基于散射轮廓傅立叶变换各向异性随机表面参量的反演
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摘要
随机表面是自然界重要的组成部分,随机表面及其散射光场的研究在材料生长、精密加工和医学诊断等许多领域具有重要的基础研究意义和实际应用意义,由随机表面散射产生的随机光场不仅是研究表面的重要手段,而且是探索光场本身特性即统计光学的重要内容,因此随机表面的特性一直是备受关注的研究课题。自仿射分形表面是一种能够更精确描述各种实际表面的模型,这种模型能同时描述随机表面长程内的颗粒状结构和短程内的自相似性,成为近年来被广泛接受和采用的表面模型。自仿射分形表面模型主要由三个统计参量来描述,即方均根粗糙度w、横向相关长度ξ和粗糙指数α,其中α描述的是随机表面短程内的分形特征。
本文针对各向异性随机表面的散射光强分布的特点,根据光波衍射的基尔霍夫理论,计算出各向异性随机表面的光散射方位曲线,并用门积分平均的散射光强轮廓采集系统沿方位曲线测量了Si(100)晶片这一典型的各向异性随机表面的散射光场,采用傅立叶变换法,通过fortran编程计算,对光的散射轮廓进行傅立叶逆变换,从而同时得到自仿射分形表面的三个统计参量,并与经原子力显微镜测量随机表面高度计算所得到的参量相比较,验证了所得数据的正确性,说明傅立叶变换法可以正确确定各向异性随机表面。本文完成的主要工作概括如下:
第一章为绪论,论述了研究随机表面及其散射光场特性的意义和随机表面的主要测量方法。
第二章介绍了自仿射随机表面模型的光散射理论,探讨了自仿射分形随机表面的散射轮廓函数的近似计算,以及如何从光的散射轮廓中提取随机表面参量。
第三章为自仿射分形随机表面的光散射特性实验研究。以Si(100)晶片的粗糙背面作为反射式随机表面样品,分别用原子力显微镜和光散射方法测量了样品表面的统计参量。在光散射实验测量中,采用光电倍增管作为探测器,测量了在入射角为40°、45°、50°、55°、60°、65°、70°、75°、80°、83°和85°时样品表面的散射光强,由数学上的对称下降函数计算得到散射光强轮廓函数。
第四章利用傅立叶变换法对光的散射轮廓进行变换,从而同时得到自仿射分形表面的三个统计参量,还用原子力显微镜对实验测量中的表面样品进行了测量和分析,并且把光散射方法和原子力显微镜测量确定的样品表面统计参量的实验结果进行了比较,实验结果表明:本方法所获得的随机表面参量值与原子力显微镜的接触法测量所得到的随机表面参量值两者符合的很好。
第五章对全文进行了客观地总结,并对下一步有关随机表面的光散射研究工作进行了展望。
The random surfaces as important parts make up of nature and random surfaces as well as their scattering light measurements are of great importance in many scientific and technological fields such as material growth, precision machining and medicine diagnosis etc. The study of optical fields scattered from random surfaces is the main content of statistical optics, so many people have payed attention to studying about random surfaces for a long time. The surface model of the self-affine fractal is demonstrated to be more adequate for the comprehensive description of a wide category of random surfaces at present. Besides the traditional parameters of root-mean-square roughness w and correlation lengthξ, a new parameter of the roughness exponentαis introduced in this model to characterize the short-range fractal properties of the surfaces.
The paper calculate the curve of the scattered light and lay out a new way to measure scattered profiles according to Kirchhoff's diffration theory. We also measured the light intensity scattered from Si(100) wafer by The average technique with gated integration and then analyze the scattering profiles of light intensity quantificationally using self—affine fractal surface model and inverse Fourier transformation ,and determinate there parameters of anisotropy surface, compare with the data obtained from AFM and verify that parameters are correct. We can determine the anisotropic random surfaces using Fourier transformation. The main contents and results of this thesis can be summarized as follows.
Chapter 1 gives a summary and review of the description of random surfaces and its measurements.
