Study On Zero-gravity Surface Figure Measurement Technology Of Optical Elements

The surface figure of optical elements manufactured on the earth will change due to the lack of gravity when they work in space.In order to predict the surface figure of optical elements in zero-gravity environment,calculation method,support method,face up and down method and horizontal rotation method have been proposed successively.However,these methods are confronted with problems such as numerical calculation error,operation risk,and so on.In view of the above problems,this paper proposes three orientations revolution model and three orientations rotation model to extract zero-gravity surface figure by any three different gravity-included angles surface figures of the tested mirror system.The main research of this thesis includes the following aspects:1.Three orientations revolution model and three orientations rotation model are proposed.This thesis attempts to establish rotational degree of freedom,coordinate system and mechanical model of the mirror system under orientations revolution model and three orientations rotation model.On this basis,the mathematical expressions of zero-gravity surface figure and surface figures at gravity-included angles 0° and 90° are derived.By substituting the special conditions of 2-rotation,3-rotation,4-rotation,6rotation into the expression of zero-gravity surface figure,the special solutions of zero gravity surface figure are derived.And the new special solutions are equal to the existing research equations.2.Researched on the relationship between the tested gravity-included angle errors and the zero-gravity surface figure.There are two approaches,surface figure model and gravity-included angle model.In surface figure model,the Angle measurement error was directly substituted into the formula to calculate the zero-gravity surface figure.In gravity-included angle model,the tested gravity-included angles were regarded as correct values and the corresponding surface figures should be calculated.These tested gravity-included angles and calculated surface figures could deduce correct zerogravity surface figure.Based on above calculation,gravity residual was proposed to characterize the zero-gravity surface figure error.3.Numerical simulation researched on three orientations revolution model and three orientations rotation model.Verified the proposed zero-gravity surface figure equation,gravity-included angles 0° surface figure equation,gravity-included angles 90° surface figure equation of three orientations revolution model and three orientations rotation model,by finite element method and numerical equations calculation.Then,the numerical results were compared with each other.4.Experimental studied on three orientations rotation model.The interferometer platform was built to measure a mirror system’s surface figures at 2-rotatoin condition and given three orientations condition.Then extracted its zero-gravity surface figures and analyzed these results.