# Reflective Inverse Diffusion
## 4 Results
### Speckle Pattern Decorrelation  
The speckle pattern produced by a fixed SLM phase map and the diffusely-reflecting sample varied with time. The decorrelation of the speckle pattern is a function of both the material properties of the diffuse reflector and the laboratory test conditions. Figure 5 shows the correlation coefficient  
Figure 4: Intensity cross-sections from the CCD using the graphite reflector performed both with and without pre-optimization. The SLM is divided into (**a**) \(4\times 4\) segments, (**b**) \(8\times 8\) segments, (**c**) \(16\times 16\) segments and (**d**) \(32\times 32\) segments.  
Figure 3: Speckle size as \(N\) increases. The SLM segment values are random. The images in (**a**) to (**e**) were created using the sandblasted aluminum reflector with \(N=2\) through \(N=32\), respectively. The images in (**f**) to (**j**) were simulated using a reflector model with a uniform phase distribution for \(N=2\) through \(N=32\), respectively.  
over time for the brushed aluminum, transmissive white paint and Spectralon\({}^{\textregistered}\) samples. As expected, the metal reflectors maintained a much higher correlation coefficient; thus, most of the decorrelation for the metal reflectors is attributed to the changing environmental conditions of the laboratory, such as temperature, air currents from the laboratory ventilation system, minute mechanical vibrations and device measurement error and noise. Previous work in the transmissive inverse diffusion shows enhancements (\(\eta\)) ranging from 50 to 1000 using both iterative and transmission matrix methods [3; 4; 6; 9; 20]. The cause of this wide range of enhancement values is still currently being investigated, with some of the disparity likely caused by noise [20].  
The total noise in the system produced small, low frequency oscillations in the correlation coefficients plotted in Figure 5. The oscillation caused microscopic shifts in the reflector. This affected the correlation of the speckle produced by the volumetric scatterers, such as Spectralon\({}^{\textregistered}\) and the white paint samples, more than the metal reflectors due to the longer internal path length changes of the material. The depth of penetration of Spectralon\({}^{\textregistered}\) has been measured at 200 \(\upmu\)m for HeNe light [21], which is over 20-times the root mean square (RMS) roughness of any of the metal samples (see Table 1). The small shifts of the reflector in concert with the larger internal path length changes in the material caused Spectralon\({}^{\textregistered}\) to initially decorrelate much faster than the other samples. This decorrelation over time adds a degree of uncertainty to the process, where previously-optimized SLM segments are in fact suboptimal by the time the process is complete. These suboptimal segments cause a decrease in the overall spot enhancement. This decorrelation effect was simulated by adding a zero-mean Gaussian-distributed random phase, with a standard deviation between 0.5\({}^{\circ}\) and 10\({}^{\circ}\), to the sample each time the intensity pattern was calculated. The standard deviation of the random phase was dependent on the severity of the decorrelation effect of the sample.