Objective   Off-axis three-mirror optical systems, based on the advantages of non-obscuration and capable of achieving a large field of view (FOV), can exhibit excellent optical performance, combined with the optical freeform surface with high degrees of freedom and strong aberration correction ability. The improvement of the imaging requirements has led to the continuous increase of the aperture and focal length of the reflective optical system, the error sensitivity of the optical system increases dramatically, resulting in higher processing difficulty and alignment sensitivity, as well as substantial time and economic costs. Error sensitivity represents the sensitivity of optical system after misalignment. The tolerance accuracy of optical system with low error sensitivity is loose. By controlling error sensitivity during the optimization process, an optimal balance can be achieved between image quality and cost. Therefore, desensitization optimization is an indispensable part of the large freeform off-axis three-mirror optical system design process.

  Methods   Low error sensitivity optical system design begins with the selection of image quality evaluation criteria that can characterize the error sensitivity. The optical path difference and wavefront error are selected as two image quality evaluation criteria, and the geometrical optics method is adopted to establish the mathematical model of ray tracing before and after misalignment (Fig.1, Fig.4). Then the mathematical relationship between the parameters of the optical system and the error sensitivity is obtained, two error sensitivity evaluation functions (S and LC) are constructed based on the mathematical relationship, and the angle optimization desensitization design method and the local curvature desensitization design method are proposed as two desensitization design methods applicable to freeform optical systems according to the evaluation functions. A desensitization design process for large freeform off-axis three-mirror optical systems is developed (Fig.5). Two proposed desensitization design methods are applied to desensitize a large freeform off-axis three-mirror optical system with a focal length of 30 000 mm, an F number of 15 and an FOV of 1°×1° (Tab.1), and the desensitization effect of the two methods is compared.

  Results and Discussions  The initial structure of the large freeform off-axis three-mirror optical system is System 1 (Fig.7), the angle optimization desensitization design method is used to obtain System 2, and the local curvature control desensitization design method is used to obtain System 3. The modulation transfer function (MTF) of all three systems is close to the diffraction limit, and the average RMS WFE of System 1, System 2, and System 3 is 0.038λ, 0.036λ and 0.039λ respectively (Fig.8), the image quality of all three systems is in the range of 0.038× (1±5%)λ and less than 1/15λ of each FOV (Fig.8).The total length of System 1, System 2, and System 3 is9 097.23 mm, 8 862.07 mm and 9 100.00 mm (Tab.2) respectively. The three systems are identical in configuration and differ slightly in total length. Under the tilt error perturbation (tangential: 0.001°, sagittal: 0.001°), the error sensitivity (ΔRMS WFE) of System 1, System 2, and System 3 is 0.089λ, 0.073λ and 0.062λ respectively (Fig.9). The error sensitivity is reduced by 17.98% using the angle optimization desensitization design method and by 30.34% using the local curvature control desensitization design method, obviously the latter method has better desensitization effect.

  Conclusions   In this paper, the angle optimization desensitization design method and the local curvature control desensitization design method are introduced to desensitize the large freeform off-axis three-mirror optical system. Systems designed with different methods are compared, and the results demonstrate that, under the condition of no significant differences in optical system configuration, both desensitization design methods exhibit excellent theoretical aberration correction results for the optical system, and the MTF of the systems is close to the diffraction limit. The two desensitization design methods can effectively reduce the error sensitivity of the optical system, and it is found that the local curvature control desensitization design method can achieve better desensitization performance. Applying the desensitization design method in the large freeform off-axis three-mirror optical system design process correctly can significantly improve the system robustness, and effectively reduce the manufacturing cost, which is of great significance for the design and construction of large optical systems.