Absolute Testing Technology Of Standard Flat Based On Shift-rotation Method

The large-aperture optical elements has been widely used in major scientific research projects,such as high-energy laser system and laser fusion,new challenges have been posed to the surface accuracy of optical components.The processing of the surface shape should be guided by measurement equipment,so the accuracy of the surface measurement technique determines the accuracy of the surface machining.The commonly used high-precision surface shape measurement method is interferometry,where the testing result is a relative measurement with the interferometer reference mirror.The absolute measurement method can eliminate the influence of the reference mirror surface shape error and realize high-precision surface shape measurement.However,the traditional three-flat testing method require the tested flat to be flipped,which easily introduces position matching errors and affects the accuracy of the surface shape solution.In order to achieve high precision surface shape measurement and to avoid the large flips in traditional three-flat testing method.The shift-rotation absolute method is the main research object of this paper,and the main contents are as follows:(1)On the basis of the traditional three-flat testing method and translation shearing method,this paper introduces the Zernike polynomial fitting shift-rotation absolute method and N equal-angle rotation shift absolute method in detail.The theoretical analysis and numerical simulations of the Zernike polynomial fitting shift-rotation method have demonstrated its high theoretical calculation accuracy.(2)Aiming at the eccentricity error introduced in the experiment,analyzed the influence and characteristics of eccentricity error and proposed an eccentricity error correction algorithm based on image alignment.This method obtains the actual amount of eccentricity error by aligning "the surface containing twice the eccentricity" with "the surface without the eccentricity" in several iterations,the actual rotation center is substituted into the shift-rotation method to achieve the correction of the surface shape.After the eccentricity error is corrected,the experiment shows that the residual surface error is within 0.35nm(RMS).Based on the four measurements of the shift-rotation absolute method,this method can realize the correction of the eccentricity error by adding only one measurement of the 180° position of the tested mirror,which is not only easy to operate but also can effectively improve the measurement accuracy.(3)Based on the correction of the eccentricity error,an experimental scheme for the shift-rotation absolute method was designed.For a standard flat with an aperture of 100mm,the surface shape error of 10.77nm(PV)and 1.96nm(RMS)was obtained by using the shift-rotation method,and the deviation was found to be 0.25nm by comparing with the absolute measurement results of the traditional three-flat testing method.Repeated measurements were carried out on the standard flat with an aperture of 320mm,and it was found that the repeatability error of the shift-rotation absolute method was 0.26nm(RMS).The main error factors in the experiment are analyzed and common measures to reduce the error are given.Through theoretical derivation,simulation analysis and experiment measurement,this paper verifies the reliability of the shift-rotation absolute method and eccentricity error correction method,and provides technical support for large-aperture high-precision optical element surface interference measurement.