Directional coherence loss coefficients for characterizing scattering distributions in enclosures

This study introduces directional coherence loss coefficients (DCLCs) to quantify the angular distribution of sound field coherence loss, which arise from localized scattering distributions within an enclosure, from a receiver's perspective. Sound fields in the room are sampled by a spherical receiver and decomposed into plane waves using spherical harmonics expansion, yielding directional impulse responses (IRs). The time-dependent coherence coefficients between directional IRs in furnished rooms and their empty counterparts are analyzed for each direction. DCLCs are derived from these coherence coefficients and decide the transition between the coherent component—mainly representing specular reflections—and the incoherent component, accounting for scattering contributions from interior elements. This research extracts DCLCs from rooms with varying transducer positions founded on wave-based simulations and measurements from rooms with different element distributions. A hybrid model is proposed to reconstruct the sound field in a room with a single diffusive wall, where the coherent component is computed from the empty room case, and the incoherent component is simulated stochastically, with their relative weighting decided by DCLCs. Directional IRs from the hybrid model exhibit agreement with ground truth in terms of reverberation time, clarity, kurtosis, and spatial cross correlation coefficients, verifying the ability of DCLCs to characterize localized scattering distributions in enclosures.