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作为一种流行的红外光学材料,硅在中短波红外光学系统中得到了广泛的应用,特别是在红外透镜的制造中。某大口径红外硅透镜元件凸面面形设计要求如下:
$$ {\textit{z}}=\frac{c{r}^{2}}{1+\sqrt{1-\left(1+k\right){c}^{2}{r}^{2}}}+A{r}^{4}+B{r}^{6}+C{r}^{8} $$ (1) 式中:r2 = x2 + y2;c=1/R, R为非球面顶点曲率半径;k为非球面系数;A、B、C为高次非球面系数。凸面非球面透镜的表面参数及精度要求如表1所示。此外,要求最终加工面形中高频误差符合如下要求:Zernike多项式36项拟合残差RMS<0.02λ;Z9<0.04λ,Z15、Z25、Z36<0.01λ。
表 1 凸非球面面形参数 (λ=632.8 nm)
Table 1. Parameters of the convex aspheric surface (λ=632.8 nm)
R/mm k A B C PV RMS 339.3331±0.1 0 −1.288E-10 −1.283E-15 6.342E-20 1/5λ λ/50 -
在透镜凸非球面的铣磨和研磨初期,其表面精度较低,可采用三坐标测量机对其面形进行离散点测量,再通过算法进行数据拟合从而获取面形误差,其测试精度极限约为PV 5 μm。随着面形精度以及表面光洁度的提高,可采用非接触式轮廓仪检测透镜凸非球面的面形。文中采用的非接触式轮廓仪检测精度优于10 nm RMS,该设备利用非接触式探头对放置于高精度气浮转台的待测光学元件表面进行螺旋扫描,从而计算光学表面的面形误差。为了保证检测精度,应控制透镜与转台的同轴度与倾斜误差分别优于50 μm和1′,环境温度应控制在(20±1) ℃,实验室防振等级不低于二级。为了控制顶点曲率半径偏差,对轮廓仪的采样结果进行数据处理时仅拟合平移、倾斜误差,对其他面形设计参数进行强制拟合。该方法用于回转类零件的高频次测试,具有操作简便、精度高、周期短等优点。但由于设备的局限性和透镜结构的特殊性,在面形精修阶段,通过气浮转台直接支撑透镜进行测试往往容易引入支撑误差,严重干扰了加工的判断。因此必须采取有效的措施实现支撑误差的解耦,从而获取准确、真实的面形误差指导进一步加工。由于铣磨和研磨阶段的面形三坐标检测工艺较为常规,因此文中不展开描述详细检测细节,将重点介绍抛光阶段的高精度轮廓面形检测工艺。
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由于透镜自身结构的特点,相比于反射类光学元件,透镜在轮廓检测过程中更易受支撑力影响发生变形。当面形加工进入抛光阶段时,随着面形精度的逐渐提高,透镜因支撑引起的变形对轮廓测试的影响逐渐增大。此时,支撑误差与真实面形误差相互耦合,且支撑误差的分布形式及量级存在较大的随机性,难以进行定量化解耦,从而严重限制了加工精度的进一步提升。针对上述问题,在粗抛阶段,在轮廓仪气浮转台上增加具有三明治结构的微柔性缓冲垫用于透镜的支撑。该方法一方面避免了透镜凹面的基准平台与气浮转台之间的直接硬接触,同时也避免了测试过程中透镜轴向和径向的微扰动,能够快速均衡各支撑点的受力,具有方便快捷的优点。
随着抛光后面形精度的提升,加之透镜自身超薄径厚比及高陡度的特点,支撑引起的透镜变形对高精度的面形测试影响逐渐增大。柔性缓冲垫与透镜凹面平台基准的作用点和作用力均无法量化,由此产生的透镜变形使得不同角度测试的面形分布趋势与数值存在较大差异,同时也难以进行准确的支撑误差分离,从而无法做出下一步针对性精修的准确判断,严重限制了加工精度的极限。因此,在透镜凸面高精度面形抛光阶段,柔性缓冲支撑方式以无法满足准确的面形误差测试需求,必须采用支撑误差可定量化分离的轮廓测试技术指导面形的高精度收敛。
在轮廓仪面形测试中,除了设备自身的系统误差,测试误差的来源主要分为两个部分,分别是透镜光轴相对轮廓仪转台的位置误差,包括平移和倾斜误差,以及透镜受支撑力作用引起的变形。其中,透镜放置的平移和倾斜误差可以通过软件算法进行定量分析和去除。支撑力引起的透镜变形属于弹性变形,相对于透镜的口径而言属于高阶小量,当作用力卸载后相应的变形量也随之消失。因此,基于弹性力学理论,假定环境温度恒定,透镜内部材料均匀且连续,则透镜内任意微小单元均满足如下平衡方程[18]:
$$ \begin{array}{c}\left\{\begin{array}{c}\dfrac{\partial {\sigma }_{x}}{{\partial }_{x}}+\dfrac{\partial {\tau }_{xy}}{{\partial }_{y}}+\dfrac{\partial {\tau }_{x{\textit{z}}}}{{\partial }_{{\textit{z}}}}+{F}_{x}=0\\ \dfrac{\partial {\tau }_{xy}}{{\partial }_{x}}+\dfrac{\partial {\sigma }_{y}}{{\partial }_{y}}+\dfrac{\partial {\tau }_{y{\textit{z}}}}{{\partial }_{{\textit{z}}}}+{F}_{y}=0\\ \dfrac{\partial {\tau }_{x{\textit{z}}}}{{\partial }_{x}}+\dfrac{\partial {\tau }_{y{\textit{z}}}}{{\partial }_{y}}+\dfrac{\partial {\sigma }_{{\textit{z}}}}{{\partial }_{{\textit{z}}}}+{F}_{{\textit{z}}}=0\end{array}\right.\end{array} $$ (2) 其中,沿镜面坐标系x、y、z方向的正应力和切应力分别为
