基于子孔径拼接的非球面检测方法研究
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摘要
随着光学技术的不断发展,非球面光学元件以其优越的光学特性被应用于多个领域,然而非球面光学元件在检测方面的困难制约了其广泛应用。子孔径拼接干涉检测技术,因具有拓展干涉仪的横向和纵向动态范围,能够对非球面进行低成本、高分辨率检测的优点而成为一个重要的研究课题。本文针对子孔径拼接干涉检测非球面开展了以下研究。
首先介绍了子孔径拼接干涉检测的基本原理,对各种子孔径形状和各种拼接模式进行了比较,在此基础上介绍了拼接算法的基本原理,包含两两拼接算法、全局误差均化算法和局部误差均化算法。其次完成了非球面子孔径拼接检测系统总体方案的设计,设计了包含非球面合成检测机构、大口径近平面非球面检测机构和小口径深度凹非球面检测机构的三种检测机构,进而设计了非球面检测流程,解决了子孔径划分模式的优化和检测机构的运动规划问题。讨论了非球面检测系统的误差修正,分析了标准球面波前误差、机构运动调整误差和成像畸变误差对非球面检测的影响并给出了修正方法。然后研究了子孔径拼接检测算法,对包括子孔径波面拟合和子孔径定位变换的拼接算法预处理方法进行了讨论,提出了基于调整误差分离模型的全孔径拼接优化算法,并用Matlab编制了包含多个模块的拼接算法程序。
最后,对平面子孔径拼接检测和非球面子孔径拼接检测进行了实验验证,测量结果PV值的误差小于十分之波长,验证了拼接算法和拼接程序的有效性,并对检测误差进行了分析。
With the continuous development of optical technology, aspheric optical elements are used in many areas for its excellent optical properties, but the wider use of this technology was constrained by the difficulties in testing. Sub-aperture stitching, as it can be used to expand the horizontal and vertical dynamic range of a interferometer, can test aspheric optical elements with low-cost and high-resolution, has become an important research topic. This thesis studies these aspects aims at aspheric surfaces testing with sub-aperture stitching testing technique as follows:
Firstly, basic principles of sub-aperture stitching have been investigated. Then we compare various sub-aperture shapes and a variety of sub-aperture stitching patterns. On this basis we introduce the basic principles of several stitching algorithms, include double sub-aperture stitching algorithm, global optimization algorithm and local optimization algorithm. Secondly we design overall plan of aspheric surfaces testing system with sub-aperture stitching method. Design three kinds of testing mechanisms, which are combined testing mechanism for aspheric surfaces, testing mechanism for large-diameter near-plane aspheric surfaces and testing mechanism for small-caliber deep concave aspheric surfaces. Put forward a process program for the measurement of non-spherical, resolve the optimization of sub-aperture partition, and the motion planning problem of testing organizations. We discuss about how to remove errors in aspheric surfaces testing system, make an assay of the inaccuracy of standard spherical wave-fronts, the inaccuracy of movement and adjustment of testing organizations, the inaccuracy of image distortion, which can influence the detection of non-spherical, and give compensation methods in addition. Make a study of algorithms of sub-aperture stitching, conduct a discussion of stitching algorithm pretreatment methods which includes sub-apertures fitting and sub-aperture orientation transformation. According to these researches, we write a stitching algorithm program with Matlab.
In the end, sub-aperture stitching tests are performed with a planar mirror and an aspheric mirror respectively, the PV value of test result has reached one tenth wavelength, which verifies the validity of the stitching algorithm and program. Besides, test errors also have been analyzed.
