Unobscured reflective optical systems with a wide field of view (FOV) have significant application values. However, the aberration increases with the increase of the system FOV, so a wide FOV system is difficult to design. In this paper, a design method that is effective in achieving off-axis three-mirror systems with ultrawide FOV is proposed. In this method, the system FOV is expanded stepwise in the design process, and the surface optical freeform polynomial terms are extended based on the judgment of image quality and some constraint conditions, and to obtain a prospective ultrawide FOV system. A freeform off-axis three-mirror imaging system with a focal length of 1000 mm, an F-number of 10, and an ultrawide FOV of $80°\times 4°$ is designed as an example. This design result shows that the system has a high imaging quality of RMS wavefront error value of $0.040\lambda (\lambda =0.633\mathrm{\mu m})$, and it demonstrates that the method is effective in achieving off-axis three-mirror systems with an ultrawide FOV.

We report on the design of an off-axis three-mirror freeform telescope with a large field of view (FOV) based on an integration mirror (IM). This design is the continuation of the authors’ previous work. Based on aberration theory, we established a suitable nonrelayed three-mirror-anastigmat initial configuration for integration mirror design. For an optical freeform surface, we analyzed the qualitative aberration correction ability of a $x\text{-}y$ polynomial surface that can provide a simple, convenient, and user-friendly relationship between freeform surface term coefficients and aberrations and then applied the $x\text{-}y$ polynomial surface on the tertiary mirror to improve the system optimization degrees of freedom. In an example with a focal length of 1200 mm, an F-number of 12, and a FOV of $1°\times 30°$, the tolerance performance was analyzed, and the system presented a good imaging performance. In addition, the IM structure and opto-mechanics support structure were designed and analyzed. The confirmatory design results showed that the integration of the primary mirror and tertiary mirror can improve opto-mechanical properties judged by multiple criteria. In conclusion, the integration of the primary mirror and tertiary mirror not only offers alignment convenience as described previously but also improves system opto-mechanical properties in multiple perspectives. We believe this large linear FOV system based on IM has broad future applications in the optical remote sensing field.

An off-axis three-mirror system (OTS) was designed based on the primary mirror and tertiary mirror (TM) integrated on a single substrate in order to solve the OTS drawbacks, such as the alignment difficulty and the large opto-mechanical weight. Furthermore, an optical freeform surface that can increase the optimizing degrees of freedom (DOF) was applied on the TM in order to achieve a wide field of view (FOV). An example with a focal length of 1200 mm, F-number of 12, and FOV of $10°\times 4°$ was given, and the maximum wave front error (WFE) RMS was $0.0126\lambda$, indicating a good imaging quality. The design result shows that the number of alignment DOF was reduced from 12 to 6, and the weight of the mirror support assembly can also be lighter. An XY polynomial, established as an even function of x, was employed as the TM surface, so we obtained an axial symmetrical imaging quality about the $x$ axis, and the axial symmetry aberration performance also brings considerable convenience to alignment and testing for the OTS.

The realization of the final performance of the optical system depends not only on the aberration correction of the optical design but more importantly on the control of the position error of the optical element during the construction process. Therefore, reducing the error sensitivity of the optical system is an important part of the optical system design process. In order to obtain an optical system with low error sensitivity, this paper proposes an evaluation function of the tilt error sensitivity of the optical system and establishes a desensitization design method for the optical system. Taking an off-axis three-mirror optical system as an example for desensitization design. By comparing the variation of wave front error (WFE) caused by the tilt error of the optical system before and after the desensitization design, the correctness of the evaluation function and the effectiveness of the desensitization design method of the optical system are proved.

An off-axis three-mirror anastigmatic optical system with the offset apertures configuration as a typical unobscured optical system is frequently used in various optical instruments. The practical applications show that this type of system has a higher sensitivity in alignment. To reduce the alignment sensitivity of the unobscured optical systems, a desensitization design method with an adjustment-optimization-evaluation process is proposed. By ray path difference analysis based on the optical system mathematical models, the mirror off-axis magnitude value is determined as a significant factor influencing system alignment sensitivity. Accordingly, in the desensitization design process, the mirror off-axis magnitude value is set as an adjustment, and the image quality and system sensitivity are set as the criteria. By a design example, it proves that the desensitization design method is effective and practical, and the design result sensitivity analysis not only verifies that the off-axis magnitude is a significant factor that influences the system alignment sensitivity, but also finds that there is a positive correlation relation between system sensitivity and off-axis magnitude value. The desensitization method can design the unobscured optical systems with less alignment sensitivity and robust tolerance.