With the continuous trend of low cost and miniaturization in satellite launch, higher requirements have been put forward for the imaging quality and overall size of the optical remote sensing imaging system which the satellite is equipped with. Under constant orbital height, reducing the pixel size and increasing the focal length of the optical system can improve the ground resolution, but this can bring rising system aperture, which increases the overall size of the imaging system and conflicts with the carrying capacity of small satellites. Compared to transmission systems with long focal length, reflective systems feature light weight, and easy installation and adjustment, without color differences. The traditional coaxial three-mirror system requires the addition of a folding mirror in the optical path to extract the image plane, resulting in secondary obstruction and an increase in overall system size. The off-axis three-mirror system can achieve a large field of view and avoid central obstruction, but the overall structure is larger in the vertical direction, with the processing and assembly cost twice that of the coaxial system. Meanwhile, the four-mirror structure can avoid image extraction and secondary obstruction simultaneously, but it has a large number of mirrors, high design difficulty, and high requirements for processing and assembly accuracy. Multi-surface integration is the process of machining multiple complex optical surfaces onto the same optical substrate, reducing the number of optical components in the imaging system and reducing assembly freedom. It is an innovative design direction for lightweight optical remote sensors.

Based on the general structure of a coaxial four-mirror optical system, the obstruction ratio and magnification of each mirror are derived. Then the aperture is set on the primary mirror, and the initial structure of the system is solved by the Gaussian geometrical optics theory. According to Seidel's aberration theory, the aberration coefficient of an optical system is obtained as a function of obstruction ratio, magnification, and conic coefficient. After determining the focal length, aperture, and overall size of the system, based on the above functions, we optimize the selection of reasonable parameters to ensure that all aberration coefficients are 0 and complete the primary aberration correction of the system. The conic coefficient of the primary mirror in a coaxial four-mirror optical system only affects the primary spherical aberration and does not contribute to other off-axis aberrations. Conic coefficients of the secondary, third, and fourth mirrors can influence the primary spherical aberration, coma, astigmatism, and distortion. Additionally, it is necessary to reasonably control the conic coefficients of the three mirrors to correct related aberrations. The primary field curvature is only related to the system structure and is independent of the aspheric coefficients of each surface. It is generally corrected by controlling structural parameters.

We carry out the design optimization in the multi-surface integration direction, and propose a coaxial four-mirror optical system with small aperture, long focal length, and high multi-surface integration degree of the primary and tertiary mirrors as same as the secondary and fourth mirrors. The field angle is 1.5°, the focal length is 737 mm, and the total system length is 150 mm, with the modulation transfer function better than 0.2 at 100 lp/mm. The image quality is close to the diffraction limit and the relative distortion is small. The final optimization results of this system design show that the curvature and cone coefficient of the primary and secondary mirrors are the same values. In actual processing, the primary and tertiary mirrors can be machined onto the same substrate material to create the same sphere, which can eliminate the tilt and eccentricity degrees of freedom between the primary and tertiary mirrors. Different high-order aspheric surfaces can be machined at different positions on the same sphere to distinguish the primary and tertiary mirrors. The situation is the same for the secondary and fourth mirrors. We analyze the system athermalization and tolerance. The assembly error of the system includes the displacement error of the four mirrors along the optical axis direction and the inclination and eccentricity error of each mirror. Compared to the traditional coaxial four-mirror optical system, the assembly error of this system is reduced from 12 items to 6 items, with reasonable tolerance allocation. The system has great advantages in terms of manufacturing and processing stability. Under varied temperatures, the conic coefficient of the aspheric surface remains unchanged, and the curvature radius at the vertex and the aspheric surface coefficients of all orders change. When the reflective substrate and mechanical support structure of the system are made of homogeneous aluminum alloy materials, there is no difference in the linear expansion coefficient. The thermal expansion of optical elements and mechanical structures caused by temperature changes can be regarded as thermal expansion or contraction in the same direction, which means the changes in the mechanical frame are synchronized with those of the system's rear intercept. Since the detector surface is still the optimal image plane of the system, the system exhibits sound thermal stability.

As an innovative design direction for light and small optical remote sensors, the integrated optical system with multiple mirrors can reduce assembly freedom and has caught widespread attention and exploration from domestic and foreign researchers. There are still some problems to be solved in the optical design, manufacturing, and testing of multi-surface integrated optical components, stray light suppression, and system assembly of the multi-surface integrated folding imaging system. The design of a multi-surface integrated optical system is a multi-objective optimization problem under multivariate constraints. The manufacturing of multi-surface integrated optical components should solve the problem of high-precision machining and detection of shape and position. The performance improvement of the proposed system needs to address stray light suppression and high-precision assembly. All of these point out the way for future research and will continue to promote the development of multi-surface integrated imaging optical systems.