Absolute Testing Of Spherical Surface With Shift-rotation Method

With the rapid development of modern electronics industry, high-precision opticshave been widely employed in optical systems, eg. Surface deviation of the opticsused in the EUV must be better than rms0.1nm. The manufacture accuracy is limitedby the testing accuracy, and it certainly requires much higher accuracy of testing.Interferometric testing is the main method to test surface deviation; its result isactually the deviation of tested surface compared to the reference surface. It is relativemeasurement. The absolute testing methods can remove the reference surfacedeviation to get the absolute surface deviation of the tested surface. As a generalabsolute testing method, the shift-rotation method belongs to null-test method, and isthe key technology in surface metrology.Based on the high repeatability of interferometers, the thesis is dedicated to solvethe key theoretical algorithm, error analysis and technical problems of absolute testingmethod of shift-rotation, and further promote the accuracy of measurements bycalibrating the surface deviation of the reference surface.The surface deviation of any optical surface can be divided into rotationallysymmetric and asymmetric components. And there are many different absolute testingmethods that are based on Zernike polynomials fitting methods, to measure therotationally asymmetric surface deviation. We introduce the principles of the methods,and analysis the theoretical errors. And we further propose a new method withtheoretical and experimental comparisons.The shift-rotation algorithm is the key of the absolute testing technologies, and itis the key content of the thesis. We briefly introduce different shift-rotation methods,and give corresponding comments.The traditional shift-rotation employs the N-position method, and it suffers thekN order angular terms errors missed by N-position method when calculates therotationally symmetric surface deviation. An optimized absolute testing method ofshift-rotation is presented in this thesis. It considers the missingkN order errors.As a result, it is more accurate than the traditional method. Experimental absolute results of spherical surfaces are given.A simple and reliable data-reduction method of absolute shift-rotation method ispresented, which relies on the decomposition of the surface deviation into rotationallyasymmetric and symmetric components. The rotationally asymmetric surfacedeviation can be simply obtained by N-position method. After that, thetwo-dimensional (2D) problem of estimating the other rotationally symmetric surfacedeviation can be simplified to a one-dimensional (1D) problem. Experimentalabsolute results of spherical surfaces are given.A pixel-level spatial frequency solution of shift-rotation method is also presentedin the thesis. With the well-organized absolute procedures, the absolute surfacedeviation of the test and reference surface can be obtained accurately with pixel-levelspatial frequency resolution. Experimental absolute results of flat surfaces are given.The absolute testing methods of flats are also introduced in the thesis. Comparedwith the traditional three-flat testing method, the shift-rotation method has its ownadvantages. With theoretical analysis, the experimental results are given.To prove the validity of shift-rotation method, we measure a same testes sphericalsurface with two different sphere transmissions (same F number, but differentqualities). Then we prove the validity of the absolute testing methods withexperiments. With three different absolute testing methods, two-sphere method,random-average-testing method and shift-rotation method, we calibrate the samespherical reference surface and make comparisons.Finally, we introduce a method to determine the shift and rotational parameters,and give error analysis of the shift-rotation method.