水下发射光束的最大发散角为1.513 mrad,水下传播20 m最大均方根(RMS)光斑半径为30.618 mm;共形窗方案的水下发射光束最大发散角为1.561 mrad,水下传播20 m最大RMS光斑半径为31.576 mm。利用物理光学传播仿真模拟了5个入射角下20 m外的光斑的图像如图11所示。光斑中心X方向能量分布如图12所示。
图 11 水下传播20 m光束截面光斑:(a)~(e)平板窗系统光斑; (f)~(j)共形窗系统光斑
Figure 11. Beam section spot after 20 m under water propagation:(a)- (e) Spot of plane window system; (f)-(j) Spot of conformal window system
图 12 光斑能量分布:(a)~(e)平板窗系统光斑能量分布;(f)~(j)共形窗系统光斑能量分布
Figure 12. Spot energy distribution: (a)-(e) Spot energy distribution of plane window system; (f)-(j) Spot energy distribution of conformal window system
像面大小统一调整为100 mm×100 mm,光束的初始能量统一设置为1 W,仿真结果表明,光斑仍近似高斯分布。不计玻璃和水介质的反射和吸收损失,到达像面的能量均达到99.9%以上,光斑最大直径均小于100 mm。
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由于镜片较多,如不镀增透膜,则出窗前因为各个光学面的反射,探测光束就将产生较大的能量损失。利用Zemax查看未镀膜时两种设计方案能量传输效率如表8所示。
表 8 未镀膜传输效率
Table 8. Coating-less transmission efficiency
${\theta _1}$/(°) Efficiency (plane window) Efficiency (conformal window) 0 47.0214% 46.9997% 8.4 47.0576% 47.0356% 14 47.1184% 47.0960% 19.6 47.1941% 47.1730% 28 47.2029% 47.2045% 从表8数据得知,未镀膜时因为各表面反射损失,出窗后的能量不足初始能量的50%。
若对各表面镀增透膜,比较0.995和0.999两种增透膜对像面能量的影响,镀膜后两种设计方案的传输效率如表9和表10所示。
表 9 0.995镀膜传输效率
Table 9. 0.995-coating transmission efficiency
${\theta _1}$/(°) Efficiency (plane window) Efficiency (conformal window) 0 90.935% 90.893% 8.4 91.006% 90.963% 14 91.132% 91.088% 19.6 91.320% 91.276% 28 91.719% 91.679% 表 10 0.999镀膜传输效率
Table 10. 0.999-coating transmission efficiency
${\theta _1}$/(°) Efficiency (plane window) Efficiency (conformal window) 0 95.803% 95.759% 8.4 95.878% 95.833% 14 96.011% 95.965% 19.6 96.210% 96.163% 28 96.629% 96.587% 镀0.995的增透膜后,能量传输效率可达90%以上;镀0.999的增透膜后,能量传输效率可达95%以上。为满足设计需求,镜组需镀99.9%增透膜保证能量传输效率。
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设置各面加工面型精度±0.1 mm,偏心±0.1 mm,各玻璃元件倾斜公差±0.1°,折射率和阿贝数采用默认设置,分别为0.001和1%。140个参数,总计140个公差数,故设蒙特卡洛仿真次数19600次。仿真的目标为RMS spot radius,仿真结果如表11、表12所示。
表 11 平板窗公差分析结果
Table 11. Tolerance analysis result of plane window
Probability RMS spot radius/mm 0° 8.4° 14° 19.6° 28° 98%≤ 9.603 9.877 9.878 18.675 18.697 90%≤ 8.895 9.092 9.074 17.993 17.986 50%≤ 7.609 7.695 7.673 16.848 16.826 10%≤ 6.324 6.324 6.309 15.760 15.734 2%≤ 5.599 5.553 5.506 15.164 15.122 表 12 共形窗公差分析结果
Table 12. Tolerance analysis result of conformal window
Probability RMS spot radius/mm 0° 8.4° 14° 19.6° 28° 98%≤ 8.713 12.909 12.969 22.557 22.596 90%≤ 7.949 12.026 12.057 21.775 21.792 50%≤ 6.584 10.507 10.521 20.498 20.511 10%≤ 5.260 9.036 9.071 19.305 19.332 2%≤ 4.537 8.241 8.263 18.683 18.684 加工和装配公差使平行光束的汇聚特性发生变化:在大多数仿真中,0°、8.4°、14° 3个场的光束发散角比设计的理论值更小,在19.6°场和28°场比设计的理论值更大。但光斑半径均小于50 mm,满足光束发散角小于5 mrad的设计需求。
由于舱内保持标准大气压,而舱外随水深不同将承受不同的压力,因此水深变化主要通过压力变化引起窗口玻璃的面型变化。通过有限元分析软件可以分析不同深度水压所引起变化对系统的影响[31-32]。使用Ansys软件数值仿真50~300 m深度水压对窗玻璃的面型影响:窗口玻璃为成都光明的H-BAK1,其杨氏模量
$E = 70.95\,{\rm{GPa}}$ ,泊松比$\mu = 0.223$ ,密度$\rho = 2.74\,{{\rm{g}} / {{\rm{c}}{{\rm{m}}^{\rm{3}}}}}$ ,窗口为直径15 mm、中心厚度5 mm圆窗;舱体和压圈采用7075铝。仿真计算得到300 m水深时,舱外水压3 MPa,窗口中心最大的面型变化为0.55 μm。将该变化引入窗口玻璃面型以及窗口玻璃内侧空气厚度间隙公差。重新计算的公差结果与表11、表12所列结果相差均小于0.1%,表明所设计的系统理论上可以适应30~300 m不同深度的光束发射需求。
