# Reflective Inverse Diffusion
## 4 Results
### Speckle Size and Pre-Optimization  
The SLM was segmented into \(N\times N\) segments, where \(N=\{2,4,8,16,32\}\), with random phase values applied to each segment and the speckle pattern recorded with the CCD. The speckle patterns in Figure 3 were produced by the sandblasted aluminum sample and show the variation of speckle pattern size as \(N\) is increased. All of the tested reflector materials showed a similar variation in speckle pattern size with respect to \(N\). Simulated images are included in Figure 3 for comparison. They were generated using Equation (15) with the reflector term, \(e^{\mathrm{i}\Theta(u,v)}\), modeled as a uniform phase distribution with a magnitude of one. Histograms of the measured and simulated intensity speckle patterns fit a negative exponential probability density function, which is expected for fully-developed speckle [17]. A transmissive inverse diffusion experiment was conducted based on [PERSON]'s original research and used as a point of comparison. Using a white paint on glass sample as the scattering media, the size of the background speckle did not change with \(N\). This was due to the imaging optics used and placed closely to the scattering sample.  
The algorithm sequentially optimized the \(N\times N\) segments of the SLM to produce a focused spot on the CCD. For cases where \(N\geq 4\), pre-optimization was accomplished, i.e., the SLM was optimized for each previous value of \(N\). After each stage of \(N\times N\) optimizations, the algorithm proceeds to the next value of \(N\) by splitting each segment horizontally and vertically into four, equally-sized, smaller segments. These smaller segments are then individually re-optimized, and the process is repeated until the desired \(N\) is reached. The spot intensity produced by a pre-optimized SLM was compared to the spot produced by an SLM that was not pre-optimized. In addition, two different phase modulation step sizes, \(\Delta\Phi=\frac{2\pi}{5}\) and \(\frac{\pi}{10}\), were used for the pre-optimization trials.  
Figure 2: Simulation validation. The diffusely-reflecting sample was replaced by a mirror to compare measured and simulated intensity patterns. A negative lens phase screen was used to position the focus onto the CCD.  
The results of pre-optimization for the graphite sample are shown in Figure 4. Pre-optimization did not appreciably affect the spot intensity for \(N\leq 8\), but improved spot intensity for \(N\geq 16\). An increase in peak intensity of approximately 40% is shown in the pre-optimized trial for \(N=32\). Computer simulations with a uniform phase reflector model showed a more modest effect with only a 5% increase in peak intensity in the pre-optimized trial for \(N=32\). A decrease in the phase modulation step size from \(\Delta\Phi=\frac{2\pi}{5}\) to \(\Delta\Phi=\frac{\pi}{10}\) improved spot intensity by 20% for the graphite reflector and by 10% in simulation. Pre-optimization was shown to increase peak intensity for all of the reflector materials for \(N\geq 16\). The amount of improvement was dependent on the individual material surface properties, such as roughness and correlation length. The exact relationship the material surface properties have on enhancement must be examined in future research.