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非球面因其自由度高、成像质量好，越来越广泛地应用于现代光学系统，如手机、相机、AR/VR眼镜等数码产品，显微物镜、内窥镜等医疗仪器、天文望远镜、遥感相机、光刻机、激光点火装置乃至激光武器[1−7]。
随着各类光学仪器的迅速发展，特别是激光点火装置、激光武器、卫星产品，其对洁净度等质量具有高要求的同时，定制型的研制模式也在向模块化、批量化研制快速转变。虽然自动化测试技术在工业生产领域已经逐渐完善，然而激光点火装置、激光武器、卫星产品等自动化测试并没有成熟方案。
作为光学系统关键部组件，非球面的批量化制造、检测与装调的自动化直接决定了批量化研制的质量和效率，对非球面的自动化检测提出了越来越高的要求[8]。
对非球面的检测方法主要有扫描法、几何光学法与干涉检测法等[9−11]。扫描法纵向精度高，但横向分辨率一般较低，为了弥补横向分辨率，需要拉长扫描路径，造成单次测量周期长，且如果采用接触式测头会有划伤被测镜的风险[12]。几何光学方法采用几何光学原理进行测量，虽然有无接触与快速测量的优势，但纵向分辨率往往不高[13]，难以满足如天文望远镜、遥感相机、激光武器等对非球面精度要求较高的场景。干涉检测因其高精度、无接触、快速、全局的特点成为非球面光学表面的常用检测方法，也是未来发展的主要趋势之一[14]。采用干涉法检测非球面时，往往采用补偿法[15]，干涉仪-补偿器-非球面三者之间相对位置的精确调整是补偿法的重要保障。
补偿干涉法的一般流程如下：1）设计并加工补偿器；2）干涉仪与补偿器对准；3）被测非球面粗对准；4）测量光路精调；5）干涉测量读取面形。测量光路精调是完成粗对准后，失调量较小，干涉图可测量时进行。分析测量波前的球差、彗差、像散等像差，求解失调量，对被测非球面位置与角度进行精细调整，最终消除球差、彗差、像散，即消除干涉仪测量波前受失调量的影响。测量光路精调需要测量人员基于经验的多轮迭代调整，往往是测量周期中耗时最多的环节。
开展非球面自动化检测可以通过更准确的软件判读与自动调整来有效降低测量时间，通过控制误失调量提高测量的一致性，并为未来的自动化遥感相机等光学系统的自动化生产提供技术支撑。
在干涉测量读取面形时，测量人员带来的空气扰动会对测量结果产生影响，往往需要施加随机扰动气流，进行多次测量求取平均来抑制测量人员带来的扰动。此外，在对洁净度和表面光洁度要求极高的高能激光领域，检测人员可能引入的颗粒物污染是极高的风险。
粉尘颗粒物会对强激光系统中的反射镜造成表面损伤，透明颗粒物会造成表面凹坑，增加表面的粗糙度。在透镜表面附着的污染物会造成透镜表面出现凹坑和损坏，使表面质量下降，还可能导致下游光学元器件的进一步损坏[16]。
为了降低测量人员和环境带来的扰动影响，无操作人员的非球面自动化干涉检测亟需实现。自动化干涉检测如图1所示，包含自动化地拾取、安装、测量、拆除、转移。在测量过程中，对非球面失调量高精度地检测与控制是关键。
图 1 非球面自动化干涉检测
Figure 1. Aspheric automated interferometry measurement
为了实现补偿干涉法中被测非球面失调量的自动求解与反馈控制，文中提出采用灵敏度矩阵求解，采用六自由度平台控制，通过迭代缩小，最终实现高洁净度超光滑非球面的自动化干涉检测的方法。
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补偿干涉法非球面面形的测量系统由干涉仪、补偿器、被测非球面组成。补偿器以被测非球面为输入进行设计，以补偿后的波前为优化目标，使之成为可以使用干涉仪直接测量的球面波或平面波。
实际非球面的测量中，需要对补偿器与被测非球面进行精密调节，使得被测非球面与补偿器光轴实现对准，满足测量精度要求。当补偿器与被测非球面存在失调量时，测量波前无法与被测非球面匹配，测量获得的波前除了受非球面面形误差的影响外，主要受失调量的影响。
根据矢量像差原理[17−19]推导出具有偏心和倾斜的共轴光学系统三阶波像差表达式，如公式(1)所示：
$$ \begin{split} W =& \Delta {W_{20}}\left( {\vec \rho \cdot \vec \rho } \right) + \Delta {W_{11}}\left( {\vec H \cdot \vec \rho } \right) \sum\limits_j {{W_{040j}}{{\left( {\vec \rho \cdot \vec \rho } \right)}^2}} +\\& \sum\limits_j {{W_{131j}}\left[ {\left( {\vec H - {{\vec \sigma }_j}} \right) \cdot \vec \rho } \right]\left( {\vec \rho \cdot \vec \rho } \right)} +\\& {\sum\limits_j {{W_{222j}}\left[ {\left( {\vec H - {{\vec \sigma }_j}} \right) \cdot \vec \rho } \right]} ^2} +\\& \sum\limits_j {{W_{220j}}\left[ {\left( {\vec H - {{\vec \sigma }_j}} \right) \cdot \left( {\vec H - {{\vec \sigma }_j}} \right)} \right]\left( {\vec \rho \cdot \vec \rho } \right)} +\\& \sum\limits_j {{W_{311j}}\left[ {\left( {\vec H - {{\vec \sigma }_j}} \right) \cdot \left( {\vec H - {{\vec \sigma }_j}} \right)} \right] \cdot \left[ {\left( {\vec H - {{\vec \sigma }_j}} \right) \cdot \vec \rho } \right]} \end{split} $$ (1) 式中：W为系统波像差；ΔW20为离焦；ΔW11为倾斜；W040为球差；W131为彗差；W222为像散；W220为场曲；W311为畸变；j表示表面j；$\vec H$为视场坐标矢量；$\vec \rho $为出瞳坐标的矢量；$ {\vec \sigma _j} $为表面j的像差中心偏移矢量。
