| Off-axis reflective optical system with its high resolution,large effective field of view,high energy utilization efficiency and stray light suppression has become an important optical path structure for the new generation of large space telescopes.The theoretical results achieved in the optical design of system,the machining accuracy of components in the optical manufacturing,the alignment accuracy in the integration phase and the operating environment in orbit combine to determine the final performance of telescopes.However,with the development and maturity of modern optical path structure design methods,mirror processing technology and optical detection means,it is crucial to achieve high precision alignment and real-time correction of in-orbit misalignment aberrations that govern system performance.To ensure the ground alignment accuracy of telescopes and the correction accuracy of misalignment aberrations during the orbit operation,computer-aided alignment technology and active optics technology have become the key technologies necessary for the construction of large-aperture off-axis reflective space telescopes.Among them,the methods of calculating the amount of misalignment using misalignment aberrations is a key part common to both techniques.Most of misalignment algorithms currently used in computer-aided alignment and active optics technology are numerical.Numerical algorithms do not consider the intrinsic mechanism of the effect of misalignments on system aberrations when constructing misalignment calculation models.For off-axis reflective optical system without a clear axis of rotational symmetry,the coupling of different types of aberrations introduced by optical element misalignments is stronger than in conventional on-axis system,and the aberration field changes caused by misalignments are more complex.Therefore,for the correction of misalignment aberrations in such optical system,numerical algorithms are often blind and uncertain in solving misalignments due to the difficulty in providing insight into the coupling mechanism of misalignment aberrations.In particular,when there is a failure of the calculation,numerical methods are often difficult to help analyze the causes of the failure due to the lack of relevant aberration theories.To this end,this paper presents an in-depth study of the correction mechanism and methods for misalignment aberrations of off-axis reflective system within the framework of nodal aberration theory.The main contents include the study of the nodal characteristics of various types of misalignment aberrations in off-axis optical system,the influence of the coupling effect of high-order misalignment aberrations and low-order misalignment aberrations in off-axis reflective system on the accuracy of misalignment calculation,the mechanism of the coupling of axial and lateral misalignments and the method of simultaneous correction of these two types of misalignments,and the compensation mechanism of different types of perturbation parameters(misalignments and figure errors)on the influence of aberrations,which will provide some theoretical reference for the correction of misalignment aberrations in large-aperture off-axis reflective space telescopes by the research idea from shallow to deep and from theory to application.Specifically speaking,this paper mainly contains the following contents:The influence of misalignment on nodal characteristics of aberration fields in off-axis system is studied.Firstly,the influence of aberration field decenter vector on the nodal characteristics of the aberration field is systematically derived and explained by expanding the field vector in different types of aberration vector expressions from the third to the fifth order.Then,by expanding the pupil vector in vector expressions of off-axis system,the derivation relationships of different types of aberrations between off-axis system and its coaxial parent system are studied.Based on this derivation,an off-axis aberration model is constructed for off-axis system by sorting the different types of aberrations according to their aperture dependencies.The constructed off-axis aberration model not only takes into account the existence of tilts and decenters in the design of off-axis reflective system,but also has a one-to-one correspondence with the Fringe Zernike polynomial.Finally,the nodal characteristics of different types of aberration fields in the constructed off-axis aberration model are analyzed based on the on the relationship between aberration field nodal characteristics and the power exponent of field vector.The influence of the coupling effect of higher-order and lower-order misalignment aberrations in off-axis system on the accuracy of the misalignment calculation is studied.Firstly,the coupling relationship between higher-order misalignment aberrations and lower-order misalignment aberrations in the off-axis aberration model is analyzed and decoupled.Then,based on the decoupled off-axis aberration model,the misalignment calculation models are constructed with and without the coupling effect of higher-order aberrations and lower-order aberrations,respectively.In addition,when constructing the calculation models,a method is proposed to introduce new astigmatic node parameter(?)by separating the third-order astigmatic node parameter(?)to deal with the problem that the number of aberration field decenter vector solution equations is insufficient because the higher-order aberration node parameters cannot be used.This method only needs to measure the Zernike coefficients of multiple fields of view to solve the aberration field decenter vectors of each surface,and does not need to measure new physical quantities(such as boresight errors).Finally,using an off-axis TMA telescope as the research object(containing designed tilts and decenters in addition to aperture off-axis),the coupling effect of higher-order aberrations and lower-order aberrations on the accuracy of misalignment calculation is quantitatively analyzed with these two models.The coupling mechanism of axial and lateral misalignments in off-axis system and the method of simultaneous correction of these two types of misalignments are studied.Firstly,the coupling effects of axial and lateral misalignments on aberration field decenter vectors and on spherical aberration,coma and astigmatism in off-axis system are analyzed,and the aberration node parameters of misaligned off-axis system are derived when both axial and lateral misalignments exist.Then,a method is proposed to calculate the axial and lateral misalignments simultaneously by fitting the partial derivative coefficient matrix of the aberration node parameters.Finally,simulation and actual computer-aided alignment experiment were conducted for the off-axis TMA telescope using the proposed method respectively,and the correctness of the proposed method was comprehensively verified.The aberration field compensation mechanism of the secondary mirror for simultaneous compensation of the third mirror misalignments and the primary mirror low-order figure errors in the off-axis TMA telescope is studied.Firstly,the third-order astigmatism(C5/C6),third-order coma(C7/C8)and third-order spherical aberration(C9)induced by different perturbation parameters(misalignments and primary mirror figure errors)in the off-axis TMA telescope are expressed analytically according to different field dependencies.Then,the reasons and feasibility of the mutual compensation of secondary mirror misalignments,third mirror misalignments and primary mirror figure errors are analyzed from the perspective of the aberration field compensation mechanism.Accordingly,an aberration compensation mechanism is proposed of the secondary mirror to compensate for the third misalignments and the primary mirror figure errors simultaneously,and the corresponding correction volume solution model is constructed.Finally,the correctness of the proposed aberration field compensation mechanism is verified by a specific simulation case and Monte-Carlo analysis.Based on the trend that the structure of future large-aperture space telescopes will be developed in the off-axis direction,this paper conducts an in-depth study on the theory of misalignment aberration correction based on the vector aberration theory to provide some extension of ideas for the development of the misalignment calculation method and,in turn,to play an active role in the development and on-orbit operation for future large-aperture off-axis reflecting space telescopes. |
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