An Image Source Method Framework for Arbitrary Reflecting Boundaries

TL;DR

This paper introduces a generalized theoretical framework for the image source method that handles arbitrary reflecting boundaries, including curved surfaces and openings, while incorporating absorption, directivity, and nonspecular reflections.

Contribution

It extends the classical image source method to arbitrary boundary shapes and properties using reflection paths and virtual source distributions.

Findings

Framework accommodates curved and open boundaries.

Incorporates boundary absorption and source directivity.

Represents room impulse response as an integral over virtual sources.

Abstract

We propose a theoretical framework for the image source method that generalizes to arbitrary reflecting boundaries, e.g. boundaries that are curved or even with certain openings. Furthermore, it can seamlessly incorporate boundary absorption, source directivity, and nonspecular reflections. This framework is based on the notion of reflection paths that allows the introduction of the concepts of validity and visibility of virtual sources. These definitions facilitate the determination, for a given source and receiver location, of the distribution of virtual sources that explain the boundary effects of a wide range of reflecting surfaces. The structure of the set of virtual sources is then more general than just punctual virtual sources. Due to this more diverse configuration of image sources, we represent the room impulse response as an integral involving the temporal excitation signal against a measure determined by the source and receiver locations, and the original boundary. The latter smoothly enables, in an analytically tractable manner, the incorporation of more general boundary shapes as well as directivity of sources and boundary absorption while, at the same time, maintaining the conceptual benefits of the image source method.