首先介绍了子孔径拼接干涉检测的基本原理,对各种子孔径形状和各种拼接模式进行了比较,在此基础上介绍了拼接算法的基本原理,包含两两拼接算法、全局误差均化算法和局部误差均化算法。其次完成了非球面子孔径拼接检测系统总体方案的设计,设计了包含非球面合成检测机构、大口径近平面非球面检测机构和小口径深度凹非球面检测机构的三种检测机构,进而设计了非球面检测流程,解决了子孔径划分模式的优化和检测机构的运动规划问题。讨论了非球面检测系统的误差修正,分析了标准球面波前误差、机构运动调整误差和成像畸变误差对非球面检测的影响并给出了修正方法。然后研究了子孔径拼接检测算法,对包括子孔径波面拟合和子孔径定位变换的拼接算法预处理方法进行了讨论,提出了基于调整误差分离模型的全孔径拼接优化算法,并用Matlab编制了包含多个模块的拼接算法程序。
最后,对平面子孔径拼接检测和非球面子孔径拼接检测进行了实验验证,测量结果PV值的误差小于十分之波长,验证了拼接算法和拼接程序的有效性,并对检测误差进行了分析。
With the continuous development of optical technology, aspheric optical elements are used in many areas for its excellent optical properties, but the wider use of this technology was constrained by the difficulties in testing. Sub-aperture stitching, as it can be used to expand the horizontal and vertical dynamic range of a interferometer, can test aspheric optical elements with low-cost and high-resolution, has become an important research topic. This thesis studies these aspects aims at aspheric surfaces testing with sub-aperture stitching testing technique as follows:
Firstly, basic principles of sub-aperture stitching have been investigated. Then we compare various sub-aperture shapes and a variety of sub-aperture stitching patterns. On this basis we introduce the basic principles of several stitching algorithms, include double sub-aperture stitching algorithm, global optimization algorithm and local optimization algorithm. Secondly we design overall plan of aspheric surfaces testing system with sub-aperture stitching method. Design three kinds of testing mechanisms, which are combined testing mechanism for aspheric surfaces, testing mechanism for large-diameter near-plane aspheric surfaces and testing mechanism for small-caliber deep concave aspheric surfaces. Put forward a process program for the measurement of non-spherical, resolve the optimization of sub-aperture partition, and the motion planning problem of testing organizations. We discuss about how to remove errors in aspheric surfaces testing system, make an assay of the inaccuracy of standard spherical wave-fronts, the inaccuracy of movement and adjustment of testing organizations, the inaccuracy of image distortion, which can influence the detection of non-spherical, and give compensation methods in addition. Make a study of algorithms of sub-aperture stitching, conduct a discussion of stitching algorithm pretreatment methods which includes sub-apertures fitting and sub-aperture orientation transformation. According to these researches, we write a stitching algorithm program with Matlab.
In the end, sub-aperture stitching tests are performed with a planar mirror and an aspheric mirror respectively, the PV value of test result has reached one tenth wavelength, which verifies the validity of the stitching algorithm and program. Besides, test errors also have been analyzed.