$ \left({\sigma }_{x},{\sigma }_{y},{\sigma }_{{\textit{z}}}\right) $ 和$ \left({\tau }_{y{\textit{z}}},{\tau }_{xz},{\tau }_{xy}\right) $ ;$ \left({F}_{x},{F}_{y},{F}_{{\textit{z}}}\right) $ 为单位体积沿各个方向的单位力。根据公式(1)的应力可得各微小单元沿x、y、z方向的正应变$ \left({\varepsilon }_{x},{\varepsilon }_{y},{\varepsilon }_{{\textit{z}}}\right) $ 和剪切应变$ \left({\gamma }_{y{\textit{z}}},{\gamma }_{x{\textit{z}}},{\gamma }_{xy}\right) $ 分别为:$$ \left\{\begin{array}{c}\begin{array}{c}{\varepsilon }_{x}=\left[{\sigma }_{x}-\left({\sigma }_{y}+{\sigma }_{{\textit{z}}}\right)\right]/E\\ {\varepsilon }_{y}=\left[{\sigma }_{y}-\left({\sigma }_{x}+{\sigma }_{{\textit{z}}}\right)\right]/E\end{array}\\ \begin{array}{c}{\varepsilon }_{{\textit{z}}}=\left[{\sigma }_{{\textit{z}}}-\left({\sigma }_{x}+{\sigma }_{y}\right)\right]/E\\ {\gamma }_{xy}={\tau }_{xy}/G\\ {\gamma }_{y{\textit{z}}}={\tau }_{y{\textit{z}}}/G\end{array}\\ {\gamma }_{x{\textit{z}}}={\tau }_{x{\textit{z}}}/G\end{array}\right. $$ (3) 式中:G为材料的剪切模量。根据各微小单元的连续位移,可得透镜沿x、y、z方向的位移分量
$ \left(u,v,w\right) $ 如下:$$ \left\{\begin{array}{c}\begin{array}{c}{\varepsilon }_{x}=\dfrac{{\partial }_{u}}{{\partial }_{x}}\\ {\varepsilon }_{y}=\dfrac{{\partial }_{v}}{{\partial }_{y}}\end{array}\\ \begin{array}{c}{\varepsilon }_{{\textit{z}}}=\dfrac{{\partial }_{w}}{{\partial }_{{\textit{z}}}}\\ {\gamma }_{xy}=\dfrac{{\partial }_{v}}{{\partial }_{x}}+\dfrac{{\partial }_{u}}{{\partial }_{y}}\\ {\gamma }_{y{\textit{z}}}=\dfrac{{\partial }_{w}}{{\partial }_{y}}+\dfrac{{\partial }_{v}}{{\partial }_{{\textit{z}}}}\end{array}\\ {\gamma }_{x{\textit{z}}}=\dfrac{{\partial }_{u}}{{\partial }_{{\textit{z}}}}+\dfrac{{\partial }_{w}}{{\partial }_{x}}\end{array}\right. $$ (4) 根据上述力学模型,针对透镜结构设计了如图2(a)所示的三点均布支撑方案,在透镜边缘平台基准处设置三个夹角为120°的刚性支撑点。支撑点与透镜之间的作用力可以简化为点作用力,从而根据公式(2)~(4)可以计算出三点支撑作用下透镜表面的微位移量[19-20],如图2(b)所示。根据Zernike多项式拟合分析,透镜表面的微位移对应的面形误差约为RMS 0.067λ,分布形式为三阶像散,如图2(c)所示。该方法利用支撑作用力迫使透镜产生确定性的面形误差,从而可以实现支撑误差的准确解耦。
High precision manufacturing and testing of large aperture silicon-based space infrared lens (invited)
