随机表面的散斑标定法与近场散斑特性的研究
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摘要
粗糙随机表面统计特性的研究是一个多年来倍受关注的问题，这一问题在如动力学的材料生长界面，由大的冲击而产生的断裂面，光学元件设计等诸多物理领域具有重要的意义。近年来，随着近场光学显微镜的快速发展，对近场光学的研究无论在理论上还是在实验上都获得了相当大的进展，但对近场散斑特性的研究还处于探索阶段。本文对随机表面，光散射轮廓特性，近场光学和近场散斑的特性及表面的标定进行了理论、实验和计算模拟的研究。全文共分四章。
第一章对随机表面的描述和标定方法、光散射轮廓特性及其重要性、近场光学和近场散射的意义和近场散斑的特性进行了综述。
第二章提出了由像面散斑平均光强提取随机表面高度—高度相关函数的方法。在理论分析和实验测量中，我们采用了变孔径的傅立叶变换和成像系统，由所得到的像面光强的解析式，建立了将平均光强随孔径的数值变化关系转化为正逆傅立叶变换对，从而恢复出表面的高度—高度相关函数。我们以对三个高斯相关的随机表面样品的实验测量为例，对该方法行了验证。所测得的结果与用原子力显微镜测量的结果符合得很好。
第三章根据基尔霍夫近似下的光散射理论，提出了从随机表面附近衍射区内的散斑场相关函数中提取随机表面参量的方法。我们首先得出了散斑相关函数的定量表达式，该式表明散斑相关函数实际上是在Van Cittert-Zernike定理中等效地将散射轮廓函数反演到散射体平面内作为散射孔径函数的结果。采用最小方差拟合的方法，将散斑相关函数的测量结果与所得到的表达式进行拟合，可以提取出随机表面参量。我们通过模拟实验，并以自仿射分形随机表面附近散斑光强的相关函数进行数值计算为例，对该理论和方法进行了验证。所得到三个表面参量粗糙度w，横向相关长度ξ和粗糙度指数α的值与所设定的值符合得较好。
在第四章中，我们提出了近场散斑的概念，并依据介质界面电磁波的格林积分
摘要
方程对自仿射分形随机表面产生的散斑光场进行了数值计算模拟研究，发现近场散斑
分形特征与自仿射分形随机表面的特性有关，且这种分形特征在非近场区域消失。同
时研究了散斑特性及其对比度随表面参数及离开介质表面的距离的演化。通过把电磁
场的积分方程和传统衍射理论中点扩展函数的类比，我们对近场散斑特性给出了初步
的定性解释。
Great attention has been paid on the study of random surfaces in many scientific and technological fields such as the growth fronts of thin films, surfaces of fabricated optical devices, and the fractured cross-section of materials, etc.. With the rapid development of near-field optical microscopy in recent years, considerable advancement has been achieved theoretically and experimentally in the studies of near-field optics. This dissertation is concentrated on theoretical, experimental and simulational studies on the characterizations of random surface by speckle methods and the properties of speckles in near-field. The whole dissertation is divided into four chapters.
In chaper 1, we give a summary and an overall review for the descriptions and measurements of random surfaces , the light scattering theory and its applications in the characterization of random surfaces, and the near-field optics and the near-field speckles.
In chaper 2, we present a method for the extraction of the height-height correlation function of random rough surfaces from the data of average intensity of image speckles. Based on the theoretical expression of the average intensity in the Fourier transforming and imaging optical system with variable aperture, an algorithm is developed to change the intensity data versus the aperture radius into the Bessel-Fourier-transform-and-the-inversion of a function of the height-height correlation function. Three samples of Gaussian correlation are used for the experimental demonstration. The extracted height-height correlation function and the random surface parameters obtained ever since conform with those obtained by the measurement of AFM
In chaper 3, based on the light scattering theory of Kirchoff approximation, we propose the method for the extraction of surfaces parameters from the correlation functions
of speckles intensity produced by light scattering in the region near the random surfaces. The quantitative expression for speckle correlation function is formulated, in which the scattered intensity profile reciprocated on the surface plane acts as the aperture function in Van Cittert-Zernike theorem. By least-squares fit of the measured data of speckle correlation function to the obtained quantitative expression, parameters of random surfaces can be extracted. The theory and the method are validated by the simulational experiments, in which the scattering from random self-affme fractal surface are simulated and the speckle intensity correlation function are calculated. The extracted values of 3 surface parameters i.e., the roughness w, lateral correlation length ξ, and roughness
exponent a are in good accordance with the set values.
Chaper 4, we put forward the concept of the near-field speckles and study their properties by the numerical solution of the integral equation based on the Green's theorem. We study the near-field speckles produced the by random self-affine fractal surfaces of dielectric medium. The speckle intensities evolve considerably in the near-field region and the local fluctuations in them disappear in the distance of a wavelength. The transition of the speckle contrast either on the surface or in the near-field and the neighborhood non-near-field regions depends on lateral correlation length ξ and the roughness
exponent a of the random surfaces. Preliminary qualitative explanations are given to the computation results based on the analogy of the integral equation to the point spread function in the conventional diffraction theory.
