Development of Debye Series for Light Scattering by a Spheroid
Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
Final Report Abstract
In this project, the Debye series is developed for light scattering by a spheroidal particle in order to decompose the far‐field into various physical processes. As an application, the Debye series has been applied to analyze the formation of rainbow caustic, transverse cusp and HU caustics for a spheroid, which provides an exact analysis tool for studying light scattering by a spheroid. Then the Debye series is generalized to non‐spherical particle with complex shape and coated non‐spherical particle respectively. Since, the EBCM is adopted which treats light scattering in spherical coordinates independent of the shape of the particle’s surface, no special coordinate system in which the vector wave equation is separable is required to match the boundary conditions of the electromagnetic field at the particle surface and Debye series could be employed to particle with arbitrary shape. Based on the understanding the physical process of light scattering by use of Debye series, the experiment is then carried out to measure the generalized rainbow pattern from oblate water droplets. According to the position of rainbow and angular frequency of the generalized rainbow pattern, the refractive index and the equatorial radius of the oblate water droplet are inverted with high measurement accuracy. It is shown that absolute error of the refractive index is less than 0.5x10‐4 and of the droplet diameter 5%. Furthermore, the relation between the curvatures of rainbow fringe and the aspect ratio of oblate droplet is established. Based on such a relation, the non‐sphericity in terms of aspect ratio of oblate droplets are inferred from the corresponding generalized rainbow patterns with the relative errors lying between ‐1% and 1%. In addition, the VRT is employed to optical caustics in the secondary rainbow region of light scattering from oblate droplets. The changes of the rainbow and HU fringes in response to shape deformation of an oblate droplet are investigated which indicates the secondary rainbow also a reliable measure of an oblate droplet. Because the droplet orientation is arbitrary in many industrial processes, theoretical and experimental investigations of abnormally oriented droplet also are worthy to carry out.
Publications
- Debye series for light scattering by a coated nonspherical particle, Phys. Rev. A 81, 063812 (2010)
Feng Xu and James A. Lock
- Debye series for light scattering by a nonspherical particle, Phys. Rev. A 81, 043824 (2010)
Feng Xu, James A. Lock, and Gérard Gouesbet
- Debye series for light scattering by a spheroid, J. Opt. Soc. Am. A 27, 671‐686 (2010)
Feng Xu, James A. Lock, and Cameron Tropea
- Optical caustics observed in light scattered by an oblate spheroid, Appl.Opt. 49, 1288‐1304 (2010)
James A. Lock and Feng Xu
- Application of generalized rainbow patterns on spheroidal droplets measurement, in Lasermethoden in der Strömungsmesstechnik, (3–5 September 2013, München)
Haitao Yu, Feng Xu, and Cameron Tropea
- Spheroidal droplet measurements based on generalized rainbow patterns, J. Quant. Spectroscopic Radiative Transfer, 105‐112 (2013)
Haitao Yu, Feng Xu, and Cameron Tropea
(See online at https://doi.org/10.1016/j.jqsrt.2012.09.012)
