Theoretical refinement of sound field diffusion indices determined from incidence directivity

This study focuses on two types of sound diffusion indices determined from incidence directivity at a receiving point: directional coefficient and isotropy indicator. The directional coefficient is determined from the directional deviation of sound intensity, where employing a normalization procedure taking account of the directional resolution of a receiver. On the other hand, the existing isotropy indicator is directly given through spherical harmonic expansion of sound intensity without the above normalization procedure. First, to resolve this inconsistency, we incorporate a similar normalization procedure into the definition of the isotropy indicator. Moreover, we revise the definition formulas of both indices in the light of mathematical applicability and physical comprehensibility. As a result, these modifications lead to an explicit correspondence between the two indices, providing a unified interpretation of them. Finally, to observe the behaviors of the two indices, we conduct numerical simulations of steady-state sound fields in a room with different absorption conditions using the fast multipole boundary element method. Numerical results demonstrate the trends of the revised indices, which suggests their validity for evaluating sound field diffuseness.