Research And Application Of Decoupling Control Technology For Multi-corrector Systems

Adaptive optics is a very efficient technology used to correct the wave-front aberration,so it has been successfully used in telescopes,the laser beam clean-up systems,and vision instruments.However,with the development of these application field,adaptive optics system should compensate both low-order and high-order wave-front aberration simultaneously.In recent years,as the key component of adaptive optics,deformable mirror has obtained a great progress,but the requirement of correction precision and correction stroke is still not satisfied with a single deformable mirror.In order to solve that problem,adaptive optics system with multi-wavefront-corrector is an efficient solution to simultaneously compensate for phase distortion with a large amplitude and high spatial frequency.However,since adaptive optics system with multi-wavefront-corrector can improve the correction precision and stroke of adaptive optcis system,it must be faced with with the cross-couple among multi-wavefront-corrector,which may induce a serious waste of the DMs' correction ability and even destroy the system stability.Based on the typical woofer-tweeter adaptive optics system in which woofer is used to correct large-stroke and low-spatial aberration and tweeter is used to correct low-stroke and high-spatial aberration,this paper focuses on the decoupling control technology for adaptive optics with woofer and tweeter,and carrys out a series of and a series of theoretical and experimental researches.The main contents of this paper is as follows:Firstly,a detailed analysis of Zernike decoupling algorithm which is the most effective method of decoupling control technology for multi-corrector systems is made from the compensation ability and correlation suppression.In terms of compensation ability,demonstrated that there is some limitations of Zernike decoupling algorithm for large stroke and high spatial frequency aberration: because woofer has different fitting precision for different order of Zernike mode,distributing aberration to woofer and tweeter through Zernike mode is difficult to take full use of woofer and tweeter and then make adaptive optics be unble to correct some aberration with a large amplitude and high spatial frequency.In terms of correlation suppression,demonstrated that there are two defects of Zernike decoupling algorithm: one is that an unreasonable distribution of aberration will make the correlation suppression of Zernike decoupling algorithm unefficient,the reason of that is also that woofer has unlike fitting precision for different order of Zernike mode;the other is that Zernike decoupling algorithm must introduce Zernike mode and accurately measure the influence function of tweeter before correlation suppression,because the first-order partial derivative term of Zernike polynomials is not orthogonal.In fact,the procee of measuring the influence function of tweeter with a large number of actuators will be tedious,but indispensable.Secondly,for the problem that Zernike decoupling algorithm must introduce Zernike mode and accurately measure the influence function of tweeter because the first-order partial derivative term of Zernike polynomials is not orthogonal,Eigenfunction of Laplacian is introduced into decoupling control technique for multi-corrector systems.A set of Eigenfunction of Laplacian for different pupil area can be achieved through solving the Eigen equation of Laplacian with different boundary conditions,then the decoupling control technique for multi-corrector systems can be applied in different pupil area through these Eigenfunctions of Laplacian.The theoretical derivation verifies the orthogonality of the first-order partial derivatives of Eigenfunction of Laplacian and proves that it is not necessary to measure the influence function surface of tweeter using Eigenfunction of Laplacian to suppress the cross-coupling.Numberical simulation validates the compensation ability and correlation suppression of Eigenfunction of lapacian decoupling algorithm.The experimental results of the actual system are consistent with the numerical simulation and prove the effectiveness of that algorithm in practical systems.Thirdly,for the problem that Zernike decouping algorithm can't take full use of the different deformable mirror in the stroke and spatial frequency due to the distribution of aberration,a slope-based decoupling algorithm is proposed.A slope-based orthogonal basis which is constructed by the response matrix of woofer can be used to not only distribute aberration reasonably,but also conveniently construct a constraint matrix without measuring the influence function surface of tweeter.The mathematic derivation proves the feasibility of that algorithm in principle firstly.Secondly,the numerical simulation results show that the algorithm has lager range of aberration correction and is more convenient to restrain the cross-coupling than Zernike mode decoupling algorithm.Finally,the compensation ability and correlation suppression of that algorithm are verified by experments.Finally,projection-based decoupling algorithm is proposed.This algorithm can directly calculate the cross-coupling voltage of tweeter which will generate the opposite shape with woofer through vector projection,then eliminate the corss-coupling voltage to restrain the cross-coupling between woofer and tweeter.The mathematic derivation proves the feasibility of that algorithm in principle and gives the precondition of that algorithm that the column of wave-front reconstruction matrix introduced must be orthogonal.The numerical simulation shows that the decoupling control method using projection-based can be not only better to suppress the coupling compensation between different deformable mirrors,but also greatly reduce the computational burden caused by the process of correlation suppression,especially when tweeter has a lage number of actuators in an adaptive optics system.The experimental results show that the projection-based decoupling algorithm can control woofer and tweeter simultaneously and restrain the coupling error very well,even under the condition of dynamic wavefront distortion changing rapidly.