## 2 Materials and Methods
The moment of inertia, \(I\), was calculated to be 0.0197 kg\(\cdot\)m\({}^{2}\) using total mass and internal radius of the ring. If the motor rotates 22.5\({}^{\circ}\) in 1.5 s, then the angular rotation per minute, \(\alpha\), would be 24 and hence, the required torque, \(T_{rad}\), is 0.4728 N-m. According to the motor specification, motor torque, \(T_{motor}\), is 0.056 N\(\cdot\)m. Therefore, the gear ratio, \(\eta_{g}\) is rounded up to 9. Mass of water inside the ring is calculated considering a density of 1000 kg/m\({}^{3}\). Other structural parameters of the circular ring are provided in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Height, \(h\) & 31 cm \\ External radius, \(r_{ext}\) & 8 cm \\ Internal radius, \(r_{int}\) & 7.5 cm \\ Motor weight, \(m_{r}\) & 5 kg \\ Total weight, \(m_{t}\) & 7.01 kg \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Structural parameters of the circular ring. Figure 2: (**a**) Flowchart of the correction technique and (**b**) calibration setup with black tape targets located above each transducer to acquire calibration PA signal for the alignment of the transducers’ signals. The motor rotates 22.5\({}^{\circ}\) in 1.5 s. The data acquisition and motor rotation are synchronized using a LabView code. Based on the laser repetition rate, 75 view angles are defined within the 22.5\({}^{\circ}\). The size of the acquired data is 1200 \(\times\) 16 bits. For reconstruction, we used filtered back projection algorithm [36; 37; 38]. The algorithm requires the scanning radius as an input. Unlike a commercial ring array, where the transducers have been perfectly manufactured to be equidistant from the center of the ring, in the proposed system, the transducers are not equidistant from the center due to the manual insertion of the transducers into the holes on the ring; i.e., if 7.5 cm is used as the radius of the ring for all the channels, the reconstruction will be imperfect and lead to a distorted image. In fact, there is a shift in the expected location of the PA signals coming from the imaging target. Therefore, the calibration method is required. The original values of radius are within 7.58-7.68 mm (please see Table 2). An easy fix will be to change the scanning radius until an image with adequate quality is obtained. This method, is however, time consuming and somewhat inefficient. To address this issue and ensure all the transducers are equidistant from the center of the circular ring, a data correction algorithm is used. The flowchart of the correction methodology is provided in Figure 2a. In this method, we image high optical energy absorbent (trimmed homogenous black tape strips made of vinyl). A small piece of black tape is attached on the inner wall of the ring above each of the 16 transducers as shown in Figure 2. While imaging, the output laser from the optical fiber had sufficient energy to produce a distinguishable PA signal from the black tape for calibration. The PA signals generated from the black tape and imaging target do not overlap because they are spatially apart. Each transducer detects a PA signal from the tape that is located 180 degrees away from the transducer. The diameter of the ring, the distance between tape and the opposite transducer, is 15 cm. As a result, the PA signal generated from the tape is supposed to occur at the sample number corresponding to such distance, for all 16 channels. Since the signal shift is the same for both PA signals coming from the tape and the imaging target, the number of samples between the peak of the PA signal from the tape and the imaging target remains the same. To align the data of each channel, the arrays are truncated to the same length (5000 samples) with the last sample being the PA signal of their respective calibration tape. Based on this methodology, a calibration algorithm is developed and applied on each channel data as shown in Figure 3.  
In order to determine the system resolution, a 0.2 mm single lead phantom is made as shown in Figure 4a.