## 2 Theoretical Background of Industrial Radiology  
According to the American Society for Nondestructive Testing (ASNT), an NDT is defined as \"the determination of the physical condition of an object without affecting that object's ability to fulfill its intended function\" [40]. There are five basic NDT methods, which are based respectively on the use of magnetic particles, penetrating fluids, radiography (X-rays or gamma-rays), and ultrasonic and eddy currents [41]. NDT based on radiography has a widespread presence in industry, being especially important, for example, in the inspection of the welded joints of pressure pipes and vessels [42]. Industrial radiology is based on applying a penetrating radiation (usually X or gamma-rays) to a part, which is placed between the radiation source and a detector or radiographic film on which the radiography is printed [41]. In this way, the radiography obtained is an orthogonal image of the piece colored in gray scale. The grayish coloration of each zone of the image depends on the radiation density, the width of the inspected object, and its chemical composition. Thus, if the radiation beam does not encounter any obstacles in its path it will reach the sensor or film with almost the same intensity as was generated at the source, creating a dark image; conversely, if the radiation beam passes through an obstacle it will reach the sensor or film with its intensity reduced, creating a light image. Using this phenomenon, it is possible to detect in a radiograph which areas of a part are formed only by the base material and which have defects inside. Defects such as cracks, voids, blowholes, or internal cavities, which are areas with lower radiation absorption than the base material, appear on radiographies as darker areas than the surrounding base material. Similarly, defects such as refractory inclusions absorb a different amount of radiation than the base material and therefore appear as areas of a different shade of gray than the base material.  
The intensity reaching the sensor or film is quantified by the Beer-Lambert equation:  
\[I=I_{0}e^{-\mu x}=I_{0}e^{-\mu_{m}\rho x} \tag{1}\]  
where \(I\) is the intensity of the radiation beam reaching the sensor or film, \(I_{0}\) is the intensity reaching the part, \(\mu\) is the linear absorption coefficient, \(\mu_{m}\) is the mass absorption coefficient, \(\rho\) is the density of the material, and \(x\) is the thickness of the material traversed by the radiation beam. Since \(\mu\) depends on the type of material, the intensity of the beam that manages to pass through a part will have one value or another, depending on whether or not it has encountered internal defects on its way through the part, since the absorption coefficient of the defects is different from that of the base material that surrounds them.  
The student who faces the study of industrial radiology must be able to analyze the different shades of gray observed in a radiograph in order to understand: (i) which zones correspond to the base material of the part; (ii) identify the internal defects of the part; (iii) spatially locate the identified defects; and (iv) classify the types of defects.