光学元件拼接测量中的定位误差校正
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摘要
为了实现大口径反射光学元件表面面形的高精度测量,建立了拼接测量方法,用以得到光学元件表面的面形数据。但拼接测量存在较多误差,其中各局部面形之间的定位误差对拼接误差影响较大,需要通过校正来减少定位误差对拼接误差的影响。首先对被测镜进行局部面形划分,按着一定顺序完成所有局部面形的测量;然后,基于BFGS算法对各子口径面形之间的定位误差进行校正求解,进而得到整体面形数据;最后,使用ZYGO菲索干涉仪搭建了拼接测量设备,对反射镜中120 mm×20 mm的区域进行测量,将直接拼接方法与位移校正拼接方法获得的面形数据与全口径整体测量获得的面形数据进行了对比,位移校正拼接方法测量面形数据与全口径拼接测量面形数据残差小,结果表明该方法可以有效提高拼接测量精度。
[Background] In order to realize the high precision measurement of large-aperture mirror, a stitching method is established. The position errors between adjacent surfaces affect the stitching results, so compensation algorithm is needed to solve this problem. [Purpose] This study aims to reduce the effect of position errors in stitching measurement by proposing a global optimization algorithm for position error compensation. [Methods]Firstly, the basic theory of stitching measurement technology is applied to dividing the whole test mirror into several parts, each part of the surface should meet the requirement of a single measurement. Then, based on BFGS algorithm,pixel motion and two-dimensional linear interpolation, a stitching method for compensating position error is established. Finally, a ZYGO Fissor interferometer is employed to construct stitching measurement equipment to measure the 120 mm × 20 mm area in reflector by using stitching measurement method. [Results] Compared with full aperture measurement, the peak-valley(PV) and root mean square(RMS) of the height residual achieved by stitching measurement are 8.7 nm and 0.5 nm, respectively. [Conclusions] The experiment result showed that this optimization method can compensate the position error more effectively than the direct stitching method.
[Background] In order to realize the high precision measurement of large-aperture mirror, a stitching method is established. The position errors between adjacent surfaces affect the stitching results, so compensation algorithm is needed to solve this problem. [Purpose] This study aims to reduce the effect of position errors in stitching measurement by proposing a global optimization algorithm for position error compensation. [Methods]Firstly, the basic theory of stitching measurement technology is applied to dividing the whole test mirror into several parts, each part of the surface should meet the requirement of a single measurement. Then, based on BFGS algorithm,pixel motion and two-dimensional linear interpolation, a stitching method for compensating position error is established. Finally, a ZYGO Fissor interferometer is employed to construct stitching measurement equipment to measure the 120 mm × 20 mm area in reflector by using stitching measurement method. [Results] Compared with full aperture measurement, the peak-valley(PV) and root mean square(RMS) of the height residual achieved by stitching measurement are 8.7 nm and 0.5 nm, respectively. [Conclusions] The experiment result showed that this optimization method can compensate the position error more effectively than the direct stitching method.
引文
1 Yumoto H,Koyama T,Matsuyama S,et al.Stitching interferometry for ellipsoidal X-ray mirrors[J].Review of Scientific Instruments,2016,87(5):6.
2彭川黔,何玉梅,王劼.基于法线追迹原理的新型高精度面形检测系统[J].核技术,2017,40(9):090101.DOI:10.11889/j.0253-3219.2017.hjs.40.090101.PENG Chuanqian,HE Yumei,WANG Jie.A novel highaccuracy deflectometric profiler system based on normal tracing principle[J].Nuclear Techniques,2017,40(9):090101.DOI:10.11889/j.0253-3219.2017.hjs.40.090101.
3 Kim C J,Wyant J C.Sub-aperture test of a large flat on a fast aspheric surface[J].Journal of the Optical Society of America,1981,71:1587.
4 Bray M.Stitching interferometer for large optics using a standard interferometer,description of an automated system[J].Society of Photo-Optical Instrumentation Engineers,1997,3047:911?918.
5 Assoufid L,Bray M,Qian J,et al.3-D surface profile measurements of large X-ray synchrotron radiation mirrors using stitching interferometry[J].Society of Photo-Optical Instrumentation Engineers,2002,4782:21?28.
6 Tang S.Stitching:high-spatial-resolution microsurface measurements over large areas[J].Society of PhotoOptical Instrumentation Engineers,1998,3479:43?49.
7 Sjodahl M,Bozenko F O.Stitching interferometric measurement data for inspection of large optical components[J].Optical Engineering,2002,41(2):403?408.
8 Yamauchi K,Yamamura K,Mimura H,et al.Microstitching interferometry for X-ray reflective optics,review of scientific instruments[J].American Institute of Physics,2003,74(5):2894?2897.
9 Mimura H,Yumoto H,Matsuyama S,et al.Microstitching interferometry for nano focusing mirror optics[J].Optical Engineering,2004,5533:171?180.
10王月珠,田义,李洪玉,等.环形子孔径拼接干涉检测非球面的建模与实验[J].光学学报,2009,29(11):3082?3087.WANG Yuezhu,TIAN Yi,LI Hongyu,et al.Modeling and experiment of testing asphere by annular subaperture stitching interferometer[J].Acta Optica Sinca,2009,29(11):3082?3087.
11张鹏飞,赵宏,周翔,等.采用立体视觉实现子孔径拼接测量的工件定位[J].光学精密工程,2010,18(2)503?511.ZHANG Pengfei,ZHAO Hong,ZHOU Xiang,et al Work-piece location in sub-aperture stitching test based on stereo vision[J].Optics and Precision Engineering2010,18(2):503?511.
