## 2 Materials and Methods
The \(u_{3}\) waveform was received and processed, from which the \(u_{1}\) waveform was computed using the Hilbert transform [14]  
\[u_{1}(\tau)=-\frac{1}{\gamma}H(u_{3}(\tau))\]  
\[H(u_{3})=\frac{1}{\pi}\text{Pr}\int\limits_{-\infty}^{\infty}\frac{u_{3}(t^{ \prime})dt^{\prime}}{t^{\prime}-t}\]  
where \(\tau=t-x_{1}/c\) is the retarded time,  
\[\gamma=\left[\frac{1-\delta/\delta_{1}}{1-\delta}\right]^{1/4}\]  
\[\delta=\left[\frac{c_{R}}{c_{T}}\right]^{2}\quad\delta_{1}=\left[\frac{c_{L}}{ c_{T}}\right]^{2}\]  
and \(c_{R}\), \(c_{T}\), and \(c_{L}\) are the Rayleigh, transverse (shear), and longitudinal wave speeds respectively. Pr represents the principal value of the integral. Then the displacement waveforms are differentiated with respect to time to obtain the \(v_{3}\) and \(v_{1}\) waveforms as was described relative to Figure 2. Scanning experiments were conducted for the baseplate and the as-built deposition in our laser ultrasound testbed (i.e., not in the DED-AM chamber). Prior work documented that wrought baseplate Ti-6 Al-4V has different nonlinearity than DED-AM as-built Ti-6 Al-4V [60]. In addition, prior experiments [59] indicate that the surface roughness affects the nonlinearity, at least partially due its effect on attenuation. In addition, an experiment was conducted at low pulse energy to clarify linear from nonlinear behavior. Selected results are presented from laser ultrasound experiments conducted inside the DED-AM chamber on depositions having the artificially changed process parameters given in Table 1. It is our experience that the speed and power of the deposition laser and the hatch spacing are important parameters relative to the mechanical behavior of the material and are readily adjustable. The changed parameters are not intended to create isolated flaws, but rather influence the material micro/meso-structure in subtle ways. Results from the four build sequences described in Table 2 are presented. The Ti-6 Al-4V and IN-718 baseplates (process parameter sets A and D respectively) are 10 mm thick and typical cross-sections are shown in Figure 5.  
Surface profilometry (using Newview NX2, Zygo, Middlefield, CT, USA) was used to quantify the surface roughness with ISO 25178-2 areal parameters: \(S_{a}\), \(S_{q}\), and \(S_{z}\), which are the arithmetic mean height, root mean square height, and maximum height respectively. The results provided in Table 3 show that the variations in process parameters had a more significant effect on roughness for IN-718 than for Ti-6 Al-4V. The effect of process parameters on surface roughness (and microstructure) is analyzed in more detail by [PERSON] et al. [63]. Clearly, the AM depositions are much rougher than their respective baseplates, but the effect that the variation in process parameters has on roughness is minor in comparison. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Set** & **Material** & **Laser Power (W)** & **Scan Speed (mm/s)** & **Hatch Spacing (mm)** \\ \hline A \({}^{1}\) & Ti-6 Al-4V & 450 & 10.6 & 0.8 \\ B & Ti-6 Al-4V & 380 & 10.6 & 0.8 \\ C & Ti-6 Al-4V & 450 & 10.6 & 0.9 \\ D \({}^{1}\) & IN-718 & 400 & 10.6 & 0.6 \\ E & IN-718 & 400 & 9.3 & 0.6 \\ F & IN-718 & 400 & 11.8 & 0.6 \\ G & IN-718 & 400 & 10.6 & 0.75 \\ H & IN-718 & 400 & 10.6 & 0.85 \\ \hline \hline \end{tabular} \({}^{1}\) Nominal processing parameters.  
\end{table} 
Table 1: Process parameter sets for DED-AM builds. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**1** & **2** & **3** & **4** \\ \hline Ti-6 Al-4V & Ti-6 Al-4V & IN-718 & IN-718 \\ baseplate & baseplate & baseplate & baseplate \\
4 layers Set A & 4 layers Set A & 4 layers Set D & 4 layers Set D \\ LU test & LU test & LU test & LU test \\
4 layers Set B & 4 layers Set C & 4 layers Set E & 4 layers Set G \\ LU test & LU test & LU test & LU test \\  & & 4 layers Set F & 4 layers Set H \\  & & LU test & LU test \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DED-AM build sequence with laser ultrasound (LU) testing.