# Deep Machine Learning for Path Length Characterization Using Acoustic Diffraction
## 1 Introduction  
An acoustic wave is the flow of pressure and velocity patterns as sound propagates through a medium. Such waves are often observed to be longitudinal, meaning the medium moves in the direction of the wave. However, under various circumstances, an acoustic wave traveling through a solid medium can exhibit transverse modes instead. With this change, the medium begins to move in a direction perpendicular to the wave. This induced movement of the medium results in a wave that carries information that can be used to gain insight into the structure of the medium. Specifically, this acoustic energy is telling of the elastic property of the medium and can be used to probe the structure of the specimen [1]. Acoustic waves have long been utilized across several fields to probe for details of the structure of materials [2, 3]. Examination of acoustic data is often accomplished by reviewing the reflection of the acoustic signal as a two-dimensional image. Such techniques typicallyemploy ultrasonic waves with frequencies ranging from 500 kHz to 10 MHz. In many cases, ultrasonic testing techniques have proven to be more efficient than rival non-destructive testing methods such as visual inspection, thermography, and shearography at detecting Barely Visible Impact Damages (BVIDs) [4]. One such method is acoustic microscopy [5]. Acoustic microscopy is a form of ultrasonic testing used to detect microscopic anomalies. Thanks to such advancements, hidden and microscopic anomalies are able to be imaged for non-destructive testing. Sound waves are observed to exhibit longer wavelengths than those seen in light waves. Because of this, achieving high spatial resolution in acoustic data is difficult. Typical acoustic analysis is limited to analysis of the amplitude of the received acoustic signal. This is problematic in cases of low acoustic reflectivity, where the acoustic impedance of the anomaly and the surrounding environment are too similar. In such cases, there will be a low contrast in the resulting image. One case of interest in which low acoustic contrast can be anticipated is the acoustic probing of biofilms. Biofilms are communities of microorganisms that accumulate via a substance called extracellular polymeric substance (EPS) at an interface between two mediums [6; 7]. Imaging biofilms is not a trivial task as the cells which contribute to the biofilm have a very similar acoustic impedance to the surrounding fluid, as both the bacterial cells and surrounding fluid are composed mainly of water [8]. The compounding of low resolution and contrast yields poor-quality images, which are very difficult for humans to interpret. Acoustic signals are characterized by two main components: amplitude and phase. Amplitude is used to understand the magnitude of energy carried by an acoustic wave. Phase, on the other hand, provides the acoustic path length. When both the original wave and the received wave are known, the two sets of data can be used together to get a more clear picture of the system. This is accomplished by calculating the transfer function as the change in the emitted signal exhibited by the received signal. Doing so illuminates the change that an acoustic signal undergoes when passing through a system. Previous research on using the phase, amplitude, transfer function phase, and transfer function amplitude to detect an acoustic anomaly shows that the transfer function phase and the transfer function amplitude provide more useful information on the nature of the anomaly than phase and amplitude alone [9]. The improved quality of information is due to the transfer function filtering out components that are common to both the emitted and received signal, thus allowing examination of just the changes due to interaction with the medium being probed. Biofilms are so thin that the resultant diffraction falls in the Fresnel range where the lateral profile of the amplitude and phase varies in a complicated fashion.