Topology Optimization Of Support Structure Of Reflective Mirror Based On Ray Tracing Method

Large aperture observation devices often have similar optical structures with their primary and secondary mirrors both being reflective ones.Hence,the accuracy of the optical reflective mirrors is one of the most important factors to guarantee a good system image quality.Research in this paper can mainly be divided into two parts.In the first one,the support structure of single mirror is taken as the topology optimization design domain.Besides,the optimization objective and constraints are all based directly on Zernike coefficients,which are derived from corresponding mirror surface deformation.In the second part,topology optimization is conducted in a Newtonian telescope.The support structure of the primary mirror is then chosen as the design domain and Zernike coefficients derived from system wavefront error form the objective and constraints in optimization model directly.In the first part of this research,where a single mirror and its support structure is taken into account,the most direct optimization model uses Zernike coefficients as its objective and constraints.Usually,the deformation and the relevant Zernike coefficients of a mirror surface are evaluated in different software.Thus,the sensitivity of topology optimization objective to its design variables is often calculated with difference method which then leads to an acceptable computational amount and a complicated calculation flow.To this point,the algorithm proposed in this paper starts from the principle of Zernike coefficients evaluation.According to the equivalence between Gaussian and Riemann integral,the classical version is reformulated within the frame of numerical finite element discretization.Based on this,the adjoint method is adopted to derive the sensitivity of optimization objective and constraints to design variables,which overcomes the bottleneck of large computational amount in sensitivity analysis when the difference method is used.Therefore,the topology optimization models can be constructed by the objectives and design constraints directly based on Zernike coefficients.In the aspect of numerical implementation,adaptive finite element basis functions and element numerical integrals can be employed to solve structural deformation and Zernike coefficients accurately and efficiently.The algorithm proposed in this paper is flexible to be applied to general structural topology optimization models with their objectives and constraints being a reasonable linear combination of Zernike coefficients.Besides,there is no extra restriction on the surface of the mirror so that the whole algorithm can be compatible with any practically used shape.In the second part of this research where the optimization objective and constraints are all based on Zernike coefficients,the key point is the coupling of ray tracing and elastic stress field.These two parts are often evaluated in different frames which brings about problems mentioned above.Besides,there are also studies employing matrix optics to trace rays and valuate reflective system image aberration.However,matrix optics can only include some special rigid body displacement modes of primary mirror surface error.Hence,for the sake of using as much the finite element method(FEM)results of the primary mirror as possible,the topology optimization algorithm here starts from principles of optics and uses a new algorithm where ray tracing is conducted according to true deformation of mirror surface.Therefore,ray tracing is integrated into FEM calculation frame.The deformation of the mirror surface in the algorithm for ray tracing here can be arbitrary instead of a few rigid body displacement modes.The Zernike coefficients of the system wavefront error,evaluated by that method,can thus be more reliable.Moreover,the algorithm here constructs clear functions between Zernike coefficients of the wavefront error and that of the mirror surface deformation.The ray tracing equations are added directly into the topology optimization model so that the sensitivity of Zernike coefficients of wavefront error to that of mirror can be evaluated using adjoint method.When combined with the algorithm in the first part,it then evolves into sensitivity of Zernike coefficients of wavefront error to topology optimization design variables.The adjoint method is used again to derive the sensitivity of wavefront error Zernike coefficients and topology optimization design variables.It also overcomes the similar bottleneck and leading to new topology optimization models with objective and constraints based directly on wavefront error Zernike coefficients.The algorithm here is flexible to apply to reflective systems with multi reflective surfaces and each support structure of optical elements can be optimized simultaneously.Also,Zernike coefficients in topology optimization models can be chosen according to practical demands.