无衍射光光轴安装基础的误差研究
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摘要
直线度误差测量是一项基本的几何公差测量,将无衍射光技术,CCD成像技术和数字图像处理技术结合起来开发的无衍射光空间直线度测量仪适合于长短距离的直线度误差测量,为了进一步提高其测量精度,本文从影响无衍射光空间直线度测量仪的测量精度的各种误差因素出发,找出其误差根本,主要研究由于地倾斜固体潮带来的无衍射光光轴安装基础的误差,旨在从实质上提高无衍射光空间直线度测量仪的中长距离的测量精度,也为无衍射光应用于地倾斜仪的设计奠定理论基础和实践的可能性。
本文采用理论推导和实验相结合的方法,首先从牛顿力学原理推导出天体之间的引潮位一般计算公式,采用球面谐函数和杜德森展开方法对引潮位进行二阶和三阶展开,利用最新的天文参数简化引潮位的展开计算,选取主要潮波并根据引潮位和地倾斜之间的关系采用MATLAB软件计算出地倾斜角变化规律,然后根据地倾斜角变化规律考虑实际情况得到无衍射光光轴安装基础的误差变化规律。
理论计算结果表明无衍射光轴安装基础的误差随24小时周期规律变化,与光轴稳定性实验结果经小波变化后结论一致,所以在无衍射光直线度测量仪测量直线度过程中是存在由地倾斜引起的误差,其最大误差可达到6.5e-8rad,在超精密测量中必须予以考虑其影响,其误差补偿方法可以采用本文所述的直接补偿法。
无衍射光光轴稳定性实验的误差分析证明了无衍射光光轴安装基础的误差存在,它也为将无衍射光应用于地倾斜仪的设计开发奠定了理论基础和实践的可能性。
Straightness error is a basic parameter of the geometric tolerance measurement, The spatial straightness error instrument is designed by using non-diffracting beam technique, CCD imaging and digital image processing technology, which is adapt to measure straightness error both in long distance and short distance. To further improve its accuracy, this paper is based on all the factors of measuring error, finding out the real causes of measuring error, mainly studying the error of the non-diffracting beam’s installment base which is caused by earth tides. The aims of this paper are improving the accuracy of spatial straightness error instrument and ready for designing non-diffracting beam tilt-meter.
This article uses the method which is unifying the theory reasoning and the experiment, at first uses Newtonian mechanics principle to infer the general formula of earth tide level between plnanets, uses the spherical surface harmonic function and the Doodson launches to carry on the tide level to second-order and third-order, uses the newest astronomy parameter to simplify the computation of the general formula, uses the MATLAB software to complete the computation of the tilt angular variation rule which is based on selecting several main tidal waves and relations between the tide level and the tilt, in the end gets out the variation rule on the error of the non-diffracting beam’s installment base which is based on the tilt variation rule and also thinking about actual situation.
The results of computation indicate that the error of the non-diffracting beam’s installment base is varied along with 24 hour periodic law, which is consistent with the result of optical axis stability trial after wavelet changing. So the installment foundation error is existed in the procedure of the straightness error measurement by spatial straightness error instrument, which is caused by tilt. Its Maximum value was 6.5e-8rad, which must be considered in the super-precision measurement, the compensated method for the error is direct compensated method which has been shown in this article.
The non-diffracting beam axis stability trial had proven the error of installment base to be existed by the analysis of error, which makes a ready for the design of non-diffracting beam tilt-meter.
本文采用理论推导和实验相结合的方法,首先从牛顿力学原理推导出天体之间的引潮位一般计算公式,采用球面谐函数和杜德森展开方法对引潮位进行二阶和三阶展开,利用最新的天文参数简化引潮位的展开计算,选取主要潮波并根据引潮位和地倾斜之间的关系采用MATLAB软件计算出地倾斜角变化规律,然后根据地倾斜角变化规律考虑实际情况得到无衍射光光轴安装基础的误差变化规律。
理论计算结果表明无衍射光轴安装基础的误差随24小时周期规律变化,与光轴稳定性实验结果经小波变化后结论一致,所以在无衍射光直线度测量仪测量直线度过程中是存在由地倾斜引起的误差,其最大误差可达到6.5e-8rad,在超精密测量中必须予以考虑其影响,其误差补偿方法可以采用本文所述的直接补偿法。
无衍射光光轴稳定性实验的误差分析证明了无衍射光光轴安装基础的误差存在,它也为将无衍射光应用于地倾斜仪的设计开发奠定了理论基础和实践的可能性。
Straightness error is a basic parameter of the geometric tolerance measurement, The spatial straightness error instrument is designed by using non-diffracting beam technique, CCD imaging and digital image processing technology, which is adapt to measure straightness error both in long distance and short distance. To further improve its accuracy, this paper is based on all the factors of measuring error, finding out the real causes of measuring error, mainly studying the error of the non-diffracting beam’s installment base which is caused by earth tides. The aims of this paper are improving the accuracy of spatial straightness error instrument and ready for designing non-diffracting beam tilt-meter.
