Diffuse Reflection Of Rays From Surfaces

The characterization of diffusion is currently undergoing considerable study. It has been assumed that a diffusing surface can be characterized by means of a coefficient, similar to the Sabine absorption coefficient, that varies between 0 (specular reflection) and 1 (complete diffusion), which can be measured in a standard way. Just as was the case with absorption, there may be different formulations depending on whether we are in a free field, having a given angle of incidence, or a diffuse field, with a random angle of incidence. To characterize the surface diffusion a scattering coefficient and measurement methodology were proposed by Mommentz and Vorlander, (1995)

Etot Espec + Ediff

The scattering coefficient is the ratio between the diffusely reflected energy and the total reflected energy. Here a diffuse reflection is defined as any nonspecular reflection, even though a perfect diffuser will radiate a portion of the incident energy in the specular direction and even though a redirection rather than perfect diffusion of the energy may be what is occurring.

Measurement of the Scattering Coefficient

The measurement of all the diffuse energy is difficult so most methods measure the specularly reflected energy and use the diffuse absorption coefficient to calculate it

Etot Etot where Espec /Einc = 1 — aspec = normalized specularly reflected energy Etot /Einc = 1 — a = normalized total reflected energy so,

1 — a which gives us a way of measuring the diffusion coefficient, 5.

Farina (2000) has suggested the technique pictured in Fig. 22.16, using a microphone 2 m above the floor that is dollied past a diffusing surface suspended 3.65 m above a loudspeaker flush mounted into the floor. Impulse response data are recorded at regular (28 mm) microphone intervals. Time windowing filters out the direct sound so that the impulse response of the reflection from the panel under test is obtained. The results from various panels are given in Fig. 22.17. Although this method yields consistent results, the technique has not been accepted as a standard. Some (e.g., D'Antonio, 1995) prefer a diffusion coefficient that characterizes the evenness of the diffused energy, based on the standard deviation of the measurements around a test surface. This approach is helpful for a comparison of products but not, as yet, particularly useful for modeling applications.

Diffuse Reflections

When a sound ray impacts a surface some of the energy is reflected specularly and some is diffused. The portion of the energy reflected specularly creates an intensity at a receiver (Naylor, 1993)

^ = 4 ^ + )2 t1 — a)(1 — 5) e—y (r1 + r2) (22.48)

Figure 22.16 Measurement Methodology for the Specular Absorption Coefficient (Farina, 2000)

Figure 22.16 Measurement Methodology for the Specular Absorption Coefficient (Farina, 2000)

Figure 22.17 Comparison of Measured and Predicted Specularly Reflected Intensities (Farina, 2000)

Flat Panel

I oo

Direct Calculated

Figure 22.17 Comparison of Measured and Predicted Specularly Reflected Intensities (Farina, 2000)

Flat Panel

I oo

Direct Calculated

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