第一章对随机表面的描述和标定方法、光散射轮廓特性及其重要性、近场光学和近场散射的意义和近场散斑的特性进行了综述。
第二章提出了由像面散斑平均光强提取随机表面高度—高度相关函数的方法。在理论分析和实验测量中，我们采用了变孔径的傅立叶变换和成像系统，由所得到的像面光强的解析式，建立了将平均光强随孔径的数值变化关系转化为正逆傅立叶变换对，从而恢复出表面的高度—高度相关函数。我们以对三个高斯相关的随机表面样品的实验测量为例，对该方法行了验证。所测得的结果与用原子力显微镜测量的结果符合得很好。
第三章根据基尔霍夫近似下的光散射理论，提出了从随机表面附近衍射区内的散斑场相关函数中提取随机表面参量的方法。我们首先得出了散斑相关函数的定量表达式，该式表明散斑相关函数实际上是在Van Cittert-Zernike定理中等效地将散射轮廓函数反演到散射体平面内作为散射孔径函数的结果。采用最小方差拟合的方法，将散斑相关函数的测量结果与所得到的表达式进行拟合，可以提取出随机表面参量。我们通过模拟实验，并以自仿射分形随机表面附近散斑光强的相关函数进行数值计算为例，对该理论和方法进行了验证。所得到三个表面参量粗糙度w，横向相关长度ξ和粗糙度指数α的值与所设定的值符合得较好。
在第四章中，我们提出了近场散斑的概念，并依据介质界面电磁波的格林积分
摘要
方程对自仿射分形随机表面产生的散斑光场进行了数值计算模拟研究，发现近场散斑
分形特征与自仿射分形随机表面的特性有关，且这种分形特征在非近场区域消失。同
时研究了散斑特性及其对比度随表面参数及离开介质表面的距离的演化。通过把电磁
场的积分方程和传统衍射理论中点扩展函数的类比，我们对近场散斑特性给出了初步
的定性解释。
Great attention has been paid on the study of random surfaces in many scientific and technological fields such as the growth fronts of thin films, surfaces of fabricated optical devices, and the fractured cross-section of materials, etc.. With the rapid development of near-field optical microscopy in recent years, considerable advancement has been achieved theoretically and experimentally in the studies of near-field optics. This dissertation is concentrated on theoretical, experimental and simulational studies on the characterizations of random surface by speckle methods and the properties of speckles in near-field. The whole dissertation is divided into four chapters.
In chaper 1, we give a summary and an overall review for the descriptions and measurements of random surfaces , the light scattering theory and its applications in the characterization of random surfaces, and the near-field optics and the near-field speckles.
In chaper 2, we present a method for the extraction of the height-height correlation function of random rough surfaces from the data of average intensity of image speckles. Based on the theoretical expression of the average intensity in the Fourier transforming and imaging optical system with variable aperture, an algorithm is developed to change the intensity data versus the aperture radius into the Bessel-Fourier-transform-and-the-inversion of a function of the height-height correlation function. Three samples of Gaussian correlation are used for the experimental demonstration. The extracted height-height correlation function and the random surface parameters obtained ever since conform with those obtained by the measurement of AFM
In chaper 3, based on the light scattering theory of Kirchoff approximation, we propose the method for the extraction of surfaces parameters from the correlation functions
of speckles intensity produced by light scattering in the region near the random surfaces. The quantitative expression for speckle correlation function is formulated, in which the scattered intensity profile reciprocated on the surface plane acts as the aperture function in Van Cittert-Zernike theorem. By least-squares fit of the measured data of speckle correlation function to the obtained quantitative expression, parameters of random surfaces can be extracted. The theory and the method are validated by the simulational experiments, in which the scattering from random self-affme fractal surface are simulated and the speckle intensity correlation function are calculated. The extracted values of 3 surface parameters i.e., the roughness w, lateral correlation length ξ, and roughness
exponent a are in good accordance with the set values.
Chaper 4, we put forward the concept of the near-field speckles and study their properties by the numerical solution of the integral equation based on the Green's theorem. We study the near-field speckles produced the by random self-affine fractal surfaces of dielectric medium. The speckle intensities evolve considerably in the near-field region and the local fluctuations in them disappear in the distance of a wavelength. The transition of the speckle contrast either on the surface or in the near-field and the neighborhood non-near-field regions depends on lateral correlation length ξ and the roughness
exponent a of the random surfaces. Preliminary qualitative explanations are given to the computation results based on the analogy of the integral equation to the point spread function in the conventional diffraction theory.
引文
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[3.1] P. Meakin, Fractal, Scaling and Growth Far From Equilibrium(Cambridge University press, Cambridge, 1998)
[3.2] J. M. López, Scaling Approach to Calculate Critical Exponents in Anomalous Surface Roughening Phys. Rev. Lett, 1999, 83:4594
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[3.4] F. Farsakolu, D M. Zengin and H. Kocabas, Grinding Process for Beveling and Lapping Operations in Lens Manufacturing , Appl. Opt, 2000, 39:1541
[3.5] Y.-P. Zhao, G. C. Wang and T.-H. Lu, Characterization of Amorphous and Crystalline Rough Surfaces: Principles and Applications ( Academic Press, New York, 2001 ).
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[3.8] C. F. Cheng, C. X. Liu, S. Y. Teng, N. Y. Zhang and M. Liu, Half-width of intensity profiles of light scattered from self-affine fractal random surfaces and simulational verifications,Phys. Rev E, 2002, 65:061104
[3.9] M. Giglio, M. Carpineti and A. Vailati, Space Intensity Correlations in the Near Field of the Scattered Light: A Direct Measurement of the Density Correlation Function g(r), Phys. Rev. Lett, 2000, 85:1416
[3.10] M. Giglio, M. Carpineti, A. Vailati and D. Brogioli, Near-field intensity correlations of scattered light, Appl. Opt, 2001, 40:4036
[3.11] D. Brogioli, A. Vailati and M. Giglio, Heterodyne near-field scattering, Appl. Phys. Lett, 2002, 81:4109
[3.12] D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, C. F. Cheng, Morphological analysis by atomic force microscopy and light scattering study for random scattering screens, Acta Physica Sinca, 2000, 49:1260
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