Physics-Informed Identification and Interpolation of the Directivity of Sound Sources

The radiation characteristics of sound sources are important, for example, for the simulation and auralization of sound fields or for the design of sound reinforcement systems. They are usually determined by measurements in an anechoic chamber with a discrete grid of microphones on a spherical surface and subsequent interpolation. This manuscript introduces a physically informed method for source directivity identification and interpolation based on source modeling using the adjoint Euler equations in a finite-difference time-domain approach. Synthetic analyses are used to investigate the properties of the method under different parameters: the number of microphones used, the effect of measurement noise and microphone misalignment, off-center source positioning, and the presence of reflecting walls. In addition, the method is applied to a real-world scenario involving the analysis of a musical instrument. The method is found to be a versatile and robust approach to sound source directivity analysis. Its particular strengths are its flexibility in microphone placement, its adaptability to non-centered sound sources, and its ability to account for non-anechoic environments.