DIFFUSION COEFFICIENT

In 1994, RPG launched the publication of Diffuse Reflections with Volume 1 Issue 1 to share our vision, acoustics research, product development, application and standards activities. Over the years we have described the various steps in an evolving process to characterize the degree to which a surface uniformly scatters sound. In this issue, we summarize this research and describe a procedure and diffusion coefficient that the AES SC-04-02 Working Group on the Characterization of Acoustical Materials will be submitting as a potential standard. Please contact the AES Standards Committee (www.aes.org/standards) if you would like to participate in this process.

Diffusor Geometry

Diffusors are tested for their ability to scatter into two orthogonal planes or a hemisphere. Two orthogonal planes should be used when the diffusor is expected to display distinct anisotropic behavior, as might be the case for a cylinder, and two diffusion coefficcients given. When the diffusor is isothropic, hemispherical evaluation is needed and a single diffusion coefficient is given.

Near Field - Far Field

Diffusors are usually applied in situations where some sources and receivers are in the near field. If this is the case, then measurements should be carried out in the far and near field. Far field measurements monitor diffusion, while measurements in the near field monitor abberations, particularly focusing. The far field condition is obtained if the distances from the source and receiver fulfill the following requirements:

D_max is the largest dimension of the diffusor, is the wavelength and r is the distance from either the source or receiver to the measurement position. The near field may extend further for oblique sources and receivers.

True far field conditions require very large measuring distances, further than can be realistically achieved for many test geometries. If true far field conditions can not be achieved, it is necessary to ensure that at least 75% of receiver positions are outside the specular zone. If achievable within the above constraints, the source to reference point distance should be 10m and the receiver's semi-circle or hemisphere should have a radius of 5m.

Measurement should be made with a receiver angular resolution of 5⁰. To obtain random-incidence diffusion coefficient, source positions should be measured with an angular separation of 10⁰ covering a semi-circle or hemisphere.

Measurement

In Volume 5 Issue 1 we described the measurement goniometers needed. To avoid measurement errors caused by sound reflecting objects, an anechoic chamber or large non-anechoic reflection-free zone may be used. Boundary measurements may be carried out in a reflection free zone when one plane data are required. For each source and receiver pair the following measurements are required:

1. h₁(t), impulse response with diffusor present
2. h₂(t), impulse response without diffusor present
3. h₃(t), impulse response of source/microphone pair, with source in diffusor position on axis with each microphone The diffusor impulse response, h₄(t), is obtained by the inverse Fourier Transform, IFT, of the ratio of the Fourier transform of the sample diffusor plus background, h₁(t), minus the background, h₂(t), divided by the Fourier transform of the source/mic impulse response. The data reduction process was described in Volume 5 Issue 2.

Directional Diffusion Coefficient

For a fixed source position, in each 1/3-octave band, the directional diffusion coefficient, d, can be calculated from the set of levels L_i, from the n receivers. A diffusor that scatters sound completely will have a diffusion coefficient of 1. When the scattered level is concentrated in one measurement location, the diffusion coefficient approaches zero.

Random Incidence Diffusion Coefficient

When a sufficient number of source positions are chosen over a complete semi-circle or hemishpere, then the directional diffusion coefficient may be averaged over all source positions to obtain a random-incidence diffusion coefficient.

In the next issue of Diffuse Reflections, we will describe the random-incidence scattering coefficient, , which quantifies the percentage of the reflected energy that is scattered into non-specular directions. can be used in geometrical model programs.