Accurately Predicting the Reflectance of Rough Metal Surfaces From One-Dimensional Surface Profile Measurements

Abstract

This thesis investigates the problem of using surface microgeometry measurements to predict the reflectance of rough metal surfaces. Because light cannot penetrate much into metals, the observable reflectance of a metal surface is due almost entirely to interfacial reflection, i.e., light reflection at the interface between the metal and air. According to the laws of optics, interfacial reflection is determined completely by surface topography and material refractive index. Hence this thesis seeks to accurately predict the reflectance of metals, as observed and measured by a gonioreflectometer, from topographic measurements and material refractive index alone. In order to achieve accurate prediction, it is vital to acquire accurate topographic measurements as input. This thesis identifies why modern profilometers based on white light interferometry (WLI) and atomic force microscopy (AFM) are unlikely to measure the two-dimensional topography of real-world rough surfaces with sufficient fidelity to allow accurate reflectance prediction. A new experimental procedure for accurately measuring the one-dimensional surface profiles using AFM is consequently proposed. This thesis then derives how reflectance of a two dimensional surface is related to one-dimensional surface profiles, resulting in an ill-posed linear inverse problem. Two algorithms are subsequently designed for solving this inverse problem: The first algorithm introduces and employs the shaped microfacet model, an extension to the classic microfacet model under the Kirchhoff approximation, to provide the necessary priors for tackling the inverse problem using optimization; The second algorithm employs the Fourier slice theorem to construct a solution to the inverse problem in its Fourier domain using simple interpolation. Both algorithms require no back-fitting of free parameters to reflectance measurements, thereby allowing reflectance computation from profilometer measurements to be truly predictive. This thesis also experimentally evaluated the proposed measurement procedures and computational algorithms on surface samples manufactured via metallic coating using off-the-shelf leafing aluminum flakes and polyurethane binder. The proposed methods, including both algorithms, achieved much higher prediction accuracy than demonstrated before for non-precision-fabricated real-world two-dimensionally rough surfaces.