Research On Active Optical Wavefront Control Methods For Off-axis Reflective Astronomical Telescopes

With the increase in the aperture size of the emerging generations of astronomical telescopes,active optics systems have been widely used in astronomical telescopes in the last two decades,which can sense and correct mirror figure errors and misalignments during observing periods.Active optical wavefront control methods are of great importance to active optics systems,which mean the suitable ways or methods of correcting and compensating for those aberrations induced by figure errors and misalignments.Active optical wavefront control method mainly contains two aspects,i.e.,the selection of the type of the compensator and the computation of the value of each compensator needed for compensating for those aberrations induced by misalignments and figure errors.Off-axis telescopes with unobscured pupil have many advantages over those on-axis,axisymmetric ones,such as lower scattering property,larger emissivity throughput,higher dynamic range,and so on.Besides,with the development of astronomy,more and more attention is paid to the measurement of weak gravitational lensing.Unobscured off-axis telescopes have simpler and sharper diffraction pattern,meaning not only higher resolution but also some advantages in ellipticity performance,which is of cardinal importance for weak gravitational lensing measurement.However,the active optical wavefront control methods for off-axis astronomical telescopes are not mature enough compared to those for on-axis ones.Therefore,we need to present an in-depth discussion on active optical wavefront control methods for off-axis astronomical telescopes and provide some valuable insights to them.This will greatly contribute to the development of active optics systems for off-axis astronomical telescopes.Based on the framework of nodal aberration theory,this dissertation carries on theoretical research on active optical wavefront control methods for off-axis astronomical telescopes.This dissertation first presents an in-depth and systematic discussion on the effects of figure errors and lateral misalignments.The analytic expressions for these effects are derived,and the principles of aberration compensation between the effects of different perturbations are discussed,which can be used to select proper types of compensators and compute the value of each compensator needed for correcting the wavefront error.Then these analysis and discussions are applied to the development of active optical wavefront control methods for off-axis two-mirror and three-mirror astronomical telescopes.Relevant simulations are conducted to demonstrate the efficiency of the proposed strategies.Specifically,the main contents of this dissertation are presented as follows:This dissertation presents an in-depth and systematic discussion on the impacts of figure errors on the net aberration fields.The quantitative theoretical formulations for net aberration contributions induced by freeform surfaces are derived,which can be located away from the aperture stop and decentered from the optical axis.On this basis,on one hand,the principle of aberration compensation between figure errors(mainly astigmatic and trefoil figure errors)at different positions are discussed;on the other hand,an analytic method of computing astigmatic figure error on primary mirror,trefoil figure errors on primary and secondary mirror and misalignments of the secondary mirror is proposed.The results show that its computation accuracy is higher than the non-linear least square fitting algorithms.This dissertation presents a systematic and in-depth discussion on the aberration fields of unobscured astronomical telescopes with offset pupils induced by lateral misalignments.Based on the framework of nodal aberration theory and a system level pupil coordinate transformation,the aberration functions through 3rd-order and 5th-order for misaligned off-axis telescopes are derived.Some specific aberration field characteristics induced by lateral misalignments for off-axis two-mirror and three-mirror anastigmatic telescopes are presented,mainly including astigmatism,coma,medial focal surface and trefoil aberration,where the differences between the aberration fields of misaligned off-axis systems and the on-axis ones are further illustrated.The comparisons between the results calculated with our 3rd-order model and 5th-order model and the ray-tracing data for each aberration field are made.The reasons for the discrepancies between the three set of data are also explicitly explicated.Some valuable insights and theoretical guidance for the optical design,alignment and active compensation and alignment of off-axis telescopes are proposed based on the knowledge of the aberration fields induced by lateral misalignments.At last,by analyzing the inherent relationships between the astigmatic and coma aberration fields induced by lateral misalignments,this dissertation demonstrates that the aberrations induced by astigmatic figure error on the primary mirror can be compensated by lateral misalignments to some extent.Discussions on how to quantitatively determine the lateral misalignments used for compensating the effects of primary mirror astigmatic figure error are also presented.This dissertation discusses the development of active optical wavefront control methods for off-axis two-mirror and three-mirror astronomical telescopes under different perturbation cases.On one hand,the proper types of compensators are selected according to the principle of aberration compensation presented in this dissertation for different perturbation cases;on the other hand,the values of different compensators needed for compensating for the wavefront error are computed.Detailed simulations are conducted to demonstrate the efficiency of the proposed strategies,by comparing the mean wavefont error root mean square value over the field before and after correction.At last,simple alignment experiment is further conducted,which can tentatively verify the correctness of the computation model presented in this dissertation.This dissertation can serve as a theoretical basis for the development of active optical wavefront control methods in off-axis astronomical telescopes.