## 3 Methodology  
### Laboratory Experiments  
The primary equipment for the laboratory experiment is a laser source, an SLM, and a CCD for feedback. The laser source is a Thorlabs 5-mW HeNe laser (\(\lambda=632.8\) nm) with a linearly polarized output. The laser is beam expanded to fully and uniformly illuminate the SLM. The Meadowlark model P512 is an LCoS (liquid crystal on silicon) SLM consisting of \(512\times 512\) pixels, each capable of over 16,000 discrete phase levels over a total \(2\pi\) phase stroke. The SLM has an effective area of \(7.68\) mm \(\times\) 7.68 mm with pixel pitch of \(15\) um. Intensity feedback is recorded using a Thorlabs model 4070-GE monochrome CCD with a resolution of \(2048\times 2048\) pixels and a pixel pitch of \(7.5\) um.  
A total of five rough-surface samples were made from 1-inch aluminum squares. Each sample received a different surface preparation; the first was bead blasted, while the remaining four were polished with 100 grit, 220 grit, 320 grit, and 600 grit sandpaper. Surface profiles of each sample were measured using a Tencor stylus profiler in both the \(x\)- and \(y\)-directions. The surface roughness, \(\sigma\), was calculated as the standard deviation in surface height in each direction and then averaged together to produce a single roughness value per sample. The sample roughness, \(\sigma\), and autocorrelation length, \(\ell_{c}\), are in Table 1.  
The RM of each sample was measured in three separate locations using the optical setup shown in Figure 1. This is the same optical setup used in the original reflective inverse diffusion experiments where the rough-surface reflector was placed at the focus of lens \(L_{1}\)[7]. The RM measurements were also repeated using the optical setup shown in Figure 2, where the single lens system produces a \(\
icefrac{{1}}{{8}}\)-scale image of the SLM on the rough-surface reflector. The RM was then used to refocus light individually to each of the \(M\) segments of the observation plane. The average and maximum intensity enhancement for each sample is shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Aluminum Samples** & **Roughness** & **Correlation** & **Slope** & **Correlation** & **Focal-Plane** & **Image Plane** \\  & \(\sigma\)/\(\mu\)m & \(\ell_{c}\)/\(\mu\)m & **s** & \(\ell_{\lambda 1/2}\)/\(\mu\)m & \(\eta_{avg}\) & \(\eta_{max}\) & \(\eta_{avg}\) & \(\eta_{max}\) \\ \hline
100 Grit & 2.13 & 54.25 & 0.143 & 2.21 & 1.6 & 7.2 & 2.2 & 10.1 \\
220 Grit & 1.67 & 35.25 & 0.141 & 2.24 & 1.5 & 5.8 & 3.1 & 13.3 \\ Bead Blasted & 1.04 & 30.25 & 0.105 & 3.00 & 2.2 & 8.5 & 6.1 & 22.5 \\
320 Grit & 0.63 & 13.75 & 0.107 & 2.97 & 1.3 & 4.5 & 4.3 & 16.7 \\
600 Grit & 0.45 & 16.00 & 0.066 & 4.79 & 1.3 & 6.0 & 5.4 & 24.2 \\ \hline \end{tabular}
\end{table}
Table 1: Summary table for the five aluminum samples. Roughness (\(\sigma\)) is the standard deviation of the sample surface height. Correlation (\(\ell_{c}\)) is the autocorrelation shift to reduce the maximum value by \(e^{-1}\). Slope (s) is the RMS (root mean square) surface slope. Correlation (\(\ell_{\lambda/2}\)) is the lateral distance required to change the surface height by \(\
icefrac{{\lambda}}{{2}}\) at the RMS slope (s). The samples average enhancement (\(\eta_{avg}\)) and maximum enhancement (\(\eta_{max}\)) achieved with each optical setup is included.  
Figure 1: Focal-plane optical setup for reflective inverse diffusion. A vertically polarized HeNe laser is expanded, collimated, and normally incident on the SLM (spatial light modulator). The phase modulated beam is then focused onto the rough-surface reflector with positive lens (\(L_{1}\)) and the reflected speckle pattern is recorded by the CCD (charged-coupled device). The mirror (\(M_{1}\)) and the NPBS (non-polarizing beam splitter) are used to allow normal incidence with the SLM. For focal-plane experiments and simulations, the lens focal length, \(f\), is 500 mm, and the distances \(Z_{1}\) and \(Z_{2}\) are \(15\pm 0.5\) cm and \(50\pm 0.5\) cm, respectively.