A Wave Optics Based Fiber Scattering Model

Mengqi (Mandy) Xia¹, Bruce Walter¹, Eric Michielssen², David Bindel¹, Steve Marschner¹

¹Cornell University, ²University of Michigan

ACM Transactions on Graphics (SIGGRAPH Asia 2020)

This figure shows a spiderweb iridescence example. The left image is a photograph of this effect by Marianna Armata. The middle image is rendered using our wave-based BCSDF and the image on the right is rendered using a previous ray-based BCSDF. Our wave optics fiber scattering model is able to produce strong color effects with hues similar to the photograph while the ray model produces a colorless appearance. Similar iridescence effects can also be seen in eyelashes or a Dandelion seed head.

Abstract

Existing fiber scattering models in rendering are all based on tracing rays through fiber geometry, but for small fibers diffraction and interference are non-negligible, so relying on ray optics can result in appearance errors. This paper presents the first wave optics based fiber scattering model, introducing an azimuthal scattering function that comes from a full wave simulation. Solving Maxwell's equations for a straight fiber of constant cross section illuminated by a plane wave reduces to solving for a 3D electromagnetic field in a 2D domain, and our fiber scattering simulator solves this 2.5D problem efficiently using the boundary element method (BEM). From the resulting fields we compute extinction, absorption, and far-field scattering distributions, which we use to simulate shadowing and scattering by fibers in a path tracer. We validate our path tracer against the wave simulation and the simulation against a measurement of diffraction from a single textile fiber. Our results show that our approach can reproduce a wide range of fibers with different sizes, cross sections, and material properties, including textile fibers, animal fur, and human hair. The renderings include color effects, softening of sharp features, and strong forward scattering that are not predicted by traditional ray-based models, though the two approaches produce similar appearance for complex fiber assemblies under many conditions.

Results

1. Forward scattering

Compared to the wave optics predictions, the previous ray model has less energy in the forward scattering direction and this results in appearance differences, especially in the backlit setting. We show a video of orbit renderings with a head of curly black hair under an area light and an environment light. The ray result is lacking energy near the forward direction and results in a dimmer appearance on the edge of the hair model. When the light source rotates to be partially blocked by the hair model, one can observe the biggest appearance differences between the two results.

2. Highlight shape

This figure shows renderings of a head of elliptical red hair lit by an environment light. We show the full-scale render using our wave BCSDF on the top left. On the bottom left, we zoom in on hair ends and show the comparison between the ray and the wave renders. On the right, we zoom in near the root of hair. Comparing to the ray render, the wave render has different highlight patterns and a softer appearance.

3. Interactive comparison

Hamster fur has six different colors of elliptical fibers with semi-major axis 16um and semi-minor axis 10um.

Silk sofa

Polyester sofa (type 1)

Polyester sofa (type 2)

4. Gaussian beam

We illustrate two examples of a Gaussian beam illuminating a circular cross section. In the first row, we have a circle with radius 1um and a Gaussian beam with waist 5um. In the second row, we have a circle with radius 10um and a Gaussian beam with waist 1um and a center offset 5um. In both cases, the Gaussian beams have wavelength 400nm and transverse-magnetic (TM) polarization. They are normally incident on the circular cross sections. We plot the z component of the electric fields at a particular time. The first column is the incident field, the second column is the scattered field, and the third column is the total field. Non-positive values are shown as black.

Acknowledgement

The authors would like to thank Zechen Zhang and Francesco Monticone for their helpful discussion on this project. We thank Sitian Chen for generating the woven pattern used in the sofa scene and Lingqi Yan for letting us use the converted hamster scene. We would also like to thank Under Armour for providing the textile sample. This work was supported by the National Science Foundation under grant IIS-1909467.