Absolute Testing Of Optical Plane Surface Based On Shift Differential Method

With the rapid development of precision optical manufacturing technology,high-precision planar optical elements are widely used in national major scientific projects,and their surface shape accuracy requirements have reached the nanometer level,which poses a new challenge to the optical element surface shape testing technology.Interferometry is a high-precision surface shape testing technology.Its measurement result is a relative measurement based on the reference mirror shape error.In order to eliminate the system error,the absolute surface shape of the tested mirror is obtained by using the absolute testing technology,so as to achieve higher precision surface shape testing.There are many problems in the traditional optical element surface shape absolute testing technology,such as complex steps,many error sources and spatial frequency loss.In order to achieve high efficiency and high precision wide-band surface absolute testing target,this paper makes a profound study on the shift differential surface absolute testing technology.The main work includes:(1)On the basis of the research on the absolute testing of shift differential surface shape and differential wavefront reconstruction methods,the conjugate shift differential method based on differential Zernike fitting and Fourier transform is numerically simulated to verify the effectiveness of the algorithm.The influence of two kinds of wavefront reconstruction algorithms and experimental errors on surface reconstruction results is simulated and analyzed,which provides theoretical guidance for the selection of reconstruction algorithms and error suppression under different measurement conditions.(2)As a key parameter in the conjugate shift differential method,the value of shift directly affects the accuracy of surface shape measurement.In order to determine the optimal shift interval under different measurement conditions,a method for determining the optimal solution of shift based on inverse optimization strategy is proposed.Firstly,the error model of shift and surface reconstruction is established under the condition of noise;Then,the optimal shift interval under the allowable error of surface reconstruction is solved by taking the estimated value of the measured surface shape and random noise as variables;Finally,the comparative experiment of plane absolute testing under different shift is carried out.The experimental results show that 0.6-4.6mm is the general optimal shift interval of the measured surface shape error PV value is better than that of the plane optical element with the aperture of 100 mm.The measurement results in this shift interval are basically consistent with the three-sided mutual inspection method.It is proved that the proposed method can effectively suppress the influence of noise on the measurement results,so as to improve the surface shape measurement accuracy.(3)The wavefront reconstruction algorithm based on Fourier transform is one of the important methods to measure the wide-band surface error of optical elements.Aiming at the problems of spectrum loss and measurement error in this method,the conjugate double shift differential technique is studied.Firstly,the Fourier reconstruction process is studied,and the spectrum missing problem of conjugate single shift differential method is analyzed;Then the formula of conjugate double shift differential method is derived,and the shift constraints are given;Finally,the reconstruction accuracy of various spectrum compensation methods is compared.The experimental results show that the larger the shift,the more obvious the spectrum loss.Compared with the direct zero filling method and the adjacent point averaging method,the conjugate double shift differential method has the smallest measurement error.It is proved that this method can accurately evaluate the wavefront information in the wide frequency band,and is helpful to promote the application of Fourier transform in the process of wavefront reconstruction.