由公式（1）可以得到以下推论：
1）离焦和球差仅受光瞳坐标影响，即球差不受元件偏心与倾斜影响，仅受元件在光轴方向的位置影响；
2）倾斜、彗差、像散、场曲、畸变同时受元件倾斜、偏心与光轴方向的位置的影响，不同像差倾斜与偏心的影响阶次不同。
灵敏度矩阵法[20−21]简单有效，是光学装调中广泛使用的方法。虽然在失调量较大时，像差与失调量的线性关系被破坏，难以使用，但在失调量较小的精调中，像差和失调量的线性关系较好，可以获得较高精度的快速收敛。
补偿干涉法非球面面形测量光学系统可以视为干涉仪、补偿器、被测非球面三者组成的光学系统，测量时的精调环节可以视为光学系统的精装调。
在采用透射式补偿器的同轴非球面面形测量系统中，球差主要受干涉仪与补偿器间距影响，离焦主要受补偿器与被测非球面间距的影响，X(或Y)倾斜和X(或Y)彗差主要受被测镜平移和倾斜的影响。
采用灵敏度矩阵，利用干涉仪测量获得的干涉图对被测非球面失调量进行求解与调整的流程如图2所示。
图 2 自动化干涉检测流程图
Figure 2. Automatic interferometry measurement flowchart
倾斜像差较大时，调节被测非球面X或Y方向平移；离焦像差较大时，调节被测非球面轴向平移；球差较大时，调节干涉仪轴向位置；当倾斜控制到较小、离焦与球差接近于0后，调节被测非球面的倾斜，使彗差与倾斜最小，完成补偿干涉检测光路的精细调节。
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仿真实验中，被测非球面选用一个接近抛物面的长轴二次椭球面，相关参数如表1所示。
表 1 被测非球面参数
Table 1. Parameters of aspheric surface under test
Parameter Value Radius of curvature/mm 896.826 Conic coefficient −0.9630 Outer diameter/mm 338 Inner diameter/mm 108 以被测非球面参数为输入设计补偿器，补偿器采用平行光入射，由两个球面透镜组成，设计参数如表2所示。
表 2 补偿器设计参数
Table 2. Parameters of designed compensator
Surface serials Radius of curvature Thickness/mm Material 1 208.23 mm 13.00 H-K9L 2 −108.36 mm 185.70 3 PLANO 8.00 H-K9L 4 −348.21 mm 838.57 补偿镜最后一面距离被测镜顶点838.57 mm，补偿干涉系统光路图如图3所示。平行光入射两片球面镜组成的补偿器，出射光为与被测镜匹配的发散光，经被测镜返回后二次进入补偿镜组，形成平面波返回干涉仪。
图 3 补偿干涉系统布局图
Figure 3. Layout of compensation interferometry system
干涉仪测量波前如图4所示。波前PV值和RMS值分别为0.011λ和0.003λ，波长λ=632.8 nm。
图 4 补偿干涉系统设计波前
Figure 4. Designed wavefront of compensation interferometry system
可以认为补偿干涉系统为零补偿干涉系统。利用仿真获得灵敏度矩阵，结果如表3所示。其中，Z为光轴方向，X为水平方向，Y为竖直方向，α为绕X轴旋转，β为绕Y轴旋转。
表 3 灵敏度矩阵
Table 3. Sensitive matrix
Aberration ΔX ΔY ΔZ α β Tilt X 12.57 0 0 0 −304.78 Tilt Y 0 12.57 0 304.5 0 Power 0.07 0.07 27.12 16.99 17.90 Astigmatism at 45° 0.06 −0.06 0 −14.11 14.11 Astigmatism at 0° 0 0 0 0 0 Coma_X 6.55 0 0 0 −159.85 Coma_Y 0 6.55 0 159.72 0 Spherical −1.10E-04 −1.09E-04 0.26 −0.66 −0.34 对非球面失调量设置五组随机误差，包含主镜三个维度的平移与两个角度的偏摆，对五组随机失调量状态的波前进行Zernike分解，获得对应的2~9项如表4所示。
以各项参数误差为初始状态，按照自动化干涉检测流程对被测非球面位置姿态进行调整，收敛后调整结果如表5所示，表中括号内为调整结果相对误差设置值的偏差。
表 4 误差设置
Table 4. Error settings
