The use of acoustic phase grating surfaces, Schroeder diffusers, to attenua
te specular reflections has been investigated. The concept of primitive roo
t diffusers is reviewed and developed. Some guidelines for proper design ar
e given, and the limitations of the diffusers identified. A modification to
the primitive root sequence is suggested which results in a null in the sp
ecular reflection direction at multiples of the design frequency. This impr
oves the performance of the phase gratings particularly for modulated perio
dic arrangements. The use of optimisation to achieve better broadband notch
diffusers is detailed. (C) 2000 Elsevier Science Ltd. All rights reserved.