Non-Circular Domain Surface Figure Analysis of High-Dynamic Scanning Mirrors Under Multi-Physics Coupling

The use of large-aperture scanning mirrors for high-resolution and wide-swath imaging represents a major trend in Earth observation technology. However, to improve dynamic response performance, scanning mirror assemblies are highly lightweighted, resulting in reduced overall stiffness. This makes the mirror surface susceptible to thermal and inertial loads during operation, leading to degraded surface accuracy and poor imaging quality. Moreover, dynamic scanning mirror has the multi-disciplinary coupling effects and non-circular structural characteristics. It poses significant challenges for surface figure analysis. To address these issues, this paper proposes a surface analysis method for high-dynamic scanning mirrors under multi-physics coupling in non-circular domains. First, a finite element model of the mirror assembly is established based on the minimum aperture and angular velocity parameters. Through finite element analysis, the surface response of the scanning mirror assembly under thermal loads, dynamic inertial loads, and their coupled effects is quantitatively investigated. Subsequently, an analytical approach, which combines rigid-body displacement separation and Gram–Schmidt orthogonalization, is developed to construct non-circular Zernike polynomials, enabling high-precision fitting and reconstruction of the mirror’s dynamic surface distortions. Numerical experiments validate the accuracy of the model. Results show that for a scanning mirror with an aperture of 466 mm × 250 mm under the coupled condition of a 5 °C temperature rise and 50 N·mm torque, the surface figure achieves RMS < 2 nm and PV < 22 nm, with a fitting accuracy achieves 10−6. These results verify the accuracy and reliability of the proposed method. The surface analysis approach presented in this study provides theoretical guidance and a design framework for subsequent image quality evaluation and assurance.