Parameter No. 1 2 3 4 5 Misalignment ΔX/mm 0.0548 −0.0332 −0.0910 0.0894 −0.0790 ΔY/mm 0.0154 0.0448 0.0005 −0.0994 −0.0730 ΔZ/mm 0.0676 0.0918 −0.0270 0.0530 0.0678 α/(°) −0.0576 −0.0318 0.0940 −0.0122 −0.0132 β/ (°) −0.0292 0.0998 −0.0908 −0.0440 −0.0474 Aberration Tilt X 9.585 −30.771 26.460 14.540 13.464 Tilt Y −17.360 −9.113 28.574 −4.967 −4.941 Power 2.577 4.492 1.451 1.952 2.232 Astigmatism at 45° −0.301 1.347 −0.231 0.301 0.207 Astigmatism at 0° −0.523 0.830 2.254 −0.261 −0.214 Coma X 5.026 −16.137 13.904 7.624 7.066 Coma Y −9.107 −4.781 15.011 −2.602 −2.589 Spherical −4.199E-03 −1.788E-02 −9.320E-02 3.167E-03 8.457E-03 表 5 调整结果
Table 5. Adjust results
Parameter No. 1 2 3 4 5 ΔX/mm 0.0513(−0.0035) −0.0381(−0.0049) −0.0986(−0.0076) 0.0890(−0.0004) −0.0804(−0.0014) ΔY/mm 0.0087(−0.0067) 0.0349(−0.0099) 0.0031(+0.0026) −0.0985(+0.0009) −0.0703(+0.0027) ΔZ/mm 0.0675(−0.0001) 0.0916(−0.0002) −0.0269(+0.0001) 0.0533(+0.0003) 0.0678(+0.0000) α/(°) −0.0573(+0.0003) −0.0314(+0.0004) 0.0939(−0.0001) −0.0127(−0.0005) −0.0133(−0.0001) β/(°) −0.0293(−0.0001) 0.0996(−0.0002) −0.0911(−0.0003) −0.0446(−0.0006) −0.0475(−0.0001) 五组调整结果与设置结果基本一致，其中平移偏差小于0.01 mm，角度偏差小于3″，达到了人工测量时的对准精度，初步验证了方法的可行性。
这里的偏差主要是波前采样精度与Zernike拟合舍入位数造成的影响，这些误差影响在实际测量中也会体现。
另外，在实际测量中，被测非球面本身存在一定的面形误差，参考标准镜也存在较小的面形误差，其中，像散、彗差等非回转对称误差会对失调量求解造成一定影响，需开展实验验证。
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实验使用的被测镜与补偿镜参照仿真实验，具体参数分别如表1和表2所示。
实验采用一个定制的载重可达50 kg的Stewart平台，如图5所示。平台的X、Y轴行程范围为±25 mm，Z轴行程范围为±12.5 mm，绕X、Y、Z轴转动行程范围为±5°，最小平移运动增量1 μm，平移重复定位精度±2 μm，最小角度旋转增量1″，角度重复定位精度±2″。Stewart平台具有高负载能力、高精度、高刚性的特点，虽然工作空间有限，但足以满足精调时的位移与角度调节。
图 5 Stewart平台与背板。(a)安装在Stewart平台上的一体化背板；(b)被测非球面通过快插接口安装在背板上；(c)安装后的被测非球面、背板与Stewart平台
Figure 5. Stewart stage with backplane. (a) Integrated backplane mounted on the Stewart stage; (b) Aspheric surface mounted on the backplane via a snap-in connector; (c) Aspheric surface, backplane and Stewart stage after installation
Stewart平台固定安装一体化测试背板，如图5(a)所示，背板上留有与被测非球面相连的三个快插接口，安装时将被测非球面镜插入锁死，如图5(b)所示。安装后的被测非球面、Stewart平台与一体化测试背板如图5(c)所示。
实验系统如图6所示。由干涉仪、补偿器和被测非球面镜组成测量光路，4D干涉仪计算机作为上位机进行测量和控制。
图 6 实验装置
Figure 6. Experimental device
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将被测非球面安装在一体化测试背板上之后，测试人员离开测试光路，开始自动化测试，自动化检测过程如图2中的流程所示。因为补偿镜为平行光入射，无需通过调整干涉仪与补偿器之间的距离调整球差。软件界面如图7所示，界面中左上图为测量波前，右上表为计算获得的前16项泽尼克系数，左下为更新文件位置与计算获得的旋转与平移量，右下图为去除倾斜和离焦的波前。
图 7 软件界面
Figure 7. Software interface
实验过程如表6所示。测量初始波前有较大的倾斜，如表6(a)所示。通过调整被测非球面离轴平移调节倾斜像差，得到表6(b)中的波前，此时波前有较明显的离焦，通过调整被测非球面的轴向平移将离焦调小。
表 6 测量过程与结果
Table 6. Measurement process and results
Steps Wavefront Zernike coefficients Aberrations (a) Intial state 
PV=8.737
RMS=2.017Tilt X=−0.3329
Tilt Y=1.6998
Power=3.3714
Astigmatism at 45°=0.0319
Astigmatism at 0°=0.0575
Coma X=−0.1968
Coma Y=0.8690
Spherical=−0.0364ΔX= −0.027 mm
