### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 1pPA6. Extension of the Huygens--Fresnel principle to a virtual space.

**Mitsuhiro Ueda
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*Intl. Cooperation Ctr. for Sci. and Technol., Tokyo Inst. of Technol.,
O-okayama, Meguro-ku, Tokyo 153, Japan
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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.