低频液体表面波激光的干涉和衍射研究
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摘要
与液体体相相比，液体表面具有特殊的性质。对于液体表面特性的研究，已经引起了人们广泛的关注。本文运用光学手段，主要研究液体表面低频波动特性。具体内容包括：针对几十赫兹液体表面波，发现了表面波对光的干涉效应，建立了干涉光强分布与液体表面波的关系。利用这种干涉效应，研究液体表面张力、振幅、波长、表面波的衰减等物理特性：其次针对几百赫兹的低频液体表面波，发现了表面波对光的衍射效应，建立了衍射光强分布与表面波的关系。并研究在几百赫兹下的低频液体表面波的衰减问题。通过研究，本文得到以下的实验现象和结论：
1 当频率为几十赫兹时，首次发现了液体表面波对其入射光产生干涉效应，并在实验上获得了清晰的调制干涉图样。基于这一发现，提出了一种适应测量低频表面声波特性及表面张力的实用方法。相对于较为成熟的高频条件下的声光衍射技术和低频条件下的激光扫描技术而言，频率为几十赫兹的低频表面波，上述两种方法均不适应。而本文所提出的基于表面波干涉技术的测量方法填补了这一波段的空白。
2 针对表面波对光的干涉效应，根据波动光学原理，理论上得到低频液体表面波的波长，振幅等特性参数与干涉图样分布的解析关系。根据CCD所采集的干涉图样的实验数据，通过对表面波的波长，振幅等特性参数与干涉图样分布的解析关系编程，实现了表面波参数的自动化测量。
3 本文还研究了低频表面波的衰减特性。实验上改变入射光点与表面波振源之间的距离，同时检测相应位置上干涉图样中相临亮纹的间距和干涉图样的范围。理论上推导出表面波的振幅与条纹间距和条纹区间的关系，通过计算机编程处理实验数据，得到表面波振幅随波传播距离的变化曲线，拟合数据得到几十赫兹频率下的表面波的衰减系数。
4 当液体表面波频率为几百赫兹时，观察到了表面波对入射光的衍射效应，并根据这一效应对表面波进行测量。实验上得到了中间亮，两边暗的高反衬度衍射条纹。当移动振源改变入射点与振源之间的距离时，发现衍射图样中一级衍射条纹消失。再移动振源改变入射点与振源之间的距离，还发现衍射图样中零级衍射条纹消失，这意味着此时的衍射效率接近100％。用一级条纹缺级时零级条纹的光
强度来标定出所对应的表面波振幅值，根据贝塞尔函数中振幅与强度的变化关
系，得到表面波振幅与传播距离的变化曲线，拟合数据得到几百赫兹频率下液体
表面波的衰减系数。
本文基于低频液体表面波的干涉和衍射效应，结合现代光电检测技术和计算
机技术，建立了液体表面参数的测量理论和测量技术，实时地测量了液体的表面
张力、衰减系数、振幅、波长等低频液体表面的参数。
Optical method is an important technique to detect the substance properties. Of course, this method is a good choice for the surface research as well. When the optical effects, including interference and diffraction, occuring on the liquid surface, many fantastic phenomena will emerge,which may be used to measure some parameters of liquid, such as surface tension, SAW wavelength, amplitude, and so on. Therefore, optical methods have been adopted extensively in many fields.
In this thesis, we studied liquid surface using optical methods: When a capillary wave propagating along the air-liquid interface, a grating will form on the surface under certain condition. When a collimated-beam illuminated upon the liquid surface, interference or diffraction patterns may be observed. Based on the relationship between the distrib- ution of intensity and the surface wave, we can study the liquid properties.
In our research, the major phenomena and conclusions were obtained as follows:
1 For the SAWs at the region of a few tens Hertz, neither diffraction technique nor the laser scanning slope method is suitable since the scan- ning laser beam neither illuminates a part of the acoustical wavelength (geometrical optics case), nor illuminates many wavelengths (pure diffraction case). Thus, few techniques are available for SAW at these frequencies. A practicable method for liquid-surface acoustic-wave at the frequencies of a few tens Hertz, based on the combination of optical interference and scanning wave slope, has been developed.
