Relationship Between the Scattering Coefficients Determined with Coherent Averaging and with Directivity Correlation

There exist three kinds of methods to determine the scattering coefficients of architectural surfaces: 1) the reverberation room method, using coherent averaging of room impulse responses during sample rotation, 2) the freefield method, using coherent averaging of reflected responses during sample rotation, 3) the free-field method, using directivity correlation between reflected fields with a sample and with a flat reference surface. This paper discusses the relationship among the scattering coefficients determined by the three methods. Numerical simulation demonstrates that the two free-field methods give little different values at mid and high frequencies for a 1D sinusoidal surface, but not to the same extent for a 2D sinusoidal surface. Subsequently, this disagreement is examined in comparison with experimental results obtained by the reverberation room method and with theoretical ones. Theoretical consideration reveals that the dominant reason for the disagreement is due to different averaging processes in the three methods, which take the arithmetic mean or the quadratic mean of specular reflection factors with respect to azimuthal incidence angle, respectively.