Study On Techniques Of High-accuracy Radius Interferometric Measuremen

The radius of curvature(ROC), as a fundamental parameter of spherical optical elements, has a critical effect on the performance of optical systems. With the extensive application in metrology, projection lithography system and other high-tech fields, the requirement of ROC measurement accuracy of spherical optical elements is more and more stringent. Interferometric testing is the main method to test radius, it identifies confocal position and cat’s eye position by interferometric technique. The distance between the two positions is tested by displacement measuring system, and then the ROC is determined. The main study of this thesis is high-accuracy interferometric radius measurement. For this purpose, the environmental disturbance effects, position errors and test aperture effects are theoretically analyzed and compensated, in order to further promote the accuracy of interferometric radius measurements. The major research efforts are summarized in the following points.1. The domestic and overseas development status about the radius measurement is investigated. The theory of the contacted methods and noncontact methods is discussed, and various radius measurement techniques are compared and analyzed.2. Based on radius interferometric measurement, key theoretical and technical problems are discussed. Every part in interferometer is analyzed systematically and every error source that affects on radius measurement is classified. The main errors have been determined.3. According to Edlén equation, the effects of the variation of environmental parameters on refractive index of air are theoretically analyzed, including system error of interferometry and thermal self-deformation of spherical optical elements. The self-deformation is simulated by finite element analysis method and the error compensational equation is built up, then the synthetic error is calculated. Cross-check test is carried out on a set of elements with different ROC, in order to obtain the effects of thermal field on radius interferometric measurement.4. In order to improve the position precision, a single analytical expression for position errors is presented in terms of various error contributions, including phase measuring interferometer errors, wavefront errors of transmission sphere, surface figure error and adjustment errors. The comparative experiments indicate that after controlling the adjustment errors, the linear trend of both power and radius are changed to the random trend, and the radius variation is reduced by a scale. The result shows that the adjustment errors are the main error contributors. The power can be effectively controlled by minishing adjustment errors. Thus the interferometric radius precision is improved.5. Because of the incompletely testing at confocal position of spherical optical elements, test aperture effects on radius measurement are theoretical analyzed. And aberration compensate approach based on Zernike polynomial fitting is proposed. Experimental result shows that test aperture effects can be corrected by aberration compensate approach.6. Multiple repeated measurements are carried out on a set of elements with different ROC. Each error component is estimated or assumed, and error compensation is applied, the result shows that the system errors can be effectively compensated. Then uncertainty propagation law was employed to combine several error sources in the paper and an uncertainty budget was given. Relative standard uncertainty is up to 4ppm. Here the uncertainty of nonideal surface wavefront errors and adjustment errors are the largest, and then is the uncertainty of Type A evaluations and self-deformation.