Geometrical-optics Approximation Of Light Scattering By Particles

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.