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When evaluating or optimising the accuracy of sound field synthesis, it is commonplace to only consider the error in the pressure field that is reproduced. While this is justifiable perceptually - pressure is what we hear - it neglects error in particle velocity. Acoustic energy density includes both these quantities, so is less sensitive to locations where one or other quantities is zero and has been shown to be outperform pressure in some adaptive noise control applications.  Acoustic cross-energy density was suggested in 2014 as a measure of common energy between waves, generalising spatially the notion of cross-covariance between signals. It’s counterpart quantity, acoustic cross-intensity, is a measure of common energy flux. The two are connected by an energy flux relation, meaning similar information can be computed over a domain or a boundary. Cross-intensity generalises several double-layer microphone array designs that have previously been limited to planar, cylindrical or spherical geometries. Applications of it since published includes a boundary integral equation that is based on wave reflection and satisfies reciprocity, and encoding of a sound field computed by boundary element method to allow auralisation. This paper will study a generalisation of the ordinary coherence function based on acoustic cross-energy, which is computed spatially for waves. It is shown to be a bounded metric that measures wave similarity, and hence can be used to quantity the physical accuracy of sound field synthesis systems.

Optimising Sound Field Synthesis using Acoustic Cross-Energy Metrics