# Active Optics and Aberration Correction Technology for Sparse Aperture Segmented Mirrors
## 5 Conclusions  
In the paper, the active optics and aberration correction technology for sparse aperture segmented mirrors are investigated and analyzed using a GMT-type segmented mirror model as an example. The sparse aperture orthogonal polynomial is derived using Gram-Schimdt orthogonalization based on the single-aperture Zernike polynomial. From the hard spot theorem, the active optical model of the sparse aperture segmented mirror based on the variation of the edge sensor position is established. The active optical control of the segmented mirror is proposed with the segmented mirror aberration as the evaluation function. The correction principle of the WH technique is derived by taking a Whiffletree triangular plate as an example. By improving the existing ridge estimation and the differential evolution algorithm, the ridge parameters and the weight matrix in the iterative process of the correction volume are solved by combining the two methods. Through theoretical analysis and simulation verification, the following conclusions can be drawn. 1. The active optical control model based on aberration evaluation mode and the active optical control model based on the change of edge sensor position can realize the active optical correction of segmented mirrors. However, the aberration evaluation mode has a relatively high correction accuracy. It does not depend on the edge sensor, which reduces the complexity of the co-phase maintenance method and improves the cost performance of the technique;
2. Compared with the traditional segmented mirror aberration correction method, the proposed aberration correction mode with the segmented mirror aberration as the correction target, which has a simple correction method, a wider target aberration range and a better correction effect;  
Figure 8: The mirror deformation cloud of the SiC segment after correction by the two schemes, (**a**) Scheme 1, deformation of mirror surface in Y condition, (**b**) Scheme 1, deformation of mirror surface in Z condition, (**c**) Scheme 2, deformation of mirror surface in Y condition, (**d**) Scheme 2, deformation of mirror surface in Z condition. 3. The combination of the improved generalized ridge estimation proposed in this study and the improved differential evolution algorithm can be used to efficiently and accurately solve the correction quantity. Introducing the ridge parameter and the weight matrix results in a full-rank normal matrix and dramatically improves the degree of the sickness of the control matrix;
4. SiC material is superior to Zerodur material for thin mirror technology and support system adaptability. Using SiC as a segmented mirror material can effectively reduce the quality of the support system while improving the face shape accuracy of the segmented mirror after co-phase. It is shown that the active optical control model based on the aberration evaluation model of the segmented mirror can be used to maintain the co-phase. The WH technique is used to correct the residual aberration of the segmented mirror after co-phase. The combination of generalized ridge estimation and differential evolution algorithm is used to solve the correction quantity, which can effectively reduce the number of normal matrix conditions and achieve an accurate Solving accuracy. Using SiC material for the segmented segment can effectively reduce the support system mass and improve the adaptability of the gravity load on the segmented mirror surface. This study provides a new solution to the problem of co-phase maintenance q e and aberration correction of the segmented mirror surface and the choice of mirror material. Conceptualization, B.Z. and F.Y. ; methodology, B.Z. and F.W. ; software, B.Z. ; validation, B.Z., F.Y. and B.L. ; formal analysis, B.Z. ; investigation, B.Z. ; resources, B.Z. ; data curation, B.Z. ; writing--original draft preparation, B.Z. ; writing--review and editing, B.Z. ; visualization, B.Z. ; supervision, B.Z. ; project administration, B.Z. ; funding acquisition, F.Y. and F.W.