Design of 4f emission optical system for underwater laser circumferential scanning
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摘要: 针对水下激光周视扫描环窗设计的缺点,提出一种转移扫描基点的发射光学系统设计方法。该方法基于开普勒望远镜的结构,通过对物镜和目镜组分别采用像方远心方法进行共轭设计并加以畸变控制,对光束的发散角及其分布均匀性进行了优化。在优化设计的基础上,分别仿真分析了平板窗和共形窗对光束质量的影响,以及镀膜对能量传输效率的影响。最后,对不同窗口设计进行了公差分析和水压受力仿真。光学和力学仿真结果表明,该方法有效减小了壳体表面开窗面积,避免了环窗设计造成的扇形探测盲区,对水下激光周视扫描发射系统的工程设计具有一定的指导意义。Abstract: Aiming at the shortcomings of the design of the underwater laser peripheral scanning ring window, a design method of the transmitting optical system that shifted the scanning base point was proposed. This method was based on the structure of Kepler telescope. The divergence angle of the beam and its distribution uniformity were optimized by adopting the image-side telecentric method for the conjugated design and distortion control of the objective lens and the eyepiece group. On the basis of the optimized design, the influence of the flat window and the conformal window on the beam quality and the influence of the coating on the energy transmission efficiency were simulated and analyzed respectively. Finally, tolerance analysis and hydraulic simulation of different window designs were carried out. The simulation results of optics and mechanics show that the method effectively reduces the window area of the shell surface, avoids the blind area of the fan-shaped detection caused by the design of the ring window, and has certain guiding significance for the engineering design of the underwater laser peripheral scanning emission system.
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表 1 初始结构参数
Table 1. Parameter of original structure
Former group parameter Value Latter group parameter Value Image height/mm 40 Image height/mm 40 f1/mm 37.615 f2/mm 22.370 Total length/mm ≤90 Total length/mm ≤60 Field/(°) ±28 Field/(°) ±41.799 表 2 初步优化后的参数
Table 2. Parameter after primary optimization
Former group parameter Value Latter group parameter Value Image height/mm 40.000 Image height/mm 40.000 f1/mm 39.669 f2/mm 27.045 Total length/mm 90.000 Total length/mm 60.000 Field/(°) ±28 Field/(°) ±41.799 表 3 前、后组像高
Table 3. Image height of former and latter group
${\theta _1}$ /(°)Former group image height/mm ${\theta _2}$ /(°)Latter group image height/mm 0 0 0 0 8.4 5.826 12.540 5.903 14 9.743 20.900 9.863 19.6 13.729 29.259 13.706 28 19.990 41.799 19.932 表 4 平板窗发射系统设计方案
Table 4. Prescription for transmitting system with plane window
Lens Surface Surface type Radius/mm Thickness/mm Material Semi-diameter/mm Stop Standard Infinity 20.000 Air 0.577 L1 1 Standard −64.875 7.999 H-BAK1 10.736 2 Standard 245.825 4.563 Air 14.397 L2 3 Standard −62.429 5.870 H-ZF7LA 15.940 4 Standard −28.195 1.844 Air 17.045 L3 5 Standard 83.148 8.000 H-BAK1 20.280 6 Standard −65.614 41.725 Air 20.513 Focus plane Standard Infinity 16.725 Air 20.000 L4 7 Standard 72.584 6.308 H-BAK1 20.196 8 Standard −178.896 1.000 Air 19.981 L5 9 Standard 35.081 7.426 H-ZF7LA 18.457 10 Standard 83.958 15.541 Air 16.967 L6 11 Standard 13.985 8.000 H-BAK1 8.067 12 Standard 22.229 10.000 Air 4.536 L7 13 Standard Infinity 5.000 H-BAK1 4.816 14 Standard Infinity 20000.000 Water 7.233 Image Standard Infinity 0.000 Water 11552.561 表 5 共形窗发射系统设计方案
