2.2.3. Differential Absolute Contrast (DAC) Evaluation

A Modified Differential Absolute Contrast (DAC) method was used to process the measured data. This allows partial elimination of heat source unevenness, such as reflections from the surroundings (e.g., IR camera, flash lamps) and emissivity distribution on the surface. The DAC method compares the temperature of the tested place containing the defect, with the theoretical value of the temperature if there were no defect in the place being tested. This theoretical temperature is calculated on the basis of the 1D form of the Fourier equation of heat conduction in a semi-infinite medium from the measured temperature, at a point in time where the temperature defect does not manifest itself [12]. The standard DAC method works with the temperature at that point in time just before the manifestation of the defect, which, however, usually requires the manual intervention of the test operator. This thermal contrast is calculated according to Equation (11) below, which describes the relation of temperature *T*(*t*) at the observed time *t* and the temperature *T*(*t'*) at the reference time *t'* for each individual pixel of the record [28].

$$
\Delta T\_{DAC}(t) = T(t) - \sqrt[b]{\frac{t'}{t}} T(t') \tag{11}
$$

Since the theoretical temperature decrease using the standard DAC method does not involve heat transfer by radiation, but only by conduction, this decrease is significantly lower than in reality. For this reason, the square root in Equation (11) was replaced by a power with the general parameter *b* representing the slope of the temperature decrease (12).

$$
\Delta T\_{DAC}(t) = T(t) - \left(\frac{t'}{t}\right)^b T(t') \tag{12}
$$

This parameter was determined from experimental data based on the approximation of the cooling curve on the reference gauge for the thickness *z* = 2.30 mm, which represents the adhesive joint without any defect. The reference time for calculating the contrast is the time *t'* = 0.15 s, which corresponds to the thickness just behind the interface between the skin and the adhesive, and the value of the parameter *b* = 0.65. The whole calculation is performed for temperatures normalized to the maximum and minimum temperatures reached during the measurement from excitation to a steady state at the end of the measurement, over the entire measured area. Figure 13 shows the actual and theoretical cooling curves plotted using Equation (11) for three different thicknesses on the reference gauge (Figure 13a) and the DAC curves for all the thicknesses on the reference gauge (Figure 13b).

**Figure 13.** Cooling curves for the reference gauge: (**a**) linear time axis; (**b**) Differential Absolute Contrast (DAC) curves.

As in Figure 12, the following graph in Figure 14 shows the DAC profile normalized to the temperature range from the highest temperature (curve for *z* = 0.25 mm) to the lowest temperature (curve for *z* = 2.3 mm) at each measurement point. This graph shows the dimensionless contrast within the data obtained at a given time. A comparison of the two graphs shows that the DAC contrast calculation does not have a significant effect on the resulting image contrast.

**Figure 14.** DAC image contrast curves for the reference gauge.

Figure 15 shows a comparison between the raw thermogram image and the modified DAC-processed image. These images represent the same test area (end of the front wing spar) at the same time after excitation. In the first image, the reflection of the IR camera is visible in the lighter parts (the foam sandwich area, blue circle), and in the dark area (the area of the adhesive joint), a significant unevenness in the emissivity of the surface can be observed (green marking). The effect of the heating unevenness is marked by a red circle. These imperfections have been largely eliminated by the application of the DAC method.

**Figure 15.** Comparison of the resulting images: (**a**) RAW thermal data; (**b**) modified DAC-processed data.

### *2.3. Experimental System Description*

A modular test system was designed and employed for the PT NDE method. The experimental setup can be seen in Figure 16. The basic hardware elements of this system consist of a FLIR A325SC bolometric uncooled IR camera (resolution 320 × 240 pixels; NETD < 50 mK; maximum scanning frequency, 60 Hz), an instrument unit equipped with a PC for test control and data recording and two flash lamps (2 × 1200 Ws).

**Figure 16.** Pulse Thermography (PT) method experimental configuration.

The instrument unit works as the communication interface between the PC, IR camera and excitation lamps. It consists mainly of the cDAQ measuring and control system from National Instruments, equipped with analog output cards (for excitation lamp control) and digital input/output as well as other necessary auxiliary electronics.

A program was specifically created for this purpose in the LabView environment from National Instruments, and this was used to control the test's processes and record the measured data. The processing and evaluation of the obtained data were performed in the MATLAB environment from MathWorks [29].
