# The Potential of Focusing Acoustic Retroreflectors for Architectural Surface Treatment
## 3 Results
### Large Ideal Reflector Array
#### 3.1.1 Retroreflected Energy Levels  
The distributions of speech-A-weighted retroreflected energy levels (\(L_{\text{retro}}\)) for the 25 source-receivers in a square offset from the large reflector are shown in Figure 5 (boxplots for 2 m and 4 m surface distances) and Figure 6 (energy averages for space-reversed and space-reversed focusing patches, 1.5-4 m surface distances). The'simple' (neither spatially reversed nor focusing) patch size had no effect, because the patches involve no change. The range of reflected energy for a given surface distance was very small in the simple case for  
Figure 4: The seven large parabolic trihedron array and its shadow on the source-receiver plane (blue). The shadow of the small array is also shown (green). Single trihedron cases only use the one in the respective array center. Sources are within the yellow area (2.4 \(\times\) 2.4 m). The red dotted line traces the central source-to-vertex distance, which was extended for clarity. all tested surface distances. Results deviated by less than 0.1 dB from theory (Equation (3)) for each of the six surface distances. The results for focusing patches were strikingly different. For small patches (e.g., 0.3 m) the patches were too small to have a substantial focusing effect. As the patch size increased, the maximum (at the focus of a patch) increased, but the range of values increased even more dramatically. Hence, the results describe a reflector that introduces a highly variable retroreflected energy level over the source-receiver plane, which does not have an obvious useful application in architectural contexts. The single 7.2 m patch spans the entire reflector, with an extremely large range of values over the 2.4 \(\times\) 2.4 m source-receiver square. The  
Figure 5: Distribution of retroreflected energy levels for 25 collocated source-receivers. The reflector is a 7.2 \(\times\) 7.2 m square, and 24 source-receivers are in a 2.4 \(\times\) 2.4 m square centered on the reflector at (**a**) 2 m or (**b**) 4 m distance. One source-receiver is at the focus of a 3.6 m patch on the same plane, beyond the 2.4 \(\times\) 2.4 m square. Values are speech-A-weighted. Figure 6: Spatially averaged retroreflected energy levels at collocated source-receivers for space-reversal and focusing space-reversal surface configurations. Twenty-four source-receivers are located within a 2.4 \(\times\) 2.4 m square offset from the centroid of a 7.2 \(\times\) 7.2 m reflector, and one is located at the focus of a 3.6 m patch. Distances from source-receiver to reflector are indicated by the \(x\)-axis. Dashed lines show theoretical expectations (Equations (2), (4) and (5)). Values are speech-A-weighted. maximum value for the single patch was consistently less than theory (Equation (4)), but within 0.7 dB. Note that the bulk of the 3.6 m focusing patch results are very low, partly because the patch's focus is beyond the 2.4 \(\times\) 2.4 m source-receiver square. Results for space-reversal patches show increased medians, and relatively small ranges, which is consistent with retroreflection. Retroreflection was most efficient for 0.6 m to 1.2 m patch sizes. The single 7.2 m patch was ineffective in boosting the retroreflected energy, yielding results slightly lower than the simple reflector. The reason for the slightly reduced \(L_{\text{retro}}\) is that spatial reversal introduces retroreflection at incidence angles larger than 0\({}^{\circ}\). The focusing space-reversal patches had the most promising retroreflected energy levels. The maximum for the 7.2 m patch was the same as that for the focusing patch without space reversal, which is expected when the source is at the patch focus. However, at a 2 m surface distance the extreme range of single 7.2 m focusing space-reversal values makes it an unlikely design choice; whereas at a 4 m distance the range is less extreme. The subdivided reflector patches provided strong retroreflected energy with a usefully small ranges of values over the source-receiver plane.