Bidirectional surface scattering coefficients

The prediction and modeling of sound propagation rely heavily on accurate representations of surface scattering. Traditional scattering coefficients, often based on random-incidence assumptions, fail to capture the directional dependence of sound reflections from rough surfaces. This paper introduces a methodology for determining and representing bidirectional surface scattering coefficients, moving beyond the limitations of existing Lambertian-based approaches. We propose a framework that leverages numerical simulations and physical measurements to compute bidirectional scattering coefficients from reflected sound pressure distributions with finite-size samples. The methodology is validated using a well-documented sinusoidal test surface, comparing our results with analytical solutions for infinite-size samples and former random-incidence scattering coefficient measurements. Additionally, we propose a data storage format compatible with the Spatially Oriented Format for Acoustics (SOFA) to facilitate the integration of bidirectional scattering coefficients into sound propagation models. This work provides a foundation for improved acoustic simulations in applications ranging from room acoustics to urban noise control.