Research On Misalignment Correction In Off-axis Reflective Systems Based On Nodal Aberration Theory

Off-axis reflective systems with large aperture have become the main choice of space astronomical telescopes because of their high resolution,wided field of view and unobscured characteristic in recent years.For this kind of space optical system,active optics system is a key technology.The image quality of optical system can be maintained by detecting wavefront,determining correction values and implementing correction when it is degraded.Among them,determining correction values is an important procedure.Active optics aims at maintaining the image quality of optical system with minimum cost of engineering.To achieve it,reasonable correction strategies need to be formulated.And correction values need to be calculated pointedly.Three steps are mainly included: calculating surface figure errors and position errors,choosing appropriate correction types(based on the idea of system recovery or system compensation),determining the needed correction values.However,most of the algorithms of determining correction values are numerical in the engineering.The model of numerical algorithms is usually simple,resulting that numerical algorithms are widely used.But most of the numerical algorithms are based on linear approximation,which omits the higher order terms.For some conditions(misalignments are larger),the calculation precision of these algorithms is limited.Meantime,the coupling effect between optical elments is not considered for most of the numerical algorithms based on linear approximation.Aberrations may be compensated in the process of determining correction values.As a result,the determined surface figure errors and position errors are not correct.Therefore,it is necessary to research an analytical algorithm to determine correction values.In this dissertation,several reseaches are carried out on the basis of nodal aberration theory(NAT)of on-axis reflective systems.These researches are composed of the NAT of off-axis reflective systems,the correction values solution of off-axis reflective systems based on the idea of system recovery,the correction values solution of off-axis reflective systems based on the idea of system compensation,the correction values solution of off-axis reflective systems with decented or tilted optical elements and freedom surfaces.Specifically speaking,the contents of this dissertation are presented as follows:Based on the NAT of on-axis reflective systems,the algorithm of calculating lateral misalignments is modified.Besides,an algorithm of calculating axial misalignments is proposed and the algorithm of calculating figure errors is summarized.By simulating a 5m aperture on-axis three-mirror reflective system,the calculation precision of these three algorithms is validated.Aberration theory of off-axis reflective systems is studied on the basis of NAT of on-axis reflective systems.An off-axis system is just regarded as an off-axis section of an on-axis parent system.The aberration expression of off-axis reflective systems can be deduced by pupil transformation.By decomposing 3rd-order terms and 5th-order terms of aberration expression into Zernike polynomial,it is found that the higher order terms of aberration expression have contributions to both higher order terms and lower order terms of Zernike polynomial for off-axis reflective systems.The algorithm of determining correction values of off-axis reflective systems based on the idea of system recovery is presented.Both figure errors and position errors need to be determined in the process of system recovery.Considering the contributions of higher order aberration terms to lower order Zernike terms,models of determining correction values of off-axis reflective systems based on 3rd-order and5th-order NAT are established respectively.For a 6m focal length off-axis three-mirror reflective system,simulations of the two models are conducted.And the model using 5th-order NAT is compared with sensitivity table method(STM).What’s more,the model using 5th-order NAT is also demonstrated by experiment.It’s shown that the model of determining correction values of off-axis reflective systems based on 5th-order NAT is highly analytical and owns high calculation precision.The algorithm of determining correction values of off-axis reflective systems based on the idea of system compensation is presented.In the process of system compensation,the compensating element and the compensated element of optical systems need to be confirmed.And the adjusting values of the compensating element need to be determined(sencondary mirror is usually regarded as the compensating element for off-axis reflective systems).Based on the NAT of off-axis reflective systems,models of determining correction values of secondary mirror to compensate the perturbed system when primary mirror is deformed and tertiary mirror is misaligned are established respectively.For the same off-axis three-mirror reflective system mentioned above,simulations of the two models are conducted.And the model of compensating the misaligned tertiary mirror by secondary mirror using NATis demonstrated by experiment.It’s shown that the perturbed system can be well compensated based on the presented algorithms.The algorithm of determining correction values of off-axis reflective systems with decented or tilted optical elements and freedom surfaces based on NAT is presented.For off-axis reflective systems with decented or tilted optical elements and freedom surfaces,models of determining correction values of this kind of optical systems is established combined with the idea of STM.By simulating an off-axis reflective system with decented or tilted optical elements and freedom surfaces,it’s shown that the model of determining correction values of this kind of optical systems is correct.