2 High visibility stationary interference fringes and two extremely bright spots at the edges in the reflection field were experimentally observed. The SAW characteristics of wavelength and amplitude are obtained directly from the measured divergence angle and angular separation of the interference fringes. And we have derived the expression of the light intensity.
3 Light interference method is used to determine the attenuation coefficient of the tens hertz Liquid Surface Acoustic Wave in real time.
4 The high visibility diffraction patterns were observed experimentally in the case of the hundreds hertz Liquid Surface Acoustic Wave. Furthermore, the disappearance of zero-order diffraction was obtained, which was corresponding to the 100% diffraction efficiency. We can use Bessel function to calculate attenuation coefficient.
1 当频率为几十赫兹时，首次发现了液体表面波对其入射光产生干涉效应，并在实验上获得了清晰的调制干涉图样。基于这一发现，提出了一种适应测量低频表面声波特性及表面张力的实用方法。相对于较为成熟的高频条件下的声光衍射技术和低频条件下的激光扫描技术而言，频率为几十赫兹的低频表面波，上述两种方法均不适应。而本文所提出的基于表面波干涉技术的测量方法填补了这一波段的空白。
2 针对表面波对光的干涉效应，根据波动光学原理，理论上得到低频液体表面波的波长，振幅等特性参数与干涉图样分布的解析关系。根据CCD所采集的干涉图样的实验数据，通过对表面波的波长，振幅等特性参数与干涉图样分布的解析关系编程，实现了表面波参数的自动化测量。
3 本文还研究了低频表面波的衰减特性。实验上改变入射光点与表面波振源之间的距离，同时检测相应位置上干涉图样中相临亮纹的间距和干涉图样的范围。理论上推导出表面波的振幅与条纹间距和条纹区间的关系，通过计算机编程处理实验数据，得到表面波振幅随波传播距离的变化曲线，拟合数据得到几十赫兹频率下的表面波的衰减系数。
4 当液体表面波频率为几百赫兹时，观察到了表面波对入射光的衍射效应，并根据这一效应对表面波进行测量。实验上得到了中间亮，两边暗的高反衬度衍射条纹。当移动振源改变入射点与振源之间的距离时，发现衍射图样中一级衍射条纹消失。再移动振源改变入射点与振源之间的距离，还发现衍射图样中零级衍射条纹消失，这意味着此时的衍射效率接近100％。用一级条纹缺级时零级条纹的光
强度来标定出所对应的表面波振幅值，根据贝塞尔函数中振幅与强度的变化关
系，得到表面波振幅与传播距离的变化曲线，拟合数据得到几百赫兹频率下液体
表面波的衰减系数。
本文基于低频液体表面波的干涉和衍射效应，结合现代光电检测技术和计算
机技术，建立了液体表面参数的测量理论和测量技术，实时地测量了液体的表面
张力、衰减系数、振幅、波长等低频液体表面的参数。
Optical method is an important technique to detect the substance properties. Of course, this method is a good choice for the surface research as well. When the optical effects, including interference and diffraction, occuring on the liquid surface, many fantastic phenomena will emerge,which may be used to measure some parameters of liquid, such as surface tension, SAW wavelength, amplitude, and so on. Therefore, optical methods have been adopted extensively in many fields.
In this thesis, we studied liquid surface using optical methods: When a capillary wave propagating along the air-liquid interface, a grating will form on the surface under certain condition. When a collimated-beam illuminated upon the liquid surface, interference or diffraction patterns may be observed. Based on the relationship between the distrib- ution of intensity and the surface wave, we can study the liquid properties.
In our research, the major phenomena and conclusions were obtained as follows:
1 For the SAWs at the region of a few tens Hertz, neither diffraction technique nor the laser scanning slope method is suitable since the scan- ning laser beam neither illuminates a part of the acoustical wavelength (geometrical optics case), nor illuminates many wavelengths (pure diffraction case). Thus, few techniques are available for SAW at these frequencies. A practicable method for liquid-surface acoustic-wave at the frequencies of a few tens Hertz, based on the combination of optical interference and scanning wave slope, has been developed.