引文
1辛企明.光学非球面透镜在一些光电仪器中的应用.光学技术. 1998, 22(1):74~76
2唐健冠,伍凡,吴时彬.大口径非球面精磨表面形状检测技术研究.光学技术. 2001(11):1~6
3 H. J. Tiziani, S. Reichelt, C. Prub, et al. Testing of Aspheric Surfaces. SPIE. 2001, 4440:109~119
4乔玉晶,吕宁.非球面及非球面测量技术.哈尔滨商业大学学报. 2005, 21(3):357~361
5谢高容.非球面镜片面形检测技术综述.光学仪器. 2007, 29(2):87~90
6 Stephan Reichelt, Christof Pruss, Hans J. Tiziani. Absolute Testing of Aspheric Surfaces. SPIE. 2004, 5252:252~263
7王朝暄.大口径光学平面干涉检测的子孔径拼接研究.南京理工大学硕士学位论文. 2007:1~2
8 Jay Kumler. Designing and Specifying Aspheres for Manufacture Ability Proceedings of SPIE. 2005, 5874(25):390~397
9 Zhang X J. Recent Progress on Asphere Manufacturing and Testing at CIOM. SPIE. 2000, 4231:24~31
10陈耀龙.非球面光学元件的制造技术.光电工程. 2002, 29(12):5~9
11杨力.《先进光学制造技术》.科学出版社.北京, 2001:1~10
12伍凡.大口径透镜凸面零检验的补偿器设计.应用光学. 1996, 17(5):511~515
13 Jeng-dang Kuang. The Testing of a General Rotationally Symmetrical Aspherical Surface by Using a Null Lens in a Zygo Interferometer Meaurment. 1994, (13):85~90
14伍凡,陈强. F/1.3抛物面零检验补偿器设计.光电工程. 2004, 31(1):12~15
15 Hua Liu, Zhenwu Lu, Fengyou Li, Yongjun Xie, Qiang Shun. Full Aperture Measurement of Convex Surfaces in Interferometric Test Using Holographic Test Plate. Opt Commu. 2004,241:231~236
16 C J.Kim Polynomial Fit of Interferograms. Appl.Opt.1982, 21(24): 4521~4525
17 J.G.Thunen, O.Y.Kwon. Full Aperture Testing with Subaperture Test Optics. Proc. Soc. Photo-Opt. Instrum. Eng.1983, 351(19):19~27
18 G. N. Lawrence, R. D. Day, Interferometric Characterization of Full Spheres:Data Reduction Techniques. Appl. Opt.1987, 26:4875~4882
19 M. Otsubo, K. Okada, J Tsujiuchi. Measurement of Large Plane Surface Shapes by Connecting Small-aperture Interferomgrams. Optical Engineering. 1994, 33:608~613
20 Michael Bray. Stitching Interferometer of Large Plano Optics Using a Standard Interferometer. SPIE. 1997, 3134:39~50
21 S.Tang. Stitching: High Spatial Resolution Microsurface Measurements Over Large Areas. Proc. SPIE. 1998,3479:43~49
22 T. H?nsel, A. Nickel, A. Schindler. Stitching Interferometry of Aspherical Surfaces. Proceedings of SPIE. 2001,4449:265~275
23 P. Murphy, et al. Stitching Interferometry: a Flexible Solution for Surface Metrology. Optics and Photonics News. May 2003, 14:38~43
24 J. Fleig, P. Dumas, P. E. Murphy, G. W. Forbes. an Automated Subaperture Stitching Interferometer Workstation for Spherical and Aspherical Surfaces. Proc. SPIE. 2003, 5188:296~307
25 Greg Forbes and Marc Tricard. Subaperture Approaches to Finishing and Testing Astronomical Optics. Proceedings of SPIE. 2004,5382: 440~448
26 Paul E. Murphy, Jon Fleig, Greg Forbes, Marc Tricard. High Precision Metrology of Domes and Aspheric Optics. Proc SPIE. 2005 ,5786: 112~121
27 Chen M Y, Cheng W M, Wang C W. Multi-aperture Overlap-scanning Technique for Large Aperture Test. SPIE. 1991, 1553: 626~635
