## 2 Research Technique
### Calculating Illumination of the Specim Surface  
The straight line showing the illumination component, obtained based on the light flux from the light sources, was calculated for the specimen surface in the zone of the obtained images. The specimen surface illuminated with the LED lamp was calculated based on the geometric scheme presented in Figure 6a. In this scheme, the LED light source (2) with its geometric and optical centre at point O is represented by a uniformly bright disk (\(d=0.158\) m) placed at a distance (\(h=OO_{1}=0.200\) m) from the surface covered by the image 1 zone. Figure 4: Dependence of the light flux on the consumed voltage for the LED source (**a**) and for the incandescent lamp (**b**). Figure 5: The light intensity curve obtained for the LED source at a consumed voltage of 12 V (**a**) and for the incandescent lamp at a consumed voltage of 220 V (**b**). \(E_{A}\) the illumination of point \(A\), which is located on the specimen surface covered by the image zone, is calculated according to the following equation [26]:  
\[E_{\text{A}}=\pi\cdot L\cdot sin^{2}\varphi, \tag{1}\]  
where \(L\) is the brightness of the LED light source; \(\varphi\) is the half value of the angle at which the LED light source is visible from the calculation point. The following ratios determine brightness:  
\[L=\frac{M}{\pi}=\frac{\frac{\Phi}{\pi\cdot\frac{d^{2}}{4}}}{\pi}=\frac{4\cdot \Phi}{\left(\pi\cdot d\right)^{2}}, \tag{2}\]  
where \(M\), \(F\) are the brightness and the light flux coming out of the LED light source, respectively. \[ \begin{split}&\varphi=\frac{1}{2}\cdot\left(\varphi_{2}-\varphi_{1} \right)=\frac{1}{2}\cdot\left(arctg\frac{l_{OA_{1}+r}}{h}-arctg\frac{l_{OA_ {1}-r}}{h}\right)=\\ &=\frac{1}{2}\cdot arctg\frac{\frac{\left(OA_{1}+r\right)}{1+ \frac{\left(OA_{1}+r\right)}{h}}-\frac{\left(OA_{1}-r\right)}{h}}{\frac{1}{2 }\cdot arctg\frac{2\cdot h\cdot r}{l_{OA_{1}}^{2}-r^{2}}},\end{split}  \tag{3}\]  
where \(l_{OA_{1}}=l_{\text{AO}_{1}}\) is the OA\({}_{1}\) segment length; \(r=\frac{d}{2}\). Substituting (2) and (3) into (1), we obtain:  
\[ \begin{split}& E_{\text{A}}=\pi\cdot\frac{4\cdot\Phi}{\left(\pi \cdot d\right)^{2}}\cdot sin^{2}\left(\frac{1}{2}\cdot arctg\frac{2\cdot h\cdot r }{h^{2}+l_{OA_{1}}^{2}-r^{2}}\right)=\\ &=\frac{\frac{4\cdot\[PERSON]}{\pi\cdot d^{2}}}{\pi\cdot d^{2}} \cdot\frac{1-cos\left(arctg\frac{2\cdot h\cdot r}{h^{2}+l_{OA_{1}}^{2}-r^{2} }\right)}{2}=\\ &=\frac{2\cdot\[PERSON]}{\pi\cdot d^{2}}\cdot\left(1-\frac{1}{\sqrt{ 1+\left(\frac{2\cdot h\cdot r}{h^{2}+l_{OA_{1}}^{2}-r^{2}}\right)^{2}}} \right)=\\ &=\frac{2\cdot\Phi}{\pi\cdot d^{2}}\cdot\left(1-\frac{h^{2}+l_{ OA_{1}}^{2}-r^{2}}{\sqrt{h^{2}+l_{OA_{1}}^{2}-r^{2}+4h^{2}\cdot r}}\right).\end{split}  \tag{4}\]  
Figure 6: Geometric schemes for estimating the illuminance level of the specimen surface lit by the LED light source (**a**) and incandescent lamp (**b**). Before obtaining images, we measured distances between points \(O_{0}\) and \(O_{1}\) along the coordinate axes. The position of the point \(O_{0}\) on the plate is shown in Figure 3. Along the abscissa axis, \({l_{O_{0}O_{1}}}^{x}=0.083\). Along the ordinate axis, \({l_{O_{0}O_{1}}}^{y}=0.112\) m.  
Then, the \(l_{AO_{1}}\) distance was determined as:  
\[ \begin{array}{l}{l_{AO_{1}}=\sqrt{\left({{x_{A}}-{x_{O_{1}}}}\right)^{2}+ \left({{y_{A}}-{y_{O_{1}}}}\right)^{2}}=}\\ =\sqrt{\left({{x_{A}}-{x_{O_{0}}}+{l_{O_{0}O_{1}}}^{x}}\right)^{2}+\left({{y_{A }}-{y_{O_{0}}}+{l_{O_{0}O_{1}}}^{y}}\right)^{2}}=}\\ =\sqrt{\left({{l_{AO_{0}}}^{x}+{l_{O_{0}O_{1}}}^{x}}\right)^{2}+\left({{l_{AO _{0}}}^{x}+{l_{O_{0}O_{1}}}^{y}}\right)^{2}},\end{array}  \tag{5}\]  
where \({l_{AO_{0}}}^{x}={x_{A}}-{x_{O_{0}}}\), \({l_{AO_{0}}}^{y}={y_{A}}-{y_{O_{0}}}\) is the difference between the relevant coordinates of points A and O\({}_{0}\). Numerical values of \({l_{AO_{0}}}^{x}\) and \({l_{AO_{0}}}^{y}\) are obtained from the following equations:  
\[