Research On Deformation Mechanism And Design Optimization Of Variable Curvature Mirrors

Variable curvature mirror（VCM）is an advanced active optics component whose radius can be adjusted by applying actuation force at the back of it.The development of VCM has been mature gradually,its application area has been broaden from improving solid laser’s beam quality degradation induced by thermal lens effect at the beginning to ground-based telescope’s laser guide star refocusing to realize wave-front monitor and in non-moving element zoom optical system design to realize continuous fast zoom and focusing with increasing performance requirements.To VCM,its radius change range,central deformation,surface figure accuracy before and after radius change and repeatability of surface figure accuracy are the core indexes have close relation ship with VCM’s structure and actuation way which determine the performance of it.This thesis takes the VCM as the research object.The research is carried out step by step on three levels on the basis of combining the basic theories of VCM.First,carry out a whole chain study to annular force actuation VCM with uniform thickness distribution from theoretical study to experimental verification.From the Theory of Plates and Shells and Roark’s Formulas for Stress and Strain,the deformation model of VCM actuated by annular line force is built.Numerical analysis is carried out for the influence to deformation and actuation force value caused by plate’s thickness and the radius of actuate ring.The optimal values of radius of actuate ring and thickness are abtained which can achieve a relative large central deformation with small actuate force.Based on the theoretical study,a prototype of VCM is designed and manufactured with 100mm diameter and 3mm thickness.Its original surface figure accuracy before actuation is nearlyλ/30（λ=632.8nm）.Although it can reach central deformation over30λ,its surface figure accuracy has a fast deterioration caused by two reseans.The first is uneven actuate force distribution which only work on part the mirror’s back.The second is the separation between VCM and actuation structure not only lead to poor contact of actuate ring and mirror’s back but also lead to compressional deformation because of asymmetric slide.Besides,from the mechanical,the ideal radius change only exist within the actuate ring and the optimal value of actuate ring’s adius is half of the effective aperture.So,the effective working aperture is lower greatly.Therefore,the annular force based VCM is used to thermal lens compensation of solid laser which can be satisfied by small aperture and radius-thickness ratio.Second,for the problem of surface figure accuracy deterioration of VCM actuated by annular line force,the VCM model actuated by uniform pressure is derived from the plate’s deformation mechanism.Also,the systematically research is done from theory to test.For the first step,build the mathematical and physical model of VCM actuated by uniform air pressure,make the basic reason of this kind model can achieve big central deformation and high surface figure accuracy clear.For the first reason,the uniform pressure can improve the local stress caused by mechanical actuate ring.For the second reason,the combination of variable thickness distribution and ultra thin collar can keep both its space stability and remove the stress out of the effective working area to keep the surface figure accuracy.For the second step,work out the analytical solution and verification of two common thickness distribution:?=?₀0)^-6⁽（）(62)and?=?₀（1-6）)^1/3,by using small parameter method under simply support edge condition.This analytical solution simplifies the solution given by Theory of Plates and Shells which is in the form of series.Also,it gives a strong theoretical support to the research of VCM.On this basis,carry out the verification for further step by comparing the analytical solution to the finite element analysis of elastic plate with variable thickness and VCM.A VCM structure which can maintain its surface accuracy during deformation is obtained by optimization to thickness distribution and structural parameters.For the last step,two alluminium alloy prototypes of VCM with 135mm diameter,8mm central thickness actuated by air pressure are manufactured using advance ultra-thin alluminium alloy process.The original surface figure accuracy of first VCM is nearλ/50（λ=632.8nm）,and the surface figure accuracy has a great deterioration when have22μm central deformation.Analysis shows that the value of original surface figure accuracy facilitates the maintenance of surface accuracy.So,during the manufacturing process of the second prototype,the ion beam figuring is applied to improve the original surface accuracy up toλ/80.The actuation test shows that when the deformation approaches to 37μm,its surface accuracy still can beλ/40.It is coincided with the theoretical analysis and verify the effectiveness of combination of uniform pressure and thickness variable design.Third,no matter the annular line force actuated VCM with uniform thickness or the air pressure actuate VCM with variable thickness,usually its deformation target is tens of microns.In this thesis,the deformation is expanded to micrometer level.A VCM actuated by central force with variable thickness is designed and optimized.Large central deformation and high surface figure accuracy are achieved at the same time.The optimization shows that VCM with 100mm diameter,central thickness 3.4mm,?=_?*（-7）9)（?（6）²）^1/3thickness distribution,when the deformation achieve 1mm,the corresponding surface accuracy is 424nm.This VCM is a beneficial expansion to the VCM actuated by uniform pressure.