## 1 Introduction
### Additive Manufacturing Process Monitoring  
Additive manufacturing (AM) is a promising technology for manufacturing a wide range of components and complex geometries directly from computer-aided design files. The rapid on-demand fabrication of parts has attracted many high-value applications in the medical, energy, aerospace, and defense sectors. However, AM technology is still maturing, and the complex physical and metallurgical processes during deposition may lead to undesired microstructure, and therefore undesirable properties (e.g., yield strength, fracture strength, fatigue strength, creep strength) in the final part. The phase transitions, thermal behavior, and melt pool behavior during the AM process strongly depend on the process parameters such as hatch spacing, processing speed, laser power and are difficult to observe in real-time [31]. Subtle changes in the process parameters can lead to undesired microstructure in a part or variability from one part to another [32]. Thus, an in-situ monitoring technique sensitive to changes in the microstructure of the part is highly desirable. A multitude of in-situ monitoring strategies have been and are actively being explored for AM, and laser ultrasonics is considered a promising candidate. Given the tremendous interest in in-situ monitoring for AM it is not possible to provide a comprehensive review in this work, but interested readers are advised to consult the numerous review articles that have been published on in-situ monitoring of AM in recent years [33; 34; 35; 36; 37; 38; 39; 40], and a few of the more important strategies are touched on below. Monitoring the deposition laser (or electron) beam characteristics, process characteristics, and motion characteristics are typical strategies used for in-situ AM monitoring [41; 42]. Another common strategy is to study the melt pool dynamics, as they are critical in determining the quality of the AM deposition. Alternatively, optical emission monitoring is developing as a means to assess process stability [43; 44]. In contrast, ultrasonic techniques for in-situ monitoring of AM are unique because they are able to detect internal defects with high sensitivity. Figure 3: Particle velocity and displacement waveform evolution predicted by [PERSON] et al. model [24] for IN-718: \(v_{1}\), \(v_{3}\), \(u_{1}\), \(u_{3}\). The nondimensional abscissa is the product of the initial monochromatic frequency and the retarded time. The nondimensional ordinate is the waveform normalized with respect to the initial amplitude of the \(v_{1}\) sinusoid. \(X\) is propagation distance normalized with respect to shock formation distance. [PERSON] and [PERSON] [45] and others [46; 47; 48; 49; 50] conducted in-depth reviews of ultrasonic techniques for nondestructive testing of AM. While most traditional ultrasonic inspection techniques are difficult or impractical for in-situ monitoring of AM, laser ultrasound is identified as one of the suitable candidates as it is noncontact [40; 51]. Thus, a significant amount of research is currently underway on laser ultrasonic characterization and monitoring of AM material [52; 53; 54; 55; 56; 57; 58]. We note that x-ray computed tomography is an excellent tool for ex-situ quality assurance testing, but it is not well-suited for process monitoring. Unique considerations for using laser ultrasound as a means to monitor the AM process include:  
* the act of monitoring should not impede the manufacturing process;
* detection of both flaws and micro/mesostructure variations that affect mechanical properties are important;
* the surface of the deposited material is rough. It is well-known that fully noncontact laser ultrasound systems are suitable for many manufacturing environments. Likewise, the scattering of Rayleigh waves from surface and near-surface flaws makes them useful for flaw detection.