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Abstract. This paper presents an approach for estimating and then removing image radial distortion. It works on a single image and does not require a special calibration. The approach is extremely useful in many applications, particularly those where human-made environments contain abundant lines. A division model is applied, in which a straight line in the distorted image is treated as a circular arc. Levenberg-Marquardt (LM) iterative nonlinear least squares method is adopted to calculate the arc's parameters. Then "Taubin fit" is applied to obtain the initial guess of the arc's parameters which works as the initial input to the LM iteration. This dramatically improves the convergence rate in the LM process to obtain the required parameters for correcting image radial distortion. Hough entropy, as a measure, has achieved the quantitative evaluation of the estimated distortion based on the probability distribution in one-dimensional θ Hough space. The experimental results on both synthetic and real images have demonstrated that the proposed method can robustly estimate and then remove image radial distortion with high accuracy. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

As one of the most-critical components in space optical cameras, the performance of space mirrors directly affects the imaging quality of space optical cameras, and the lightweight form of mirror blanks is a key factor affecting the structural quality and the surface-shape accuracy of mirrors. For the design requirements of lightweight and high surface-shape accuracy with space mirrors, this study proposes a design and manufacturing method that integrates topology-optimization with additive-manufacturing technology. This article firstly introduced the basic process and key technologies of space-mirror design and analyzed the superiority of combining a topology-optimized configuration design and additive-manufacturing technology; secondly, the topology-optimized design method of a back-open-structure mirror was used to complete the scheme design of a Φ260 mm aperture mirror; finally, the laser selective-melting manufacturing technology was used to complete the Φ260 mm aperture mirror blank. The mirror and its support structure were assembled and tested in a modal mode; the resonant frequencies of the mirror assembly were all over 600 Hz; and the deviation from the analytical results was within 2%. The optical surface of the mirror was turned by the single-point diamond-turning (SPDT) technique. The accuracy of the optical surface was checked by a Zygo interferometer. The RMS accuracy of the mirror surface was 0.041λ (λ is the wavelength; λ = 632 nm). In the test of the influence of gravity on the surface-shape accuracy, the mirror was turned over, which was equivalent to twice the gravity, and the RMS of the mirror surface-shape accuracy was 0.043λ, which met the requirement. The verification results show that the mirror designed and fabricated by the additive-manufacturing-based mirror-topology-optimization method can be prepared by the existing process, and the machinability and mechanical properties can meet the requirements, which provides an effective development method for improving the structural design and optimizing the manufacturing of space reflectors.