This paper presents an active compensation strategy for RMS wavefront error of perturbed off-axis telescopes in the framework of nodal aberration theory. First, the orthogonalized expression of the wave aberration function in the vector form for perturbed off-axis telescopes is derived by using RMS normalization. The orthogonalized aberration function is applied to analytically describe the RMS wavefront error in perturbed off-axis telescopes with circular apertures. Then, the system compensation model for perturbed off-axis telescopes is established. The compensation model takes the weighted square sum of the RMS wavefront errors at representative field points as the objective function, which is minimized to obtain the optimal compensation solution of off-axis systems with perturbation constraints. The compensation model is solved by using a particle swarm optimization algorithm. Then, the off-axis three-mirror anastigmatic telescope is taken as an example, and the system compensations for the misaligned tertiary mirror and deformed primary mirror are discussed. After compensation, the average RMS wavefront errors in the perturbed off-axis systems are greatly reduced, which can well meet the system requirements. Finally, Monte Carlo simulations of the optimal compensation method and sensitivity table method are carried out to demonstrate the correctness and accuracy of the proposed method.

Shadows in very high-resolution multispectral remote sensing images hinder many applications, such as change detection, target recognition, and image classification. Though a wide variety of significant research has explored shadow detection, shadow pixels are still more or less omitted and are wrongly confused with vegetation pixels in some cases. In this study, to further manage the problems of shadow omission and vegetation misclassification, a mixed property-based shadow index is developed for detecting shadows in very high-resolution multispectral remote sensing images based on the difference of the hue component and the intensity component between shadows and nonshadows, and the difference of the reflectivity of the red band and the near infrared band between shadows and vegetation cover in nonshadows. Then, the final shadow mask is achieved, with an optimal threshold automatically obtained from the index image histogram. To validate the effectiveness of our approach for shadow detection, three test images are selected from the multispectral WorldView-3 images of Rio de Janeiro, Brazil, and are tested with our method. When compared with other investigated standard shadow detection methods, the resulting images produced by our method deliver a higher average overall accuracy (95.02%) and a better visual sense. The highly accurate data show the efficacy and stability of the proposed approach in appropriately detecting shadows and correctly classifying shadow pixels against the vegetation pixels for very high-resolution multispectral remote sensing images.