Misalignment Corrections In Reflective Telescopes

Reflective telescopes are completely free of chromatic aberrations, and it is more viable to manufacture large-aperture optical elements and realize lightweight design for reflective systems compared to refracting ones. Therefore, large astronomical telescopes are almost invariably reflective at present. The final imaging performance of the telescopes is determined jointly by the optical design, manufacturing and alignment status, as well as their working conditions. A good alignment state is the precondition of the telescope with excellent observation performance. Besides, for large modern telescopes, the effectsof the changes in their working conditions(e.g. the gravity, thermal or wind condition) on the position and figure of the mirrors also cannot be neglected. Consequently, active optics systems are usually indispensable for modern large telescopes. The final alignment status of the optical elements in the large telescopes is determined jointly by the alignment accuracy in both optical assembly and active optical correction processes. Since both the optical assembly and active optical correctionsystems perform the correction of mirror misalignments or deformations according to the results of optical testing, they can both be termed as the misalignment correction techniques. The development of accurate and robust misalignment correction techniques is of great importance for maintaining high observing performance. This paper presents two kinds of models for the misalignment correction of the telescopes, i.e., a numerical model based on modified sensitivity matrix method and an analytical model based on nodal aberration theory.This paper does the following researches on misalignment correction techniques for telescopes: ? In the presence of large misalignments, the accuracy of the conventional sensitivity matrix model is relatively low. For this problem a modified sensitivity model is presented. The misalignment-induced aberration field characteristics are investigated for an off-axis afocal telescope. The alignment model based on the modified sensitivity matrix method is further established. An alignment simulation of 500 misaligned telescopes is performed using both the conventional and the modified sensitivity matrix models. The root mean square errors(RMSEs) between the introduced misalignment parameters and the computed values are used to evaluate the accuracy of the two alignment models. The results show that the RMSEs for the three decenter parameters using the modified model are only about 13%-24% of the RMSEs using the conventional model, and the RMSEs for the two tilt parameters using the modified model are only about 12%-13% of theRMSEs using the conventional model. Therefore, the alignment efficiency of the modified model is far better than the conventional model. Finally, the modified alignment model is utilized in the actual alignment of a two-mirror telescope. The alignment results show that the RMS WFEs of on-axis field points 0.056 ??(?=632.8 nm), while the RMS WFEs in marginal field of view are better than 0.1 ??While most of the alignment models are based on numerical methods at present, these methods can hardly lead to any insight into the aberration field dependencies that arise in the presence of the misalignments. An analytical alignment model based on third-order nodal aberration theory is presented for this problem, which can be utilized to compute the primary mirror astigmatic figure error and secondary mirror misalignmentsfor two-mirror telescopes. Alignment simulations are conducted for an R-C telescope based on this analytical alignment model. It is shown that in the absence of wavefront measurement errors, wavefront measurements at only two field points are enough, and the correction process can be completed with only one alignment action. For the case of large misalignment perturbations(decenter parameters are within 2 mm, tilt parameters are within 0.1°, and Zernike astigmatic coefficients are within 0.2 ?), the alignment efficiency is still fine. In the presence of wavefront measurement errors, increasing the field points for wavefront measurements can enhance the robustness of the alignment model. The comparison of the alignment efficiency is further made between the two alignment models based on modified sensitivity matrix and nodal aberration theory. The results show that the alignment efficiency of the two alignment models is nearly equivalent, whether there exits wavefront measurement errors or not.?n alignment model based on fifth-order nodal aberration theory is further proposed for the field-biased three mirror anastigmatic(TMA) telescopes. The analytical expressions for aberration field decenter vectors and boresight error of misaligned TMA telescopes are derived. An alignment model based on third-order nodal aberration theory is established firstly for a field-biased TMA telescope, and the alignment simulation results show that the efficiency of this model is not enough for the accurate alignment of TMA telescopes. The fifth-order aberrations should be considered in the development of the alignment model. An alignment model based on fifth-order nodal aberration theory is further established, and the corresponding alignment simulations are conducted. The results show that the wavefront can be reconstructed to the nominal state through three iterative corrections. Monte-Carlo alignment simulations are conducted, and the results show that more iterative correction times are needed as the misalignment perturbation ranges increase. In the case where the decenter parameters are within 1 mm and the tilt parameters are within 0.1°, the alignment model based on fifth-order nodal aberration theory can complete the alignment process for all the introduced misalignment cases through three iterative corrections. Comparison results also show that for the alignment of TMA telescopes, the correction residual errors of theanalytic alignment model based on fifth-order nodal aberration theory is about an order of magnitude smaller than those of the modified sensitivity matrix method.By combining the transformation of Zernike coefficients for wavefronts with circular pupils and nodal aberration theory, an alignment model for the off-axis telescopes with offset pupils is presented, which can solve the problem that nodal aberration theory cannot directly be applied to the alignment of offset aperture telescopes. The transformation matrices for the first 9th and first 16 th Fringe Zernike coefficients are derived. On this basis, an alignment model for the New Solar Telescope(NST) is established, and the alignment simulations are conducted. The results show that, if wavefront measurements at more than three field points are available, five misalignments are well reduced to within the tolerance after three iterations, and the WFEs of the telescope are reconstructed to the diffraction-limited levels.The algorithms and methods are applied to reflective telescopes, but the methods are general and can be useful for any optical imaging system.