Featuring the ability to eliminate all primary aberrations and achieve large apertures, achromaticity, and sound environmental adaptability, off-axis three-mirror anastigmat (TMA) optical systems are increasingly being adopted in space optics. To obtain target images with a larger spatial range and more spatial details, off-axis TMA optical systems are continuously evolving toward a large field of view (FoV) while pursuing high image quality. However, when it comes to the final realizability of these high-performance optical systems, the optimization design solution is only the start, and error sensitivity is a critical factor that determines whether an optical system can yield excellent as-built performance. According to the aberration theory, optical aberrations increase exponentially with the FoV, leading to dramatically increasing error sensitivity as the FoV expands. Therefore, simultaneously achieving high performance, large FoV, and low error sensitivity is of significance for the design and implementation of high-performance imaging in large FoV off-axis TMA optical systems.

Based on previous research, we modify the error sensitivity evaluation function with curvature control, and make it more concise. Meanwhile, a low error sensitivity design method that runs through the entire optical system design is proposed. By utilizing the image quality evaluation function and error sensitivity evaluation function, a non-dominated sorting genetic algorithm (NSGA-II) is employed to select the initial structure within the specified parameter ranges. This process aims to select reasonable initial structures that yield both high image quality and low error sensitivity. Subsequently, the initial structure undergoes FoV expansion and error sensitivity optimization based on specific design criteria. By integrating the FoV expansion process with error sensitivity optimization at each step, we can gradually approach the ideal balance of error sensitivity and FoV. Finally, an off-axis TMA optical system with a large FoV and low error sensitivity is achieved.

By taking the example of designing an off-axis TMA optical system with a focal length of 100 mm, an F number of 6.7, and an FoV of 40°×4°, we validate the effectiveness of the proposed method. Firstly, the NSGA-II algorithm is employed to generate the Pareto front (Fig. 4). Since there is no significant difference in image quality among the generated 500 optical systems, we uniformly select ten optical systems from the three sets of solutions. Thirty system layouts and sensitivities are shown in Fig. 5, with system II-10 corresponding to the lowest optical system error sensitivity and having a reasonable structural layout. By employing system II-10 as the initial structure, three rounds of FoV expansion are conducted, and error sensitivity is optimized during the expansion. The error sensitivity evaluation function is controlled to be below 0.0092. Characterized by large FoV and low error sensitivity, the off-axis TMA optical system that meets the requirements is named system 3 (Fig. 6). To demonstrate the necessity of error sensitivity optimization, we set up a control group. The control group still adopts system II-8 as the initial structure and undergoes the same three rounds of the FoV expansion process, thus generating system 4 (Fig. 7). The difference between system 3 and system 4 is whether the error sensitivity is optimized, and system 4 has a 46.85% lower error sensitivity than system 3 (Fig. 8), which demonstrates that both a good initial structure and subsequent error sensitivity optimization are indispensable during the optical design. Without optimizing the error sensitivity, optical designers may design a system with better performance than system 3 when expanding the FoV, or they may end up with a system that has poorer error sensitivity than system 4. Therefore, it is difficult to determine whether the final design result has low error sensitivity. The proposed method precisely provides a clear design direction for reducing error sensitivity from the beginning, thereby improving the design efficiency of the off-axis TMA optical systems with a large FoV and a low error sensitivity.

Optical systems with low error sensitivity have a strong capability to resist error interference, leading to minimal degradation in image quality caused by errors and yielding better as-built performance. We propose a method for designing an off-axis TMA optical system with a large FoV and low error sensitivity by combining initial structure selection with error sensitivity optimization. The proposed method is based on the curvature control evaluation function and the NSGA-II algorithm. Sensitivity reduction design spans the entire process from the initial structure selection to the final design result. By controlling error sensitivity at each round of FoV expansion, an off-axis TMA optical system with a large FoV, a low error sensitivity, a focal length of 100 mm, an F number of 6.7, and an FoV of 40°×4° is ultimately designed. By comparing two optical systems designed from the same low error sensitivity initial structure, error sensitivity optimization during FoV expansion can reduce error sensitivity significantly. The results indicate that a sound initial structure alone cannot determine whether the final design has low error sensitivity. In designing off-axis TMA optical systems with a large FoV and a low error sensitivity, both a good initial structure and subsequent error sensitivity optimization are indispensable. Our method combines the two aspects, thereby making it more comprehensive and practical.