In previous issues of Diffuse Reflections, we have described an approach to evaluate the degree to which a a potential diffusing surface uniformly scatters sound. This is the diffusion coefficient, . We now present another metric, called the scattering coefficient, d, which defines the fraction of the scattered energy that is diffused. Figure 1 illustrates the normalized incident enerty, denoted by a 1, the scattered sound, denoted by (1-), and the specularly reflected energy, denoted by (1-)(1-).

Figure 1. Types of scattering from a rough surface

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, described in Diffuse Reflections Volume 5 Issue 3.

The total energy, E_total, available to be scattered is given by (1-), where is the familiar and standardized random incidence absorption coefficient. The specular component, E_spec, 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 R_spec is the specular reflection coefficient.

From these equations, the scattering coefficiet, , 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, E_spec, are made every 10⁰ 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, E_total, can be estimated by the averaged pulse energy. Thus, knowing a and a from E_spec and E_total, respectively one can calculate .

In the next Issue of Diffuse Reflections, we will discuss the reverberation method in detail and show some sample results for semi-cylinders, rectangular battens and an RPG diffusor. One of the interesting aspects of the reverberation method is that it yields both the random incidence absorption coefficient and scattering coefficient. We will also examine the limitations of this method and the types of surfaces that can be evaluated using this technique.

Home: Research & Development: Research Topics: SCATTERING COEFFICIENT PART I