ΔY= +0.135 mm(b) After tilt adjustment 
PV=5.691
RMS=1.610Tilt X=0.0175
Tilt Y=0.0175
Power=2.9389
Astigmatism at 45°=0.0293
Astigmatism at 0°=0.0066
Coma X=−0.0136
Coma Y=0.0209
Spherical=−0.0082ΔZ= +0.108 mm (c) After defocus adjustment 
PV=0.384
RMS=0.064Tilt X=0.0072
Tilt Y=−0.0099
Power=0.0033
Astigmatism at 45°=0.0360
Astigmatism at 0°=0.0322
Coma X=−0.0993
Coma Y=0.0985
Spherical=−0.0695ΔX= −2.7343 mm
ΔY= −2.7516 mm
α= +0.1131°
β= −0.1124°(d) After coma adjustment 
PV= 0.261
RMS=0.042Tilt X=0.0015
Tilt Y=−0.0014
Power=0.0018
Astigmatism at 45°=0.044
Astigmatism at 0°=−0.053
Coma X=0.0011
Coma Y=−0.0012
Spherical=−0.005ΔX= −0.001 mm
ΔY= +0.002 mm
ΔZ= −0.001 mm
α= −0.0005°
β= −0.0003°倾斜与离焦调整结果如表6(c)所示，此时干涉图表现为较为明显的彗差。将平移与旋转组合起来，结合灵敏度矩阵调整彗差，即每次倾斜调整后用平移找回倾斜像差。
经过多次迭代后，彗差调整结果如表6(d)所示，此时干涉图条纹基本平行，有较小的倾斜与像散。彗差与离焦项基本为零，此时认为调整完毕，对非球面进行测量。
测量结果如表6(d)所示，PV为0.261λ，RMS为0.042λ，其中倾斜、离焦、彗差几乎为零，0°/90°像散为−0.053，±45°像散为0.044，球差为−0.005。
测量过程的PV和RMS如图8所示。波前PV与RMS同步变小，在各个过程中，倾斜像差、离焦像差、彗差逐步降低，通过调整误差的收敛，最终实现非球面自动化干涉检测。
图 8 测量过程的PV与RMS
Figure 8. The PV and RMS of measurement process
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面向高能激光领域，高洁净度超光滑非球面对自动化干涉检测的需求，文中从同轴光学系统矢量像差原理的三阶波像差表达式出发，分析了补偿法非球面测量中失调量对测量结果的影响，提出了自动化干涉检测方法。该方法利用灵敏度矩阵实现非球面的失调量求解，结合Stewart六自由度平台实现失调量的修正，最终实现了非球面的自动化检测。
选用一个同轴非球面分别进行了仿真实验与实际实验，均验证了方法的可行性，实现了只需检测人员安装，无需检测人员手动调整的半自动化精调与检测。目前该方法仅适用于初始状态波前可测的精调环节，不适用于无法有效测量波前的粗调环节，拟在后续开展基于远场像点的自动化粗调，使自动化干涉检测得到进一步完善。
Automated interferometry test of high-cleanliness ultra-smooth aspherical surfaces
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摘要: 为了实现应用于高能激光等领域对表面洁净度有着极高要求的超光滑非球面检测，排除检测人员带来的洁净度与空气扰动的影响，研究了高洁净度超光滑非球面的自动化干涉检测方法。通过建立补偿干涉法非球面失调量与波前像差之间的灵敏度矩阵，实现利用波前像差求解被测非球面失调量。以理想干涉系统的离焦、彗差与像散为优化目标，进行反馈控制，实现被测非球面的自动化调整，进而实现高洁净度超光滑非球面的自动化干涉检测。实验结果表明，在干涉图可测范围内，利用灵敏度矩阵通过几步迭代即可实现非球面失调量的收敛。结合Stewart六自由度调整台，分别实现2 μm精度的平移误差调整、2" 精度的光轴自动化对准，最终完成被测非球面的精密调整，实现高洁净度超光滑非球面的自动化干涉检测。采用灵敏度矩阵与六自由度调整的非球面自动化干涉检测方法可实现被测非球面失调量的快速求解与自动调整，降低人员和环境带来的扰动影响，提高了非球面的检测速度，并实现了高洁净度超光滑非球面的自动化干涉检测。Abstract:
Objective Aspherical surfaces are widely used in modern optical systems. With the rapid development of various optical instruments, especially laser ignition devices, laser weapons, and satellite products, which have high standards for cleanliness, smoothness, and other quality aspects, the trend in customized development is quickly shifting towards modularization and batch production. As key components of the optical system, the automation of manufacturing, inspection, and assembly of aspherical surfaces directly