# Optical and Electronic Expert System for Diagnosing Eye Pathology in Glaucoma
## 6 Physical Modeling of the Optical-Electronic System for Researching Pathologies of Fundi
Illumination of the retinal image takes place on the photomatrix, which is built with the following optical system:  
\[E^{\prime}=\frac{\tau_{os}\cdot\tau\cdot L_{c}}{4}\cdot\left(\frac{n^{\prime} }{n}\right)^{2}\cdot\left(\frac{D}{f^{\prime}}\right)^{2}\cdot\frac{\beta_{p }^{2}}{\left(\beta_{p}-\beta\right)^{2}} \tag{6}\]  
where \(\tau_{os}\) is the transmission coefficient of the optical system; \(n^{\prime}\) is the refractive index of the medium in the image space (n\({}^{\prime}=1\)); \(n\) is the index of refraction of the medium in the space of objects (n = noka); \(D\) is the diameter of the entrance pupil of the optical system; \(f^{\prime}\) is the focal length of the optical system; \(\beta_{p}\) is the linear increase in the optical system in the pupils; and \(\beta\) is the linear increase in the optical system. Substituting (5) into (6) and assuming a linear increase in the pupils \(\beta_{p}=1\), for the illumination of the retinal image on the photomatrix, we obtain  
\[E^{\prime}=\frac{\tau_{oc}\cdot\tau_{0 ka}\cdot\rho\cdot L_{c0}\cdot S_{a}^{ \prime}}{4\cdot l_{oka}^{2}}\cdot\left(\frac{D}{f^{\prime}}\right)^{2}\cdot \frac{1}{\left(1-\beta\right)^{2}} \tag{7}\]  
Let us assume that \(\tau_{eye}=0.5\), \(\tau_{os}=0.9\), \(\rho=0.2\), \(l_{gev}=24\), and diameter = 24 mm. The maximum brightness of the light source that can be transmitted when directly observed is \(7500\) cd/m\({}^{2}\). So that patients would not feel discomfort, as an illuminator, we chose an LED; Lsd = 7000 cd/m\({}^{2}\). Let us also assume that the projection of the source onto the pupil of the eye occupies 50% of its area. In this case, with a pupil diameter of 6 mm, S\({}_{\text{d,pup}}=14.13\) mm. To perceive the image, we used the 6.6 Megapixel CMOS photomatrix NOII4 SM6600A, the main indicators of which are as follows: \begin{tabular}{l l} Dimensional capacity & \(2210\times 3002\) \\ Optical format, inches & 1 \\ Range of spectral sensitivity, nm, HM & 400...1000 \\ Apparent sensitivity, V/(lx/s) & 2.01 \\ Dark signal, mV/s & 3.37 \\ \end{tabular}   
The required linear increase \(\beta\) in the optical system can be determined by the ratio that corresponds to the condition under which the retinal image occupies the largest part of the photomatrix area:  
\[\beta=\frac{H_{phm}}{D_{c}} \tag{8}\]  
where \(H_{phm}\) is the height of the photomatrix; and D\({}_{\text{retina}}\) is the diameter of the retina. The optical matrix format of 1 inch corresponds to the size of 12.8 \(\times\) 9.6 mm. The diameter of the human retina is 22 mm. Then,  
\[\beta=\frac{9.6}{22}=0.436\]  
By substituting numerical values for the definition in Expression (7), we obtain  
\[E^{\prime}=\frac{0.9\cdot 0.5\cdot 0.2\cdot 7000\cdot 14.13}{4\cdot 24^{2}} \cdot\left(\frac{D}{f^{\prime}}\right)^{2}\cdot\frac{1}{\left(1-0.436\right)^ {2}}=12.146\cdot\left(\frac{D}{f^{\prime}}\right)^{2} \tag{9}\]  
To carry out further calculations, we will determine the illumination of the photomatrix E\({}^{\prime}\) at which the value of the useful output signal will be comparable to the dark one. The minimum illumination of the image at which it is indistinguishable from the background noise is found using the sensitivity of the photomatrix and the value of the dark signal:  
\[E_{0}=\frac{3.37\cdot 10^{-3}}{2.01}=1.677\cdot 10^{-3}\]  
To obtain a good image of the retina, the illumination of the photomatrix must be at least 10 times higher than this value. Therefore,  
\[E^{\prime}=0.01677\ (\mathrm{Lx})\]  
Then, using Expression (9) for the geometric luminous intensity of the optical system, we have  
\[\left(\frac{D}{f^{\prime}}\right)^{2}=\frac{0.01677}{12.146}=1.38\cdot 10^{-3} \tag{10}\]  
In order to use the entire field of the optical system, the entrance pupil must be aligned with the plane of the eye pupil. In this case, the field aperture will be the frame of the photomatrix, and with the linear magnification selected in accordance with Expression (8), the image of the entire retina will be formed on the photomatrix.