28程维明,陈明仪.子孔径变换与多孔径扫描拼接技术.光学精密工程. 1993,1(1):54~58
29 Chen M Y, Guo H W, Yu Y J, et al. Recent Developments of Multi-aperture Overlap-scanning Technique. SPIE. 2003,5180: 393~401
30白剑,程上彝.子孔径检测及拼接的目标函数分析法.光学仪器.1997,19(4):36~39
31张蓉竹,杨春林,许乔.使用子孔径拼接法检测大口径光学元件.光学技术. 2001,27(6):516~517
32张蓉竹,杨春林,许乔.子孔径拼接干涉检测及其精度分析.光学学报. 2003,23(10):1241~1244
33 Paul E. Murphy, Thomas G. Brown, Duncan T. Moore. Optical Vernier Interferometry for Aspheric Metrology. SPIE. 1999,3676:643~652
34王孝坤,王丽辉,张学军.子孔径拼接干涉法检测非球面.光学精密工程. 2007, 15(2):192~198
35李新南,张明意.大口径光学平面的子孔径拼接技术.光学技术. 2006,32(4):514~517
36季波.子孔径拼接干涉检测非球面光学元件.南京理工大学硕士学位论文. 2008:37~38
37 Daniel Malacara. Optical Shop Testing. Third Edition. A John Wiley @ Sons Publication. 2007:651~653
38乔玉晶,谭久彬,王伟波.非球面拼接测量中偏置误差修正模型.光电子激光. 2008, 19(11):1497~1501
39 Xue Dong-lin, Zheng Li-gong, Zhang Xue-jun. Analysis of Alignment Error in Asphere Testing Using a Corrector. SPIE. 2005,5638:752~757
40 Jeong Tae Moon, Ko Do-Kyeong, Lee Jongmin. Method of Reconstructing Wavefront Aberrations by Use of Zernike Polynomials in Radial Shearing Interferometers. Optics Letters. 2007, 32(3):232~234
41 Dai Guang-Ming, Mahajan Virendra N. Orthonormal Polynomials in Wavefront Analysis:Error Analysis. Applied Optics. 2008, 47(19):3433~3445
42陈善勇.非球面子孔径拼接干涉测量的几何方法研究.国防科学技术大学博士学位论文. 2006:86~91
43戴斌飞.面形精度评价方法研究.苏州大学硕士学位论文. 2005:1~10
44董军,张蓉竹,张均.样本容量对子孔径拼接检测精度影响的分析.激光杂志. 2005, 26(3):37~38
2唐健冠,伍凡,吴时彬.大口径非球面精磨表面形状检测技术研究.光学技术. 2001(11):1~6
3 H. J. Tiziani, S. Reichelt, C. Prub, et al. Testing of Aspheric Surfaces. SPIE. 2001, 4440:109~119
4乔玉晶,吕宁.非球面及非球面测量技术.哈尔滨商业大学学报. 2005, 21(3):357~361
5谢高容.非球面镜片面形检测技术综述.光学仪器. 2007, 29(2):87~90
6 Stephan Reichelt, Christof Pruss, Hans J. Tiziani. Absolute Testing of Aspheric Surfaces. SPIE. 2004, 5252:252~263
7王朝暄.大口径光学平面干涉检测的子孔径拼接研究.南京理工大学硕士学位论文. 2007:1~2
8 Jay Kumler. Designing and Specifying Aspheres for Manufacture Ability Proceedings of SPIE. 2005, 5874(25):390~397
9 Zhang X J. Recent Progress on Asphere Manufacturing and Testing at CIOM. SPIE. 2000, 4231:24~31
10陈耀龙.非球面光学元件的制造技术.光电工程. 2002, 29(12):5~9
11杨力.《先进光学制造技术》.科学出版社.北京, 2001:1~10
12伍凡.大口径透镜凸面零检验的补偿器设计.应用光学. 1996, 17(5):511~515
13 Jeng-dang Kuang. The Testing of a General Rotationally Symmetrical Aspherical Surface by Using a Null Lens in a Zygo Interferometer Meaurment. 1994, (13):85~90
14伍凡,陈强. F/1.3抛物面零检验补偿器设计.光电工程. 2004, 31(1):12~15
15 Hua Liu, Zhenwu Lu, Fengyou Li, Yongjun Xie, Qiang Shun. Full Aperture Measurement of Convex Surfaces in Interferometric Test Using Holographic Test Plate. Opt Commu. 2004,241:231~236
16 C J.Kim Polynomial Fit of Interferograms. Appl.Opt.1982, 21(24): 4521~4525
17 J.G.Thunen, O.Y.Kwon. Full Aperture Testing with Subaperture Test Optics. Proc. Soc. Photo-Opt. Instrum. Eng.1983, 351(19):19~27
