PSI - Issue 77

João Queirós et al. / Procedia Structural Integrity 77 (2026) 475–483

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These algorithms are used to extract information that is not immediately visible in the raw thermal data. The FFT is a mathematical algorithm that converts thermal data from the time domain to the frequency domain. This transformation is the foundation of Pulsed Phase Thermography (PPT). By applying FFT to the thermal signal of each pixel, both phase and amplitude are extracted. The phase is particularly useful for damage identification as it is less sensitive to non-uniform heating and emissivity variations. The FFT is also applied to Lock-In Thermography (LT) signals. However, unlike PPT, the most prominent frequency component is already known, as it corresponds directly to the specific excitation frequency used during thermal excitation, leading to a phase analysis of the thermograms relative to that particular frequency. PCT is a statistical method that uses PCA to process raw thermal data. This algorithm classifies and decomposes the data into a new set of images called empirical orthogonal functions, which are based on the variance in space and time. This process effectively separates useful information from the noise. The first principal component, which has the highest variance, typically represents the dominant surface heating and is often discarded. Similarly, the last components, with the lowest variance, are considered noise. The key to PCT lies in the intermediate components, which contain the subtle thermal variations such as those caused by deeper subsurface damage. By isolating these specific components and using them to reconstruct a new filtered thermogram, the algorithm effectively enhances the contrast of damage, making it much easier to identify. Regardless of the thermography technique variant (Pulsed or Lock-in), both FFT and PCT algorithms allow enhancement of damage detectability. Figure 4 shows the flowchart for post-processing raw thermal data using the two distinct algorithms. For pulsed thermal data, the signal is first reconstructed using TSR. Following this, one of the algorithms is chosen to extract either the phase or a filtered thermogram from TSR or LT thermal data, depending on the requirements.

Applying Thermographic Signal Reconstruction

Yes

PCA

No

Choosing the algorithm

Raw thermal data

Pulsed thermal data?

FFT

Extracting filtered thermograms

Extracting phase

Fig. 4. Thermal data post-processing procedure.

4.2 Post-processing of Phase maps The DS system allows us to directly measure the strain field between two deformation states of a structure in the form of a raw phase map. This phase is wrapped between −π and π due to the application of the inverse tangent function during the extraction of the interference phase from a series of recorded intensity images acquired at the same instant (dos Santos and Lopes, 2024). Furthermore, these maps are significantly affected by high-frequency noise, which is primarily caused by speckle decorrelation. Internal damage in a structure causes a decrease in stiffness, which creates small, local variations in the strain field. These variations are difficult to spot in the raw phase maps because their amplitude is significantly smaller than that of the structure's overall deformation. Additionally, high-frequency noise further obscures the visualization and identification of these subtle variations. A recent novel method by Queirós et al. (2025) provides a way to isolate small damage-related variations and improve their detectability. This technique is built on a key assumption: the global deformation is considered a smooth signal, residing in the lowest spectral range, the localized damage variations fall into the middle spectral range, and