# Spot Weld Inspections Using Active Thermography
## 3 Results
### Lock-in Thermography Using Light Heating  
Since lock-in thermography is based on sinusoidal excitation, the optimal amplitude and frequency combination has to be found in order to increase the contrast of the interesting regions. The amplitude corresponds to the amount of energy injected in the sample to be inspected; the frequency on the other hand determines the time within which the heating energy is injected into the sample. A lower frequency results in a longer heating time. Multiple experiments were performed on one sample in order to find suitable parameter combinations. These experiments have shown that a lower frequency (e.g., 0.05 Hz) results in better images. Higher frequencies (e.g., 1.4 Hz) generated noisy thermograms. The influence of the amplitude was determined as well, and a minimal amplitude of 60% of the maximum power was needed to be able to perform analyses on the thermal data. For each sample, two parameter combinations were used. The used parameter sets can be found in Table 5.  
The experiments are analyzed using both fast Fourier transform (FFT) and principle component analysis (PCA). PCA is based on singular value decomposition, and the goal of this technique is to reduce the amount of variables while losing the least amount of relevant information. FFT, on the other hand, is based on the approximation of the data through the sum of harmonic waves. The phase and amplitude can be calculated from this approximation. A thorough explanation on both post-processing techniques can be found in [15; 16]. Investigating the FFT images in Figure 4, it is visible that samples 1A, 2A and 3A show a closed circular shape around the spot weld and 4A only shows a part of the circle. The images of sample 5A do not suffice for making a conclusion about the shape of the spot weld. Another interesting aspect of a spot weld is the internal material structure  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & **Front Induction Heating** & **Back Induction Heating** \\ \hline Distance camera—sample ’L1’ [m] & 0.053 & 0.55 \\ Distance sample—coil ’d’ [m] & 0.03 & 0.025 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameter values used during induction heating measurements for the inspection of spot welds. A visual representation of the parameters can be found in Figure 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameter Set 1** & **Parameter Set 2** \\ \hline
**Frequency [Hz]** & 0.05 & 0.4 \\
**Amplitude** & 80\% & 80\% \\
**Number of periods** & 2 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameter combinations used for the inspection of each sample using lock-in thermography. The number of periods is kept constant at a value of two, and the amplitude is kept constant at 80% of the maximum power.  
inside the spot weld. Spot weld should have a different internal structure in comparison to the material around it. In samples 1A, 2A and 5A, a different thermal behaviour can be detected inside and outside the spot weld, which a different material structure might suggest. In samples 3A and 4A, this phase shift is not visible. Besides the Fourier analysis, PCA is performed in order to generate relief images. In the PCA images of samples 1A and 2A, the circular shape of the spot weld is visible. Sample 2A has the most clear circle shape. Sample 3A is less visible in the PCA in comparison to the FFT analysis, but the circle around the spot weld is still visible. Sample 4A has no closed boundary, and sample 5A shows a capricious relief. The images can be seen in Figure 5.