**3. Fundamentals of Passive IRT**

In the passive IRT technique, there are two configuration modes including transmission and reflection [28]. In transmission mode, heat sources and IR cameras are placed on two opposite sides of the specimen whereas they are placed on the same side of the specimen in the reflection mode [28]. In the present work, the reflection mode is chosen (during daytime) to detect delaminations in a concrete slab because this mode is more popular and applicable for concrete bridge deck inspection, especially in cases of bridges with great heights. The mechanism of the detectability of delaminations during both daytime and nighttime is briefly explained as shown in Figure 4.

**Figure 4.** Fundamentals of defect detection using passive IRT: (**a**) during daytime; (**b**) during nighttime.

During the daytime, energy from the sun heats up the concrete surface. If a delamination exists inside the concrete structure, the volume of the trapped heat develops above the delamination because the thermal conductivity of air (approximately 0is much lower than that of the concrete (between 0.4 and 1.8 W/m◦C), then the energy from the trap.024 W/m◦C) ped heat volume turns back to the surface [1,2,45,46]. Therefore, the concrete surface above the delaminations becomes hotter than the neighborhoods during the daytime. In contrast, the heat is radiated back to the sky, thus the volume of the trapped heat is under the delamination during nighttime [1]. As a result, the concrete surface above the delamination is cooler than its surroundings during nighttime. When utilizing an IR camera to capture the thermal images at a suitable time, defects can be observed based on the difference of the surface temperature between the delaminated and surrounding areas.

The total radiation (*Wtot*) is captured by an IR camera not only from the object but also from ambient sources and the atmosphere, as shown in Equation (1) and Figure 5 [47]. The surface temperature of the object can be computed automatically by using Equation (2).

$$\mathcal{W}\_{tot} = \varepsilon \times \tau \times \sigma \times T\_{obj}^4 + (1 - \varepsilon) \times \tau \times \sigma \times T\_{amb}^4 + (1 - \tau) \times \sigma \times T\_{atm'}^4 \tag{1}$$

$$T\_{obj} = \langle \frac{\mathbb{W}\_{tot} - (1 - \varepsilon) \times \tau \times \sigma \times T\_{amb}^4 - (1 - \tau) \times \sigma \times T\_{atm}^4}{\varepsilon \times \tau \times \sigma} \rangle \; , \tag{2}$$

where <sup>ε</sup> <sup>×</sup> <sup>τ</sup> <sup>×</sup> <sup>σ</sup> <sup>×</sup> *<sup>T</sup>*<sup>4</sup> *obj* is the emission from the object, (<sup>1</sup> <sup>−</sup> <sup>ε</sup>) <sup>×</sup> <sup>τ</sup> <sup>×</sup> <sup>σ</sup> <sup>×</sup> *<sup>T</sup>*<sup>4</sup> *amb* is the reflected emission from ambient sources, (<sup>1</sup> <sup>−</sup> <sup>τ</sup>) <sup>×</sup> <sup>σ</sup> <sup>×</sup> *<sup>T</sup>*<sup>4</sup> *atm* is the emission from the atmosphere, *Tobj* is the temperature of the object, *Tamb* is the reflected temperature from ambient sources, *Tatm* is the atmospheric temperature, ε is the emissivity of the object, τ is the transmittance of the atmosphere, σ is the Stefan-Boltzmann constant (<sup>σ</sup> = 5.67 <sup>×</sup> 10 <sup>−</sup> 8 W/m2K4), thereby (1 <sup>−</sup> <sup>ε</sup>) is the reflectance of the object, and (1 <sup>−</sup> <sup>τ</sup>) is the emissivity of the atmosphere. The values of ε, *Tamb*, and *Tatm* must be set in the camera as input data.

**Figure 5.** Radiation received by an infrared (IR) camera.
