## 4 Discussion  
To improve the unambiguity of cross-correlation-based time of flight measurements through coded excitation it is important to take into consideration the boundary conditions of the experimental setup. The transfer of coded excitation sequences into a signal that the signal-generator can process reduces the complexity of the sequences. Impulse signals always have a limited width and, therefore, the resulting impulse echo shows deviations from idealized echoes. In addition, there are limitations related to the ultrasonic transducer. The transducer has an optimal operating frequency and inertia, which affect the outgoing signal. Furthermore, the linear model provided by the transfer function created by using the FFT on the impulse echo cannot completely describe the system. Simulations were a very effective way to screen a large parameter space and guide the experimental setup (Sections 3.2 and 3.3). They showed that especially sequences with signals in alternate directions yield high reductions in side maxima values. However, the transfer function of the system is a linear model of the piezo-electric ultrasonic transducer and the testing material and, therefore, limited in its capability to fully reflect the reaction of the system. The maximum of the transfer function is also not evaluated at 4 MHz as expected. This deviation is connected to the preload of the transducer and excitation in the positive direction first. The stimulation with a negative pulse instead of a positive pulse produces an echo with a maximum power spectrum closer to the expected frequency of the transducer of 4 MHz. In addition to simulations, it is very important to rely on experimental results to explore the potential of coded excitation. Table 3 shows a summary of the references and sequences with the greatest reduction in either positive or absolute side maximum in experiments on the 60 mm specimen (cf. Table 1 for all results). Both positive and absolute side maxima values were systematically evaluated throughout this work because it is not straightforward to determine which value is more important to evaluate for optimization. The absolute side maximum could be reduced by 37 percentage points and the positive side maximum by 64 percentage points. For both optimization strategies, the susceptibility \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Steel 60 mm**} & \multicolumn{2}{c}{**Steel 30 mm**} & \multicolumn{2}{c}{**Steel 15 mm**} \\ \hline  & **Positive Side** & **Absolute Side** & **Positive Side** & **Absolute Side** & **Positive Side** & **Absolute Side** \\  & **Maximum/\%** & **Maximum/\%** & **Maximum/\%** & **Maximum/\%** & **Maximum/\%** & **Maximum/\%** \\ \hline Sine wave & 88.9 & 96.6 & 88.6 & 97.7 & 80.9 & 93.8 \\ Five-pulse & 25.0 & 73.3 & 28.6 & 76.2 & 29.1 & 71.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the magnitude of positive and absolute side maximum of the CCF for the validation measurements on the steel samples with different thicknesses. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Waveform**} & **Positive Side Maximum/\%** & **Absolute Side Maximum/\%** \\ \hline Reference 1: Sine wave & 88.9 & 96.6 \\ Reference 2: Impulse & 71.0 & 90.0 \\ Pseudo noise sequence 8 & 56.8 & 87.1 \\ Pseudo noise sequence 24 & 71.2 & 91.8 \\ Linear Chirp UpDown Freq. 1–4 & 63.3 & 89.1 \\ Automatically optimized & 56.6 & 89.3 \\ Four-pulse sequence & 41.9 & 60.0 \\ Five-pulse sequence & 25.1 & 73.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of coded sequences with the best results for the CCF. to disturbance and the unambiguity of the signal could be improved. Determination of the most relevant strategy of optimization depends on the application and the desired signals. Coded excitation is influenced by experimental boundary conditions (e.g., transducer type, electronic components,... ) and even more complex phenomena occur when the sample size is reduced.