# The Potential of Focusing Acoustic Retroreflectors for Architectural Surface Treatment
## 5 Conclusions  
By generalizing the concept of an acoustic retroreflector as a space-reversal surface, this study was able to investigate ideal acoustic retroreflector array performance for various patch sizes (0.3 m and greater) and distances (1.5 to 4 m). The introduction of delay-based focusing also allowed the systematic investigation of arrays of focusing retroreflectors. Focusing retroreflector arrays were shown to outperform non-focusing counterparts. Physically realizable configurations of parabolic trihedra confirm that results similar to ideal reflector results are possible through the design of passive surfaces. The study is mostly concerned with speech-A-weighted response because the envisaged applications in buildings are for speech support. For this spectral weighting, findings include:  
* The recommended width of individual non-focusing retroreflectors in an array is in the range of 0.6 to 1.2 m (areas 0.36 to 1.44 m\({}^{2}\)) for source distances 1.5 to 4 m. An extensive array can achieve mean retroreflected energy levels of \(-1\) dB or more (up to 5 dB), however, a smaller array (a 2.4 m square, with some source-receivers near its edges) is much less effective, especially for larger distances. * The recommended width of individual focusing retroreflectors in an array is in the range of 1.2 to 2.4 m (areas 1.44 to 5.76 m\({}^{2}\)) for source distances 1.5 to 4 m. An extensive array can achieve mean retroreflected energy levels of 3.5 dB or more (up to 7.5 dB). Again, a smaller array returns significantly reduced sound, especially for larger distances. * While a single large focusing retroreflector can return the most energy to the source for a given solid angle, an array of multiple focusing retroreflectors provides a more even response for a variety of source positions. In an array, focusing retroreflectors adjacent to the nearest one contribute to the retroreflected energy. * In principle, an extensive focusing retroreflector array can achieve mean speech-A-weighted retroreflected energy levels 15-20 dB greater than an equivalent specularly reflecting surface; and a local (2.4 \(\times\) 2.4 m) reflector can achieve retroreflected energy levels more than 10 dB greater than a corresponding specular surface. These findings are promising indicators of potential solutions to supporting people's speech through architectural surface treatments. However, further research is needed to develop and evaluate practical methods to deploy the concepts introduced by this paper. Envisaged future research by the authors includes the development, characterization, and physical testing of optimal focusing retroreflector array designs for applications such as ceiling treatments. Subsequent human experiments will involve voice-regulation and acoustic qualitative testing of treated environments. Experimental results from this research project will provide the basis for recommendations on improving room acoustics for speech by incorporating high levels of voice support without excessive reverberation. Conceptualization, D.C., S.L., J.H. and M.Y. ; methodology, D.C., S.L. and J.H. ; software, J.H., S.L. and D.C.; validation, D.C. and S.L. ; formal analysis, D.C. and S.L. ; investigation, D.C. and S.L. ; data curation, D.C.; writing--original draft preparation, D.C.; writing--review and editing, D.C., S.L., J.H. and M.Y. ; visualization, D.C. and S.L.. All authors have read and agreed to the published version of the manuscript. **Funding:** M.Y. was supported by a DRG (German Research Foundation) grant - Project number 503914237. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.