【作者】 刘春香；

【导师】 程传福；

【作者基本信息】 山东师范大学 ， 光学， 2002， 硕士

【摘要】 对随机表面及其标定的研究在材料生长、工件加工和光学元件制造等科研技术的许多领域中有着重要的理论意义和应用价值。近场光学是研究距离物体表面一个波长以内(即近场区域)的光学现象的新型交叉学科，近场光学对传统的光学分辨极限产生了革命性的突破。本文对随机表面光散射及其标定和近场光学散射及近场散斑的一些特性进行了理论、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与测量标定方法、光散射的基本原理、随机光场的特性和近场光学的一些特性进行了综述。 第二章利用对称下降函数的傅利叶变换的半宽度与函数本身的半宽度成反比这一原理，得到了自仿射分形表面的散射轮廓半宽度在Ω的整个取值区域中的一般表达式。通过对自仿射分形随机表面光散射的计算模拟，得到在不同入射角下的散射轮廓，并由数学上的对称下降函数拟合，得到轮廓函数的半宽度及其随入射光波矢量的变化关系。利用这些关系和改变入射角的光学散射测量可以从实验测得的轮廓中提取随机表面的横向相关长度ζ和粗糙指数α。 第三章利用随机表面的高斯相关模型和统计光学原理，得出了弱散射体在4f成象系统中象面上的散斑对比度的表达式，提出了一种可以同时无预定标地测量高斯相关的随机表面粗糙度w和横向相关长度ζ的散斑对比度方法。实验中，测量出象面散斑对比度随滤波孔径的半径的变化。用理论结果对实验测得的关系曲线进行拟合，从而得到两个表面参量，此方法所得结果与AFM测得的结果吻合的比较好。 第四章提出了由格林函数法和边界条件来计算模拟随机表面产生的近场随机光场的方法，并将这一方法应用于对小孔衍射计算和近场光散斑场特性的研究。在小孔衍射中，得出了衍射光场在亚波长尺度范围内随着离开表面距离的增加按负指数衰减 摘要生的近场散斑场，得出近场散斑的许多特性，并模拟了离开表面不同距离处的近场散斑场的传播过程，即随机光场由近场散斑向正常散斑的演化过程，发现了近场散斑不同于远场散斑的一些现象，并对近场散斑场的这些特性和现象给出了定性的解释。更多还原

【Abstract】 The random surfaces are of great importance in many science and technology fields such as the growth of thin films, the fine machining, the manufacture of optical devices, and etc. Near-field optics is a new interdisciplinary subject which studies the optical phenomena within one wavelength, and it breaks free from the limitation of conventional optical resolution. This paper is concentrated on theoretical, experimental and simulational studies on the measurement of random surface and the properties of near-field light scattering and its speckle field. The whole paper is divided into four chapters.Chapter 1 gives a summary and review of the description of random surfaces and its measurements, the fundamental theories of light scattering, the statistical properties of random light fields and near-field optics.In chapter 2, Based on the principle that the half-width of the Fourier transform of a symmetrical decay function is inversely proportional to the half-width of the function itself, we derive the generic expression for the half-width of the intensity profiles scattered from the self-affine fractal random surfaces. The intensity profiles are obtained at different angles of incidence by simulating light scattering from random surfaces, and by fitting these simulated profiles with a symmetrical decay function we obtain the variation of the half-width of the corresponding profiles versus the wave vector. Based on this variation and metrical results of light scattering, the lateral correlation length ? and the roughness exponent a of a random surface sample can be extracted synchronously.Chapter 3 gives a method of image speckle contrast for the non-precalibration measurement of the root-mean-square roughness and the lateral correlation length of random surfaces with Gaussian correlation. Based on the Gaussian correlation model of random surfaces and the fundamental theories of statistical optics, we obtain the expression of image speckle contrast in the 4 / optical filtering system. In the experiment, we measureexperimentally measured curve with the derived theoretical expression we can extract simultaneously the two surface parameters. The results obtained by this method conform well to the results measured with AFM.Chapter 4 proposes a method with Green functions for the simulational generation of light scattering from random surface with arbitrary parameters, and applies this method to pinhole diffraction and near-field light scattering and speckle field. In pinhole diffraction, we obtain the law that the diffracted intensity attenuates with the distance increasing from the surface according to the negative exponent decay within sub-wavelength range. We simulate light scattering from 16 self-affine fractal surface samples with different surface parameters and different length, and then study in detail the properties of scattered intensities and the near-field speckle patterns. We also simulate the transmission of light scattering with different distance from the surface, namely the evolution of the speckle patterns from near field to far field, and discover some phenomena in near-field speckles which differ from those of the well-understood far-field speckles. Some qualitative explanations are given for the analysis of these properties and phenomena.更多还原