# Modelling the Interaction of Illuminations with a Sensor Matrix Used in Vision Systems
## 2 Materials and Methods  
### Description of the Measuring Station  
The research began with measurements made for the Ring Light industrial illuminator Ring Light type VLR-10 RK0211 of SICK company. This ring construction is shown in the first figure. The LEDs of the illuminator are installed ring wise around the hole intended for mounting the lens. The optical axis of each diode is set parallel to the axis of the illuminator housing opening. The illuminance was measured as part of the research to determine the illuminator's photometric body. Then, tests were carried out using a spectroradiometer to determine the spectrum of electromagnetic radiation emitted by the illuminator. The tested illuminator, according to the manufacturer's data, CCS, emits radiation in the visible light range of white colour (Figure 1). Figure 1: (**a**) Illuminator cross-section and sensor array and (**b**) view of the position with the illuminator marked and the illuminated surface. For the illuminator, a photometric solid was determined using a goniophotometer. The luxmeter used in measurement was SONOPAN L-400. The photometric body was measured using a goniophotometer under PN EN 13032-1. It is used to determine the luminosity of electromagnetic radiation in a system called C--gamma, used in work to carry out measurements [13]. During the measurements, the angle C between two closest half-planes was 15\({}^{\circ}\), the difference between the two closest gamma angle was 2\({}^{\circ}\), and the distance between the centre of light and the lux meter was 10 m (Figure 2). The centre of the light is the point characterizing the light source. Most often, it is located at the intersection of the axis of symmetry of the output hole of a given source. Angle C is a double-sided angle between the output half-plane and a given half-plane. The output half-plane is referred to as the 0-half-plane. The angle by which we define it is the angle C0. The measure of angle C is determined depending on the number of half-planes. For example, for 25 half-planes (twice including the half-plane for the angle C = 0\({}^{\circ}\), which is the same as the half-plane for the angle of 360\({}^{\circ}\)), the angle C between the half-planes is 15\({}^{\circ}\). It is calculated from the following relationship: 360\({}^{\circ}\)/(n - 1). The letter n denotes the half-planes, which for the tests performed in work is 25. The gamma angle is a plane angle lying on each half-plane. It is determined between the semi-straight line being the optical axis of a given illuminator with a beginning in the centre of illumination of the illuminator and a semi-straight line with a start in the centre of illuminators in any direction while maintaining a constant gamma angle. The gamma angle is between 0\({}^{\circ}\) and 180\({}^{\circ}\). It should be noted that the goniophotometer measurement is performed in the dark-room with fixed measurement parameters, such as the temperature of 25+/-1 \({}^{\circ}\)C and airflow velocity of 0.2 m/s. A photometric darkroom is a large room painted in black. Black absorbs radiation and ensures that light does not reach the meter from other directions. A goniometer and a lux meter are in the photometric darkroom at a given distance between the devices. The luminaire is mounted on the goniometer holder, which allows rotation by angle C and gamma angle and moves the luminaire. The illuminance with subsequent points of space around the industrial illuminator is measured using a lux meter. Then, using the law of the inverse of the square of the distance, the luminous intensity of a given measuring point is calculated. A detailed description discussing the use of the law of the inverse of the square of the distance in measurements is discussed in the work of [PERSON] [14]. Figure 2: Diagram showing the method of goniophotometer measurement. Using a lux meter and goniometer measurement allows you to measure the illuminance E in a given direction at a photometer distance. The measurement data of each measuring point are saved to a file.