# Research on Performance Evaluation and Optimization Theory for Thermal Microscope Imaging Systems
## 1 Introduction  
Infrared imaging technology shows great advantages in target detection and is widely used in agriculture [1], medicine [2], military [3, 4], industrial [5, 6, 7] and other fields [8]. Due to the limitation of the manufacturing process of infrared imaging detectors, the performance of the infrared imaging system needs to be optimized. Therefore, it is necessary to optimize the design of the infrared imaging system according to different application fields [9, 10]. The theoretical research of infrared imaging systems is the theoretical basis for the development of infrared imaging technology [11, 12]. Among them, the performance evaluation theory can provide theoretical guidance for the design and optimization of the infrared imaging system [13, 14]. MRTD (minimum resolvable temperature difference) and MDTD (minimum detectable temperature difference) have been important parameters for evaluating the performance of infrared imaging systems, mainly because they can quantify the temperature resolution capability of infrared imaging systems [15, 16, 17, 18, 19]. MRTD is defined as a standard four-bar blackbody target pattern with a certain spatial frequency and a height ratio of 7:1 in a uniform blackbody background (as shown in Figure 1) [20, 21, 22]. When observed for a long time, the temperature difference between the target and the background gradually increases from zero until the observer confirms thatthe target pattern with four-bars can be distinguished (50% probability). The temperature difference between the target and the background is the minimum resolvable temperature difference at that frequency. MDTD is defined as when the observer can just distinguish the shape and position of a square or round black-body target with a certain size through the display screen without time limitation (as shown in Figure 2). The temperature difference between the black-body target and the black-body background is called the MDTD [23; 24; 25; 26]. MRTD and MDTD calculations help in the design of detectors and actual systems. The first mature infrared imaging system performance prediction model (the Ratches Model) was named after the proposer of the theory, and was developed by the American Night Vision Laboratory in 1975 [27]. The FLIR92 model is widely used in the performance evaluation of infrared imaging systems because it adds a three-dimensional noise model, which can predict the performance of scanning and staring imaging systems. By introducing a modulation transfer function and a new human eye model, it adds an analysis of the effect on sampling to better evaluate gaze imaging systems [28; 29]. However, the evaluation models of infrared imaging systems are mostly for infrared imaging systems in telephoto mode. Due to the lack of comprehensively considering 1) the characteristics of the TMISs (thermal microscope imaging systems) and 2) the difference in spectral radiant flux, which are factors that cannot be ignored, none of the above-mentioned methods can accurately and comprehensively evaluate the performance of the TMISs, and so there is currently no standard method for evaluating the performance of the TMISs. The imaging device can only be selected based on experience when designing the TMISs, which leads to the failure of the best performance of the imaging device in the process of designing the system, and the inability to select appropriate design schemes for different detection targets. Figure 1: Image of the four-bar pattern for calculating MRTD. Figure 2: Test chart for calculating MDTD. In this paper, we studied the performance evaluation and optimization theory of TMISs. The thermal microscope imaging process was analyzed, and the performance evaluation model suitable for TMISs was further deduced and established. Based on the performance evaluation theory, we conducted simulation analysis and obtained theoretical results suitable for performance evaluation and optimization of TMISs.