2 High visibility stationary interference fringes and two extremely bright spots at the edges in the reflection field were experimentally observed. The SAW characteristics of wavelength and amplitude are obtained directly from the measured divergence angle and angular separation of the interference fringes. And we have derived the expression of the light intensity.
3 Light interference method is used to determine the attenuation coefficient of the tens hertz Liquid Surface Acoustic Wave in real time.
4 The high visibility diffraction patterns were observed experimentally in the case of the hundreds hertz Liquid Surface Acoustic Wave. Furthermore, the disappearance of zero-order diffraction was obtained, which was corresponding to the 100% diffraction efficiency. We can use Bessel function to calculate attenuation coefficient.
引文
[1] 陆家和，陈长彦，《表面分析技术》，电子工业出版社，1988
[2] A．W．亚当森，《物理化学教程》，高等教育出版社，1981
[3] Q. Li, M. Zhao, S. Tang, S. Sun, and J. Wu, Two-dimensional scanning laser slope gauge: measurements of ocean-ripple structures, Appl. Opt., 1993, 32, 4590-4597.
[4] D.S.W. Kwoh, B.M. Lake, A deterministic, coherent, and dual-polarized laboratory study of microwave backscattering from water waves, part Ⅰ: short gravity waves without wind, IEEE J. Oceanic Eng., 1984, OE-9,291-308.
[5] 苗润才，杨宗立，液体表面波物理特性及其光学效应的研究，物理学报，1996，45(9)，1521-1525．
[6] R.C. Miao,Z.L. Yang, J.T. Zhu and C.Y. Shen, Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction, Appl. Phys. Lett., 2002, 80(17).
[7] 苗润才，杨宗立，局域弯曲液体表面反射光的黑洞效应，光子学报，1995，24(Z4)，18-21．
[8] R.C. Miao, G. Xu, The distribution variation of reflection light field of the local curve surface, SPIE, 1999,3862, 68-69.
[9] 苗润才，朱京涛，杨宗立 液体表面的遮光效应及其应用，光子学报，2002，31(4)．
[10] 杨永正，液体表面波光栅的研究，光学学报，1990，10(2)，183-186
[11] 苗润才，徐光，吕且妮The distribution variation of reflection light field of the local curve surface. SPIE, 1999,3862,68-69
[12] J.D. Barter, P.H.Y. Lee, Real-time wave-amplitude spectrum analyzer for air liquid interfaces, Appl. Phys. Lett., 1994, 64, 1896-1898.
[13] J.D. Barter, P. H.Y. Lee, Imaging surface-wave analyzer for liquid surfaces, Appl. Opt., 1997, 36(12), 2630-2635.
[14] A.R, Korpel A, and P.Desmares,An instrument for making surface waves visible, IEEE Trans. Sonics Ultron,1968,SU-15,157-161.
[15] A.Korpel, L.J.Laub, and H.C.Sievering, Measurement of acoustic surface wave propagation characteristics by reflected light, Appl. Phys. Lett, 1967,10,295-298
[16] K.Yamanaka and H.Cho, Precise velocity measurement of surface acoustic waves on bearing ball, Appl.Phys.Lett,2000,76(19),2797-2799
[17] D. A. Larson, T.D. Black, and M.Green, Optical modulation by a traveling surface acoustic wave and a holographic reference grating. J. Opt. Soc. Am. A.1990, 7, 1745-1750
[18] Devolder S, Wevers M, DeMeester D, Thin layer thinkness measurements based on the acaustic-optic technique, Appl. Phys.Lett,1996, 68(12): 1732-1734.
[19] Brier R, Leroy O, Surface roughness determination using the acoustic -optic technique: theory and experiment Appl.Phys.Lett. ,1997,75(5) : 599-601.
[20] Lee PHY, Barter J D, Beach K L, Hindman C L, Resent advance in ocean-surface characterization by a scanning-laser slope gauge, in Optics of the Air-Sea Interface: Theory and Measurement, L. Estep , ed., Proc. SPIE , 1992 ,1749: 234-224.
[21] B.D. Duncan, Visualization of surface acoustic waves by means of synchronous amplitude-modulated illumination, Appl. Opt., 2000,39(17), 2888-2895.
[22] G. Weisbuch, F. Garbay, Light scattering by surface tension waves, Am. J. Phys., 1979, 47, 355.
