# Modelling the Interaction of Illuminations with a Sensor Matrix Used in Vision Systems
## 2 Materials and Methods
### Simulation Test Method  
A diagram of the measuring station used to conduct simulation tests is presented in Figure 4.  
In the first step, the light centre for the illuminator was defined. The centre of light is located in the illuminator's geometric centre. In the case of the illuminator under test, this is the centre of the opening that is located in it. Diodes are placed around the hole in three rows. The simulation model defined the luminous centre in such a way that a solid was made: a cylinder with a base diameter of 1 mm and a height of 1 mm. It was given the material properties available in the Speos 2023 R1 software and that the material was set as opaque. The parameter defining the reflection from the material from which the luminous centre is modelled is also set to 0%. The sensor matrix was placed at a distance of d = 500 mm from the base of the cylinder (centre of light). The die was laid parallel to the base of the cylinder (Figure 5). The optical axis of the illuminator and the axis passing through the intersection of the axis of symmetry of the matrix coincided. In the Speos 2023 R1 software, it is possible to give parameters to model radiation. The surface-emitting radiation was the surface of the base of the cylinder. The radiation emitted by it was given features such as a photometric body and electromagnetic radiation spectrum, which were measured in experimental studies. The luminous flux of the illuminator tested experimentally was approximately 337 lm. Figure 4: Diagram of the measuring station. Figure 3: Diagram of the measuring station showing the position of the illuminator to the spectroradiometer. Simulation tests were carried out on a sensor matrix with dimensions of 24.576 \(\times\) 24.576 mm, for two-pixel sizes, and with dimensions x and y: 12 \(\times\) 12 \(\upmu\)m and 24 \(\times\) 24 \(\upmu\)m. The number of pixels on the sensor matrix was 2048 \(\times\) 2048 for a smaller pixel. However, the number of pixels on the sensor matrix was 1024 \(\times\) 1024 for a larger pixel (Figure 6). The tests were carried out for two groups of simulations, i.e., for the number of generated rays. The generated radius is a vector with a length corresponding to the distance between the sensor matrix (at a given point) and the centre of the light. Rays are emitted from the light centre. The generation of rays is carried out pseudorandomly: \(2\times 10^{5}\), \(2\times\ 10^{9}\). The Speos 2022 R1 software allows you to perform simulations with various parameters. There are three main types of simulation studies, which are called direct simulation, inverse simulation, and interactive simulation. The \"direct simulation\" simulation allows you to perform tests in which the rays are emitted from the source of electromagnetic  
Figure 5: Diagram showing a model of the light centre and sensor matrix with the solid photometric model marked. Figure 6: Diagram showing an example of a sensor matrix and a single sensor (pixel). radiation and fall on the sensor matrix. The \"direct simulation\" simulation was chosen to perform the simulation. The \"inverse simulation\" simulation allows you to perform a simulation in which rays are propagated from a camera or sensor towards a light source. This is known as reverse simulation. The third possibility, i.e., interactive simulation, allows visualization of the behaviour of light rays in the optical system. The visualization consists of the fact that the beams and their direction are visible in terms of the direction the rays propagate after passing through, for example, a diffuser or other material. The main assumption of this research Is to change the parameters of the sensor matrix to gain knowledge about how the average irradiance of electromagnetic radiation falling on the sensor matrix will change. We chose a simulation method called direct simulation. The described simulation method involves such elements as the source of electromagnetic radiation, the irradiance sensor, and the light centre [15; 16].