Abstract
A novel stitching machining method for ion beam figuring of optical mirrors is presented in this paper. Problems that should be dealt with in the stitching process such as shaping principle, algorithm for dwell time calculation, parameter identification and compensation for positioning errors are discussed. Based on Computer Controlled Optical Surfacing (CCOS) principle, the finite field nonlinear model is deduced from the stitching shaping mechanism; with the superposition property in the model, a modified Richardson-Lucy iterative algorithm is presented to deconvolute the dwell time for the stitching process; the effect of the positioning errors and the removal rate on the machining accuracy and shape is modeled and then the identification and compensation algorithm for these parameters is proposed based on this model. With these studies, shaping theory and algorithm are constructed, and then the stitching process for ion beam figuring comes into being. Figuring experiments are made on planar samples; the process convergence ratio is 10, which is similar to that in full aperture figuring. Theoretical and experimental studies indicate that the stitching theory and algorithm in the ion beam figuring process presented in this paper are a novel method for fabrication of precision mirrors with lower cost.
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References
Jiao C J, Li S Y, Xie X H, et al. Material removal property in ion figuring process for optics components. Opt Precision Eng, 2007, 15(10): 1520–1526
Allen L N, Keim R E. An ion figuring system for large optic fabrication. SPIE, 1989, 1168: 33–50
Tock J P, Collette J P, Gailly P, et al. Figuring sequences on a super-smooth sample using ion beam technique. SPIE, 1999, 3739: 132–141
Jiao C J, Xie X H, Li S Y, et al. Design of ion beam figuring machine for optics mirrors. Key Eng Mater, 2008, 365–366: 756–761
Yang L. Advance Optics Manufacturing Technology (in Chinese). Beijing: Science Press, 2001. 46–52
Carnal C L, Egert C M, Hylton K W. Advanced matrix-based algorithm for ion beam milling of optical components. SPIE, 1992, 1752: 54–62
Jiao C J, Li S Y, Xie X H, et al. Bayesian based dwell time algorithm for ion beam figuring of low gradient mirrors. Chin J Mech Eng (in press)
Zhou L, Dai Y F, Xie X H, et al. Model and method to determine dwell time in ion beam figuring. Nanotechnol Precision Eng, 2007, 5(2): 107–112
Xiao T Y, Yu S G, Wang Y F. Numerical Methods for Inverse Problem (in chinese). Beijing: Science Press, 2003. 11
Gonzalez R C, Woods R E, Eddins S L. Digital Image Processing Using MATLAB (in chinese). Beijing: Publishing House of Electronics Industry, 2005. 103
Richardson W H. Bayesian-based iterative method of image restoration. J Optical Soc Am, 1972, 62: 55–59
Lucy L B. An iterative technique for rectification of observed distribution. Astron J, 1974, 79(6): 745–765
Hylton K W, Carnal C L, Jackson J R, et al. Ion beam milling of silicon carbide optical components. SPIE, 1994, 1994: 16–26
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Supported by the National Natural Science Foundation of China (Grant No. 50775216)
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Li, S., Jiao, C., Xie, X. et al. Stitching algorithm for ion beam figuring of optical mirrors. Sci. China Ser. E-Technol. Sci. 52, 3580–3586 (2009). https://doi.org/10.1007/s11431-009-0309-8
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DOI: https://doi.org/10.1007/s11431-009-0309-8