Research On The Key Technology On High Precision Interferometric Testing Of Special Spherical Surface

Compared with aspherical optical elements and freeform optical elements,the spherical optical elements with simpler structure,lower fabrication cost,easy assembly and adjustment,makes it to be one of the basic optical elements which are preferentially selected in the modern optical system.Spherical optical system is not only prevailing in civilian products such as digital cameras and medical devices,but also plays an important role in high and frontier technology field such as lithography projection objectives and high power laser systems.The spherical optical elements,used in lithography projection objectives and high power laser systems,are developing rapidly in the extreme state of large numerical aperture and large radius of curvature,which belongs to special spherical surface.In this dissertation,in-depth research about the problems in interferometric testing of arge numerical aperture and large radius of curvature special spherical surface is carried out.To measure the high numerical aperture spherical surface with sub-nanometer accuracy,in this paper,the principle of pinhole point diffraction interferometer which is based on natural spherical wavefront is investigated.The effects of parameters and adjustment errors of the pinhole on the quality of the diffractive wavefront were analyzed by Finite Difference Time Domain Method(FDTD).The pinhole point diffraction interferometer was built up in the laboratory,which is helpful for the development of prototype of pinhole point diffraction interferometer with the accuracy of 0.1 nm.The lensless image method of the pinhole point diffraction interferometer,the Radon transform is used to get the image distance,is proposed.This work avoids the technical difficalties in interferometry image system development,the theoretical analysis,numerical simulation and experiments analysis were investigated.In high numerical aperture spherical surface measurement,the traditional one order correction method for spherical surface position error is no longer applicable and can not meet the sub-nanometer measurement accuracy.This paper presents a high order correction technology for position error of high numerical aperture spherical surface measurement.The theoretical model of high order adjustment error caused by the position error of the high numerical aperture spherical surface is discussed,and the correction method of the high order adjustment error is proposed.During the absolute measurement of high numerical aperture spherical surface,the high order adjustment error at different position in the measurement process is removed.Based on the simulation analysis and ecperimental verification,high order correction technique for position error ensures the accuracy of sub-nanometer measurement of high numerical aperture spherical surface.UV lithography projection objectives have double requirement of the radius of curvature and focal length testing for high numerical aperture spherical surface.This paper presents a high precision wavefront differential interferometry method for the radius of curvature and focal length testing for high numerical aperture spherical surface.The wavefront differential theory model is established to analyzed the mathematical relationship between the radius of curvature and focal length of the high numerical aperture spherical optics and the Zernike polynomial coefficients of the differential wavefront.Expermetal verification of the wavefront differential interferometry method for radius of curvature and focal length measurement is performed.This work provides a high precision interferometry method for mutual verification of high numerical aperture spherical surface measurement during the development of UV lithography projection objectives.For the large radius of curvature spherical surface used in high power laser systems,the radius of curvature is the kay parameter that affects the quality of the laser beam.Based on virtual Newton rings,a non-null interferomenter model for large radius of curvature for spherical surface was proposed.Converting the circular carrier Newton rings to a linear carrier interferogram,the radius of curvature for a spherical surface is calculated by the moire frings.The experimental apparatus of our non-null interferometric system was setted up and the retrace errors in non-null interferometric system is calibrated.The results show that the measurement accuracy is better than 0.18%for a mirror used in laser resonator with the radius of curvature is 41400 mm.