determines the quality and efficiency of mass production. The automated optical inspection of aspherical surfaces has also raised increasingly higher requirements. Interferometry, especially compensation methods, is a rapid, precise, and non-contact technique with the potential for automated test of aspheric surfaces. In order to meet the stringent requirements for surface cleanliness of ultra-smooth aspherical surfaces used in high-energy lasers and other fields, and to eliminate the impact of cleanliness and thermal disturbances introduced by inspectors, researchers have developed an automated interferometric detection method for ultra-smooth aspherical surfaces with high cleanliness. Methods The mathematical relationship between the amount of misalignment and wavefront aberration is determined by the compensation method based on the theory of vector wavefront aberration. Spherical and defocus aberrations are only affected by the position of the compensator or aspheric surface under test along the optical axis direction. Tilt, coma, astigmatism, field curvature, and distortion aberrations are influenced by the tilt and eccentricity of the optical elements. The order of the effects of tilt and eccentricity on aberrations varies. Based on the analysis, the automated interferometry test method is proposed. By establishing the sensitivity matrix between the misalignment amount of the aspheric surface and the wavefront aberration of the compensated interferometric method, it is possible to utilize the wavefront aberration to calculate the measured misalignment amount of the aspheric surface. The design utilizes the Stewart platform integrated test backplane to achieve the adjustment of the measured aspherical surface in six degrees of freedom. Taking the out-of-focus, coma, and dispersion of the ideal interference system as the optimization objectives, feedback control is implemented to achieve the automated adjustment of the measured aspherical surface. Subsequently, the automated interferometric detection of the high-cleanliness ultra-smooth aspherical surface is achieved. Results and Discussions Simulation and experiment utilize the same aspheric surface under test, which is an ellipsoidal surface. The compensation consists of two lenses with plane wave incidence. In the simulation, random misalignment of the aspheric surface is introduced, which includes positional errors along the optical axis, tilt errors, and eccentricity errors. The wavefront aberrations, i.e., Zernike coefficients, can be obtained