Debye series for light scattering by a spheroid

Xu, Feng; Lock, James A.; Tropea, Cameron

doi:10.1364/josaa.27.000671

Cited by 47 publications

(27 citation statements)

References 36 publications

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“…There has been other work focusing on the light scattering by nonspherical particles [Mishchenko et al 2000;Xu et al 2010] but none of them focuses on the physically-based geometries of water drop particles and their effect on the appearance of rainbows. To the best of our knowledge, we are the first to simulate the light scattering by physically-based water drop shapes.…”

Section: Previous Workmentioning

confidence: 99%

Physically-based simulation of rainbows

et al. 2012

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In this article, we derive a physically-based model for simulating rainbows. Previous techniques for simulating rainbows have used either geometric optics (ray tracing) or Lorenz-Mie theory. Lorenz-Mie theory is by far the most accurate technique as it takes into account optical effects such as dispersion, polarization, interference, and diffraction. These effects are critical for simulating rainbows accurately. However, as Lorenz-Mie theory is restricted to scattering by spherical particles, it cannot be applied to real raindrops which are nonspherical, especially for larger raindrops. We present the first comprehensive technique for simulating the interaction of a wavefront of light with a physically-based water drop shape. Our technique is based on ray tracing extended to account for dispersion, polarization, interference, and diffraction. Our model matches Lorenz-Mie theory for spherical particles, but it also enables the accurate simulation of nonspherical particles. It can simulate many different rainbow phenomena including double rainbows and This research has been partially funded by NSF Project GreenLight (award no. 0821155), a Marie Curie grant from the Seventh Framework Programme (grant agreement no. 251415), the Spanish Ministry of Science and Technology (TIN2010-21543) and the Gobierno de Aragn (projects OTRI 2009/0411 and CTPP05/09). Authors' addresses: I. Sadeghi (corresponding author), University of California, San Diego; email: iman@graphics.ucsd.edu; A. Munoz, Universidad de Zaragoza; P. Laven, Horley, UK; W. Jarosz, Disney Research Zürich and University of California, San Diego; F. Seron and D. Gutierrez, Universidad de Zaragoza; H. W. Jensen, University of California, San Diego. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. supernumerary bows. We show how the nonspherical raindrops influence the shape of the rainbows, and we provide a simulation of the rare twinned rainbow, which is believed to be caused by nonspherical water drops.

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Section: Previous Workmentioning

confidence: 99%

Physically-based simulation of rainbows

et al. 2012

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“…The p ¼ 2 portion of the scattered intensity was numerically computed using the method described in [18] for side-on incidence of a plane wave on an oblate spheroid. For the geometry illustrated in Fig.…”

Section: Computed Caustic Patterns In the Scattered Intensitymentioning

confidence: 99%

“…The oblate spheroid has refractive index n ¼ 1:334 þ ið1:2 × 10 −9 Þ, horizontal radius a ¼ 6μm, and various values of the vertical radius b. It should be noted that, in [18], the standard definition of spheroidal coordinates has the z axis coincident with the particle's symmetry axis, rather than being the direction of the incoming light, which is perpendicular to the spheroid's symmetry axis for side-on incidence. As a result, the intensity was computed as a function of the spheroidal coordinate system scattering angles and then had to be converted to the scattering angles Θ and Φ for the orientation of the axes in Fig.…”

Section: Computed Caustic Patterns In the Scattered Intensitymentioning

confidence: 99%

“…The electromagnetic fields scattered by a spheroid can be decomposed into an infinite series of terms known as the Debye series, where the individual contributions to wave scattering corresponding to diffraction-plus-reflection, transmission, and transmission following p − 1 internal reflections can be isolated and studied individually [18]. Each scattering caustic is associated with a single Debye process.…”

Section: Introductionmentioning

confidence: 99%

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Optical caustics observed in light scattered by an oblate spheroid

Lock

2010

Appl. Opt.

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The electromagnetic fields scattered when a plane wave is incident on an oblate spheroid in the side-on orientation may be calculated using a generalization of Mie theory, and the results may be decomposed in a Debye series expansion. A number of optical caustics are observed in the computed scattered intensity for the one internal reflection portion of the Debye series for scattering angles in the vicinity of the firstorder rainbow, and are analyzed in terms of the rainbow, transverse cusp, and hyperbolic umbilic caustics of catastrophe optics. The specific features of these three caustics are described, as is their assembly into the global structure of the observed caustics for spheroid scattering. It is found that, for a spheroid whose radius is an order of magnitude larger than the wavelength of the incident light, the interference structure accompanying the transverse cusp and hyperbolic umbilic caustics is only partially formed.

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“…[23,24], respectively. Recently, the Debye series for both plane-wave incidence and shaped-beam incidence on a homogeneous spheroid was worked out and verified [25].…”

Section: Introductionmentioning

confidence: 98%

Debye series for light scattering by a nonspherical particle

Lock

Gouesbet

2010

Phys. Rev. A

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The Debye series is developed for scattering of light by a homogeneous nonspherical particle to interpret the angular dependence of the scattered intensity in terms of various physical processes. In contrast to the previously developed Debye series for several regularly shaped particles that mirror the orthogonal curvilinear coordinate system where the variable-separation method can be applied, we develop and verify the Debye series in a coordinate-independent way using the extended boundary condition method. Verification computations are made for an oblate spheroidal water droplet of equivalent-volume sphere radius 10 µm.

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Debye series for light scattering by a spheroid

Cited by 47 publications

References 36 publications

Physically-based simulation of rainbows

Physically-based simulation of rainbows

Optical caustics observed in light scattered by an oblate spheroid

Debye series for light scattering by a nonspherical particle

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