Alignment Technique For Off-axis Reflective Systems Based On Zernike Vector Polynomials

With its advantages of high energy concentration,high resolution and wide field of view,unobstructed off-axis reflective system has been widely applied in the field of space and aerial remote sensing.However,the non-rotationally symmetric layout brings great difficulty to the alignment of off-axis reflective system.It is difficult for the traditional alignment method which relies on manual experience to meet the position tolerance requirement.Computer aided alignment technique must be used to realize high precision alignment.The core of computer aided alignment lies in the accurate calculation of the misalignments.Existing misalignment calculation methods fall into two categories: numerical method and analytical method.The numerical method relies on mathematical approximation and optimization iteration.The accuracy of solution is dependent on the accuracy of model and optimization algorithm.On the other hand,the analytical method builds analytical misalignment solution model based on aberration theory.Accurate solutions of misalignment can be obtained.However,the analytical model is too complicated,limiting the application of this method.In this dissertation,the misalignment-induced aberrations of off-axis system are studied.By constructing Zernike vector polynomials,a misalignment calculation method that combines the advantages of numerical method and analytical method is proposed.The proposed method is then applied to the alignment of an off-axis three mirror system.The specific research work is as follows:1.Based on the Nodal Aberration Theory,the aberration properties of misaligned off-axis reflective system are studied.Based on the vector aberration expressions of coaxis system and coordinate transformation of the pupil vector,the vector aberration expressions of off-axis system are derived.Transformation rules of aberration terms for pupil decentered system are summarized.The effects of pupil decenter,surface decenter,tilt and piston on the aberration fields and nodal properties of third order aberration terms(spherical aberration,coma and astigmatism)are analyzed.The couplings among different misalignment freedoms are revealed.Theoretical guidance for the alignment of off-axis reflective systems are provided.2.Misalignment calculation model based on Zernike vector polynomials is built.Zernike vector polynomials which describe the aberration fields of misaligned systems are built first.Based on the equivalence of the vector aberration expressions and the Zernike vector polynomials,analytical expressions of Zernike coefficient vectors are derived.The Zernike coefficient vectors are expressed as functions of the field vector,and the aberration field decenter vectors.Then an analytical misalignment calculation model is built.In order to avoid complex function operations,a numerical method is introduced to calculate the coefficient matrix in the model.The deriving steps of the misalignment are described in detail.Numerical simulations on a co-axis two mirror system are conducted.The validity of the proposed method is verified.Then the effects of figure errors on the calculation of misalignment are analyzed,demonstrating that the proposed calculation model can effectively eliminate the influence of the surface figure errors.Exact solution of the misalignments can be obtained.3.A transformation method of Zernike polynomial coefficients for decentered pupil is proposed.Based on which,the misalignment calculation model of off-axis reflective system is built.The normalized coordinate transformation functions between the polar coordinates of the transformed pupil and the Cartesian coordinates of the original pupil are given.Based on the Cartesian and polar representations of Zernike polynomials,the coefficients transformation matrix that accounts for the effects of scaling,translation,and rotation simultaneously is derived.The first 36 terms of standard Zernike polynomials are used to validate the proposed method.For different types of transformation,transformation rules of individual Zernike terms are systematically analyzed.Numerical examples are presented to demonstrate the validity of the proposed method.Using the Zernike coefficients transformation matrix corresponding to the third order aberrations,the misalignment calculation model of off-axis system is established.Numerical simulations on an off-axis three mirror system are conducted to demonstrate the validity of the proposed method.4.Opto-mechanical design and alignment of an off-axis three mirror system are accomplished.Based on the principle of exact constraint design,a supporting structure for nonmetallic mirror is designed.The supporting structure exactly constrains the rigid body displacement degrees of freedom while releases the degree of freedom of thermal deformation,which realizes the high-stiffness and low-stress support of the mirror and has good environmental adaptability.Considering the structural stability,processing technology and the convenience of alignment,the structure of the main frame is designed.The finite element models of the system are built.Simulation analysis under various working conditions verify the stabilities of surface figure and position accuracy of the mirrors.According to the layout of the optical system and the characteristics of the structure,the alignment scheme is designed.The processes of surface figure testing,calibration of the optical axis,coarse and fine alignment of the mirrors are described in detail.The proposed misalignment calculation model of off-axis system is used to direct the fine alignment of the secondary and tertiary mirrors.Finally,the wavefront aberration RMS over the full FOV of the system is smaller than 0.1?(?=632.8nm).The MTF of the whole system with detector installed is better than 0.1(@12cyc/mrad).Good quality of exterior imaging is obtained.