## 2 Materials and Methods
### FFT Imaging Processing  
Once the image sequence has been automatically acquired, a Python (version 3.13.3) script is used to process the pictures. Common processing approaches are based on square wave signal modulation, where each image is classified as either a high or low emission state [12]. High and low signal images are averaged separately and then subtracted to extract the luminescence signal. The implementation of fast FFT for processing not only allows the extraction of the luminescence signal waveform used during modulation but also eliminates the need to classify the images within the sequence.  
The FFT is applied to each pixel individually, analyzing the evolution of its intensity throughout the sequence. The pixel intensities in the final EL image correspond to the amplitude of the FFT at the index associated with the modulation frequency (4 Hz), where a peak is expected. Therefore, background signals generated by sunlight can be removed.  
The python script is also able to automatically adjust the brightness of the final EL picture and apply a perspective correction and crop by identified solar module corners.  
In order to quantitatively evaluate the quality of the final EL image, the signal-to-noise ratio (SNR) can be calculated using the FFT [35]. The SNR of each pixel is determined using the following Equation (1):  
\[\mathrm{SNR}=10\mathrm{log}_{10}\left(\frac{\mathrm{Peak~{}amplitude}^{2}}{ \mathrm{Var}(\mathrm{Noise})}\right) \tag{1}\]  
where the peak amplitude is defined as the difference between the amplitude at the modulation frequency (_f_) and the average amplitude within the frequency range [_f_/2, _2f_], excluding the modulation frequency itself (_f_). The noise is estimated as the variance of the amplitude within the same frequency range [_f_/2, _2f_], also excluding the modulation frequency (_f_). To calculate the SNR of the entire image, the pixel SNR values corresponding to the PV module area are averaged, ensuring that the signal evolution in non-relevant pixels is not considered. In this SNR approach, a value higher than 10 dB can be considered indicative of a sufficiently high-quality image. The flow diagram of the processing approach implemented can be seen in Figure 3.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{Camera Parameters (Hamamatsu C12741-03)} \\ \hline Image size & 640 \(\times\) 512 pixels \\ Stack size & 1000 images \\ Exposure time & 2 ms \\ Acquisition speed & 53 fps \\ Filter & Bandpass filter (1100 nm\(-\)1250 nm) \\ \hline \multicolumn{2}{c}{Signal modulation parameters} \\ \hline Frequency & 4 Hz \\ Waveforms & Square, half sine and full sine \\ \hline PV characteristics (Trina Solar TSM-235-PC05A) \\ \hline Module Power (STC) & 235 V \\ Module V\({}_{\mathrm{OC}}\) (STC) & 37.2 V \\ Module I\({}_{\mathrm{SC}}\) (STC) & 8.55 A \\ String size & 10 modules \\ Inverter type & String inverter \\ \hline \multicolumn{2}{c}{Weather conditions} \\ \hline Irradiance & 1030–1150 W/m\({}^{2}\) \\ Cloudiness & Clear-sky conditions \\ Temperature & \(\approx\)14 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of camera settings, modulation parameters, PV characteristics and weather conditions during the measurements.