光学非球面坐标测量关键技术研究
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摘要
非球面光学零件具有校正像差、改善像质、扩大视场和增大作用距离的优点,同时还能够减轻系统重量、减小占用空间,因此在现代光学系统中得到了广泛应用。随着光学系统性能要求的不断提高,对非球面光学零件口径、相对口径、加工精度、轻量化程度、加工效率和生产成本等方面都提出了更高要求。坐标测量技术作为光学非球面研磨与抛光前期阶段面形误差的主要检测手段,是决定非球面加工效率的关键因素。目前,坐标测量技术在解决大口径、大相对口径和高陡度非球面镜的检测方面仍有一些问题需要解决,例如测量精度与效率较低、镜面的高陡度特征给测量带来一定困难等,这些问题的存在严重影响了光学非球面的加工精度和效率。本论文研究工作的主要任务就是要有效解决坐标测量技术目前存在的问题,使坐标测量技术得以完善,提高我国非球面光学零件的加工检测能力。论文的研究工作包括以下几个部分：
1.针对大口径非球面的检测问题,研究了直角坐标测量方法的基本原理、精度分析与建模。系统分析了直角坐标测量系统的关键部件——长气浮导轨6自由度误差对测量结果的影响模型,并据此开发了高精度测量实验系统。针对其中长气浮导轨直线度误差的高精度测量问题,建立了使用短基准的高精度测量方法,分析研究了测量过程中测量误差、采样频率、重叠区域长度等因素对测量精度的影响规律,实现了导轨直线度误差的高精度测量与校正。最后对口径500mm、相对口径1：3的抛物面镜进行了测量实验。
2.针对大口径、大相对口径非球面镜的检测问题,分析仿真了摆臂式测量方法的基本测量原理。建立了测量臂的挠性变形、回转轴系的跳动误差等因素对测量精度的影响模型,并开发了摆臂式测量实验系统。通过对测量原理的深入研究,利用被测非球面名义面形与测量数据建立了测量参考球面半径优化算法,在获得非球面面形误差的同时以较高精度得到了被测非球面顶点曲率半径的最优估计值。最后对口径500mm、相对口径1：1的深型镜面进行了测量实验。
3.针对高陡度非球面的检测问题,提出了基于多段拼接的高陡度光学非球面坐标测量方法。建立了基于多段拼接的高陡度光学非球面坐标测量方法的数学模型。分析仿真了重叠区域二次采样点匹配误差对测量结果的影响规律。针对重叠区域二次采样点匹配误差对测量精度具有较大影响的问题,提出了基于向量空间压缩映射原理的迭代收敛算法。分析研究了工件面形轮廓的自动划分方法并在Matlab下对测量算法进行了仿真。通过对现有测量系统的改进,建立了高精度的测量实验系统,并对口径120mm,长径比1.2的加工样件进行了测量实验。
4.分析建立了测量系统与被测工件之间相对位姿误差的数学模型,并在Matlab下进行了仿真分析。利用模型参数估计的方法,建立了截线测量位姿误差的优化分离算法,消除了测量过程中位姿误差等因素的影响,提高了测量结果的精度。在此基础上,建立了以截线测量结果为基础,综合截线位姿误差优化参数以及各截线相互平移量为参数的三维面形优化方法,得到了合理的三维面形误差分布结果,为CCOS的局部修形提供了可靠的测量数据。
5.分析研究了直角坐标测量和高陡度非球面测量过程中测量力对接触式测头测量不确定度的影响模型；分析研究了摆臂式测量过程中扫描速度对测量不确定度的影响；对实际测量过程中的温度、振动等环境误差因素对测量不确定度的影响进行了分析实测。在综合上述分析结果的基础上,对测量结果的合成标准不确定度进行了估算。最后,作为一个应用实例,介绍了与实验室自行研制的加工机床AOCMT合作完成的0500mm,f/3,K9玻璃抛物面镜的加工过程,在233小时内成功加工出抛物面反射镜,加工后的面形精度达到9.4nm RMS (λ/67 RMS,λ2=632.8nm ),表面粗糙度为1.5nm RMS,顶点曲率半径偏差控制在1.2mm(0.4‰),其结果符合预期要求。
Aspheric optics are being used more and more widely in modern optical systems, since they can correct aberrations, enhance the image quality, enlarge the field of view and extend the range of effect, at the same time of reducing the weight and volume of the optical systems. With the ever-increasing demands on optical system performances, requirements for aspheric optical components are more and more critical, which involve aperture, relative aperture, accuracy, lightweight extent, manufacturing efficiency and cost. As the main measurement method of aspherics in grinding and pre-polishing process, the coordinate measurement technique is the key factor affecting the manufacturing efficiency. However, there are still some problems about the coordinate measurement technique, such as the relatively low accuracy and efficiency, the difficulty to test steep aspherics, which have blocked the application of aspherics seriously. This thesis is dedicated to solving the problems mentioned above, in order to perfect the coordinate measurement technique and improve the capability for manufacturing large and steep aspheric surfaces. The major research efforts include the following aspects.
