# Deep Machine Learning for Path Length Characterization Using Acoustic Diffraction
## 1 Introduction
### Theory  
To perform the necessary assessment of how machine learning algorithms perform when producing an estimate of acoustic path length, we use a surrogate experiment with which acoustic diffraction data can be more quickly and cost-efficiently produced and analyzed. In this experiment we compare two machine learning approaches for using acoustic diffraction data collected on thin metallic specimens in both the Fresnel and Fraunhofer regimes to estimate the acoustic path length of the anomaly. Producing the ability to estimate such a complex feature is an important step toward enabling the automated estimation of density and thickness of biofilm specimens. The experiment is carried out using steel rings as shown in Figure 1 and the dimensions of each ring used can be found in Table 1. The controlled anomalies for which the acoustic path length will be calculated are holes with diameters of 6.47 mm and 2.17 mm. Figure 1: The two sets of rings used in this experiment with the three 6.47 mm anomalies on the left and the three 2.17 mm anomalies on the right. Each set of rings contains 3 different thicknesses: 0.68 mm (top), 1.32 mm (middle), and 6.46 mm (bottom). The steel rings are placed in the center of the experiment, directly over the transmitter on the bottom. The transmitter emits signals at 1 and 5 MHz in order to increase the number of acoustic path lengths induced in the experiment. Data are then collected from a steel observation plate on top of the specimen where the receiver sweeps from left to right to pick up the transmitted signal. This setup can be seen in Figure 2. A layer of water is kept between all components to increase the acoustic coupling of the system. More details on the experimental setup can be found in Section 2. Figure 3 depicts the acoustic wave traveling from an acoustic emitter into a medium containing a known acoustic anomaly and then to the receiver on top. In this figure, the axis X denotes the direction in which the receiver scans across the observation plate. The axis Z denotes the axis of propagation for the acoustic signal. The receiver detects the signal as it scans the observation plane. At the location of the anomaly, the acoustic wave is partially reflected. Due to this reflection, the wavefront is deformed by the time it is picked up by the receiver. The change in the wavefront depends on the shape of the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Disc Height (mm)** & **Disc Diameter (mm)** & **Anomaly Width (mm)** \\ \hline
0.68 & 58.75 & 6.47 \\ \hline
0.68 & 58.75 & 2.17 \\ \hline
1.32 & 58.75 & 6.47 \\ \hline
1.32 & 58.75 & 2.17 \\ \hline
6.46 & 58.75 & 6.47 \\ \hline
6.46 & 58.75 & 2.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions of specimens used in data collection. Figure 2: The experimental setup used for data collection. In the main portion of the figure we see the emitter at the bottom of the system with the steel ring directly on top followed by a steel observation plate and the receiver on top of that. In the depiction of the observation plate in the lower left corner, the receiver (solid circle) is shown at its starting position of \(-2\) cm and the arrow across the center depicts the motion of the sweep. A trace of the steel specimen that lies beneath the plate is depicted with the dotted circle to give perspective on the position of the sweeping receiver relative to the specimen. The transmitter, shown as the bottom component in the main image, lies directly beneath the center of the steel specimen. interface and the acoustic impedance of the anomaly. In many situations, these are generally unknown; however, in this experiment, the acoustic impedance of the anomaly and size of the anomaly are controlled. Because of this, we can approximate the change experienced due to acoustic impedance. The surface of the emitter is PZT and the medium used in this experiment is steel. Within the steel is an anomaly in the form of a hole drilled through the center.