through simulation. The misalignment is addressed through simulation and continuously adjusted until the misalignment and aberration reach an acceptable level. Simulation initially verifies the feasibility of the automated interferometry test method. In the experiment, the aspheric surface is mounted on the back plane of the Stewart platform using a snap-in interface. The interferogram can be obtained through simple coarse adjustment as the initial state of the experiment. The experimental results show that within the measurable range of the interferogram, the convergence of the aspherical surface misalignment can be achieved through a few iterative steps using the sensitivity matrix. Combined with Stewart's six-degree-of-freedom adjusting stage, the system enables translation error adjustment with a precision of 2 μm and automated optical axis alignment with a precision of 2". Finally, the precision adjustment of the measured aspherical surface is completed, achieving automated interferometric detection of the high-cleanliness ultra-smooth aspherical surface. Conclusions The automated interference detection method for aspherical surfaces utilizes a sensitivity matrix and adjustments in six degrees of freedom to enable a rapid solution and automatic correction of measured misalignments of aspherical surfaces. This method eliminates the influence of cleanliness and thermal perturbations introduced by inspectors, enhances the detection speed of aspherical surfaces, and achieves automated interference detection of ultra-smooth aspherical surfaces with high precision. -
图 5 Stewart平台与背板。(a)安装在Stewart平台上的一体化背板；(b)被测非球面通过快插接口安装在背板上；(c)安装后的被测非球面、背板与Stewart平台
Figure 5. Stewart stage with backplane. (a) Integrated backplane mounted on the Stewart stage; (b) Aspheric surface mounted on the backplane via a snap-in connector; (c) Aspheric surface, backplane and Stewart stage after installation
表 1 被测非球面参数
Table 1. Parameters of aspheric surface under test
Parameter Value Radius of curvature/mm 896.826 Conic coefficient −0.9630 Outer diameter/mm 338 Inner diameter/mm 108 
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表 2 补偿器设计参数
Table 2. Parameters of designed compensator
Surface serials Radius of curvature Thickness/mm Material 1 208.23 mm 13.00 H-K9L 2 −108.36 mm 185.70 3 PLANO 8.00 H-K9L 4 −348.21 mm 838.57
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表 3 灵敏度矩阵
Table 3. Sensitive matrix
