Intl. Cooperation Ctr. for Sci. and Technol., Tokyo Inst. of Technol., O-okayama, Meguro-ku, Tokyo 153, Japan
The quantitative description of diffraction started with Fresnel, who introduced the interference effect to Huygens' principle where diffracted waves are expressed by an integral of secondary wavelets over an opening in an opaque screen. Although this diffraction formula is an approximate one, it has given precise estimation of waves diffracted by the opening. Most diffraction phenomena arise from 3-D objects. However, attempts to apply the diffraction theory to 3-D objects are unsuccessful since, in these cases, the region for integration of secondary wavelets cannot be determined clearly. In order to explain the diffraction by polyhedrons, a hypothetical observer is assumed at an observation point and the Huygens--Fresnel principle is extended to a space seen by the observer virtually. In this virtual space the observer can see real images and mirror images through facets of the polyhedron and every point in real and mirror images is considered as a center of the secondary wavelets. The new representation of sound field diffracted by 3-D objects that satisfies both the wave equation and boundary conditions is derived by this extension [J. Acoust. Soc. Am. 95, 2354--2362 (1994)]. The algorithm to obtain solutions from this representation will be discussed in detail.