## 1 Introduction  
Laser cutting is a well-stablished technology in the market, but as [PERSON] et al. concluded [1] when monitoring the process, some general considerations on the requirements of process diagnostics should be taken into account. Developments of various monitoring systems have been reported, including the direct measurement of the light emitted from the cutting front with an optical fiber [2], the analysis of the acoustic and optical signals for evaluating the cut quality [3], and the development of optical systems that use photodiodes and NIR (Near InfraRed) cameras as sensors for real-time monitoring [4]. In recent years, an increase in the use of photodiodes to monitor the laser cutting process has been observed. This increase in their use is mainly based on the enormous potential of these sensors, together with their easy mounting, and the existing demand to incorporate monitoring systems in industrial applications. [PERSON] et al. [5] and [PERSON] et al. [6] demonstrated the capability of InGaAs photodiodes for detecting penetration losses and the appearance of cutting defects, respectively, whereas [PERSON] et al. [7] employed Si photodiodes for monitoring the laser cutting process and evaluating quality. In all cases, these sensors provided a high detection rate and minimal errors. Therefore, photodiodes could be used as indicators of the cut quality in real industrial applications. The understanding of the cutting process dynamics and the determination of cut quality has been an issue for many years. For instance, [PERSON] and [PERSON] [8] described in their work the main physical phenomena involved in the laser cutting process and the monitoring basis. In the same vein, [PERSON] et al. [9] used an IR camera to monitor the laser cutting process of a steel plate and they proposedan analytical model that considered the phase change, transformation energy, and heat transfer by conduction and radiation. The study of the kerf was also addressed by [PERSON] et al. (2010), who employed an Analysis of Variance (ANOVA) to study the combined effect of the process parameters. [PERSON] employed the same procedure for the laser cutting of hot stamping boron steel blanks ([PERSON] et al., 2012). [PERSON] et al. (2012) used high-speed imaging techniques to visualize the flow conditions within the cut region and correlated the developed flow conditions with the corresponding process parameters and the resulting quality. Through monitoring of the cutting process, it is possible to extract relevant information on the quality of the cut in-situ during the process and different alternatives have been proposed. On the one hand, [PERSON] and [PERSON] (2013) analyzed the cut quality based on the light emitted from the cut kerf coaxially with the laser beam. On the other hand, [PERSON] and [PERSON] (2014) performed a similar analysis based on the infrared radiation coming from the cut region. [PERSON] et al. (2015) studied the surface striation formation in the laser cutting process through an optical stereoscopic microscope and determined that there was an optimal range of the laser energy per length unit that ensured an acceptable cut quality. In addition, [PERSON] (2016) experimented to evaluate the laser cutting quality and studied the generated kerf, postulating the first and second law efficiencies for laser cutting. In addition, acoustic signals have also been employed for laser cutting monitoring. For instance, [PERSON] et al. (2017) employed both acoustic and optical signals, for ensuring the full penetration of the laser beam. [PERSON] and [PERSON] (2018) also employed acoustic signals for monitoring laser cutting, after the application of the appropriate band filter to avoid the contribution of the assist gas flow. Advances in laser cutting monitoring have allowed the development of adaptive feed-back control systems, improving the laser process robustness and productivity, as well as enhancing the resulting part quality ([PERSON] et al., 2019).