## 3 Experiment Setup  
Turbulent free-space image sets and attenuated underwater sets of data are used in this study. Free-space turbulent data is collected using the following configuration. The imagery is collected using a 635-nm 5-mW laser, a Dalsa GigE camera, several Forth Dimension Displays binary phase ferroelectric spatial light modulators (SLMs), and standard optical tools such as mirrors, pinhole filters, and diffraction order filters. The SLMs are programmed with a binary phase hologram. Simulated turbulence is also added to the holograms. MATLAB is used to generate signals that synchronize the laser, SLMs, and camera. The lab setup, originally shown in Ref. [2], is displayed in Figure 1. The images generated by the free-space camera are 512 \(\times\) 512 pixels and subsequently cropped to 256 \(\times\) 256 pixels. They are resized to 128 \(\times\) 128 for computational efficiency. The free-space OAM images consist of 32 different patterns, created through multiplexing beams passed through combinations of five different phase plates with modes [\(-4\), \(-1\), \(2\), \(5\), \(8\)]. OAM patterns from this set are shown in Figure 2.  
Figure 1: Bench setup for free-space configuration. The free-space set is composed of three distinct data collects, where each group is collected at a specific turbulence level. Turbulence is simulated and imparted through inserting phase screens in the OAM beam path. The turbulence levels are \(D/r_{0}=5\), \(D/r_{0}=10\), and \(D/r_{0}=15\). Where \(D\) represents the linear dimension of the SLM and \(r_{0}\) is the [PERSON]'s parameter, which measures a signal's quality of transmission through the atmosphere. Thus, higher values in the ratio \(D/r_{0}\) represent increased turbulence and signal displacement, which amounts to signal crosstalk. Examples of OAM patterns at different turbulence levels are showing in Figure 3. The data collects will be referred to as TB5, TB10, and TB15, where each data collect includes images from each of the 32 patterns. Underwater data is collected using the following hardware setup. The laser source used in these measurements was a diode pumped solid state laser that operates at 532-nm and produces 5 nS pulses with 250 uJ/pulse. The intensity patterns are captured by a high performance, fast-frame-rate camera (Photron FASTCAM SA-Z). The camera is synchronized with the laser pulses at a rate of 1 kHz. As shown in Figure 4, the laser beam splits into four coherent beams and is expanded to pass through and fill vortex phase plates where an OAM phase is imparted to each beam. After leaving the phase plates, the beams are recombined using beamsplitters. The multiplexed OAM beam passes through a 1.2-m water tank and is routed to the camera using mirrors. Polyamid beads are added to the water to introduce signal scattering while small pumps agitate the water to ensure that the particles remain in suspension and homogeneously distributed. Attenuation length is measured by running a 15 mW, 532 nm CW probe laser parallel to the beam that is incident on a sensor. The OAM modes used for this configuration are [1, 4, \(-\)6, \(-\)8]. Images created by the camera for this setup are 1024 \(\times\) 1024 pixels. The images are cropped and then resized to 128 \(\times\) 128 pixels. Underwater OAM images consist of 16 unique patterns derived from combinations of four different phase plates. Examples of the OAM patterns are shown in Figure 5.  
The underwater set is composed of four different data collects, where each group is collected at a specific level of attenuation. Attenuation is created by adding polyamid beads designed for scattering light. Attenuation length sets are composed of levels 0, 4, 8, and 12. The sets will be referred to as AL0, AL4, AL8, and AL12. Each set includes images representing each of the 16 OAM patterns. Figure 6 shows attenuated patterns at the four levels of interest. Figure 2: Example of OAM patterns from the free-space data set. Figure 4: Bench setup for underwater OAM communication configuration.