1. For the measurement of aspherics with a large aperture, the basic measurement principle and the accuracy analysis of a right-angle coordinate measurement technique is introduced. The effect of the 6 DOF errors of a long air guide-way, which is the critical component of a right-angle coordinate measurement system, on the measurement accuracy is analyzed, and an experimental set-up is built. For the ultra-precise measurement of the straightness error of the long air guide-way, the measurement method with a short benchmark is put forward. The effect of such factors as the testing errors, the sampling frequency and the overlap length, on the measurement accuracy is studied. With this method, we can measure and correct the straightness error of a long air guide-way accurately. Finally, a concave paraboloid with aperture= 500 mm and relative aperture= 1:3 is tested.
2. For the measurement of aspherics with a large aperture and a large numerical aperture, the measurement principle of a swing-arm profilometer is researched and simulated. The effects of the bending of the measurement arm and the runouts of the air-bearing on the accuracy are analyzed and an experimental set-up is built. With the nominal figure and the measured data, the nonlinear optimal model of the radius of the measuring reference circle is built, and the convergence error of the model is analyzed. With this method, we can get the value of the vertex radius of an asphere, at the same time of getting the surface error. Finally, a concave sphere with aperture= 500 mm and relative aperture=1:1 is tested.
3. For the measurement of steep aspherics, the coordinate measurement technique using profile matching method is put forward. The mathematical model of the profile matching technique is built, and the effect of the consistent errors of the dual-sampled points in the overlaps is analyzed and simulated. Since these errors affect the measurement accuracy quite seriously, an iteration algorithm with the compression mapping principle of the vector space is put forward. After that, the dividing method of the global profile is researched and the algorithm is simulated with Matlab. With the existed equipments, an experimental set-up is built and a steep conformal optics (diameter= 120mm, length/diameter=1.2) is tested.
4. The effect of the relative posture errors in 6 DOF between the measurement system and the workpiece is researched and simulated. With the method of model parameter estimation, the optimization and separation algorithm of the relative posture errors of a meridian is put forward, with which the effects of the relative posture errors on the result are eliminated and the accuracy of the result is improved. After that, since sometimes the distribution of the 3D surface error is needed, the reconstruction method of the 3D surface error with several meridians is researched, with which the relative posture errors and the relative translations of the meridians are the optimal parameters. Simulations and experiments indicate that, with this method, we can get the reasonable distribution of the 3D surface error and provide the reliable data for CCOS.
5. The effect of the measuring force on the uncertainty of the right-angle coordinate measurement method, and the effect of the scanning velocity of a contacting probe on the uncertainty of the swing-arm profilometer are analyzed and simulated. The effect of the environmental factors such as the temperature and the vibration is researched and tested too. With these results, we calculated the combined standard uncertainty of the right-angle coordinate measurement method and the swing-arm profilometer. Finally, as a practical example, the manufacturing process of a paraboloid (0500mm,f/3, K9) is introduced. During 233 hours, the workpiece is manufactured successfully, with the surface error 9.4nm rms, the roughness 1.5nm rms, the error of the vertex radius 1.2mm (0.4‰), which has satisfied the expected requirements.
1.针对大口径非球面的检测问题,研究了直角坐标测量方法的基本原理、精度分析与建模。系统分析了直角坐标测量系统的关键部件——长气浮导轨6自由度误差对测量结果的影响模型,并据此开发了高精度测量实验系统。针对其中长气浮导轨直线度误差的高精度测量问题,建立了使用短基准的高精度测量方法,分析研究了测量过程中测量误差、采样频率、重叠区域长度等因素对测量精度的影响规律,实现了导轨直线度误差的高精度测量与校正。最后对口径500mm、相对口径1：3的抛物面镜进行了测量实验。
2.针对大口径、大相对口径非球面镜的检测问题,分析仿真了摆臂式测量方法的基本测量原理。建立了测量臂的挠性变形、回转轴系的跳动误差等因素对测量精度的影响模型,并开发了摆臂式测量实验系统。通过对测量原理的深入研究,利用被测非球面名义面形与测量数据建立了测量参考球面半径优化算法,在获得非球面面形误差的同时以较高精度得到了被测非球面顶点曲率半径的最优估计值。最后对口径500mm、相对口径1：1的深型镜面进行了测量实验。
3.针对高陡度非球面的检测问题,提出了基于多段拼接的高陡度光学非球面坐标测量方法。建立了基于多段拼接的高陡度光学非球面坐标测量方法的数学模型。分析仿真了重叠区域二次采样点匹配误差对测量结果的影响规律。针对重叠区域二次采样点匹配误差对测量精度具有较大影响的问题,提出了基于向量空间压缩映射原理的迭代收敛算法。分析研究了工件面形轮廓的自动划分方法并在Matlab下对测量算法进行了仿真。通过对现有测量系统的改进,建立了高精度的测量实验系统,并对口径120mm,长径比1.2的加工样件进行了测量实验。
4.分析建立了测量系统与被测工件之间相对位姿误差的数学模型,并在Matlab下进行了仿真分析。利用模型参数估计的方法,建立了截线测量位姿误差的优化分离算法,消除了测量过程中位姿误差等因素的影响,提高了测量结果的精度。在此基础上,建立了以截线测量结果为基础,综合截线位姿误差优化参数以及各截线相互平移量为参数的三维面形优化方法,得到了合理的三维面形误差分布结果,为CCOS的局部修形提供了可靠的测量数据。
5.分析研究了直角坐标测量和高陡度非球面测量过程中测量力对接触式测头测量不确定度的影响模型；分析研究了摆臂式测量过程中扫描速度对测量不确定度的影响；对实际测量过程中的温度、振动等环境误差因素对测量不确定度的影响进行了分析实测。在综合上述分析结果的基础上,对测量结果的合成标准不确定度进行了估算。最后,作为一个应用实例,介绍了与实验室自行研制的加工机床AOCMT合作完成的0500mm,f/3,K9玻璃抛物面镜的加工过程,在233小时内成功加工出抛物面反射镜,加工后的面形精度达到9.4nm RMS (λ/67 RMS,λ2=632.8nm ),表面粗糙度为1.5nm RMS,顶点曲率半径偏差控制在1.2mm(0.4‰),其结果符合预期要求。
