Physically-based simulation of rainbows

Abstract

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.

On the electromagnetic scattering of arbitrary shaped beams by arbitrary shaped particles: A review

“…Chang et al studied the optical force on an ellipsoidal particle subjected to a loosely focused laser beam using a dynamic ray tracing method [200]. Sadeghi et al [201] used an extended ray tracing method allowing one to account for dispersion, polarization, interference, and diffraction in order to carry out a physically-based simulation of rainbows. Jiang et al dealt with scattering of a Gaussian beam by an elliptical cylinder using the vectorial complex ray model which describes waves by rays transporting information on the curvature of the wavefront [202].…”

Multi-scale modeling and rendering of granular materials

“…Condensing aggregate scattering behavior of complex geometric structures into more compact scattering functions has long been a research problem in computer graphics. Reflection from complex surfaces can be modeled using analytic micro-facet models [Torrance and Sparrow 1967], or by tabulating light scattered off real [Matusik et al 2003] or virtual [Westin et al 1992;Ashikhmin et al 2000;Kimmel and Baranoski 2007;Sadeghi et al 2012] surfaces. We also use a Monte Carlo approach to tabulate compact scattering functions for a single grain.…”

BRDF Estimation of Structural Color Object by Using Hyper Spectral Image

“…al. [17] calculated the refracted ray in moisture by ray tracing, and then represented the rainbow more correctly. Furthermore, Cuypers et.…”