Research On High Accuracy Figure Metrology Of Large Reflecting Optics

With the rapid development of3rdgeneration synchrotron radiation sources andFree Electron Lasers, large optical surfaces which reflect x-ray at extreme grazingincidence angles have been more widely used, especially for the large flat mirrorswhich could be bent to multiple shapes of optical surfaces by bending mechanisms.Surface figure deviation which is closely related to focus size of x-ray has been amajor consideration in high-performance synchrotron beam line instrumentation. Theworld-class aims of secondary beam lines instrumentation of Shanghai synchrotronradiation facility have placed an unprecedented high precision demand on opticalcomponents of which slope errors have been required below0.6μrad/1000mmgenerally, while even call for0.1μrad/180mm in Dream line. Therefore, it necessitatesthe use of absolute testing techniques to reach subnanometer accuracy in large surfacefigure measurement.Owing to the nature of grazing incidence x-ray optics which usually have a longtangential dimension with up to1m or more, many conventional methods for largesurface figure measurement are not easily employed in the absolute testing. In thedissertation, absolute interferometric metrology based on mirror rotational symmetryusing oblique incidence setup has been researched comprehensively, showing thecapability of the approach to achieve high accuracy for flatness measurement of theoverall2D large surface. Our works are presented as following.i. Considering the limitation of various absolute interferometric techniques, amodified method based on mirror rotational symmetry is developed to determine theabsolute flatness deviations of noncircular optical elements, extending the range ofapplications in three-flat tests. The theoretical derivation, measurement design anderror analysis are expatiated, and then simulation and experiments are performed toverify the method. It is found that our method could achieve an accuracy of10-5λ(λ=632.8nm) root mean square (rms) on height and better than0.1μrad (rms) on slopeerror measurement from simulated results. Experiments on high precision rectangular flat are finally carried out. Compared with the measurement results obtained byZygo′s three-flat application, the results of our method test coincide well both in thesurface map and slope error.ii. We demonstrate a simple method for measuring absolute figure of the largeoptical flat surface in synchrotron radiation by small aperture Fizeau interferometer.Proposed as an alternative to overcome the aperture limitation, the oblique incidenceinterferometry combined with multiple rotating measurements at N equally spacedpositions is performed to determine absolute flatness of the overall2D large surface. Unlikethe typical three-flat test, it is convenience that the reference flat in our method is notrequired to dismantle throughout the testing procedure. The uncertainty analysis associatedwith systematic errors and random errors is given in detail. Moreover, numericalsimulations have been provided for quantifying the order of magnitude for systematicerrors by the finite rotating number and the oblique incidence angle. Besides, we discussthe application range of oblique incidence test and estimate the curvature limit forcylindrical surface measurement. Finally, experiments on high accuracy rectangle flat arecarried out at four different oblique incidence angles with varied rotating numbers,checking the results available against the prediction given by simulations. In addition, fromcomparison with modified three-flat test results, the difference between two methods isestimated to be better than0.7nm (rms). An uncertainty estimate for the absolute obliqueincidence measurement at81.7°with twelve-position rotational averaging has also beenworked out. It is pointed out that the random error relating to environment stability is thedominating error source compared with systematic errors. As compared to other methodsof the large surface figure measurement, the absolute oblique incidence test is particularsimple. This approach could be implemented to facilitate the task of absolute flatnessmeasurement of large synchrotron beam line optics.iii. A novel method based on pseudo-shear in oblique incidence interferometry ispresented to test the absolute slope error of the large optical surface straight, which avoidserrors accumulation in traditional pseudo-shear interferometry. We also illustrate themethod by theoretical derivation and error analysis. It is indicated that systematic errors aremainly introduced by tilt error and displacement error of the translation stage. When tilt error is0.2′and displacement error is0.1pixel, the relative rms value error of slope error is0.2from simulations, showing the accuracy of the method is5times better than the originalaccuracy of optical surface. In conclusion, our method is valid and feasible as a newalternative to the well known method of slope measurement for large plane optics by use ofLTP.