This article uses the method which is unifying the theory reasoning and the experiment, at first uses Newtonian mechanics principle to infer the general formula of earth tide level between plnanets, uses the spherical surface harmonic function and the Doodson launches to carry on the tide level to second-order and third-order, uses the newest astronomy parameter to simplify the computation of the general formula, uses the MATLAB software to complete the computation of the tilt angular variation rule which is based on selecting several main tidal waves and relations between the tide level and the tilt, in the end gets out the variation rule on the error of the non-diffracting beam’s installment base which is based on the tilt variation rule and also thinking about actual situation.
The results of computation indicate that the error of the non-diffracting beam’s installment base is varied along with 24 hour periodic law, which is consistent with the result of optical axis stability trial after wavelet changing. So the installment foundation error is existed in the procedure of the straightness error measurement by spatial straightness error instrument, which is caused by tilt. Its Maximum value was 6.5e-8rad, which must be considered in the super-precision measurement, the compensated method for the error is direct compensated method which has been shown in this article.
The non-diffracting beam axis stability trial had proven the error of installment base to be existed by the analysis of error, which makes a ready for the design of non-diffracting beam tilt-meter.
引文
[1]谢铁邦,李柱,席洪卓.互换性与技术测量[M].第三版.武汉:华中理工大学出版社,1998.103～104
[2] GB/T 11336-2004.直线度误差检测[S].北京:中国国家标准化管理委员会, 2004
[3] ZHANG XINBAO, ZHAO BIN, LI ZHU. Measurement method of spatial straightness error using non-diffracting beam and moiré-fringe technology [J]. Opt. A: Pure Appl. Opt. 2004, 6(1):121–126
[4]张新宝.空间直线度误差无衍射光莫尔条纹测量方法的研究[D].武汉:华中科技大学,2002
[5]宁延平,刘战锋.国内外高精度直线度测量技术的研究现状[J].现代制造工程,2005,(6):82-84
[6]李钰.激光测量大尺寸物体直线度的新方法[J].中国激光,1985,12(6),365-368
[7]刘兴占,梁晋文,陈博一等.双光束补偿准直系统[J].计量技术.1999(1),12-15
[8]方仲彦,殷纯水,梁晋文.高精度激光准直技术的研究(一)[J].航空计测技术,1997, 17(1): 3-6
[9]章恩耀,张玉坤,李岩,方仲彦.双LD调制宽光束准直法[J].光学技术,1993. 2:71-73
[10] Zhang Xinbao, Zhao Bin , Li Zhu .Study of the tolerance of the non-diffracting beam to laser beam deflection[J]. J. Opt. A: Pure Appl. Opt. 4.2002 78–83
[11]匡萃方,冯其波,刘斌等.一种共路补偿激光漂移的直线度测量方法[J].光电工程,2005,32(4):32-35
[12] Akira ISHIDA. Apparatus for measuring straightness[P]. US Patent: 5333053.1994
[13] Michael Reid SOGARD. Lasers interferometer having a sheath for the laserbeam[P]. US Patent:5708505, 1998
[14]杨友堂,曾理江,殷纯永.自适应除噪技术在激光准直中的应用研究[J].仪器仪表学报,1995, Vol16(4): 370-374.
[15] BORN MAX, WOLF EMAIL. Principles of Optics[M]. New York: Pergamon, 1964:752-754
[16] M.V. PEREZ. Diffrraction patterns and zone plates produced by thin linear axicons[J]. Optica Acta, 1986, 33(9), 1161-1176.