Aberration ΔX ΔY ΔZ α β Tilt X 12.57 0 0 0 −304.78 Tilt Y 0 12.57 0 304.5 0 Power 0.07 0.07 27.12 16.99 17.90 Astigmatism at 45° 0.06 −0.06 0 −14.11 14.11 Astigmatism at 0° 0 0 0 0 0 Coma_X 6.55 0 0 0 −159.85 Coma_Y 0 6.55 0 159.72 0 Spherical −1.10E-04 −1.09E-04 0.26 −0.66 −0.34
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表 4 误差设置
Table 4. Error settings
Parameter No. 1 2 3 4 5 Misalignment ΔX/mm 0.0548 −0.0332 −0.0910 0.0894 −0.0790 ΔY/mm 0.0154 0.0448 0.0005 −0.0994 −0.0730 ΔZ/mm 0.0676 0.0918 −0.0270 0.0530 0.0678 α/(°) −0.0576 −0.0318 0.0940 −0.0122 −0.0132 β/ (°) −0.0292 0.0998 −0.0908 −0.0440 −0.0474 Aberration Tilt X 9.585 −30.771 26.460 14.540 13.464 Tilt Y −17.360 −9.113 28.574 −4.967 −4.941 Power 2.577 4.492 1.451 1.952 2.232 Astigmatism at 45° −0.301 1.347 −0.231 0.301 0.207 Astigmatism at 0° −0.523 0.830 2.254 −0.261 −0.214 Coma X 5.026 −16.137 13.904 7.624 7.066 Coma Y −9.107 −4.781 15.011 −2.602 −2.589 Spherical −4.199E-03 −1.788E-02 −9.320E-02 3.167E-03 8.457E-03
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表 5 调整结果
Table 5. Adjust results
Parameter No. 1 2 3 4 5 ΔX/mm 0.0513(−0.0035) −0.0381(−0.0049) −0.0986(−0.0076) 0.0890(−0.0004) −0.0804(−0.0014) ΔY/mm 0.0087(−0.0067) 0.0349(−0.0099) 0.0031(+0.0026) −0.0985(+0.0009) −0.0703(+0.0027) ΔZ/mm 0.0675(−0.0001) 0.0916(−0.0002) −0.0269(+0.0001) 0.0533(+0.0003) 0.0678(+0.0000) α/(°) −0.0573(+0.0003) −0.0314(+0.0004) 0.0939(−0.0001) −0.0127(−0.0005) −0.0133(−0.0001) β/(°) −0.0293(−0.0001) 0.0996(−0.0002) −0.0911(−0.0003) −0.0446(−0.0006) −0.0475(−0.0001)
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表 6 测量过程与结果
Table 6. Measurement process and results
Steps Wavefront Zernike coefficients Aberrations (a) Intial state
PV=8.737
RMS=2.017Tilt X=−0.3329
Tilt Y=1.6998
Power=3.3714
Astigmatism at 45°=0.0319
Astigmatism at 0°=0.0575
Coma X=−0.1968
Coma Y=0.8690
Spherical=−0.0364ΔX= −0.027 mm
ΔY= +0.135 mm(b) After tilt adjustment
PV=5.691
RMS=1.610Tilt X=0.0175
Tilt Y=0.0175
Power=2.9389
Astigmatism at 45°=0.0293
Astigmatism at 0°=0.0066
Coma X=−0.0136
Coma Y=0.0209
Spherical=−0.0082ΔZ= +0.108 mm (c) After defocus adjustment
PV=0.384
RMS=0.064Tilt X=0.0072
Tilt Y=−0.0099
Power=0.0033
Astigmatism at 45°=0.0360
Astigmatism at 0°=0.0322
Coma X=−0.0993
Coma Y=0.0985
Spherical=−0.0695ΔX= −2.7343 mm
ΔY= −2.7516 mm
α= +0.1131°
β= −0.1124°(d) After coma adjustment
PV= 0.261
RMS=0.042Tilt X=0.0015
Tilt Y=−0.0014
Power=0.0018
Astigmatism at 45°=0.044
Astigmatism at 0°=−0.053
Coma X=0.0011
Coma Y=−0.0012
Spherical=−0.005ΔX= −0.001 mm
ΔY= +0.002 mm
ΔZ= −0.001 mm
α= −0.0005°
β= −0.0003°
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