Aspheric optics are being used more and more widely in modern optical systems, since they can correct aberrations, enhance the image quality, enlarge the field of view and extend the range of effect, at the same time of reducing the weight and volume of the optical systems. With the ever-increasing demands on optical system performances, requirements for aspheric optical components are more and more critical, which involve aperture, relative aperture, accuracy, lightweight extent, manufacturing efficiency and cost. As the main measurement method of aspherics in grinding and pre-polishing process, the coordinate measurement technique is the key factor affecting the manufacturing efficiency. However, there are still some problems about the coordinate measurement technique, such as the relatively low accuracy and efficiency, the difficulty to test steep aspherics, which have blocked the application of aspherics seriously. This thesis is dedicated to solving the problems mentioned above, in order to perfect the coordinate measurement technique and improve the capability for manufacturing large and steep aspheric surfaces. The major research efforts include the following aspects.
1. For the measurement of aspherics with a large aperture, the basic measurement principle and the accuracy analysis of a right-angle coordinate measurement technique is introduced. The effect of the 6 DOF errors of a long air guide-way, which is the critical component of a right-angle coordinate measurement system, on the measurement accuracy is analyzed, and an experimental set-up is built. For the ultra-precise measurement of the straightness error of the long air guide-way, the measurement method with a short benchmark is put forward. The effect of such factors as the testing errors, the sampling frequency and the overlap length, on the measurement accuracy is studied. With this method, we can measure and correct the straightness error of a long air guide-way accurately. Finally, a concave paraboloid with aperture= 500 mm and relative aperture= 1:3 is tested.
2. For the measurement of aspherics with a large aperture and a large numerical aperture, the measurement principle of a swing-arm profilometer is researched and simulated. The effects of the bending of the measurement arm and the runouts of the air-bearing on the accuracy are analyzed and an experimental set-up is built. With the nominal figure and the measured data, the nonlinear optimal model of the radius of the measuring reference circle is built, and the convergence error of the model is analyzed. With this method, we can get the value of the vertex radius of an asphere, at the same time of getting the surface error. Finally, a concave sphere with aperture= 500 mm and relative aperture=1:1 is tested.
3. For the measurement of steep aspherics, the coordinate measurement technique using profile matching method is put forward. The mathematical model of the profile matching technique is built, and the effect of the consistent errors of the dual-sampled points in the overlaps is analyzed and simulated. Since these errors affect the measurement accuracy quite seriously, an iteration algorithm with the compression mapping principle of the vector space is put forward. After that, the dividing method of the global profile is researched and the algorithm is simulated with Matlab. With the existed equipments, an experimental set-up is built and a steep conformal optics (diameter= 120mm, length/diameter=1.2) is tested.
4. The effect of the relative posture errors in 6 DOF between the measurement system and the workpiece is researched and simulated. With the method of model parameter estimation, the optimization and separation algorithm of the relative posture errors of a meridian is put forward, with which the effects of the relative posture errors on the result are eliminated and the accuracy of the result is improved. After that, since sometimes the distribution of the 3D surface error is needed, the reconstruction method of the 3D surface error with several meridians is researched, with which the relative posture errors and the relative translations of the meridians are the optimal parameters. Simulations and experiments indicate that, with this method, we can get the reasonable distribution of the 3D surface error and provide the reliable data for CCOS.
5. The effect of the measuring force on the uncertainty of the right-angle coordinate measurement method, and the effect of the scanning velocity of a contacting probe on the uncertainty of the swing-arm profilometer are analyzed and simulated. The effect of the environmental factors such as the temperature and the vibration is researched and tested too. With these results, we calculated the combined standard uncertainty of the right-angle coordinate measurement method and the swing-arm profilometer. Finally, as a practical example, the manufacturing process of a paraboloid (0500mm,f/3, K9) is introduced. During 233 hours, the workpiece is manufactured successfully, with the surface error 9.4nm rms, the roughness 1.5nm rms, the error of the vertex radius 1.2mm (0.4‰), which has satisfied the expected requirements.
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