[17]管泽霖,宁津生.地球重力场在工程测量中的应用[M],第一版,武汉:测绘出版社,1990.165-201
[18]周莉萍,赵斌,李柱.圆锥透镜加工误差对光束传输变换的影响[J].华中科技大学学报,2001,29(3):61-63
[19]赵斌,李柱.无衍射光路中axicon透镜倾斜允差的计算[J].华中理工大学学报,1997,25(10):10-12
[20]郭俊义.地球物理学基础[M].第一版.北京:地震出版社,2001.247-249
[21]傅承义.陈运泰.祁贵仲.地球物理学基础[M].第一版.北京:科学出版社,1985.10-25
[22]肖峻.高精度垂直摆倾斜仪及其应用研究[D],武汉:中国科学院测量与地球物理研究所,2002
[23] E.C.Di Mauro.L S Karatzas .M J Usher.Optical tiltmeter[J]. Meas. Sci. Technol (UK).1991.2.346-351
[24] Doodson A T.The harmonic development of the tide generating potential[J]. International Hydrographic Revue. Monaco 1954, 31(1):37-61
[25] Harrison, J. C. Earth tides[M],New York :Van Nostrand Reinhold Co.,c1985. 150-176
[26]方俊.固体潮[M].第一版.北京:科学出版社,1984:1-118
[27]毛惠琴.固体潮水平分量理论值的计算[J].测量与地球物理集刊,1981(3):64-71
[28]中国科学院地质研究所计算组.固体潮理论值计算及其应用[J].地质科学,1974(3):246-268
[29]王庆宾,黄广平,徐朋.固体潮引潮位的计算机演绎展开[J],测绘学院学报2003,20(2):83-86
[30] Mays, J. Microcomputer tide prediction [J] .IEEE: Science-Engineering-Adventure, 1986,2: 373-378
[31]万永革,黄猛.固体潮汐理论值算法在VB 6. 0中的应用与实现[J].地震地磁观测与研究,2006,Vol27(16):97-103
[32] Hass R, Schuh H. Determination of frequency dependent Love and Shida numbers from VLBI data[J]. Geophys. Res. Lett,1996, 23(12): 1509-1512
[33]张捍卫,许厚泽,刘学谦.固体潮Love数的基本理论和数值结果[J].地球物理学进展,2004,19(2):372-378
[34] Pekeris, C.L.The bodily tide and the yielding of the Earth due to tidal loading [J], Geophysical Journal of the Royal Astronomical Society(UK),1978,52(3):471-478
[35] Accad, Y. Pekeris, C.L.Solution of the tidal equations for the M2 and S2 tides in the world oceans from a knowledge of the tidal potential alone[J] ,Philosophical Transactions of the Royal Society of London A (Mathematical and Physical Sciences) (UK) ,1978,290(1368):235-266
[36] Stavinschi, M.Souchay, J.Some correlations between earthquakes and earth tides[J] ,Acta Geodaetica et Geophysica Hungarica, 2003,38(1):77-92
[37] Arabelos, D.Comparison of Earth-tide parameters over a large latitude difference in Blackwell Science for R. Astron[J].Geophysical Journal International,2002,151(3) : 950-956
[38]李涛,贺勇军,刘志俭.Matlab工具箱应用指南——应用数学篇[M].第一版.北京:电子工业出版社,2000.250-277
[39]陈亚勇.MATLAB信号处理详解[M].第一版.北京:人民邮电出版社, 2001. 36-43.183-200
[40]潘晓辉,陈强.MATLAB全攻略宝典[M].第一版.北京:中国水利水电出版社2000.258-282
[41]张宜华.精通MATLAB5[M].第一版.北京:清华大学出版社, 1999. 51-54
[42]郭仕剑,王宝顺,贺志国等.MATLAB7.X数字信号处理[M].第一版.北京:人民邮电出版社,2006.29-50
[43]董长虹,高志,余啸海.Matlab小波分析工具箱原理与应用[M].第一版.北京:国防工业出版社,2004.209-212
[44]葛哲学,陈仲生.Matlab时频分析技术及其应用[M].第一版.北京:人民邮电出版社,2006.180-235
[2] GB/T 11336-2004.直线度误差检测[S].北京:中国国家标准化管理委员会, 2004
[3] ZHANG XINBAO, ZHAO BIN, LI ZHU. Measurement method of spatial straightness error using non-diffracting beam and moiré-fringe technology [J]. Opt. A: Pure Appl. Opt. 2004, 6(1):121–126
[4]张新宝.空间直线度误差无衍射光莫尔条纹测量方法的研究[D].武汉:华中科技大学,2002
[5]宁延平,刘战锋.国内外高精度直线度测量技术的研究现状[J].现代制造工程,2005,(6):82-84
[6]李钰.激光测量大尺寸物体直线度的新方法[J].中国激光,1985,12(6),365-368
[7]刘兴占,梁晋文,陈博一等.双光束补偿准直系统[J].计量技术.1999(1),12-15
[8]方仲彦,殷纯水,梁晋文.高精度激光准直技术的研究(一)[J].航空计测技术,1997, 17(1): 3-6
[9]章恩耀,张玉坤,李岩,方仲彦.双LD调制宽光束准直法[J].光学技术,1993. 2:71-73
[10] Zhang Xinbao, Zhao Bin , Li Zhu .Study of the tolerance of the non-diffracting beam to laser beam deflection[J]. J. Opt. A: Pure Appl. Opt. 4.2002 78–83
[11]匡萃方,冯其波,刘斌等.一种共路补偿激光漂移的直线度测量方法[J].光电工程,2005,32(4):32-35
[12] Akira ISHIDA. Apparatus for measuring straightness[P]. US Patent: 5333053.1994
[13] Michael Reid SOGARD. Lasers interferometer having a sheath for the laserbeam[P]. US Patent:5708505, 1998
[14]杨友堂,曾理江,殷纯永.自适应除噪技术在激光准直中的应用研究[J].仪器仪表学报,1995, Vol16(4): 370-374.
