Study Of Null Interferometry Based On Conjugate Differential Method For Absolute Test Of Optical Surfaces

As a relative test method,optical null interferometry has been widely applied in the high precision test of optical elements.To eliminate the influence of the interferometer system errors(including the reference surface error),some absolute test methods have been used to obtain the absolute shape of the test surface.In the traditional absolute test methods called three-flats test,the absolute surface is measured by large movement of the test surface such as rotation and flip,which will reduce the precision due to the non-negligible location matching error.In order to get the absolute surface of the test surface without huge motions,the conjugate differential absolute test method with micro-displacement based on null interferometry is presented,including the conjugate differential absolute test method of optical flats,the compensating wavefront transformation of CGH for the conjugate differential absolute test method using in aspherical surfaces test,and the conjugate differential absolute test method of optical cylindrical surfaces.In order to avoid position mismatch induced by the huge motions in the traditional absolute test methods,the conjugate differential absolute test method with micro-displacement based on null interferometry is proposed,where the differential absolute test method with a pair of measurements groups at conjugate positions is introduced.With four times of micro-displacement less than one millimete along two orthogonal directions,four results in two groups at conjugate positions can be obtained.By the subtraction in each group,the systematic errors can be eliminated and the differential wavefront of the test surface are also obtained.And than the absolute surface can be calculated from the differential wavefront reconstruction.Comparing with the traditional differential absolute test method,the conjugate one shows higher precision in the simulations.The major error sources in the actual measurement are analyzed,and the conjugate differential absolute test method is used to test a flat surface in the experiment.The test result is verified by the three-flats method,where the max RMS value of the deviation is less than 0.2nm,better than ?/3164.To expand the application range of the conjugate differential absolute test method to aspherical surfaces,the compensating wavefront transformation technique using CGH is studied to make sure the test surfaces are working in null interferometry.Considered the off-axis aspherical surface as the freedom surface,the design and fabrication of CGH which can generate related freeform wavefront are completed.The measurement repeatability of the freeform surface with null interferometry test is better than ?/1428(RMS),the reconstructed freeform wavefronts error is less than ?/111,and the measurement uncertainty calculated by square and root synthesis is less than ?/77.Compared with the result of Offner compensation method which is considered as reference value,the deviation is less than ?/104.In addition,a cylinder absolute test method is proposed to improve the precision of cylindrical surface,which is based on CGH wavefront transformation,cylindrical surface aided alignment,and conjugate differential absolute test method.The cylindrical compensate CGH is fabricated to accomplish the null interferometry test of cylindrical surface.To improve the alignment accuracy,the mis-adjustments are combined with the Chebyshev polynomial coefficients in the model of cylindrical null interferometry.Therefore the mis-adjustments can be analyzed to guide the alignment.The conjugate differential absolute test method is applied to the cylindrical surfaces test by satisfying null interferometry condition with CGH.The test surface is firstly translated along the centre line and secondly rotated around the centre line,so that two groups of conjugate measurements can be obtained.And then the differential wavefronts are obtained and the absolute surface is extacted from the differential wavefronts.Taking a cylindrical mirror with-100mm radius of curvature under test,the absolute surface is reconstructed by the conjugate differential method.Compared to the result of profilometer,the deviation of the surface contour is less than ?/42.