Static Analysis Of Lens Support Structure Based On The Thin Plate Theory

With the increasing progress of information technology in the new era and the industry transformation under the COVID-19 pandemic,China has an urgent need for the development of high-end lithography machine.In the research and development of lithography machine,there is a high demand for the detection accuracy of optical testing equipment.As an important component of optical testing equipment,the surface quality of optical lens is the most direct key factor affecting the performance of testing equipment.The surface shape of the lens is closely related to the accuracy of its support structure.A complete optical and mechanical system will inevitably produce errors in the process of manufacturing,assembly and use,etc.The impact of the errors on the support structure and the lens itself is the focus of this paper.In this paper,the influence of the morphology error of the supporting structure on the surface shape of the lens is analyzed by the calculation method of plate and shell mechanics.Firstly,this paper studies the surface shape of the lens under the action of point support,uses the thin plate theory and the reciprocity theorem of work to theoretically deduce the surface deformation of the lens under the uniform and non-uniform interior point support,and verifies the accuracy of the results with the finite element software.In the calculation example,this paper introduces a variety of accuracy evaluation indexes including mechanics and optics,such as PV value,RMS value,Zernike coefficient,deflection,etc.,to ensure the rationality of the calculation example.Through comparison and verification,the solution error of the lens surface deformation expression derived in this paper is within 10% under the condition of uniform support at interior points,and can be controlled within 15% for the case of non-uniform support at interior points.Secondly,considering the lens assembly conditions,the influence of the lens support structure under the external error is studied.Through the step calculation method,the deformation of frame of optical machine system is theoretically deduced,and the displacement expression of frame surface is obtained,and then the influence of displacement error of frame on the deformation of shrapnel is considered.Software was used to simulate the working condition of the frame subjected to displacement error,and the displacement of some points on the frame was extracted and compared with the analytical solution derived from theoretical derivation.Under the working conditions of the two displacement error functions given in this paper,the calculation error of this paper is less than 20%.Under the working conditions after combining the two functions,the calculation error of this paper is less than 10%.Finally,the influence of frame assembly error on the contact force between "elastic support element-lens" is studied.Through the proposed lens rigid body assumption,the equilibrium equations,geometric equations and physical equations of the statically indeterminate space between the elastic support element and the lens are obtained,and the analytical expression of the force between the lens and the elastic support element is deduced.By establishing a complete simulation model of "frame-elastic support element-lens",the force between the lens and the elastic support element is obtained,and the surface shape of the lens is analyzed.By comparing the finite element simulation with the analytical solution,the calculation error of the supporting force is generally less than 20%,and the error of the surface shape parameter is also controlled below 20%.The accuracy of this method in solving the deformation problem of frame assembly is verified.Based on the above research content,the solution idea of lens surface shape change caused by assembly error is given based on theoretical derivation.The calculation results of this paper show that the error of the proposed method in calculating the inner point support of the lens is less than 15%,and the error in calculating the surface shape of the lens frame assembly is less than 25%,which has important guiding significance for the design of solid lens support structure.