粒子光散射的几何光学近似方法研究
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摘要
大量的工业过程(如燃烧、流体、化学反应等)、大气测量、环境检测等许多领域要求对微小粒子的形状、浓度、光学特性及尺寸分布进行快速准确的测量。作为粒子光散射研究中的一种近似算法,几何光学近似方法(Geometrical-optics approximation,简称GOA)具有计算速度快,程序结构简单等优点,在计算大尺寸粒子和非均匀粒子的散射强度时尤其明显,因此GOA方法在粒度在线测量中具有独特优势。同时,对于一些结构相对复杂的粒子,在严格的电磁散射理论求解困难时,几何光学近似方法可以相对简单地得到其散射强度分布。本文将在均匀球粒子GOA方法的基础上,系统研究梯度折射率球粒子对平面波和在轴高斯波束散射的GOA方法;利用光线追迹方法研究均匀椭球粒子的几何光学彩虹角;开展了非同轴无限长柱光散射的GOA方法研究。本文主要研究工作和成果如下:
1.在均匀球粒子散射GOA方法基础上,总结了具有一定普遍性的GOA方法算法实现流程;研究了粒子光散射理论中的散射角间隔选择方法,基于这种方法给出了GOA方法中的最大入射角间隔计算公式,提高了GOA方法的计算效率。
2.推导了梯度折射率球粒子对平面波散射的GOA方法,选择了合适的数值算法有效地解决了散射角公式和光程公式中的奇异积分问题;针对两种典型的折射率模型,分别研究了前向散射GOA方法的有效范围;比较了Mie理论、Debye级数和GOA方法的计算速度。在此基础上,利用GOA方法计算了梯度折射率球粒子对平面波全角度散射强度分布。
3.将梯度折射率球粒子对平面波散射的GOA方法扩展到在轴高斯光束入射的情况。对于梯度折射率球粒子,推导出了高斯波束入射情况下的散射角和相位公式,给出了算法流程,得到了各阶散射光线在特定角度的散射振幅函数;最终得到了在轴高斯波束入射梯度折射率球的散射强度分布。
4.基于光线追迹方法,推导了适用于任意长短轴之比椭球的光线追迹公式,研究了平面波正入射和斜入射到长短轴比较大椭球的条件下一阶几何光学彩虹角随着长短轴比的变化关系。研究结果表明,对于平面波入射到长椭球的情况,当长短轴之比在一定范围内,不存在一阶几何光学彩虹角,并且这个范围随着粒子折射率增大而增大。最后,简单分析了平面波正入射时的椭球粒子的二阶散射光线散射角随着长短轴之比的变化情况。
5.基于平面波对均匀柱光散射的GOA方法,开展具有非同轴柱特性的熊猫型保偏光纤前向散射强度分布研究,并与实验测量结果进行了比较,分析了误差产生原因。
For many practical applications such as combustion, environmental control, fluid mechanics, and chemical reaction, we need to measure the properties of particles such as size and refractive index-temperature ratio quickly and precisely. As a approximation method of a rigorous light scattering theory, geometrical-optics approximation (GOA) is used widely because of high speed calculation and simple procedure structure. The GOA method is suitable for light scattering by large particles. For particles with complex structure, scattering intensity is calculated by GOA while the rigorous light scattering theories are difficult to calculate. On the basis of GOA method for homogeneous spheres, this thesis is devoted to the systemic research on GOA of plane wave and on-axis gaussian beam scattering by gradient index spherical particles. The geometrical optics rainbow angles are studied on the base of ray tracing and GOA of plane wave scattering by infinite eccentric cylinder is derived. The main works and achievements are summarized as follows:
1. On the basis of GOA of light scattering by homogeneous spheres, the simple flow chart is given. The scattering angle step is studied to promote the calculation speed of rigorous light scattering theory. Based on the scattering angle step selection formula, the incident angle step of GOA is analyzed. By use of these angle step formulas, the calculation speed is promoted.
2. GOA of plane wave scattering by gradient-index spherical particles is derived. The integration algorithm is selected to calculate the function which has endpoint singularities. For two typical refractive index models, the valid rangle is studied. Finally, the calculation speeds of GOA, Mie theory and Debye series are compared.
3. Within the framework of geometrical optics, we present a further extension of the method to the scattering of a gradient-index spherical particle with the symmetric axis Gaussian beam as the incident beam. The phase formulas and scattering angle formula are obtained and the detailed algorithm is given. On the basis of above work, the scattering amplitude of separate order rays is obtained. Finally, the scattering intensity of a gradient-index sphere with the on-axis Gaussian beam as the incident beam is given.
