The infrared search and track (IRST) system has characteristics such as good concealment, long detection range, and strong anti-jamming capabilities, and is widely used in airborne, shipborne, vehicle-mounted, and spaceborne systems. The operating range is an important indicator of the detection capability of IRST systems. Accurately analyzing the operating range is significant for improving design quality and evaluating comprehensive performance. Traditional operating range models for IRST systems generally do not consider the spectral radiation characteristics of both the target and the background. Many studies have made improvements in this area, but they have not simultaneously considered both the efficiency of target radiation received by the pixels and the short-term random errors in system tracking. In response to the current research gap, this study establishes an optimization model for the operating range of a staring IRST system and presents a novel method for solving this range. The model accounts for both the number of pixels occupied by the target’s image on the focal plane and the efficiency with which these pixels receive the target’s radiation. During the solution process, the theoretically calculated target spectral radiation intensity and background spectral radiation brightness are normalized and treated as weights, which are then multiplied by the actual measurement results. This approach balances the advantages of both theoretical calculations and actual measurements, thus improving calculation accuracy. We hope that this model can serve as a reference for analyzing factors related to the operating range of IRST systems and assist in the optimization and performance evaluation of such systems.

We improve the existing IRST system operating range model by using the number of pixels n occupied by the target to handle the system’s short-term random tracking errors, and by using the pulse visibility factor (PVF) to address the efficiency of pixel response due to target radiation. During the solution process of the operating range model, a normalization method is proposed. First, the target radiation intensity and background radiation brightness, obtained from theoretical calculations, are separately normalized to obtain the normalized target radiation intensity and normalized background radiation brightness. These values are then used as weights and multiplied by the actual measurement results to derive new spectral radiation characteristics for the target and background. The integral part is then fitted to obtain a hidden function equation that is only related to distance, which is then solved. Finally, the optimized operating range model and normalization method are used for example calculations and experimental verification.

According to the optimized operating range model and solution method proposed in this study, the operating range is calculated to be 15.4461 km, with a relative error of 2.97%. In contrast, if the unoptimized solving method is used, the operating range is calculated to be 17.5512 km, with a relative error of 17.01%. Therefore, the calculation results based on the optimized operating range model and solution method in this study are closer to the measured values. Without changing other conditions, the relationship between n and the entrance pupil diameter and operating range (Fig. 7) shows that the operating range decreases as n increases, but the rate of decrease slows down; it increases as the entrance pupil diameter increases, though the rate of increase also slows down. Therefore, optimizing the IRST system tracking device can reduce the short-term random errors in system tracking, lower the n value, and thereby increase the operating range. The operating range of the IRST system can also be increased by appropriately enlarging the optical system’s aperture.

We establish an optimization model for the operating range of a gaze-type IRST system. The operating range model corrects the traditional derivation method, which assumes a uniform distribution of the energy of the speckle pattern formed by point targets on the focal plane, while also considering the speckle effect caused by short-term random tracking errors, thereby improving the accuracy of the calculations. Finally, the operating range model is applied to calculate instances of aircraft targets, and the effect of the number of pixels n occupied by the target on the focal plane, as well as the optical system aperture, on the operating range, is analyzed. The calculation results indicate that the operating range decreases as n increases, but the rate of decrease slows down; the operating range increases as the entrance pupil diameter increases, though the rate of increase also slows down. Finally, the reliability of the operating range model is verified through field experiments. The research indicates that both the number of pixels occupied by the target on the focal plane and the efficiency of these pixels in receiving target radiation are important factors affecting the operating range of IRST systems and should be considered in calculations. The theoretically calculated target spectral radiation intensity and background spectral radiation brightness fully take into account the spectral radiation characteristics of the target and background. However, there may be some deviation between theoretical calculations and actual measurements. While actual measurements are highly accurate, they often reflect the overall radiation characteristics and cannot reveal the detailed spectral radiation characteristics. Normalizing the theoretical calculation values as weights for the actual measurement values can yield new spectral radiation characteristics for the target and background. This method combines the advantages of both theoretical calculations and actual measurements, which makes it more aligned with real-world situations. Additionally, optimizing the IRST system tracking device or appropriately increasing the optical system aperture can enhance the operating range of the IRST system. For large-aperture optical systems, further increasing the system aperture will have a diminishing effect on the improvement of the operating range.