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摘要: 随着红外技术的不断发展,空间大口径红外光学元件的需求日益增长,其各项制造指标也逐渐接近可见光级光学元件的制造要求,由此对新型空间红外光学元件的加工和检测技术均提出了更高的挑战。针对大口径
的高陡度超薄硅基红外透镜,提出了以超声铣磨-机器人研抛-离子束精抛为工艺链路的加工方案,改善了传统红外工艺路线存在的低效率、表面高频误差等问题。针对凸非球面轮廓检测中支撑引起的测试误差,在粗抛和精抛阶段分别采用了柔性缓冲支撑与三点强迫位移支撑方法,有效解决了大口径高陡度超薄透镜测试中的支撑变形问题。经过理论仿真与实验验证,证明该测试方法具有较好的一致性。通过改进的轮廓检测方法,实现了轮廓测试中支撑误差的准确分离,有效提升了加工的极限精度。最终大口径红外透镜凸非球面加工精度达RMS λ/50 (λ=632.8 nm),满足设计指标要求。 Abstract: With the development of infrared technology, the demand for large aperture space infrared optics is increasing. Their manufacturing indexes are approaching the manufacturing requirements of visible optics gradually, which poses a higher challenge to the processing and testing technology of new infrared optics. A processing scheme of ultrasonic milling, robot griding and ion beam polishing was proposed for the manufacturing of large diameter ultra-thin silicon-based infrared lens with high gradient. This method overcame the defects of low efficiency and high frequency surface error caused by single process. In order to avoid the testing error caused by supporting force in contour testing of the aspherical convex side, flexible buffer supporting and three-point forced displacement supporting were applied in rough and fine polishing phases respectively, which effectively solved the supporting deformation problem in the testing of large aperture and high gradient ultra-thin lens. Through theoretical simulation and experimental verification, it was proved that the testing method had good consistency. An improved contour detection method was adopted to achieve accurate separation of supporting error in contour testing, and has effectively improved the limit accuracy of manufacturing. Finally, the machining accuracy of convex aspheric surface with large diameter mm infrared lens reached RMS λ/50 (λ=632.8 nm), which satisfied the design requirements.-
Key words:
- optical manufacturing /
- space infrared lens /
- contour test /
- supporting error
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表 1 凸非球面面形参数 (λ=632.8 nm)
Table 1. Parameters of the convex aspheric surface (λ=632.8 nm)
R/mm k A B C PV RMS 339.3331±0.1 0 −1.288E-10 −1.283E-15 6.342E-20 1/5λ λ/50 -
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