## 3 Analysis
In practice, any peaks that were closer than one-half of the expected peak-to-peak separation from the designed raster height of 0.35 mm were removed. This yields an array of time values \(t_{n}^{*}\) for the \(N\) layer interfaces and the back wall where \(n\in\{1,2,\dots,N\}\). Next, a spatial C-scan was defined for each of the time values \(t_{n}^{*}\) as  
\[C_{n}(x_{1},x_{2})=\int\limits_{\overset{\sim}{t}_{n}}^{\overset{\sim}{t}_{n }+\Delta t_{n}}\hat{F}(t,x_{1},x_{2})^{2}dt \tag{4}\]  
where the parameter \(\overset{\sim}{t}_{n}\) was a function of the interface time value \(t_{n}^{*}\). It was found that using \(\overset{\sim}{t}_{n}=t_{n}^{*}\) was ineffective as both the \(n-1\) and the \(n\) layer reflections were in the reflected signal simultaneously. Selecting the parameter \(\overset{\sim}{t}_{n}\) as  
\[\overset{\sim}{t}_{n}=t_{n}^{*}-\delta \tag{5}\]where \(\delta=40\) ns, which was appropriate for analyzing the \(n^{\text{th}}\) layer in this work. In general, the parameter \(\Delta t_{n}\) in Equation (4) was selected to capture as much of the acoustic energy of the reflections from the \(n\)th layer as possible without including signal transmission from a previous and/or subsequent layer reflection. For the work herein, \(\Delta t_{n}=\frac{2}{3}\big{(}t_{n+1}^{*}-t_{n}^{*}\big{)}\) was found to be sufficient for the analysis, but additional work could be performed to optimize this parameter. This approach allows for adjusting \(\Delta t_{n}\) in each layer, as not all layers have an equal acoustic width due to the mode conversions of the waveform in the initial signal reflections. A representative example of the spatial C-scan \(C_{n}(x_{1},x_{2})\) is shown in Figure 3a for the third layer of a scan of part A made from PCTG, a designed 10 degree orientation state. Figure 2: (**a**) Representative A-scan showing gating in time; (**b**) enlarged portion of the representative A-Scan depicted in (**a**). Next, a two-dimensional Fourier transform was used to automate of the analysis of the raster orientation. The two-dimensional Fourier transform is defined as  
\[\mathcal{C}_{n}(\omega_{1},\omega_{2})=\int\limits_{0}^{L_{2}}\int\limits_{0}^{ L_{1}}C_{n}(x_{1},x_{2})e^{-i\omega_{1}x_{1}-i\omega_{2}x_{2}}dx_{1}dx_{2} \tag{6}\]  
where \(i\) is the complex number \(\sqrt{-1}\). The two-dimensional Fourier transform yielded a signal \(\mathcal{C}_{n}(\omega_{1},\omega_{2})\) that was originally in the spatial domain \((x_{1},x_{2})\) and cast it in the spatial frequency space \((\omega_{1},\omega_{2})\). The interpretation of the spatial frequency is that the values for \((\omega_{1},\omega_{2})\) correspond to the periodicity of features within a two-dimensional space. The specific interest in the present study is the rastered depositions. For example, the individual rows of rasters of the third layer of part A_01 can be observed in Figure 3a. The angle in the \((\omega_{1},\omega_{2})\) plane of \(\mathcal{C}_{n}(\omega_{1},\omega_{2})\) corresponds to the angle at which the rasters are orientated, whereas the magnitude \(\overline{\omega}=\sqrt{\omega_{1}^{2}+\omega_{2}^{2}}\) of a given peak corresponds to the spatial frequency of a periodic feature of the spatial C-scan, \(C_{n}(x_{1},x_{2})\). To aid in the automatic feature extraction, a simple band-pass filter in the frequency space was utilized. This was performed by taking the as-designed deposition width of 0.8 mm and removing spatial frequencies from \(\frac{1}{0.8\,\mathrm{mm}}=1.25\) mm\({}^{-1}\) in the Fourier domain \(\mathcal{C}_{n}(\omega_{1},\omega_{2})\). This is shown in Figure 3b, where it was found that a band of \(\frac{1}{0.9\,\mathrm{mm}}\) to \(\frac{1}{0.7\,\mathrm{mm}}\) was sufficient in the present study, but this band could be further optimized in future studies. The results of the transform \(C_{n}(x_{1},x_{2})\) with the bandpass filter imposed for the third layer of part A made from PCTG are shown in Figure 3b.