The Diffusion Coefficient, D, is a measure of the degree to which a potential diffusing surface uniformly scatters sound. We now describe another metric, called the scattering coefficient,
.
The ISO/TC 43/SC 2/WG25 working group, of which Dr. D'Antonio is a member,
is now evaluating an approach to measure the random incidence scattering
coefficient of surfaces. This scattering coefficient is intended to be used
in room acoustic calculations and simulation / auralization models. The
scattering coefficient, ,
defines the fraction of the scattered energy that is uniformly diffused.
Figure 1 illustrates the normalized incident energy, denoted by a 1, the scattered sound, denoted by (1-
),
and the specularly reflected energy, denoted by (1-)(1-).
Diffusor Geometry
Recently, Mommertz and Vorlander suggested a novel and elegant measurement scheme for determining the random-incidence scattering coefficient, which is needed in geometrical room modeling programs. This scattering coefficient of rough or structured surfaces is defined as the ratio of non-specularly reflected sound energy and totally reflected energy. The scattering coefficient does not include any information about the directivity of the scattered energy. This information is provided by the diffusion coefficient, D.
The total energy, Etotal, available to be scattered is given by (1-
),
where
is the familiar and standardized random incidence absorption coefficient.
The specular component, Espec, can be described in terms of the
directional scattering coefficient, .
The energies (normalized with respect to a reflection from a rigid plane
plate) can be expressed in terms of: 
The quantity a can be called a "pseudo-specular absorption coefficient" and Rspec is the specular reflection coefficient.
From these equations, the scattering coefficient,
,
can be determined by: 
Free Field And Reverberation Room Methods
The principle of both the free-field and reverberation methods can best be shown in the time domain, by looking at the effect of a structured surface on reflected, band-limited pulses. Figure 2 shows three reflected pulses obtained in front of a surface covered with randomly distributed rectangular battens. The curves were measured for different orientations of the sample. It can be seen that the first part of the reflection shows a high correlation. This corresponds to the specularly reflected component. In contrast, the scattered part contains delayed sound waves, which depend on the structure of the sample. This is changed by varying the orientation and hence the scattered components may be assumed to be incoherent.
Figure 2. Exemplary reflected pulses (10 kHz 1/3-octave band) obtained for different sample orientations.
By means of phase-locked averaging of n pulses (n>10) obtained for different orientations of the sample, the incoherent scattered sound is eliminated by destructive interference and the coherent specularly reflected sound component is obtained. In the free field method, measurements of the specular energy, Espec, are made every 100 degrees in azimuth for a given angle of elevation. Paris' formula can be used to average data collected at different elevation angles. The total reflected energy, Etotal, can be estimated by the averaged pulse energy. Thus, knowing a and
from Espec and Etotal, respectively one can calculate
.
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Evolution of the Scattering Coefficient
Introduction
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