[23] J.D.Barter "A capacitive antenna for measurement of the dispersion relation of capillary waves on water" Rev.Sic.Instrum.64,556-560(1993)
[24] J. D. Barter, K. L. Beach, and P. H. Y. Lee "Collocated and simultaneous measurement of surface slope and amplitude of water waves" Rev. Sci. Instrum.64,2661-2665 1993
[25] O. H. Shemdin and H. M. Tran, "Measuring short surface waves with stereophotgraphy," Photogramm.Eng.Remote Sens.58,311-316(1992)
[26] P.H.Y.Lee ,J.D.Barter,K.L.Beach, "X-band microwave backscattering from ocean waves," J.Geophys.Res. 100,2591-2611 (1995)
[27] G Weisbuch, Light scattering by surface tension wave. Am J Phys 1979,355-356
[28] 吴崇试，《数学物理方法》，北京大学出版社，1999，407．
[29] 林敏，黄建军，光栅衍射表面张力系数测试系统，计量与测试技术，2000，No．4，9．
[30] JJ朗道 E．M．栗弗席茨 《流体力学》 高等教育出版社 1978
[31] J．F．Douglas J．M．Gasiorek J．A．Swaffield，《流体力学》，高等教育出版社，1979
[32] M. Born and E. Wolf, Principles of Optics, Sixth edition, 1980
[33] Lighthill MJ, WAVES IN FLUIDS, 1978
[34] J.W. Goodman, Introduction to Fourier Optics, McGraw-Hill, 1968
[35] R. C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998
[36] 张智星《Matlab程序设计与应用》 清华大学出版社 2002
[37] 陈怀琛《MATLAB及其在理工课程的应用指南》 西安电子科技大学，2000
[38] 李兰友，庄国俞，秦卫光，《Visual Basic绘图与图像处理》，人民邮电出版社，1999
[39] 肖莜南 赵来军 党林立 《现代数值计算方法》 北京大学出版社 2003
[40] 张开明，顾昌鑫，《计算物理学》，复旦大学出版社，1987
[41] 施吉林，刘淑珍，陈桂芝，《计算机数值方法》，高等教育出版社，1999
[42] 周世勋，《量子力学》，高等教育出版社，1979
[43] F．S．克劳福德，《波动学》(下册)，科学出版社，1981
[44] 姚启均，《光学教程》，高等教育出版社，1989
[2] A．W．亚当森，《物理化学教程》，高等教育出版社，1981
[3] Q. Li, M. Zhao, S. Tang, S. Sun, and J. Wu, Two-dimensional scanning laser slope gauge: measurements of ocean-ripple structures, Appl. Opt., 1993, 32, 4590-4597.
[4] D.S.W. Kwoh, B.M. Lake, A deterministic, coherent, and dual-polarized laboratory study of microwave backscattering from water waves, part Ⅰ: short gravity waves without wind, IEEE J. Oceanic Eng., 1984, OE-9,291-308.
[5] 苗润才，杨宗立，液体表面波物理特性及其光学效应的研究，物理学报，1996，45(9)，1521-1525．
[6] R.C. Miao,Z.L. Yang, J.T. Zhu and C.Y. Shen, Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction, Appl. Phys. Lett., 2002, 80(17).
[7] 苗润才，杨宗立，局域弯曲液体表面反射光的黑洞效应，光子学报，1995，24(Z4)，18-21．
[8] R.C. Miao, G. Xu, The distribution variation of reflection light field of the local curve surface, SPIE, 1999,3862, 68-69.
[9] 苗润才，朱京涛，杨宗立 液体表面的遮光效应及其应用，光子学报，2002，31(4)．
[10] 杨永正，液体表面波光栅的研究，光学学报，1990，10(2)，183-186
[11] 苗润才，徐光，吕且妮The distribution variation of reflection light field of the local curve surface. SPIE, 1999,3862,68-69
[12] J.D. Barter, P.H.Y. Lee, Real-time wave-amplitude spectrum analyzer for air liquid interfaces, Appl. Phys. Lett., 1994, 64, 1896-1898.