In chapter 2 We introduce the theory of self—affine fractal surface model, discuss the approximate calculation of the scattering light intensity and how to attain the parameters of random surfaces.
In chapter3,We discuss the scattered light properties of self—affine fractal surface model. In the experiment to measure the light scattering from the reflection-mode random surface, we adopt the roughness backside of Si(110) wafer as the sample of self-affine fractal random surface. CCD detects the light intensities scattered from the sample surface at the incidence angles of the 40°, 45°, 50°, 55°, 60°, 65°, 70°, 75°, 80°, 83°and 85°. The scattering light intensity profiles at different incident angles are calculated by the symmetric decline function in mathematics.
In chapter4,the scattering profiles of light intensity quantificationaly using self—affine fractal surface model and inverse Fourier transformation and parameters of anisotropy surface are determined. Comparing with the data obtained from AFM, We verify that parameters are correct.
In chapter 5,we give the summary of this paper and put forward the further goal.
本文针对各向异性随机表面的散射光强分布的特点,根据光波衍射的基尔霍夫理论,计算出各向异性随机表面的光散射方位曲线,并用门积分平均的散射光强轮廓采集系统沿方位曲线测量了Si(100)晶片这一典型的各向异性随机表面的散射光场,采用傅立叶变换法,通过fortran编程计算,对光的散射轮廓进行傅立叶逆变换,从而同时得到自仿射分形表面的三个统计参量,并与经原子力显微镜测量随机表面高度计算所得到的参量相比较,验证了所得数据的正确性,说明傅立叶变换法可以正确确定各向异性随机表面。本文完成的主要工作概括如下:
第一章为绪论,论述了研究随机表面及其散射光场特性的意义和随机表面的主要测量方法。
第二章介绍了自仿射随机表面模型的光散射理论,探讨了自仿射分形随机表面的散射轮廓函数的近似计算,以及如何从光的散射轮廓中提取随机表面参量。
第三章为自仿射分形随机表面的光散射特性实验研究。以Si(100)晶片的粗糙背面作为反射式随机表面样品,分别用原子力显微镜和光散射方法测量了样品表面的统计参量。在光散射实验测量中,采用光电倍增管作为探测器,测量了在入射角为40°、45°、50°、55°、60°、65°、70°、75°、80°、83°和85°时样品表面的散射光强,由数学上的对称下降函数计算得到散射光强轮廓函数。
第四章利用傅立叶变换法对光的散射轮廓进行变换,从而同时得到自仿射分形表面的三个统计参量,还用原子力显微镜对实验测量中的表面样品进行了测量和分析,并且把光散射方法和原子力显微镜测量确定的样品表面统计参量的实验结果进行了比较,实验结果表明:本方法所获得的随机表面参量值与原子力显微镜的接触法测量所得到的随机表面参量值两者符合的很好。
第五章对全文进行了客观地总结,并对下一步有关随机表面的光散射研究工作进行了展望。
The random surfaces as important parts make up of nature and random surfaces as well as their scattering light measurements are of great importance in many scientific and technological fields such as material growth, precision machining and medicine diagnosis etc. The study of optical fields scattered from random surfaces is the main content of statistical optics, so many people have payed attention to studying about random surfaces for a long time. The surface model of the self-affine fractal is demonstrated to be more adequate for the comprehensive description of a wide category of random surfaces at present. Besides the traditional parameters of root-mean-square roughness w and correlation lengthξ, a new parameter of the roughness exponentαis introduced in this model to characterize the short-range fractal properties of the surfaces.
The paper calculate the curve of the scattered light and lay out a new way to measure scattered profiles according to Kirchhoff's diffration theory. We also measured the light intensity scattered from Si(100) wafer by The average technique with gated integration and then analyze the scattering profiles of light intensity quantificationally using self—affine fractal surface model and inverse Fourier transformation ,and determinate there parameters of anisotropy surface, compare with the data obtained from AFM and verify that parameters are correct. We can determine the anisotropic random surfaces using Fourier transformation. The main contents and results of this thesis can be summarized as follows.
