A Light Scattering Model for Large Particles with Surface Roughness

The scattering of light from particles with roughened surfaces occupies a gap in our understanding because they have size dimensions spanning multiple length scales. Subtle changes in the symmetries and features of a particles geometry can lead to significant changes in its optical properties. Combined with the fact that many applications of light scattering are concerned with the bulk properties of an ensemble of particles with varying shapes and sizes, this makes it particularly challenging to study them through experiment and to model via simulation. The goal of this work is to develop a model to solve a multi-scale problem in an approximate yet fast and computationally feasible manner, to aid in characterising the optical properties of particles with surface roughness. Accomplishing this will enhance current modelling capabilities and offer the potential to compute single scattering parameters with greater accuracy, leading to a deeper understanding across a wide range of applications. For particles with size much larger than the wavelength, the existing work is generally limited to ray-tracing approaches based on geometric optics, as well as some physical-optics hybrid methods based on an equivalence between the orientation averaged scattering of roughened and distorted smooth particle geometries. The use of geometric optics is a good approximation if the particle size dimensions are much greater than the wavelength of light, but the accuracy decreases with decreasing size dimension. To address this limitation, the model developed in this study, the Parent Beam Tracer method, improves upon geometric optics by accounting for diffraction effects, which become important when the length scale becomes comparable to the wavelength. The basic principles of pioneering ray-tracing studies provide the inspiration for the model, which also includes a novel ray backtracing technique for application to particles with a variety of surface textures. It utilises a surface integral diffraction equation, allowing it to capture the interplay between wavelength, surface roughness, and overall particle shape in the computation of 2D scattering patterns. It is the first physical-geometric optics hybrid method of its kind to compute the full Mueller matrix from particles with surface roughness, which can be achieved in a time reduced by several orders of magnitude compared to other methods, such as the discrete dipole approximation. By comparison of 2D scattering patterns measured by experiment with those predicted by the model, the prospective user may be able to better characterise particles beyond the capabilities of current resolution-limited imaging techniques. In summary, this report details the key findings based on the development of a physical-optics hybrid light scattering model for particles with overall size(1) much larger than the wavelength of light, but with surface roughness on a scale comparable to the wavelength. In addition, this work describes new evidence showing that the length scale of surface roughness has a negligible effect on the orientation averaged scattering, suggesting that surface roughness can be quantified solely by an amplitude. This report is structured into the following sections: First, a range of applications are introduced in Section 1, and the motivation for developing the model is discussed. A brief review of existing literature is given, with particular emphasis on the difficulties encountered in representing the size, shape, and surface texture of particles in theoretical light scattering models. The analysis of 2D scattering patterns as a means of characterising particles beyond the resolution of current imaging techniques is also discussed. Second, an introduction to some basic scattering theory is given in Section 2, which may be a useful resource for the reader for a better understanding of the proceeding sections. Third, Section 3 gives a brief review of some existing theoretical methods, with a greater depth of focus on the principles of geometric optics. These principles are then leveraged in Section 4, which describes and explains the novel techniques in the Parent Beam Tracer method. Section 5 discusses applications of the model; 2 benchmark studies comparing its accuracy against the numerically exact discrete dipole approximation are presented, as well as a study on the single scattering properties of roughened, thin hexagonal plates across a range of sizes and refractive indices. The work is summarised in Section 6, which concludes this report.

(1)Overall size is intended to be the largest characteristic length scale of the particle, which may be loosely interpreted as the diameter of a sphere with the same volume.