Table 5. Prescription for transmitting system with conformal window
Lens Surface Surface type Radius/mm Thickness/mm Material Semi-diameter/mm Stop Standard Infinity 20.000 Air 0.577 L1 1 Standard −64.875 7.999 H-BAK1 10.736 2 Standard 245.825 4.563 Air 14.397 L2 3 Standard −62.429 5.870 H-ZF7LA 15.940 4 Standard −28.195 1.844 Air 17.045 L3 5 Standard 83.148 8.000 H-BAK1 20.280 6 Standard −65.614 41.725 Air 20.513 Focus plane Standard Infinity 15.812 Air 20.000 L4 7 Standard 76.049 6.190 H-BAK1 20.184 8 Standard −172.721 1.000 Air 19.982 L5 9 Standard 35.089 8.000 H-ZF7LA 18.487 10 Standard 76.462 16.200 Air 16.750 L6 11 Standard 12.782 7.798 H-BAK1 7.894 12 Standard 20.508 10.000 Air 4.523 L7 13 Toroidal −235.145 5.000 H-BAK1 4.710 14 Toroidal −160.000 20000.000 Water 7.117 Image Standard Infinity 0.0000 Water 11552.735 表 6 平板窗设计光束发散角
Table 6. Plane window design beam divergence
${\theta _1}$ /(°)X beam size/mm X divergence/mrad Y beam size/mm Y divergence/mrad 0 30.618 1.513 30.618 1.513 8.4 26.931 1.313 27.227 1.311 14 20.746 0.986 22.333 1.026 19.6 12.784 0.584 18.375 0.786 28 10.098 0.446 27.975 1.034 表 7 共形窗设计光束发散角
Table 7. Conformal window design beam divergence
${\theta _1}$ /(°)X beam size/mm X divergence/mrad Y beam size/mm Y divergence/mrad 0 26.402 1.303 31.576 1.561 8.4 22.553 1.097 27.943 1.346 14 16.208 0.768 22.732 1.044 19.6 9.028 0.413 18.611 0.797 28 14.700 0.649 29.755 1.101 表 8 未镀膜传输效率
Table 8. Coating-less transmission efficiency
${\theta _1}$ /(°)Efficiency (plane window) Efficiency (conformal window) 0 47.0214% 46.9997% 8.4 47.0576% 47.0356% 14 47.1184% 47.0960% 19.6 47.1941% 47.1730% 28 47.2029% 47.2045% 表 9 0.995镀膜传输效率
Table 9. 0.995-coating transmission efficiency
${\theta _1}$ /(°)Efficiency (plane window) Efficiency (conformal window) 0 90.935% 90.893% 8.4 91.006% 90.963% 14 91.132% 91.088% 19.6 91.320% 91.276% 28 91.719% 91.679% 表 10 0.999镀膜传输效率
Table 10. 0.999-coating transmission efficiency
${\theta _1}$ /(°)Efficiency (plane window) Efficiency (conformal window) 0 95.803% 95.759% 8.4 95.878% 95.833% 14 96.011% 95.965% 19.6 96.210% 96.163% 28 96.629% 96.587% 表 11 平板窗公差分析结果
Table 11. Tolerance analysis result of plane window
Probability RMS spot radius/mm 0° 8.4° 14° 19.6° 28° 98%≤ 9.603 9.877 9.878 18.675 18.697 90%≤ 8.895 9.092 9.074 17.993 17.986 50%≤ 7.609 7.695 7.673 16.848 16.826 10%≤ 6.324 6.324 6.309 15.760 15.734 2%≤ 5.599 5.553 5.506 15.164 15.122 表 12 共形窗公差分析结果
Table 12. Tolerance analysis result of conformal window
Probability RMS spot radius/mm 0° 8.4° 14° 19.6° 28° 98%≤ 8.713 12.909 12.969 22.557 22.596 90%≤ 7.949 12.026 12.057 21.775 21.792 50%≤ 6.584 10.507 10.521 20.498 20.511 10%≤ 5.260 9.036 9.071 19.305 19.332 2%≤ 4.537 8.241 8.263 18.683 18.684 -
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