18 G. N. Lawrence, R. D. Day, Interferometric Characterization of Full Spheres:Data Reduction Techniques. Appl. Opt.1987, 26:4875~4882
19 M. Otsubo, K. Okada, J Tsujiuchi. Measurement of Large Plane Surface Shapes by Connecting Small-aperture Interferomgrams. Optical Engineering. 1994, 33:608~613
20 Michael Bray. Stitching Interferometer of Large Plano Optics Using a Standard Interferometer. SPIE. 1997, 3134:39~50
21 S.Tang. Stitching: High Spatial Resolution Microsurface Measurements Over Large Areas. Proc. SPIE. 1998,3479:43~49
22 T. H?nsel, A. Nickel, A. Schindler. Stitching Interferometry of Aspherical Surfaces. Proceedings of SPIE. 2001,4449:265~275
23 P. Murphy, et al. Stitching Interferometry: a Flexible Solution for Surface Metrology. Optics and Photonics News. May 2003, 14:38~43
24 J. Fleig, P. Dumas, P. E. Murphy, G. W. Forbes. an Automated Subaperture Stitching Interferometer Workstation for Spherical and Aspherical Surfaces. Proc. SPIE. 2003, 5188:296~307
25 Greg Forbes and Marc Tricard. Subaperture Approaches to Finishing and Testing Astronomical Optics. Proceedings of SPIE. 2004,5382: 440~448
26 Paul E. Murphy, Jon Fleig, Greg Forbes, Marc Tricard. High Precision Metrology of Domes and Aspheric Optics. Proc SPIE. 2005 ,5786: 112~121
27 Chen M Y, Cheng W M, Wang C W. Multi-aperture Overlap-scanning Technique for Large Aperture Test. SPIE. 1991, 1553: 626~635
28程维明,陈明仪.子孔径变换与多孔径扫描拼接技术.光学精密工程. 1993,1(1):54~58
29 Chen M Y, Guo H W, Yu Y J, et al. Recent Developments of Multi-aperture Overlap-scanning Technique. SPIE. 2003,5180: 393~401
30白剑,程上彝.子孔径检测及拼接的目标函数分析法.光学仪器.1997,19(4):36~39
31张蓉竹,杨春林,许乔.使用子孔径拼接法检测大口径光学元件.光学技术. 2001,27(6):516~517
32张蓉竹,杨春林,许乔.子孔径拼接干涉检测及其精度分析.光学学报. 2003,23(10):1241~1244
33 Paul E. Murphy, Thomas G. Brown, Duncan T. Moore. Optical Vernier Interferometry for Aspheric Metrology. SPIE. 1999,3676:643~652
34王孝坤,王丽辉,张学军.子孔径拼接干涉法检测非球面.光学精密工程. 2007, 15(2):192~198
35李新南,张明意.大口径光学平面的子孔径拼接技术.光学技术. 2006,32(4):514~517
36季波.子孔径拼接干涉检测非球面光学元件.南京理工大学硕士学位论文. 2008:37~38
37 Daniel Malacara. Optical Shop Testing. Third Edition. A John Wiley @ Sons Publication. 2007:651~653
38乔玉晶,谭久彬,王伟波.非球面拼接测量中偏置误差修正模型.光电子激光. 2008, 19(11):1497~1501
39 Xue Dong-lin, Zheng Li-gong, Zhang Xue-jun. Analysis of Alignment Error in Asphere Testing Using a Corrector. SPIE. 2005,5638:752~757
40 Jeong Tae Moon, Ko Do-Kyeong, Lee Jongmin. Method of Reconstructing Wavefront Aberrations by Use of Zernike Polynomials in Radial Shearing Interferometers. Optics Letters. 2007, 32(3):232~234
41 Dai Guang-Ming, Mahajan Virendra N. Orthonormal Polynomials in Wavefront Analysis:Error Analysis. Applied Optics. 2008, 47(19):3433~3445
42陈善勇.非球面子孔径拼接干涉测量的几何方法研究.国防科学技术大学博士学位论文. 2006:86~91
43戴斌飞.面形精度评价方法研究.苏州大学硕士学位论文. 2005:1~10
44董军,张蓉竹,张均.样本容量对子孔径拼接检测精度影响的分析.激光杂志. 2005, 26(3):37~38