【作者】 李海霞；

【导师】 程传福；

【作者基本信息】 山东师范大学 ， 光学， 2012， 博士

【摘要】 长期以来随机表面的光学散射一直受到人们的关注。它被广泛应用在很多领域，例如遥感、雷达成像、声纳探测、工业非接触检测和生物医学诊断等领域。对随机表面光散射的研究，主要是随机表面的形貌特征和光散射强度分布之间的关系。目前的理论和模型已经可以解释绝大多数自然和人工表面的散射强度特征。在已知表面形貌特征的情况下，可以预测出散射强度分布；在已知散射强度的空间分布的情况下，可以比较表面的特征参量的大小。但是，在表述这两者关系的时候，无论是理论上还是实验中，大多数研究者都是从实空间的散射角和光强空间分布的关系来计算的。这种方法在表现形式上看起来很复杂，也不能建立表面和强度分布的确定关系。如果光波用波矢量来表示，在波矢空间研究随机表面的光散射特性，二者的关系式就变得相对简单了。本论文正是基于波矢空间的随机表面和散射强度的空间分布之间的对应关系，研究波矢空间的各向同性和各向异性表面的光散射现象。根据实空间的散射光强空间分布，提取波矢空间的散射强度轮廓，然后根据基尔霍夫近似理论和自仿射分形随机表面模型，得到波矢量规律变化的散射强度的轮廓，研究根据散射强度随波矢量变化的规律，提取表征表面形貌的统计参量的理论和实验。本文的主要研究工作如下：1.用原子力显微镜对各向异性粗糙样品进行了表面形貌的测量，根据测量数据分析了各向异性随机表面样品具体的形貌特征，并把这种样品表面按其特征分为几种典型的类型，对每一类型对光散射图样的影响做了分析并编程模拟了不同类型的表面的不同参量对散射轮廓的影响。2.讨论一种典型的各向异性微结构——棱台型结构表面的光散射现象和光的遮挡效应。根据反射光波的角度关系，利用空间向量的运算公式推导出了光的反射分量在测量平面内应该满足的曲线方程，并用反射镜和圆柱形光纤的光散射实验证实了这一曲线方程。3.根据波矢空间的随机表面的光散射理论，设计了一种垂直波矢量保持不变、平行波矢量逐渐变大的角分辨的面内光散射测量方法，可以更好地测量各向同性随机表面的统计参量。我们利用计算机控制的二维移动平台带动探测器沿平行于样品平面的一条圆弧的移动，这条圆弧以样品表面的法线和观察面的交点为圆心，以反射光线和观察面的交点为起点。在这条圆弧上，散射光的垂直波矢量保持不变，平行波矢量逐渐变大，这种实验方法消除了以往光散射测量方法中垂直波矢量近似不变的误差，并将其应用于各向同性随机表面的光散射测量，提高了测量的精度。4.设计了一种方便可行的粗糙表面光散测量的实验方法。该方法采用接收屏接收散射图样，用透镜对呈现在接收屏上的散射图样进行成像，并用CCD采集该散射图样。把得到的散射图样转化为波矢空间的光强度，提取出光散射轮廓。分别以各向同性和各向异性的粗糙硅片背面作为样品，用此实验系统获得了它们的散射轮廓。对于各向异性的表面样品，散射轮廓的提取沿着接收屏上的方位曲线进行。沿此条方位曲线，波矢量规律变化。利用角分辨散射的理论和方法，对样品的表面参量进行了提取，并与AFM测量得到的结果进行了对比。总之，本文系统地研究了基于波矢空间的波矢量变化的随机表面的光散射的理论和实验测量方法，特别是对各向异性随机表面光散射的研究，对整个随机表面光散射研究的进展具有十分重要的意义。更多还原

【Abstract】 The light scattering of random surface has been subject to attention for a long time. It iswidely applied in many fields, such as remote sensing, radar imaging, sonar detection,industrial non-contact detection and biomedical diagnostics and other fields. Therelationship between the morphology of the random surface and the distribution lightscattering intensity is important for the study of random surface light scattering. The presenttheoretical and numerical models can explain the characteristics of the scattering intensity ofthe vast majority of natural and artificial surface. To simulate the scattering intensitydistribution, surface characteristics need to be known; in the case of known space distributionof the scattering intensity, the surface characteristic parameters can be extracted. However, inthe formulation between the surface parameters and the distribution of scattering intensity,regardless of theory and experiment, most of the researchers to calculate the relationshipbetween the scattering angle and the spatial distribution of light intensity in the realspace. This expression form looks complicated; it can not indirectly determine the relationshipbetween the surface and the intensity distribution. Thus, according to the wave-particleduality of photons, the light wave with wave vector to represent the random surface of thelight scattering properties of the wave vector space, the relationship becomes relativelysimple.This paper is based on the correspondence between the spatial distribution of wavevector space of random surfaces and the scattering intensity in the wave vector space and lightscattering of the isotropic and anisotropic surface is been researched. According to thescattering light intensity distribution in the real space, the intensity profile curve of lightscattering is extracted in the vector space, and then based on the Kirchhoff approximationtheory and self-affine fractal random surface model, theoretical and experimental study isdone about the statistical parameters for the surface. The main research works are as follows:1. Surface topography for anisotropic rough samples is measured with atomic forcemicroscopy and the specific morphology of the anisotropic random surface samples is analyzedusing the measurement data. The surface of the sample is sorted into several typical the type according to their characteristics. The relationship between different types of surfaces ofdifferent parameters and light scattering pattern is simulated using computer program.2. The light scattering and light shielding effect of a typical anisotropic microstructure ofthe surface is discussed. According to the law of reflection of light, the scattering orientationcurve is deduced using the operation relations of space-vector. The reflection component inthe measurement plane should satisfy the curve equation, and the theory is verified by thelight scattering experiments of the mirror and cylindrical fiber.3. Based on light scattering theory of random surfaces in the wave vector space, anexperimental method that vertical wave vector remains constant is designed andangle-resolved light scattering measurement method can better measure the statisticalparameters of an isotropic random surface. We made the detector driven by two-dimensionalmobile platform controlled by computer move along a circular arc paralleling to the sampleplane. This arc of a circle normal to the sample surface and observe the intersection of thesurface to reflect light and observe the intersection of the surface as a starting point. In this arc,the vertical wave vector of the scattered light remains unchanged, eliminating the previouslight scattering measurements the vertical wave vector approximation the same error.4. A convenient experimental method measuring light scattering pattern of rough surfaceis designed. Using the receiver screen to receive the scattering pattern, the lens to image thescattering pattern on the receiver screen, the scattering pattern is collected with the CCD. Thescattering pattern is transformed into the light intensity of the wave vector space, and the lightscattering profile is extracted. The scattering profiles of isotropic and anisotropic roughsilicon surface are obtained with this experimental system. For the anisotropic surfacesamples, the scattering profiles are extracted along the orientation curve on the screen. Resultsare compared with measurement of AFM and methods of angle-resolved scattering.The theory and experiment method of light scattering on random surface based on variedwave vector in wave vector space is studied in this paper. It is very important for thedevelopment of the light scattering on random surface to study the light scattering onanisotropic random surface.更多还原