Study On Key Techniques Of Coordinate Measurement For Optical Aspherics

Aspheric optics are being used more and more widely in modern optical systems, since they can correct aberrations, enhance the image quality, enlarge the field of view and extend the range of effect, at the same time of reducing the weight and volume of the optical systems. With the ever-increasing demands on optical system performances, requirements for aspheric optical components are more and more critical, which involve aperture, relative aperture, accuracy, lightweight extent, manufacturing efficiency and cost. As the main measurement method of aspherics in grinding and pre-polishing process, the coordinate measurement technique is the key factor affecting the manufacturing efficiency. However, there are still some problems about the coordinate measurement technique, such as the relatively low accuracy and efficiency, the difficulty to test steep aspherics, which have blocked the application of aspherics seriously. This thesis is dedicated to solving the problems mentioned above, in order to perfect the coordinate measurement technique and improve the capability for manufacturing large and steep aspheric surfaces. The major research efforts include the following aspects.1. For the measurement of aspherics with a large aperture, the basic measurement principle and the accuracy analysis of a right-angle coordinate measurement technique is introduced. The effect of the 6 DOF errors of a long air guide-way, which is the critical component of a right-angle coordinate measurement system, on the measurement accuracy is analyzed, and an experimental set-up is built. For the ultra-precise measurement of the straightness error of the long air guide-way, the measurement method with a short benchmark is put forward. The effect of such factors as the testing errors, the sampling frequency and the overlap length, on the measurement accuracy is studied. With this method, we can measure and correct the straightness error of a long air guide-way accurately. Finally, a concave paraboloid with aperture= 500 mm and relative aperture= 1:3 is tested.2. For the measurement of aspherics with a large aperture and a large numerical aperture, the measurement principle of a swing-arm profilometer is researched and simulated. The effects of the bending of the measurement arm and the runouts of the air-bearing on the accuracy are analyzed and an experimental set-up is built. With the nominal figure and the measured data, the nonlinear optimal model of the radius of the measuring reference circle is built, and the convergence error of the model is analyzed. With this method, we can get the value of the vertex radius of an asphere, at the same time of getting the surface error. Finally, a concave sphere with aperture= 500 mm and relative aperture=1:1 is tested.3. For the measurement of steep aspherics, the coordinate measurement technique using profile matching method is put forward. The mathematical model of the profile matching technique is built, and the effect of the consistent errors of the dual-sampled points in the overlaps is analyzed and simulated. Since these errors affect the measurement accuracy quite seriously, an iteration algorithm with the compression mapping principle of the vector space is put forward. After that, the dividing method of the global profile is researched and the algorithm is simulated with Matlab. With the existed equipments, an experimental set-up is built and a steep conformal optics (diameter= 120mm, length/diameter=1.2) is tested.4. The effect of the relative posture errors in 6 DOF between the measurement system and the workpiece is researched and simulated. With the method of model parameter estimation, the optimization and separation algorithm of the relative posture errors of a meridian is put forward, with which the effects of the relative posture errors on the result are eliminated and the accuracy of the result is improved. After that, since sometimes the distribution of the 3D surface error is needed, the reconstruction method of the 3D surface error with several meridians is researched, with which the relative posture errors and the relative translations of the meridians are the optimal parameters. Simulations and experiments indicate that, with this method, we can get the reasonable distribution of the 3D surface error and provide the reliable data for CCOS.5. The effect of the measuring force on the uncertainty of the right-angle coordinate measurement method, and the effect of the scanning velocity of a contacting probe on the uncertainty of the swing-arm profilometer are analyzed and simulated. The effect of the environmental factors such as the temperature and the vibration is researched and tested too. With these results, we calculated the combined standard uncertainty of the right-angle coordinate measurement method and the swing-arm profilometer. Finally, as a practical example, the manufacturing process of a paraboloid (0500mm,f/3, K9) is introduced. During 233 hours, the workpiece is manufactured successfully, with the surface error 9.4nm rms, the roughness 1.5nm rms, the error of the vertex radius 1.2mm (0.4‰), which has satisfied the expected requirements.