The sample may be mounted on a turntable and placed in reverberation chamber, Figure 1. Room impulse responses are measured for fixed loudspeaker and microphone positions with the sample rotated from one measurement to the next.
Figure 1: (a) Extract from sample structures (batten width/mean distance > 0.5). (b) Experimental set-up indicating different sample orientations.
Assuming a plane surface, under ideal conditions, the room impulse responses are fully correlated. In contrast, when measuring rough surfaces, the decorrelation increases with increasing time. Assuming statistical independence between specular and scattered sound components, it can be shown that after additions of "n" room impulse responses, the short-time averaged energy E(t) of the resulting impulse response can be expressed by:
Assuming sufficient averaging (n>30-100), the second exponential term can be neglected (Figure 2 (ii)). Regarding the test sample, the impulse response contains only those sound waves that were specularly reflected.
Figure 2. (a) Impulse responses measured in the reverberation chamber (10 kHz 1/3 - octave band), [i] one measurement [ii] after phase-locked addition of 94 room impulse responses(b) Corresponding "integrated impulse responses".
In principle, the sample has a pseudo-specular absorption coefficient a, which can be determined from the reverberation time in the same way as this is usually done (e.g. following ASTM C423/ISO 354). Thus, for the determination of scattering coefficients, three reverberation times (RT) have to be evaluated: the RT's of the empty room (
empty),
the RT's of the room with sample inserted (sample)
and the RT's after phase-locked superposition of many different room impulse
responses (asample). Provided that these three "absorption
coefficients" have been determined, the scattering coefficient can be calculated
according to: 
Figure 3 shows the scale model results obtained for the two different surfaces. The data were obtained after averaging the absorption coefficients for six different microphone - loudspeaker positions.
Figure 3. Scattering coefficients measured for two different test samples.
Scale model measurement for an RPG QRD® 734 Diffusor are shown in Figure 4.
Figure 4. Scale model random incidence absorption and scattering coefficient measurements of an RPG QRD® 734 Diffusor.
Measurements have also been carried out in a full-scale reverberation chamber using a sample surface of 8 square meters. In these experiments the sample orientation was manually changed. It was shown that the method can also be applied in the full-scale reverberation room. Several practical problems are still under investigation. These include the influence of sound propagation conditions, such as temperature variations, edge effects due to rotating full-scale commercial products that cannot be altered into round samples, restrictions on surface topology depth to width ratios,the ability to rank surfaces properly, and in general which sample topologies are conducive to being evaluated by the method.
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Evolution of the Scattering Coefficient
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