## 5 Conclusions  
[PERSON]'s method for measuring transmission matrices was successfully implemented to measure an RM. The method only requires the optical system to be linear. Both the focal-plane and the imaging systems produced RM capable of refocusing light onto the CCD. The RM is capable of enhancing a single CCD segment, or multiple segments simultaneously. For single segment enhancement, the focal plane system achieved a maximum intensity enhancement of 8.5 and the imaging system achieved a maximum intensity enhancement of 24.2.  
Simulations showed that the focal-plane system achieves higher levels of enhancement for specific lateral surface dimensions (\(\ell_{\lambda/2}\)); outside of this optimum range, the imaging system produces better enhancement. Laboratory data showed that the imaging system consistently produced higher levels of enhancement than the focal-plane system on all of the samples tested. This was expected as simulations predicted the imaging system would achieve higher levels of enhancement at lower values of \(\ell_{\lambda/2}\).  
The enhancement for both the focal-plane and imaging systems was significantly lower than that predicted by Equation (3) for the ideal simulated results. The primary cause of this was minute mechanical vibrations in the optical setup. This problem is accentuated due to the much longer propagation distances associated with reflective inverse diffusion and are not found in the transmissive case. Although enhancement for both methods was affected, incorporating a simple random vibration in the simulation model showed that the imaging system was capable of greater enhancement values in this non-ideal case. This is corroborated by the higher enhancement values achieved by the imaging system in the laboratory.  
Further research is required to solidify the RM measurement method. Improving the vibration isolation of the optical system will be key to improving the RM enhancement performance. Mathematical methods for combating the effects of vibration, such as DDDAS [23], should also be explored as a more cost-effective solution. Ideally, in the imaging case, the incident light is scattered by the same part of the rough surface regardless of which CCD segment is enhanced. Since the rough surface is assumed to be static, the scattering is deterministic [4]. Further research may yield methods of exploiting the deterministic process and lead to methods of reconstructing missing portions of the RM from partial data, or expanding an RM to include additional CCD segment locations without requiring the RM to be re-measured.  
This work is supported by the Air Force Office of Scientific Research. The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. [PERSON] developed the mathematical model, conducted the MATLAB(r) simulations, laboratory experiments, and wrote the paper. [PERSON] contributed to the idea, the mathematical model, and organization of the research. [PERSON] contributed to development of the mathematical model. [PERSON] supplied laboratory test samples and assisted with the interpretation of the experimental results. The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
AFIT Air Force Institute of Technology  
DMD digital mirror device  
LCoS liquid crystal on silicon  
SLM spatial light modulator  
HeNe helium-neon  
CCD charge-coupled device  
NPBS non-polarizing beam splitter  
BNS Boulder Nonlinear Systems  
DFT discrete Fourier transform