12汪利华,吴时彬,任戈,等.子孔径拼接检测光学系统波前机械定位误差补偿算法[J].光学学报,2012,32(1)0112003.WANG Lihua,WU Shibin,REN Ge,et al.Location error compensation algorithm for measuring optical system wave front by sub-aperture stitching[J].Acta Optica Sinca,2012,32(1):0112003.
13闫力松,王孝坤,罗霄,等.采用三角剖分算法的子孔径拼接检测技术[J].红外与激光工程,2013,42(7):1793?1797.YAN Lisong,WANG Xiaokun,LUO Xiao,et al.Subaperture stitching testing technolohy based on triangulation algorithm[J].Infrared and Laser Engineering,2013,42(7):1793?1797.
14张敏,隋永新,杨怀江.用于子口径拼接干涉系统的机械误差补偿算法[J].光学精密工程,2015,23(4):934?940.ZHANG Min,SUI Yongxin,YANG Huaijiang.Mechanical error compensation algorithm for subaperture stitching interferometry[J].Optics and Precision Engineering,2015,23(4):934?940.
15 Otsubo M,Katsuyuki O,Jumpei T,et al.Measurement of large plane surface shape with interferometric aperture synthesis[J].Society of Photo-Optical Instrumentation Engineers,1992,1720:444?447.
16陈宝林.最优化理论与算法[M].北京:清华大学出版社,2005.CHEN Baolin.Optimization theory and algorithm[M].Beijing:Tsinghua University Press,2005.
2彭川黔,何玉梅,王劼.基于法线追迹原理的新型高精度面形检测系统[J].核技术,2017,40(9):090101.DOI:10.11889/j.0253-3219.2017.hjs.40.090101.PENG Chuanqian,HE Yumei,WANG Jie.A novel highaccuracy deflectometric profiler system based on normal tracing principle[J].Nuclear Techniques,2017,40(9):090101.DOI:10.11889/j.0253-3219.2017.hjs.40.090101.
3 Kim C J,Wyant J C.Sub-aperture test of a large flat on a fast aspheric surface[J].Journal of the Optical Society of America,1981,71:1587.
4 Bray M.Stitching interferometer for large optics using a standard interferometer,description of an automated system[J].Society of Photo-Optical Instrumentation Engineers,1997,3047:911?918.
5 Assoufid L,Bray M,Qian J,et al.3-D surface profile measurements of large X-ray synchrotron radiation mirrors using stitching interferometry[J].Society of Photo-Optical Instrumentation Engineers,2002,4782:21?28.
6 Tang S.Stitching:high-spatial-resolution microsurface measurements over large areas[J].Society of PhotoOptical Instrumentation Engineers,1998,3479:43?49.
7 Sjodahl M,Bozenko F O.Stitching interferometric measurement data for inspection of large optical components[J].Optical Engineering,2002,41(2):403?408.
8 Yamauchi K,Yamamura K,Mimura H,et al.Microstitching interferometry for X-ray reflective optics,review of scientific instruments[J].American Institute of Physics,2003,74(5):2894?2897.
9 Mimura H,Yumoto H,Matsuyama S,et al.Microstitching interferometry for nano focusing mirror optics[J].Optical Engineering,2004,5533:171?180.
10王月珠,田义,李洪玉,等.环形子孔径拼接干涉检测非球面的建模与实验[J].光学学报,2009,29(11):3082?3087.WANG Yuezhu,TIAN Yi,LI Hongyu,et al.Modeling and experiment of testing asphere by annular subaperture stitching interferometer[J].Acta Optica Sinca,2009,29(11):3082?3087.
11张鹏飞,赵宏,周翔,等.采用立体视觉实现子孔径拼接测量的工件定位[J].光学精密工程,2010,18(2)503?511.ZHANG Pengfei,ZHAO Hong,ZHOU Xiang,et al Work-piece location in sub-aperture stitching test based on stereo vision[J].Optics and Precision Engineering2010,18(2):503?511.
12汪利华,吴时彬,任戈,等.子孔径拼接检测光学系统波前机械定位误差补偿算法[J].光学学报,2012,32(1)0112003.WANG Lihua,WU Shibin,REN Ge,et al.Location error compensation algorithm for measuring optical system wave front by sub-aperture stitching[J].Acta Optica Sinca,2012,32(1):0112003.
13闫力松,王孝坤,罗霄,等.采用三角剖分算法的子孔径拼接检测技术[J].红外与激光工程,2013,42(7):1793?1797.YAN Lisong,WANG Xiaokun,LUO Xiao,et al.Subaperture stitching testing technolohy based on triangulation algorithm[J].Infrared and Laser Engineering,2013,42(7):1793?1797.
14张敏,隋永新,杨怀江.用于子口径拼接干涉系统的机械误差补偿算法[J].光学精密工程,2015,23(4):934?940.ZHANG Min,SUI Yongxin,YANG Huaijiang.Mechanical error compensation algorithm for subaperture stitching interferometry[J].Optics and Precision Engineering,2015,23(4):934?940.
15 Otsubo M,Katsuyuki O,Jumpei T,et al.Measurement of large plane surface shape with interferometric aperture synthesis[J].Society of Photo-Optical Instrumentation Engineers,1992,1720:444?447.
16陈宝林.最优化理论与算法[M].北京:清华大学出版社,2005.CHEN Baolin.Optimization theory and algorithm[M].Beijing:Tsinghua University Press,2005.