High-Precision Aspheric Surface Measurement Using Scanning Deflectometry: Three-Dimensional Error Analysis and Experiments
Tingzhi Hu*, Muzheng Xiao*,†, Xicheng Wang*, Chao Wang**, Zhijing Zhang*, and Kiyoshi Takamasu***
*School of Mechanical Engineering, Beijing Institute of Technology
5 South Zhongguancun Street, Haidian District, Beijing, China
**BAIC MOTOR SALES Co., Ltd., Beijing, China
***Department of Precision Engineering, School of Engineering, The University of Tokyo, Tokyo, Japan
Interferometers are widely used to measure large aspheric surfaces because of their high accuracy and high efficiency. However, they cannot be used for aspheric surfaces with large curvature and asphericity. In this paper, we propose a method for measuring aspheric surfaces using scanning deflectometry with an autocollimator. A rotary stage is used to enlarge the measurement range of the autocollimator, so that aspheric surfaces with large slope changes can be measured. Three-dimensional error analysis is performed. We use an autocollimator with a measurement range of 21500 μrad (4500 arcsec) to measure a spherical surface with a curvature radius of 400 mm to perform the experiment. Experimental results showed that the average root-mean-square error was approximately 100 nm.
-  H. Suzuki, “Multi-Axis Controlled Ultraprecision Machining and Measurement,” Int. J. of Automation Technology, Vol.3, pp. 227-232, 2009.
-  J. G. Tang and F. Wu, “Research on surface shape detection technology of large diameter aspheric surface,” Optical Technique, Vol.27, p. 509-511, 2001.
-  K. Li, X. Wu, S. Wang, and C. Zhang, “A Survey of Current Aspheric Measurement Methods,” Technology Foundation of National Defence, 2010.
-  Y.-T. Liu, H.-L. Wu, J.-Y. Wang, and Y. Yamagata, “Contact-Type Profile Measuring Device Using Laser Interferometry System Incorporating Hybrid Actuating System,” Int. J. of Automation Technology, Vol.7, pp. 489-497, 2013.
-  X. Wang, L. Wang, L. Yin, B. Zhang, D. Fan, and X. Zhang, “Measurement of large aspheric surfaces by annular subaperture stitching interferometry,” Chinese Optics Letters, Vol.5, 2007.
-  F. Gao, Z. Jiang, Z. Zhao, and B. Li, “Measurement of aspheric surface combining point diffraction interferometry and annular subaperture stitching,” Optical Engineering, Vol.54, 2015.
-  P. Thomsen-Schmidt, M. Schulz, and I. Weingaertner, “Facility for the curvature-based measurement of the nanotopography of complex surfaces,” Int. Society for Optics and Photonics, pp. 94-101, 2000.
-  M. Xiao, T. Takamura, S. Takahashi, and K. Takamasu, “Random error analysis of profile measurement of large aspheric optical surface using scanning deflectometry with rotation stage,” Precision Engineering, Vol.37, pp. 599-605, 2013.
-  K. Ishikawa, T. Takamura, M. Xiao, S. Takahashi, and K. Takamasu, “Profile measurement of aspheric surface using scanning deflectometry and rotating autocollimator with wide measuring range,” Meas. Sci. Technol., Vol.25, 2014.
-  M. Xiao, S. Jujo, S. Takahashi, and K. Takamasu, “Nanometer profile measurement of large aspheric optical surface by scanning deflectometry with rotatable device: Uncertainty propagation analysis and experiments,” Precision Engineering, Vol.36, pp. 91-96, 2012.
-  W. S. Cleveland and S. J. Devlin, “Locally weighted regression: an approach to regression analysis by local fitting,” J. of the American Statistical Association, Vol.83, pp. 596-610, 1988.