Investigation On The Key Techniques Of On-machine Measurement For Optical Surfaces

Optical surface have been widely used in the field of aviation, spaceflight and nationaldefense. In recent years, with the improving development of the design of optical system, therequests of production cost, machining accuracy and weight reduction are getting higher andhigher. The production quality of optical surface elements does not only depend on theaccuracy of machining, but also the measurement technology. In a sense, if there are notprecise measurement equipment and advanced measuring method corresponding with themachining technology, it is difficult to achieve the high quality of optical surface. Therefore,the measurement of the optical surface has been one of the key issues in the field ofprecision engineering.With the developed ultra-precision polishing platform, the investigation on the keytechniques of on-machine measurement for optical surfaces is carried out and theon-machine measurement system is developed for the measurement of optical surface basedon LM50laser interferometer effectively. The design and development of hardware andcontrol software, the error modeling of measurement system, the processing of measuringdata and planning of measurement trajectory are studied in a series of innovative work.Based on the Windows XP system, the control software for the data acquisition of thesurface information is developed, which integrates the A3200motion controller with theLM50laser interferometer. The classical measurement method of optical surface—Cartesiancoordinate measuring method is analyzed and the corresponding mathematical expressionsof the relationship between the measurement data, the target profile and the practical profileis established based on mathematical modeling method.The error source of on-machine measurement system for optical surface is analyzed.The main sources of system error are classified based on the statistical method and themathematical modeling for the vertical correction and central correction error of the probeand the error of curvature radius is set up based on mathematical modeling method. The XL-80laser interferometer of RENISHAW is used for calibrating the position error andrepetitive positioning error of the air floated platform of the measurement system and theprocessing of measurement data is carried out. The repetitive error of LM50laserinterferometer is calibrated and the straightness error of on-machine measurement system iscalibrated by scanning optical flat.Based on the fitting principle of moving least squares method and moving total leastsquares method, adaptive moving total least squares method is proposed which combineswith the error theory and takes into account the error of all variables. This method is suitablefor curve fitting under different conditions of the variable error, which is verified by thenumerical cases and measurement experiments. Interms of the disadvantage of the movingtotal least square method for surface fitting, improved moving least squares method isproposed for solving the problem of low efficiency and high calculation. This methodpreserves the advantages of adaptive moving total least squares method for the inhibition of variable errors, which is verified by numerical cases.The measurement trajectory for the curve and surface is generated. The uniformdistribution of measurement points is determinated for the spherical optical element and theuniform distribution and radial distribution of measurement points are used for the off-axisthree-mirror surface in polishing phase. According to the trajectory planning, the sphericalgeneratrix is measured based on the on-machine measurement system. The measurementdata is processed by the curve fitting and radius compensation. The calculated peak-to-valleyvalue by OMM is compared with the result of PGI1240. For the measurement data of theoff-axis three-mirror surface, the surface information is obtained with the improved movingleast-square method for surface fitting and radius compensation.The theoretical and experimental work in this article shows that the on-machinemeasurement for optical surface can achieve the measurement of the optical surface andsatisfy the requirement of the polishing process. The developed measurement system isstable and reliable and the proposed algorithms—adaptive moving total least squares methodand improved moving least squares method have good generality, which can meet the fittingaccuracy of the complex surface and provide new technology and solution for the processingof measurement data.