[15] BORN MAX, WOLF EMAIL. Principles of Optics[M]. New York: Pergamon, 1964:752-754
[16] M.V. PEREZ. Diffrraction patterns and zone plates produced by thin linear axicons[J]. Optica Acta, 1986, 33(9), 1161-1176.
[17]管泽霖,宁津生.地球重力场在工程测量中的应用[M],第一版,武汉:测绘出版社,1990.165-201
[18]周莉萍,赵斌,李柱.圆锥透镜加工误差对光束传输变换的影响[J].华中科技大学学报,2001,29(3):61-63
[19]赵斌,李柱.无衍射光路中axicon透镜倾斜允差的计算[J].华中理工大学学报,1997,25(10):10-12
[20]郭俊义.地球物理学基础[M].第一版.北京:地震出版社,2001.247-249
[21]傅承义.陈运泰.祁贵仲.地球物理学基础[M].第一版.北京:科学出版社,1985.10-25
[22]肖峻.高精度垂直摆倾斜仪及其应用研究[D],武汉:中国科学院测量与地球物理研究所,2002
[23] E.C.Di Mauro.L S Karatzas .M J Usher.Optical tiltmeter[J]. Meas. Sci. Technol (UK).1991.2.346-351
[24] Doodson A T.The harmonic development of the tide generating potential[J]. International Hydrographic Revue. Monaco 1954, 31(1):37-61
[25] Harrison, J. C. Earth tides[M],New York :Van Nostrand Reinhold Co.,c1985. 150-176
[26]方俊.固体潮[M].第一版.北京:科学出版社,1984:1-118
[27]毛惠琴.固体潮水平分量理论值的计算[J].测量与地球物理集刊,1981(3):64-71
[28]中国科学院地质研究所计算组.固体潮理论值计算及其应用[J].地质科学,1974(3):246-268
[29]王庆宾,黄广平,徐朋.固体潮引潮位的计算机演绎展开[J],测绘学院学报2003,20(2):83-86
[30] Mays, J. Microcomputer tide prediction [J] .IEEE: Science-Engineering-Adventure, 1986,2: 373-378
[31]万永革,黄猛.固体潮汐理论值算法在VB 6. 0中的应用与实现[J].地震地磁观测与研究,2006,Vol27(16):97-103
[32] Hass R, Schuh H. Determination of frequency dependent Love and Shida numbers from VLBI data[J]. Geophys. Res. Lett,1996, 23(12): 1509-1512
[33]张捍卫,许厚泽,刘学谦.固体潮Love数的基本理论和数值结果[J].地球物理学进展,2004,19(2):372-378
[34] Pekeris, C.L.The bodily tide and the yielding of the Earth due to tidal loading [J], Geophysical Journal of the Royal Astronomical Society(UK),1978,52(3):471-478
[35] Accad, Y. Pekeris, C.L.Solution of the tidal equations for the M2 and S2 tides in the world oceans from a knowledge of the tidal potential alone[J] ,Philosophical Transactions of the Royal Society of London A (Mathematical and Physical Sciences) (UK) ,1978,290(1368):235-266
[36] Stavinschi, M.Souchay, J.Some correlations between earthquakes and earth tides[J] ,Acta Geodaetica et Geophysica Hungarica, 2003,38(1):77-92
[37] Arabelos, D.Comparison of Earth-tide parameters over a large latitude difference in Blackwell Science for R. Astron[J].Geophysical Journal International,2002,151(3) : 950-956
[38]李涛,贺勇军,刘志俭.Matlab工具箱应用指南——应用数学篇[M].第一版.北京:电子工业出版社,2000.250-277
[39]陈亚勇.MATLAB信号处理详解[M].第一版.北京:人民邮电出版社, 2001. 36-43.183-200
[40]潘晓辉,陈强.MATLAB全攻略宝典[M].第一版.北京:中国水利水电出版社2000.258-282
[41]张宜华.精通MATLAB5[M].第一版.北京:清华大学出版社, 1999. 51-54
[42]郭仕剑,王宝顺,贺志国等.MATLAB7.X数字信号处理[M].第一版.北京:人民邮电出版社,2006.29-50
[43]董长虹,高志,余啸海.Matlab小波分析工具箱原理与应用[M].第一版.北京:国防工业出版社,2004.209-212
[44]葛哲学,陈仲生.Matlab时频分析技术及其应用[M].第一版.北京:人民邮电出版社,2006.180-235
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