Geometric solutions for focusing retroreflectors

Abstract

Although focusing might normally be an architectural acoustician’s nightmare, combining it with retroreflection is potentially beneficial. Focusing acoustic retroreflectors concentrate early reflected sound onto arbitrarily located sources. Dihedral and trihedral retroreflectors can be made to focus by curving one or more of their faces in either one or two dimensions. The relationship between curvature and focal distance is developed empirically using analytic ray tracing and finite-difference time-domain methods. Dihedra can be made more compact by segmenting the cross-sectional curvature similar to the Fresnel lens. Complexities of fabricating doubly curved surfaces can be overcome by approximating with several flat surfaces and physical examples are constructed from bending sheet-steel. Simplified designs are shown to achieve similar performance to ideally curved focusing retroreflectors. For context, performance is compared to coherent and incoherent summation of a perfectly reflecting spherical surface of equivalent solid angle, as well as an equivalent flat surface. Results show increased speech-weighted retroreflected energy level and concentration of sound in the region surrounding the collocated source-receiver over the upper range of typical human speech (1 kHz–8 kHz octave bands) when compared to non-focusing retroreflectors, and substantial increases in reflected energy level compared to a specular reflection at normal incidence.