An Introduction to Numerical Modeling of Infrared Array-Based Object Detectors for Free-form Surface Installations

Infrared-based scanners are utilized as a promising method for detecting objects that contact on a surface. In this system, infrared transmitters and receivers are positioned at opposite ends of the plane, facing each other. Traditionally, this system employed a one-to-one scanning method, where a single infrared transmitter emits a light signal that is detected by a corresponding receiver on the opposite side. While this method offers advantages such as fast response times and system simplicity, it is limited by its inability to detect multiple objects simultaneously. To address this limitation, recent applications have adopted the one-to-many scanning. In this scanning method, a single infrared transmitter emits a light signal that is detected by multiple receivers on the opposite side. The results are then read in real-time to determine the position and size of the object. With the recent advancements in computing power, the response speed and accuracy of one-to-many scanning have significantly improved. However, in most cases, this method has been limited to object detection on simple planes, and there is no analytical method available to support performance prediction when considering various sensor installation configurations with various form-factors. In this study, we mathematically modeled an infrared sensor array system to predict the performance of various sensor configurations installed on two-dimensional planes or curved surfaces. Additionally, we assess the critical effect of inevitable positional errors (including orientation mismatches) on the system's performance. The unique approach introduced in this paper will provide highly reliable quantitative predictions, aiding in the design of sensor network form factors tailored for various applications in the future.