Design of Off-axis Three-mirror Optical System Based on Controlled Genetic Algorithm

With the rapid development of optical technology，the application demand of high-performance optical systems in various fields is growing steadily. Especially in the fields of aerospace remote sensing，astronomical observation，scientific exploration and other fields，the performance requirements of optical systems are becoming more and more stringent. These systems are expected to have larger fields of view and broader detection bands. Reflective optical systems，which are free from chromatic aberration and can achieve large apertures while being lightweight，have garnered significant attention in satellite remote sensing. At present，in optical design，it is commonly used to find an initial structure that is similar to the design goal as a starting point for optimal design. The damping least squares method employed by optical design software in the optimization process is more sensitive to the selection of initial values. If the initial values are not selected properly，the optimization process may fail to converge or may converge to a local optimal solution，thereby failing to reach the global optimal solution. The initial structure of the off-axis reflection system is small and it is difficult to find the initial structure. Therefore，it is commonly used to design the coaxial system first and then optimize the off-axis system. To address this problem，this paper proposes a solution that combines traditional optical design with optimization algorithms. This solution makes up for the shortcoming that design software easily falls into local optimal solutions，so that the final optical system not only guarantees the global optimal solution to the greatest extent，but also has strict ray tracing calculations. Firstly，the relationship between system parameters and structural form，main mirror type，and imaging times is analyzed to provide a more reasonable range for parameter selection during the initial structure calculation process，thereby reducing the amount of calculation. Secondly，based on the aberration analysis of the coaxial three-mirror optical system，the initial structure of the system is calculated through a controlled genetic algorithm using the sum of the weighted third-order aberrations as the fitness function. Compared with the traditional Genetic Algorithm，which generally tends to have the characteristics of individuals with better fitness，the Controlled Genetic Algorithm also tends to select individuals with lower fitness values but can increase the diversity of the population，which is more conducive to the entire solution space. Find the optimal initial structure within the range. Compared with the method of directly substituting the constraints into the optimization software，the initial structure obtained by this method is more reasonable and the image quality is better. After the initial structure is determined，the aperture and field of view of the system are off-axis，and the field of view is gradually expanded while ensuring that the light is not blocked. Free-form surfaces are introduced to correct the asymmetric aberrations produced by the off-axis system. Compared with traditional spherical，the freeform surfaces have the characteristics of non-rotational symmetry and can be of any shape. They can correct the asymmetric aberration produced by the non-rotation symmetric optical system in the meridional direction，and ultimately achieve high-quality large field of view imaging. Taking an optical system with a field of view of 30°×20°，a focal length of 110 mm，an F number of 2.2，and an operating band of 3 to 5 μm as an example，the fringe Zernike polynomial is used to describe the free-form surface. Each term of the Zernike polynomial is related to aberrations have a direct correspondence. In the design process，not only can new higher-order terms be added during the optimization process to describe the free-form surface without affecting the coefficients of other terms，but terms with very small contributions can also be found to appropriately delete the design. The results indicate that the Optical Transfer Function（MTF）is near the diffraction limit and exceeds 0.6 at the Nyquist frequency of 25 lp/mm. The maximum Root Mean Square（RMS）spot radius value in the full field of view is about 6.3 μm，and the maximum distortion is less than 10%. Finally，the tolerance analysis was conducted，and under reasonable tolerance conditions，the image quality met the requirements. The effectiveness of this method in the design process of large-field off-axis three-mirror optical systems has been verified，and it has certain reference significance for the design of large-field off-axis optical systems. © 2024 Chinese Optical Society. All rights reserved.