One of the important uses of being able to quantify the 3D backscattered sound is to evaluate potential architectural acoustic surfaces. The following data clearly reveal the differences between specular scattering, re-direction and diffusion.
Specular ScatteringIn Figure 1 we illustrate a periodic array of (16) 3.5" (90 mm) x 3.5" (90 mm) x 23.625" (600 mm) battens oriented parallel to the x-axis of the 3D scattering pattern for normal incidence in the 2 kHz 1/3-octave band shown in Figure 2. The scattering along x is essentially specular, wheras the battens offer modest diffusion parallel to the y-axis.
Figure 2: 3D scattering pattern from a parallel array of rectangular
battens aligned parallel to x at normal incidence in the 2 kHz 1/3-octave
band. 
RedirectionFigure 4 shows an example of the type of scattering obtained using the 3D goniometer for a square-based pyramid, shown in Figure 3, 4.92' (1.5 m) x 4.92' (1.5 m) x 1.15' (0.35 m) at normal incidence in the 2 kHz 1/3-octave band. Note that the four-fold symmetry of the square-based pyramid is revealed in the four symmetrical scattering lobes. The absence of appreciable specular scattering for normal incidence is also indicated by the dip in the center of the scattering pattern. By contrast, the parallel battens scatter a significant amount of energy into the specular direction. While pyramids are often classified as diffusors, they essentially provide redirection. This redirection contributes to the diffusivity of the sound field, but large 2' x 2' and 4' x 4' pyramids do not produce diffuse reflections.
Figure 4: Backscattered pressure from a square based pyramid at normal
incidence in the 2 kHz 1/3-octave band 
DiffusionThe number theoretic diffusor offers an elegant and efficient means of obtaining diffuse reflections and uniform diffusivity. RPG's 2' (568 mm) x 2' (568 mm) x 6 3/8" (162 mm) 2D Skyline® diffusor is pictured in Figure 5. The 3D scattering pattern obtained with the 3D goniometer from an array of (4) Skyline® units is shown in Figure 6. The Skyline® is an optimized primitive root diffusor. The 2D phase grating consists of 156 distinct phase blocks. Notice the uniform scattering into the diffraction directions, indicated by the outward pointing lobes, at normal incidence in the 2 kHz 1/3-octave band. The Skyline® can be used for wall or ceiling diffusion.
Figure 6: Backscattered pressure from a 2D optimized primitive root RPG
Skyline® diffusor at normal incidence in the 2 kHz 1/3-octave band
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