## 2 Pulse-Compression Thermography (PuCT)  
Historically, pulse-compression (PuC) was introduced in radio detection and ranging (RADAR), and later applied in acoustic, SONAR and several NDT techniques, including IRT, an example being PuCT [20; 21; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37]. In this paper, the PuCT is used for minimizing the temperature increment \(\Delta T\) of the sample surface while assuring enough SNR at the same time. By adopting the system theory approach, the PuC is a measurement technique for characterizing a linear time-invariant (LTI) system by estimating its impulse response. The peculiarity of this approach, with respect to the more traditional ones, e.g., using a short-pulse or a step excitation, is that coded signals are employed to modulate the heat source. This in turn introduces high control of both the delivered power and the excitation bandwidth, so that these can be chosen to both optimize the defect detection and minimize the temperature increment of the sample. The basic theory underlying PuC is introduced below, together with a step-by-step guide for replicating the experimental activity, highlighting also the differences with respect to standard active IRT excitation schemes. For a thorough overview of the PuC, the reader is referred to the above-cited research. As the starting point to introduce the PuC algorithm, it should be considered that pulsed-thermography (PT) [38] is the most common yet effective approach used in active IRT. High-power flash lamps are used in PT for exciting the sample, provoking a quick change of the sample's surface temperature. The flash duration is significantly shorter than the typical heat diffusion time duration within the sample, so that the heating is quasi-instantaneous, while the cooling trend is regulated by the local thermal properties of the inspected sample, i.e., specific heat, density and thermal conductivity [39; 40]. By adopting again the system theory approach, the pulsed excitation is a good approximation of the Dirac Delta function \(\delta(t)\), thus an impulse response \(h(t)\) is directly obtained for each \(\left(j_{x},j_{y}\right)\) pixel captured via an infrared (IR) camera as time elapses. The presence of defects/anomalies can be inferred either via frequency and/or time domain analysis. In other words, the LTI system is completely described by its impulse response \(h(t)\), thus the sample under test (SUT) is completely characterized by measuring the set of its \(\left\{h\middle(j_{x},j_{y},t\right)\right\}\). PT is thus a very powerful, reliable and simple (perhaps expensive) method for inspecting a huge variety of samples. However, the main drawback in applying PT for inspecting artworks and CH goods is that the achieved SNR level is directly related to the flash lamp power. In common NDT applications, PT is carried out by using systems of high-power flash lamps, which are commonly capable of providing several kJ of energy within a few millisecond (ms), meaning that a potential thermal shock can be provoked onto the CH sample's surface [21; 28]. Furthermore, if the flash power is increased more than enough to ensure the needed SNR, non-linear phenomena can be originated, a fact that must be completely avoided when dealing with CH items. Moreover, the onset of a non-linear behavior limits the use of PT data to build prognostic models that can be useful for further analysis. For these reasons, it is highly desired to unlink the final SNR from the heat source peak power and spread the overall amount of energy over a longer time interval. One can argue that this can be achieved by using step-heating or lock-in, another two conventional active IRT techniques, but such methods are not able (lock-in) or good enough (step-heating) to retrieve the SUT's impulse response (the provided information is limited).