# Reflective Inverse Diffusion
## 4 Results
### Reflector Materials  
The spot intensity enhancement (\(\eta\)), measured surface roughness (\(R_{rms}\)) and final FWHM spot size are summarized in Table 1 for each of the reflector materials. The spot intensity is the RMS value of the CCD pixels inside the FWHM radius. The background intensity is the RMS value of the CCD pixels at a radius of three-times the FWHM and beyond. The algorithm ran with pre-optimization starting with \(N=2\) through \(N=32\) for all six reflector materials. The spot enhancement was calculated after each segment was optimized and is shown in  
Figure 5: The correlation coefficient of the speckle pattern produced by an unoptimized phase map as a function of time. Phase maps for \(N=16\) and 32 are shown for the brushed aluminum, transmissive white paint on glass and Spectralon\({}^{\textregistered}\) samples. Figure 6. The smaller optimized segments in the \(N=32\) case produced no improvement compared to the \(N=16\) case for the graphite and Spectralon\({}^{\text{\textregistered}}\) reflectors. The enhancement for the white paint reflector continued to increase slowly during the initial segment optimization of the \(N=32\) stage, but began to decrease midway through the optimization process. At the completion of the \(N=32\) stage, the enhancement for the white paint reflector is only slightly higher than the \(N=16\) enhancement. Decorrelation is believed to be the cause for the lack of enhancement for the Spectralon\({}^{\text{\textregistered}}\) reflector. As a bulk scatterer rather than a surface reflector, Spectralon\({}^{\text{\textregistered}}\) causes light to undergo multiple scattering events before exiting. Studies have produced penetration depth estimates of 200 \(\upmu\)m for HeNe light in samples of Spectralon\({}^{\text{\textregistered}}\)[21]. This depth is approximately 20-times the thickness of the white paint sample used in transmissive inverse diffusion experiments, which indicates that larger internal path length changes occur in the Spectralon\({}^{\text{\textregistered}}\) sample. The greatest enhancement was achieved using the brushed aluminum reflector. The spot optimization for the brushed aluminum reflector is shown in Figure 7 along with the normalized intensity cross-section. The intensity cross-sections are shown as the algorithm completes each stage of \(N\times N\) optimizations. The cross-sections are normalized by the RMS intensity produced by a random \(N\times N\) phase map applied to the SLM. A single transmissive inverse diffusion experiment was conducted based on [PERSON]'s experimental setup [9]. The white paint on glass sample was used for enhancement comparison between transmissive and reflective inverse diffusion. The results of the spot optimization and corresponding intensity cross-section are shown in Figure 8. In reflection, background speckle size decreased as \(N\) was increased; however, in the transmission trial, the background speckle was relatively constant for all \(N\). The algorithm failed to produce additional enhancement during the \(N=32\) stage for the baseline white paint transmission trial. Again, this is believed to be due to the decorrelation of the speckle pattern. The spot for the \(N=32\) stage was larger than the previous \(N=16\) spot. Decorrelation of the individual background speckles produced a smearing effect that produced an overall larger target spot. Figure 6: Reflective inverse diffusion enhancement for each of the six reflector materials. The \(N=16\) iterations are highlighted in gray. The \(N=32\) iterations are highlighted in yellow. As the algorithm completes each stage of \(N\times N\) optimizations, the enhancement is plotted as a function of total optimized SLM segments and compared with Equation (10). The results of a simulation using a uniformly-distributed random phase reflector model with reflectivity of one are show in Figure 9 without any added noise or decorrelations effects. The simulation and experimental data show similar trends, but less enhancement than predicted by Equation (10).