Measurements Of Topography Of A 1.5m Flat Mirror And Control Of Errors

In general,large flat mirror refers to flat mirror with aperture greater than 1 m.Large flat mirror has been widely used in fields including optical detection,space optics,and astronomical optics,etc.It’s required to measure topography of large flat mirror to ensure the good quality.However,topography measure of large flat mirror has always been a problem in optical field for a long time.Existing measuring methods is immature in technology,with insufficient measuring accuracy,high cost,long measuring period,which cannot meet measuring demand of topography of large flat mirror.To solve these problems,the paper studied technologies of measuring of topography of a 1.5m flat mirror and control of errors.The detection system and the detection method was designed.It proposed the method about how to detect the surface angle of 1.5m aperture flat topography by using the single pentaprism scanning to measure the difference of tilt angle in the surface,and combines the zernike polynomial partial derivative to make equations,calculate the two dimensional full aperture directly.This method uses a single pentaprism differential scanning to measure the difference in surface tilt angle,which can eliminate all the first-order effects of tilt error,the influence of pentagon prism manufacturing angle difference and most of the environmental impact,and has a strong ability of error suppression.The method adopts a round-trip scaning and a step-by-step scanning,makes the measurement of the two pairing points be close in time and no longer measured in sequence according to the order of the measuring points,which reduces the influence of environmental changes.In algorithm,this method uses the difference of the surface tilt angle,and combines the zernike polynomial partial derivative to make equations to calculate the two dimensional full aperture directly,which avoiding trivialities of the Fourier transform algorithm and the errors accumulation of recursive algorithm and splicing algorithm.In addition,this method also automatically monitors and adjusts the inclination change amount of the pentaprism during scanning,and reduces the tilt error of the pentaprism.This paper also analyzes the principle of selection of each detection parameter,especially the principle of selection of the distance d between two pairing points.It points out that the choice of d needs to take into account both the suppression of environmental impact and the suppression of relative error;Four sets of testing parameters with different frequency levels were designed for a 1.5m aperture flat topography.The Testing parameters of different frequency levels correspond to different frequency detection requirements,and the parameters of the highest frequency level are selected for detection,so that the surface shape information of the measured plane mirror can be detected more completely;finally,the detection method is simulated and analyzed.The results show that the principle error of the detection method is only 2.3nm rms,which verifies the correctness of the detection method.The paper studied error characteristics of pentaprism.The paper studied impact of rotation error of pentaprism on emergent light direction using action matrix and coordinate conversion formula,and obtained important conclusion: drift angle of emergent light within principal section is almost not influenced by rotation error of pentaprism,while drift angle of emergent ligh in the direction perpendicular to the principal section is greatly influenced by rotation error of pentaprism.The paper also studied impact of manufacturing angular difference of pentaprism on emergent light direction using unfolding of pentaprism and optical path calculation,and obtained important conclusion: manufacturing angular difference of pentaprism would generate fixed drift angles in the two directions of emergent light,which are constants irrelevant with angle of incidence.The paper derived error formula of pentaprism basic system using vectorial ray tracing,which laid the foundation for system adjustment and error analysis.The paper studied fine adjustment technology of the measuring system.The paper designed rough adjustment procedure based on direction of guide rail and rotating plane of whirling arm.The paper analyzed content,benchmark and target of fine adjustment,studied fine adjustment method based on autocollimator 1,mainly focused on studying yaw and roll testing during fine adjustment process,and designed fine adjustment procedure.The paper analyzed error of the measuring system,including tilt error,measuring error of autocollimator 1,position error of measuring point,manufacturing angular difference of pentaprism,and error brought by environment changes,obtained total error of surface tilt angle difference is 81.3 nrad rms,on this basis,the paper adopted simulation method and determined that topography measuring error brought by error of surface tilt angle difference is 7.8 nm rms,and then compounded it with error of the measuring method itself,and obtained the final topography measuring precision,which is 8.1 nm rms.The paper adopted this measuring system to measure topography of a flat mirror with 1.5 m of aperture for totally five times,calculated the average standard deviation,which is 4.3 nm,to verify fine repeatability of the measuring method.The paper compared measuring results with the ones using Ritchey-Common method,obtained difference of topography results of the two methods,which is 7.6 nm rms,less than topography measuring precision of this paper’s measuring system,and proved correctness of the measuring method and measuring system proposed in this paper.