4. A general ray-tracing method for homogeneous spheroids with arbitrary axial-ratios is presented on the basis of geometrical optics, and is employed to study the variation of primary rainbow angle with the axial-ratio of spheroids with larger axial-ratio at both normal and oblique incidences. For the prolate spheroid normally illuminated by plane waves, when the axial ratio is in certain range, no primary rainbow angle exists. The research shows that the axial ratio range increases with the refractive index of the spheroid. With increase of tilt angle, the symmetry of the two primary rainbow angles changes. Finally, the variation of secondary rainbow angle with axial ratio for the spheroid at normal incidence is generally introduced.
5. The scattering intensity of PANDA fiber is calculated by geometrical-optics approximation. The result is compared with measurement data and the reason that causes errors is analyzed.
1.在均匀球粒子散射GOA方法基础上,总结了具有一定普遍性的GOA方法算法实现流程;研究了粒子光散射理论中的散射角间隔选择方法,基于这种方法给出了GOA方法中的最大入射角间隔计算公式,提高了GOA方法的计算效率。
2.推导了梯度折射率球粒子对平面波散射的GOA方法,选择了合适的数值算法有效地解决了散射角公式和光程公式中的奇异积分问题;针对两种典型的折射率模型,分别研究了前向散射GOA方法的有效范围;比较了Mie理论、Debye级数和GOA方法的计算速度。在此基础上,利用GOA方法计算了梯度折射率球粒子对平面波全角度散射强度分布。
3.将梯度折射率球粒子对平面波散射的GOA方法扩展到在轴高斯光束入射的情况。对于梯度折射率球粒子,推导出了高斯波束入射情况下的散射角和相位公式,给出了算法流程,得到了各阶散射光线在特定角度的散射振幅函数;最终得到了在轴高斯波束入射梯度折射率球的散射强度分布。
4.基于光线追迹方法,推导了适用于任意长短轴之比椭球的光线追迹公式,研究了平面波正入射和斜入射到长短轴比较大椭球的条件下一阶几何光学彩虹角随着长短轴比的变化关系。研究结果表明,对于平面波入射到长椭球的情况,当长短轴之比在一定范围内,不存在一阶几何光学彩虹角,并且这个范围随着粒子折射率增大而增大。最后,简单分析了平面波正入射时的椭球粒子的二阶散射光线散射角随着长短轴之比的变化情况。
5.基于平面波对均匀柱光散射的GOA方法,开展具有非同轴柱特性的熊猫型保偏光纤前向散射强度分布研究,并与实验测量结果进行了比较,分析了误差产生原因。
For many practical applications such as combustion, environmental control, fluid mechanics, and chemical reaction, we need to measure the properties of particles such as size and refractive index-temperature ratio quickly and precisely. As a approximation method of a rigorous light scattering theory, geometrical-optics approximation (GOA) is used widely because of high speed calculation and simple procedure structure. The GOA method is suitable for light scattering by large particles. For particles with complex structure, scattering intensity is calculated by GOA while the rigorous light scattering theories are difficult to calculate. On the basis of GOA method for homogeneous spheres, this thesis is devoted to the systemic research on GOA of plane wave and on-axis gaussian beam scattering by gradient index spherical particles. The geometrical optics rainbow angles are studied on the base of ray tracing and GOA of plane wave scattering by infinite eccentric cylinder is derived. The main works and achievements are summarized as follows:
1. On the basis of GOA of light scattering by homogeneous spheres, the simple flow chart is given. The scattering angle step is studied to promote the calculation speed of rigorous light scattering theory. Based on the scattering angle step selection formula, the incident angle step of GOA is analyzed. By use of these angle step formulas, the calculation speed is promoted.
2. GOA of plane wave scattering by gradient-index spherical particles is derived. The integration algorithm is selected to calculate the function which has endpoint singularities. For two typical refractive index models, the valid rangle is studied. Finally, the calculation speeds of GOA, Mie theory and Debye series are compared.
3. Within the framework of geometrical optics, we present a further extension of the method to the scattering of a gradient-index spherical particle with the symmetric axis Gaussian beam as the incident beam. The phase formulas and scattering angle formula are obtained and the detailed algorithm is given. On the basis of above work, the scattering amplitude of separate order rays is obtained. Finally, the scattering intensity of a gradient-index sphere with the on-axis Gaussian beam as the incident beam is given.
4. A general ray-tracing method for homogeneous spheroids with arbitrary axial-ratios is presented on the basis of geometrical optics, and is employed to study the variation of primary rainbow angle with the axial-ratio of spheroids with larger axial-ratio at both normal and oblique incidences. For the prolate spheroid normally illuminated by plane waves, when the axial ratio is in certain range, no primary rainbow angle exists. The research shows that the axial ratio range increases with the refractive index of the spheroid. With increase of tilt angle, the symmetry of the two primary rainbow angles changes. Finally, the variation of secondary rainbow angle with axial ratio for the spheroid at normal incidence is generally introduced.
5. The scattering intensity of PANDA fiber is calculated by geometrical-optics approximation. The result is compared with measurement data and the reason that causes errors is analyzed.
引文
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