Chapter 1 gives a summary and review of the description of random surfaces and its measurements.
In chapter 2 We introduce the theory of self—affine fractal surface model, discuss the approximate calculation of the scattering light intensity and how to attain the parameters of random surfaces.
In chapter3,We discuss the scattered light properties of self—affine fractal surface model. In the experiment to measure the light scattering from the reflection-mode random surface, we adopt the roughness backside of Si(110) wafer as the sample of self-affine fractal random surface. CCD detects the light intensities scattered from the sample surface at the incidence angles of the 40°, 45°, 50°, 55°, 60°, 65°, 70°, 75°, 80°, 83°and 85°. The scattering light intensity profiles at different incident angles are calculated by the symmetric decline function in mathematics.
In chapter4,the scattering profiles of light intensity quantificationaly using self—affine fractal surface model and inverse Fourier transformation and parameters of anisotropy surface are determined. Comparing with the data obtained from AFM, We verify that parameters are correct.
In chapter 5,we give the summary of this paper and put forward the further goal.
引文
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[2] Minghui Hu, Suguru Noda, and Hiroshi Komiyama, Amorphous-to-crystalline transition during the early stages of thin film growth of Cr on SiO2, J. Appl. Phy., 2003, 93(11): 9336-9344.
[3] German Drazer and Joel Koplik, Permeability of self-affine rough fractures, Phys. Rev. E, 2000, 62(6): 8076-8085.
[4] Arjen Amelink, Henricus J. C. M. Sterenborg, Martin P. L. Bard and Sjaak A. Burgers, In vivo measurement of the local optical properties of tissue by use of differential path-length spectroscopy, Opt. Lett., 2004, 29(10): 1087-1089.
[5]王运华,郭立新,吴振森,改进的二维分形模型在海面电磁散射中的应用,物理学报,2006, 55(10): 5191-5199.
[6] Jin-Yuan Liu, Chen-Fen Huang and Ping-Chang Hsueh, Acoustic plane-wave scattering from a rough surface over a random fluid medium, Ocean Engineering, 2002, 29(8): 915-930.
[7] Kouveliotis N. K., Trakadas P. T., Stefanogiannis A. I., Capsalis C. N., Field prediction describing scattering by a one-dimensional smooth random rough surface, Electromagnetics, 2002, 22(1): 27-35.
[8] A. Khenchaf, Bistatic reflection of electromagnetic waves from random rough surfaces: Application to the sea surface and snowy-covered, Eur. Phys. J. AP, 2001, 14(1): 45-62.
[9] JoséRicardo Arias-González, Manuel Nieto-Vesperinas, and Alberto Madrazo, Morphology-dependent resonances in the scattering of electromagnetic waves from an object buried beneath a plane or a random rough surfaces, J. Opt. Soc. Am. A., 1999, 16(12): 2928-2934.
[10] Raúl García-Llamas and César Márquez-Beltran, Scattering of s-polarized electromagnetic plane waves from a film with a shallow random rough surfaces on a perfect conductor, Appl. Opt. 2000, 39(25): 4698-4705.
[11] Mady Elias and Michel Menu, Experimental characterization of a random metallic rough surfaces by spectrophotometric measurements in the visible range, Opt. Communications, 2000,
[12] Yiping Zhao, Gwo-Ching Wang, and Toh-Ming Lu, Characterization of Amorphous and Crystalline Rough Surface: Principles and Applications, London: Academic Press, 2001.
[13] Chuanfu Cheng, Deli Liu, Dongping Qi, Light scattering microscopy of surface and its computational simulation, Chinese Physics Letters, 1999, 16(6): 397-399.
[14] D. J. Whitehouse, J. F. Archard, The properties of random surfaces of significance in their contact. Proc. Roy. Soc., 1970, A316(1524): 97-121.
[15] M. L. Boyd, R. L. Deavenport, Forward and specular scattering from a rough surface: theory and experiment, J. Acoust. Soc. Am., 1993, 53(5): 791-801.
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