## 4 Results and Analysis
### Predicted vs. Measured Enhancement  
The best enhancement values from the aluminum samples were 10 to 24 times the RMS background intensity, which is less than 10% of the average enhancement of 300 to 400 achieved in simulation. Device error does not account for this discrepancy. Simulations included a random intensity fluctuation of \(\pm 5\%\) for each CCD pixel, while SLM pixels included a similar \(\pm 5\%\) fluctuation in phase. For both the imaging and focal-plane simulations, this random device error of \(\pm 5\%\) only decreased the average enhancement by approximately 10%. The RM is measured using the temporal FFT of intensity measurements from the CCD. Since the random intensity fluctuations do not occur at a specific frequency, the noise does not have a significant effect on the RM coefficients. The aluminum samples are assumed to be stable for much longer than the five minutes it takes to measure the RM. However, mechanical sources in the laboratory, such as the ventilation system, fume hoods, cooling fans, water and compressed air lines, produce micro-vibrations in the optical  
Figure 6: Observation plane intensity patterns (**a–c**) are computer simulations of the focal-plane system and (**d–e**) are laboratory results of the imaging system with the 600 grit aluminum sample. Above each spot are the (row, column) coordinates of the given observation plane segment. Phase maps generated by the RM (reflection matrix) are used to refocus light to single or multiple segments in the observation plane. (**a**) a simulated single-segment enhancement of \(\eta=348\) over background speckle; (**b**) simulation of two foci optimized simultaneously at \((72,72)\) and \((96,96)\) with enhancements of \(\eta=47\) and \(56\), respectively; (**c**) simulation of three foci generated with increased background speckle at \((72,72)\), \((96,96)\), and \((120,120)\) with enhancement values of \(\eta=26\), \(32\), and \(29\), respectively; (**d**) demonstrated single-segment enhancement of \(\eta=18\) over background speckle using the imaging system with the 600 grit aluminum sample (**e**) two segments are optimized simultaneously, measured enhancement for both foci is \(\eta=10\); (**f**) three foci are generated with increased background speckle at \((24,24)\), \((32,32)\), and \((40,40)\), enhancement values are \(\eta=7\), \(6\), and \(7\), respectively. setup that cause the incident light to shift on the rough-surface reflector. The oscillation of the RM measurement area produces intensity measurements that belong to several different RMs. For the imaging system with a simulated rough-surface lateral dimension of \(\ell_{\lambda/2}=7.8\) um, incorporating a random vertical and horizontal shift of the sample by 23.4 um, reduces average enhancement to \(\eta_{avg}=6\) and maximum enhancement to \(\eta_{max}=43\). For the focal-plane system with a simulated rough-surface lateral dimension of \(\ell_{\lambda/2}=10.3\) um, a simulated vibration magnitude of 20.6 um produces maximum enhancement of \(\eta_{max}=12\) and an average enhancement of \(\eta_{avg}=2.3\). The lateral surface dimension (\(\ell_{\lambda/2}\)) for the aluminum samples is much smaller than can be simulated without an unacceptable increase in processing time. However, trends between enhancement and \(\ell_{\lambda/2}\) from the experiments and simulations were extended and plotted for comparison in Figure 7. The imaging system shows the best alignment between experimental and simulation trends for maximum enhancement. The imaging system average enhancement trend lines for experimental and simulation data have matching slope despite the increase in separation. The experimental data for the focal-plane system showed very low enhancement with predominately flat trends for both average and maximum measured enhancement. Similar enhancement levels are achieved in simulation for \(\ell_{\lambda/2}=10.3\) um with the addition of the random vibration oscillation of 20.6 um. Simulations show enhancement increases for \(\ell_{\lambda/2}>10.3\) um.