# Reflective Inverse Diffusion
## 4 Results
### Reflector Materials
This was expected and similar to transmission experiments [9], since the 21 phase values used for optimization represent an extremely small sample of the total phase space. The enhancement predicted by the computer simulations corroborates the experimental data. The effects of speckle decorrelation were simulated by adding a zero-mean random Gaussian-distributed phase to the reflector model each time the intensity was calculated. The standard deviation (\(\sigma\)) of the random phase fluctuation was dependent on the severity of decorrelation time of the material. Brushed aluminum maintained the highest correlation coefficient over time (see Figure 5), thus experiencing the lowest amount of enhancement loss attributed to speckle decorrelation. Simulations of the metal samples corresponded to a Gaussian phase fluctuation with standard deviation of \(0.5^{\circ}\) to \(2^{\circ}\). The  
Figure 8: Optimized spot intensities for transmissive inverse diffusion for the white paint on glass sample for \(N=4\) through 32 (top) and corresponding intensity cross-sections (bottom). Background speckle size is relativity constant as \(N\) increases. Figure 7: Optimized reflective inverse diffusion spot intensities for the brushed aluminum reflector for \(N=4\) through 32 (top) and corresponding intensity cross-sections (bottom). more diffuse samples, such as graphite and white paint, matched with a standard deviation of \(3^{\circ}\) to \(5^{\circ}\). Figure 10 shows enhancement per iteration for a given standard deviation of the Gaussian phase fluctuation. Figure 10: Simulations of reflective inverse diffusion enhancement with zero-mean Gaussian distributed random phase fluctuations added to the reflector model. With the exception of \(\sigma=8^{\circ}\), all reflector models are unimodular with a uniformly-distributed random phase. For \(\sigma=8^{\circ}\), both the uniformly-distributed random phase model (red) and the circular Gaussian model (blue) are shown. The \(N=16\) iterations are highlighted in gray. The \(N=32\) iterations are highlighted in yellow. Figure 9: The enhancement produced from a pre-optimized SLM for a given number of segments is plotted for computer simulations and experimental data for various reflector materials. Equation (10) is plotted (dotted-dashed line) for comparison. Spectralon\({}^{\textregisteredregistered}\), with its high depth of light penetration and multiple reflections, was considered similar to the random paths experienced by light when transmitted through a scattering medium. Simulations of both the circular Gaussian model from transmissive inverse diffusion and uniform phase model produced similar enhancement with the same phase fluctuation standard deviation deviation of \(\sigma=8^{\circ}\) (see Figure 10). The enhancement for the uniform phase model does initially rise faster than the circular Gaussian model, which is expected based on the slopes of Equations (3) and (10). However, due to the decorrelation effects and limited number of phase values used in the optimization process, neither model was significantly better than the other at simulating the Spectralon\({}^{\textregistered}\) results.