[13] J.D. Barter, P. H.Y. Lee, Imaging surface-wave analyzer for liquid surfaces, Appl. Opt., 1997, 36(12), 2630-2635.
[14] A.R, Korpel A, and P.Desmares,An instrument for making surface waves visible, IEEE Trans. Sonics Ultron,1968,SU-15,157-161.
[15] A.Korpel, L.J.Laub, and H.C.Sievering, Measurement of acoustic surface wave propagation characteristics by reflected light, Appl. Phys. Lett, 1967,10,295-298
[16] K.Yamanaka and H.Cho, Precise velocity measurement of surface acoustic waves on bearing ball, Appl.Phys.Lett,2000,76(19),2797-2799
[17] D. A. Larson, T.D. Black, and M.Green, Optical modulation by a traveling surface acoustic wave and a holographic reference grating. J. Opt. Soc. Am. A.1990, 7, 1745-1750
[18] Devolder S, Wevers M, DeMeester D, Thin layer thinkness measurements based on the acaustic-optic technique, Appl. Phys.Lett,1996, 68(12): 1732-1734.
[19] Brier R, Leroy O, Surface roughness determination using the acoustic -optic technique: theory and experiment Appl.Phys.Lett. ,1997,75(5) : 599-601.
[20] Lee PHY, Barter J D, Beach K L, Hindman C L, Resent advance in ocean-surface characterization by a scanning-laser slope gauge, in Optics of the Air-Sea Interface: Theory and Measurement, L. Estep , ed., Proc. SPIE , 1992 ,1749: 234-224.
[21] B.D. Duncan, Visualization of surface acoustic waves by means of synchronous amplitude-modulated illumination, Appl. Opt., 2000,39(17), 2888-2895.
[22] G. Weisbuch, F. Garbay, Light scattering by surface tension waves, Am. J. Phys., 1979, 47, 355.
[23] J.D.Barter "A capacitive antenna for measurement of the dispersion relation of capillary waves on water" Rev.Sic.Instrum.64,556-560(1993)
[24] J. D. Barter, K. L. Beach, and P. H. Y. Lee "Collocated and simultaneous measurement of surface slope and amplitude of water waves" Rev. Sci. Instrum.64,2661-2665 1993
[25] O. H. Shemdin and H. M. Tran, "Measuring short surface waves with stereophotgraphy," Photogramm.Eng.Remote Sens.58,311-316(1992)
[26] P.H.Y.Lee ,J.D.Barter,K.L.Beach, "X-band microwave backscattering from ocean waves," J.Geophys.Res. 100,2591-2611 (1995)
[27] G Weisbuch, Light scattering by surface tension wave. Am J Phys 1979,355-356
[28] 吴崇试，《数学物理方法》，北京大学出版社，1999，407．
[29] 林敏，黄建军，光栅衍射表面张力系数测试系统，计量与测试技术，2000，No．4，9．
[30] JJ朗道 E．M．栗弗席茨 《流体力学》 高等教育出版社 1978
[31] J．F．Douglas J．M．Gasiorek J．A．Swaffield，《流体力学》，高等教育出版社，1979
[32] M. Born and E. Wolf, Principles of Optics, Sixth edition, 1980
[33] Lighthill MJ, WAVES IN FLUIDS, 1978
[34] J.W. Goodman, Introduction to Fourier Optics, McGraw-Hill, 1968
[35] R. C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998
[36] 张智星《Matlab程序设计与应用》 清华大学出版社 2002
[37] 陈怀琛《MATLAB及其在理工课程的应用指南》 西安电子科技大学，2000
[38] 李兰友，庄国俞，秦卫光，《Visual Basic绘图与图像处理》，人民邮电出版社，1999
[39] 肖莜南 赵来军 党林立 《现代数值计算方法》 北京大学出版社 2003
[40] 张开明，顾昌鑫，《计算物理学》，复旦大学出版社，1987
[41] 施吉林，刘淑珍，陈桂芝，《计算机数值方法》，高等教育出版社，1999
[42] 周世勋，《量子力学》，高等教育出版社，1979
[43] F．S．克劳福德，《波动学》(下册)，科学出版社，1981
[44] 姚启均，《光学教程》，高等教育出版社，1989