ABSTRACT
One of the most significant occurrences in the design of diffusers, if not the most important event, was the invention of the phase grating diffuser by Schroeder [1, 2]. Apart from very simple constructions, previous diffusers had not dispersed sound in a predictable manner. The Schroeder diffuser offered the possibility of producing so-called optimum diffusion and also required only a small number of simple to use design equations. D’Antonio and Konnert [3] presented one of the most readable reviews of the far field diffraction theory of Schroeder’s number theoretic surfaces, experimentally measured their performance and described their application in critical listening environments. Most crucially, they commercialized Schroeder diffusers and so made them widely available. Since the publication of Reference 3, there have been many new developments which have not been brought together and documented in one place. Therefore the intention of this chapter is to tell the whole story of Schroeder diffusers. Much of this chapter featured as a review article in the journal Building Acoustics [4]. The chapter will start by outlining a largely qualitative view of the diffuser, how it
works and the basic design principles. Following this, a more detailed quantitative and theoretical analysis of the diffuser will be given. In these descriptions, the ingenuity of the original design concept will hopefully become apparent. In addition, more recent developments will be presented, illustrating weaknesses in the original design which can be overcome by modifying the design procedure, sometimes using one of Schroeder’s favourite subject area of number theory. Finally, it will be shown that better phase gratings can be made using an optimization procedure.
