## 2 Test Objects and Methods
### Radioscopic Transparency of the Test Object
#### 2.2.1 Basic Formulas  
The signals at the output of total absorption detectors for counting \(I_{N}\) and integral \(I_{E}\) modes of registration of X-ray radiation behind the test object are estimated by the formulas similar to [40]  
\[I_{N}(E_{\text{max}},\rho H,Z)=\left[N_{0}\int\limits_{0}^{E_{\text{max}}}f_{N} (E,E_{\text{max}})\exp(-m(E,Z)\rho H)dE\right], \tag{3}\]  
\[I_{E}(E_{\text{max}},\rho H,Z)=N_{0}\int\limits_{0}^{E_{\text{max}}}Ef_{N}(E,E _{\text{max}})\exp(-m(E,Z)\rho H)dE, \tag{4}\]  
where \([x]\)--integer part \(x\), \(f(E,E_{\text{max}})\)--numerical energy spectrum of X-rays with maximum energy \(E_{\text{max}}\); \(\rho H\)--mass thickness of TO; \(m(E,Z)\)--mass attenuation coefficient (MAC) of photons with energy \(E\) for materials with effective atomic number \(Z\); \(N_{0}\)--the number of photons incident on the front surface of the detector during registration. The parameter \(N_{0}\) is called the loading of the radiometric detector. Formulas (3) and (4) imply that  
\[\int\limits_{0}^{E_{\text{max}}}f_{N}(E,E_{\text{max}})dE=1\]  
In accordance with the definition of the expression for the dependences of radioscopic transparencies for counting \(T_{N}\) and integral \(T_{E}\) recording modes on the parameters of the radiation source and TO, they have a form similar to [40; 41]  
\[T_{N}(E_{\text{max}},\rho H,Z)=\frac{[I_{N}(E_{\text{max}},\rho H,Z)]}{[I_{N}( E_{\text{max}},0,Z)]}\approx\int\limits_{0}^{E_{\text{max}}}f(E,E_{\text{max}}) \exp(-m(E,Z)\rho H)dE, \tag{5}\]  
\[T_{E}(E_{\text{max}},\rho H,Z)=\frac{I_{E}(E_{\text{max}},\rho H,Z)}{I_{E}(E_{ \text{max}},0,Z)}=\frac{\int\limits_{0}^{E_{\text{max}}}Ef(E,E_{\text{max}}) \exp(-m(E,Z)\rho H)dE}{\int\limits_{0}^{E_{\text{max}}}Ef(E,E_{\text{max}})dE}, \tag{6}\]  
From the analysis of expression (3)-(6), it follows that the estimates of radioscopic transparency \(T\) for the registration modes under consideration depend on the maximum energy of X-ray radiation \(E_{\text{max}}\), on the description of the numerical energy spectrum of X-ray radiation \(f(E,E_{\text{max}})\), mass thickness \(\rho H\) and effective atomic number \(Z\) of the TO material, as well as from registration mode. It is known that in the range of maximum energies of X-ray radiation, which is typical for industrial digital radiography (DR) and X-ray CT, the MAC of radiation \(m\) increases with increasing \(Z\). From the analysis of Equations (3)-(6) and the previous remark, it follows that the functions \(T_{N}(E_{\max},\rho H,Z)\) and \(T_{E}(E_{\max},\rho H,Z)\) are decreasing in \(\rho H\) and \(Z\). From this conclusion, it is natural to conclude that a decrease in the values of signals from the detectors to levels that lead to the appearance of metal artifacts in the X-ray CT is achieved not only by increasing the effective atomic number \(Z\) of the TO material but also by increasing the mass thickness \(\rho H\) of the object. This means that a metal artifact can be observed for objects not only with metal fragments. From the above, it follows that in order to study the conditions for the appearance of metal artifacts in the X-ray CT and ways to reduce the levels of these artifacts, it is necessary to vary the values of the main parameters of the fragments of the TO, that is, the mass thickness \(\rho H\) and the effective atomic number \(Z\). The estimates of \(T_{N}\) and \(T_{E}\) according to formulas (3)-(6) are idealized; that is, they do not take into account some of the nuances associated with the technical implementation of digital imaging in the DR and projections in the X-ray CT. We'll discuss this in the next section. .2.2 Influence of Parameters of Detectors and Pre-Filters on the Radioscopic Transparency Estimation  
Detectors in DR and X-ray CT systems are, as a rule, far from total absorption detectors. In addition, pre-filters are used to harden the X-ray emission in order to reduce the corresponding artifact.