Study On The Effect Mechanism Of Structure Bias Error And The Stitching Method In The Stitching Interferometric Measurement Of Aspheric Surfaces

Large aperture aspheric optical elements have become key parts in the area of space optics. Accurate measurements of large aperture aspheric surfaces associate with precise manufacture and effective application. However, The current aspheric surface testing methods, such as contact scanning testing method and null testing method are restricted by measurement range, efficiency and cost, which restricts the further development of accurate measurement of large aspheric surfaces. For this reason, it is urgent to find a faster and more accurate measurement method to solve the above key technology.The subject,"study on the effect mechanism of structure bias error and the stitching method in the stitching interferometric measurement of aspheric surfaces", which aims to research on measuring large aperture aspheric surfaces accurately using the stitching method. The paper mainly focuses on studying the realization of a stitching method for large aperture aspheric surface measurement. Both stitching interferometric measurement model of aspheric surface and the single stitching measurement precision have been improved according to analyzing the behavior of three-direction adjustment errors and stitching structure bias error in the sub-aperture interferometric measurement of aspheric surface. These researches offer a technology scheme for testing large aperture aspheric surface precisely, and settle the theoretical foundation ultimately for implementing the precise testing large aperture aspheric surface.The behavior of three-direction adjustment errors and stitching structure bias error in the sub-aperture interferometric measurement of aspheric surface have been analyzed based on wavefront aberration theory. The analysis results show that all the components of aspheric surface wavefront distribution under test have been changed by three direction adjustment errors; these changes not only include the low order tilts and the second order defocus but produce the high order bias such as the third order longitudinal spherical, comatic aberration and so on. Therefore, the traditional correcting method of three direction adjustment errors will make the residual errors accumulated due to the high order aberrations uncorrected during the stitching process of interferometric measurement, and hence is not suitable for aspheric surface precise testing when using the standard planar and spherical wavefront in the interferometric measurement of aspheric surface.In order to separate the adjustment errors in the stitching measurement, functional relationship model between the bias error of stitching positioning mechanism and corresponding movement freedom is established. The presented model with quadratic surface as its testing object, describes integrally how the stitching positioning mechanism affects the interferometric measurement results with quantified mathematical expression by analyzing the spatial combined motion mechanism of stitching positioning structure. Moreover, the model provides the basis of theoretical analysis for the mechanism design of the stitching interferometric measurement of aspheric surface.Aberration correction method and technology for stitching measurement of aspheric surfaces have been proposed based on the influences of three-direction adjustment errors and the bias error of stitching positioning mechanism on interferometric measurement of aspheric surfaces. In this method, the stitching measurement has been successfully accomplished by established mathematical model of aberration correction. In order to implement stitching, the multiple linear regression equation has been solved to obtain the stitching coefficients, and phase fitting precision of overlapping area of sub-apertures and stitching precision of the measurement system are evaluated utilizing the statistical distribution method. The simulations and comparable experimental results show that both phase fitting precision of overlapping area of sub-apertures and stitching precision of the measurement system are higher than the current stitching measurement method based on three-direction adjustment error correction by using this proposed stitching measurement method. At last, the proposed stitching method has been validated by experiments: 1)For the stitching interferometric measurement of plane surfaces, the difference of PV values is less thanλ/10, and the difference of RMS values is less thanλ/50 comparing with full-aperture measurement results, which preliminarily verifies the validity of the experimental system and the developed software for stitching interferometric measurement. 2) A contrast experiment has been implemented to validate the superiority of the presented aberration correction stitching method. The experimental results show the single stitching measurement precision has been obviously improved by the proposed method comparing with the stitching measurement method of three-direction adjustment error correction. 3) The uncertainty of sub-aperture stitching interferometric measurement results is analyzed systematically in the last chapter of this thesis.