Edge effect of optical surfacing process with different data extension algorithms

doi:10.1007/s12200-014-0393-7

Front Optoelec

2014, Vol. 7

Issue (1) : 77-83 https://doi.org/10.1007/s12200-014-0393-7

RESEARCH ARTICLE

Edge effect of optical surfacing process with different data extension algorithms

Yang LIU¹(

), Haobo CHENG¹, Zhichao DONG¹, Hon-Yuen TAM²

1. School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China; 2. Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong, China

Download: PDF(572 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

This study presents a strategy which integrates extra polishing path (EPP) and error map extension to weaken the edge effect in the ultraprecise optical surfacing process. Different data extension algorithms were presented and analyzed. The neighbor-hood average can be selected as the frequently-used method, as it has not bad precision and time-saving performance for most surface forms through the simulation results and practical experiment. The final error map was obtained, its peak-to-valley (PV) was 0.273λ and root mean square (RMS) was 0.028λ (λ = 632.8 nm). The edge effect was weakened and suppressed well through the experiment.

Keywords edge effect convergence rate extension algorithms

Corresponding Author(s): LIU Yang,Email:chenghaobo@tsinghua.org.cn

Issue Date: 05 March 2014

Cite this article:

Yang LIU,Haobo CHENG,Zhichao DONG, et al. Edge effect of optical surfacing process with different data extension algorithms[J]. Front Optoelec, 2014, 7(1): 77-83.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-014-0393-7
https://academic.hep.com.cn/foe/EN/Y2014/V7/I1/77

Fig.1 Schematic diagram of Gaussian extension method

Fig.2 Schematic diagram of neighborhood extension method

Fig.3 Results with Gerchberg’s 1-D algorithm. (a) Initial data; (b) data after extended

Fig.4 Schematic diagrams with different extension methods (with low edge gradient). (a) Setting zero; (b) Gaussian extension; (c) neighborhood extension; (d) Gerchberg-pupil extension

Fig.5 Schematic diagrams with different extension methods (with high edge gradient). (a) Setting zero; (b) Gaussian extension; (c) neighborhood extension; (d) Gerchberg-pupil extension

Fig.6 Results comparison of surface form with low and high edge gradient with different extensions. (a) Results of and ; (b) results of convergence rate (m_1: setting zero; m_2: Gaussian extension; m_3: neighborhood extension; m_4: Gerchberg-pupil extension)

Fig.7 Surface error map. (a) Initial surface error map: , ; (b) final surface error map: ,

1	Johns M. The giant magellan telescope (GMT). In: Proceedings of SPIE, Extremely Large Telescopes: Which Wavelengths? Lund, Sweden , 2008, 6986: 696803-1-696803-12
2	Clampin M. Status of the James Webb space telescope (JWST). In: Proceedings of SPIE, Astronomical Telescopes and Instrumentation: Synergies Between Ground and Space. France , 2008, 7010: 70100L-1-70100L-7
3	Kim D W, Park W H, Kim S W, Burge J H. Parametric modeling of edge effects for polishing tool influence functions. Optics Express , 2009, 17(7): 5656-5665 doi: 10.1364/OE.17.005656 pmid:19333334
4	Jones R A. Computer-controlled optical surfacing with orbital tool motion. Optical Engineering (Redondo Beach, Calif.) , 1986, 25(6): 785-790 doi: 10.1117/12.7973906
5	Zhang X J, Yu J C, Sun X F. Theoretical method for edge figuring in computer-controlled polishing of optical surface. In: Proceedings of SPIE’s 1993 International Symposium on Optics, Imaging, and Instrumentation . 1994, 239-246
6	Luna-Aguilar E, Cordero-Davila A, Gonzalez J, Nunez-Alfonso M, Cabrera V, Robledo-Sanchez C I, Cuautle-Cortez J, Pedrayes M H. Edge effects with Preston equation. In: Procedings of SPIE, Astronomical Telescopes and Instrumentation . 2003, 4840: 598-603
7	Cordero-Dávila A, González-García J, Pedrayes-López M, Aguilar-Chiu L A, Cuautle-Cortés J, Robledo-Sánchez C. Edge effects with the Preston equation for a circular tool and workpiece. Applied Optics , 2004, 43(6): 1250-1254 doi: 10.1364/AO.43.001250 pmid:15008526
8	Wang T, Cheng H B, Feng Y P, Dong Z C. Simulation analysis of edge effect in typical processing. Transactions of Beijing Institute of Technology , 2011, 31(9): 1100-1103
9	Shu L X, Wu F, Shi C Y. Optimization of the edge extension in dwell time algorithm for ion beam figuring. In: Proceedings of 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT) . 2012, 8416: 84162M-1-84162M-6
10	Jiao C J, Li S Y, Xie X H. Algorithm for ion beam figuring of low-gradient mirrors. Applied Optics , 2009, 48(21): 4090-4096 doi: 10.1364/AO.48.004090 pmid:19623222
11	Zhou L. Optical mirror ion beam figuring theory and technology. Dissertation for the Doctoral Degree . Hunan: National University of Defense Technology, 2008, 30-43 (in Chinese)
12	Wu J. Research on ion beam figuring technology. Dissertation for the Doctoral Degree . Jilin: Changchun Institute of optics, Fine Mechanics and Physics, Chinese Academy of Science, 2010, 13-38
13	MarksII R J, Robert J. Gerchberg’s extrapolation algorithm in two dimensions. Applied Optics , 1981, 20(10): 1815-1820 (in Chinese) doi: 10.1364/AO.20.001815 pmid:20332839
14	Wu J F, Lu Z W, Zhang H X, Wang T S. Dwell time algorithm in ion beam figuring. Applied Optics , 2009, 48(20): 3930-3937 doi: 10.1364/AO.48.003930 pmid:19593344

Viewed

Full text

Abstract

Cited

Shared

Discussed