# Modelling the Interaction of Illuminations with a Sensor Matrix Used in Vision Systems
## 1 Introduction
Issues related to the influence of electromagnetic radiation with given parameters on the speed of human reaction are described in the paper [8]. The article discusses the impact of parameters such as colour rendering index (CRI) and colour temperature (CCT) on human reaction speed. It also presents graphs of the electromagnetic radiation spectrum with different colour temperatures (CCT) and colour rendering factors (CRI). The most popular device used for measuring spectral irradiance and reflectance is a spectroradiometer [9]. In this paper, it was used to measure the spectrum of electromagnetic radiation of an industrial illuminator ring light type. The spectroradiometer, in its built form, contains a CCD matrix (charge-coupled device). The CCD matrix is used for measurement of irradiance of each wavelength [10; 11; 12]. Electromagnetic radiation in the form of photons of a certain wavelength is incident on the matrix. This is possible because of the use of a concave-holographic diffraction grating or a system of mirrors and a diffraction grating. There are different constructions of spectroradiometers. The electromagnetic radiation responds to given pixels on the matrix of sensors separated by each wavelength. It is sensitive to the measurement irradiance of each wavelength of electromagnetic radiation. In this work, an attempt was made to make a model of an industrial illuminator and a model of a sensor matrix in order to conduct preliminary research work and select the parameters of both elements for the implementation of measurement tasks. A model was adopted in which the ring illuminator emits radiation directly in the direction of the sensor matrix without the presence of a lens and additional interference in the optical path. For the model adopted in this way, simulation measurements of irradiance were made on the matrix model. The irradiance intensity at a given surface point was determined, which is the quotient of the electromagnetic radiation power and the surface area surrounding this point. The model was simplified to the light medium, which was given the parameters of the measured photometric solid and the spectrum of electromagnetic radiation. The article presents the results of simulation studies and average irradiance and irradiance at a point on the sensor matrix as well as their analysis and interpretation. For research purposes, a virtual model of the workstation was made in dedicated software. The test stand consisted of a light source and a sensor matrix distant from it by a given distance. The sensor matrix model receives electromagnetic radiation falling on it, enabling the determination of the average irradiance of radiation falling on it. The tests were carried out for equal operating parameters of the illuminator model and selected parameters of the sensor matrix. The research and simulations presented in the paper aim to develop a primary method of selecting the illuminator's operating parameters and the sensor matrix's type and parameters. This method can be used as the first step in designing vision systems to verify the assumptions made for the system. The work uses Ansys software to model optical and lighting systems. It uses a built-in module based on the Monte Carlo method to simulate electromagnetic radiation distribution. The work also uses illuminator measurements made with a goniophotometer. These measurements made it possible to enter the actual parameters of the illuminator into the simulation model. In addition, in the second chapter, research was performed and described using a spectroradiometer using the proprietary method in the photometric darkroom. Section 2 describes the method of making measurements using a goniophotometer and spectroradiometer. The measurements were made in the dark room. The goniophotometer enables measurement of the intensity of lighting radiation and electromagnetic radiation in the visible range to obtain a photometric solid. The spectroradiometer, on the other hand, made it possible to perform spectral irradiance tests.