Figure Measurement Of Aspheric Surface Based On Wavefront Aberration Calibration And Simultaneous Stitching

With the increasing aperture in modern optical system,such as space camera,astronomical telescope,the large-diameter aspheric surface is in urgent requirement.However,the measurement for large-diameter aspheric surface,especially large-diameter convex aspheric surface,is the difficulty all the while.Due to the limitation of manufacturing precision for large-aperture auxiliary mirror and compensator,the traditional testing method can not satisfy the measurement of high precision.The subaperture stitching method could avoid the application of above two elements,thus the lateral resolution and dynamic scale are increased.This method has the ability to realize the high precision measurement,however,two problems still existed: 1)Even though the reference wavefront error,alignment error and mapping error appear to be minor factor within each subaperture,significant errors could be introduced to the stitching data due to the transfer and accumulation.2)Compensators are employed for the correction of subaperture and stitching errors,unfortunately,compensators also decrease the stability of the numerical solution and cause the numerical optimization to be ill conditioned.Meanwhile,the resistibility of stitching algorithm for errors would decrease once ill quality compensators are employed.The purpose of the study on “Figure Measurement of Aspheric Surface Based on Wavefront Aberration Calibration and Simultaneous Stitching” is to propose a measurement method to inhibit the transfer of error and accumulation exist in traditional stitching,and avoid optimization becoming ill conditioned.The proposed simultaneous stitching method which is based on the calibration of wavefront aberration and constrained optimization provides theoretical foundation and technical support for the high precision measurement of largediameter aspheric surface.The followings are the major issues addressed by this study:Firstly,the even/odd synthesis method is proposed for the calibration of reference surface.Utilizing the property that surface error could be divided into rotationally symmetric and non-rotationally symmetric terms,odd and even parts of the reference surface can be obtained respectively,and the least square algorithm with dual-objective optimization function proposed is used to calibrate the measurement results at the confocal position.This method conquers the disadvantage of traditional three positions measurement method-being sensitive to experimental errors due to misalignments,such as decentration and tilt in the rotation and shifting of test surface.Furthermore,environment effects such as air turbulence and vibration can also be effectively suppressed.Experiments show: compared with the traditional three position measurement method,the calibration result of reference surface by using odd/even synthesis method highly tallies with reference value,the measurement repeatability of PV value is better than 0.003λ.Secondly,based on the calibration of wavefront aberration and constrained optimization,the simultaneous stitching method is proposed.On the foundation of corrected reference wavefront error and alignment error,global averaging error and constrained optimization are adopted to realize subaperture’s simultaneous stitching.The method decreases the influence caused by the error of subaperture,inhibits the error transfer and accumulation,and conquers the demerit of traditional stitching method-ill conditioned easily.Finally,experiments are conducted to verify relevant contents in this study.For one thing,the experiments of subaperture stitching for spherical surface testing are conducted to analysis that how the quantities of subaperture and stitching strategy influence the stitching result,and to demonstrate that the proposed simultaneous stitching method can inhibit error transfer and accumulation,and avoid optimization becoming ill conditioned.For another thing,the experiments of subaperture stitching for concave aspheric surface testing with Φ150mm are conducted to verify the stitching model based on wavefront aberration calibration.By using model,the discrepancy of overlap regions is minimized,and the mismatch of subaperture stitching is reduced.Compared the first zonal result acquired by simultaneous stitching and direct test method,discrepancy PV is 0.0764λ,and RMS is 0.0180λ.Finally,the experiments of subaperture stitching for convex aspheric surface testing with Φ200mm are conducted to verify the simultaneous stitching method based on global averaging error and constrained optimization.Under the condition that,the overlapping coefficient is more than 20%,proposed method simultaneously stitches 43 subapectures(vertex curvature radius is 125 mm,and the surface parameter k is-0.002).The mismatch of the simultaneous stitching has the 0.0601λ(PV)and 0.0064λ(RMS);compared with the unconstrained optimization method,the PV of the mismatch map is reduced by 28%,and the RMS is reduced by 38%.