Geometrical acoustics simulations are an essential tool for predicting sound propagation in rooms and urban environments. A key requirement for physically accurate simulations is an appropriate representation of surface scattering to capture wave-related phenomena at surfaces. In current acoustic practice, surface reflection is commonly described by decomposing reflected sound energy into specular and scattered components, with the scattered part modeled using Lambert’s cosine law. The amount of scattered energy relative to the total reflected energy is quantified by a scattering coefficient, which is most often determined as a random-incidence value under diffuse-field conditions according to ISO 17497-1. These coefficients typically assume sufficiently large surfaces, such that scattering behavior can be considered independent of sample size.<\/p>\n
Despite its widespread use, this conventional framework has fundamental limitations. Random-incidence averaging fails to capture scattering behavior that depends on the incidence direction. In addition, Lambertian scattering assumes an isotropic redistribution of scattered energy, independent of the incidence direction and the actual reflection pattern of the surface geometry. For many surfaces, particularly periodic or pseudo-periodic geometries, the scattering behavior depends strongly on surface geometry, incidence direction, and acoustic wavelength, producing distinct outgoing scattering directions. These simplifications are especially problematic for surfaces such as acoustic diffusers, building facades, or retroreflective elements and lead to systematic inaccuracies in geometrical acoustic simulations.<\/p>\n
Directional scattering coefficients provide additional information by accounting for the dependence on incidence direction and can be obtained with free-field methods such as the correlation method. However, these coefficients are rarely used directly in simulations and are often averaged over incidence directions to determine random-incidence values. As a result, a representation that captures both incidence and outgoing directions in a physically meaningful and practically applicable manner is still missing.<\/p>\n
To overcome these limitations, this dissertation introduces the bidirectional scattering coefficient (BSC) as an energy-based metric that explicitly accounts for incidence direction, scattering direction, and frequency dependence. Like the scattering coefficient, the BSC quantifies the fraction of reflected acoustic energy redistributed into a specific outgoing direction relative to the total reflected energy. Determining BSCs requires extending the correlation method to compute complete bidirectional scattering coefficients from numerical simulations and physical measurements on finite-sized samples. The approach is validated using a well-documented sinusoidal test surface, allowing direct comparison with analytical solutions for infinite surfaces and previously reported random-incidence scattering coefficients.<\/p>\n
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