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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 15 — May. 20, 2013
  • pp: 3624–3636

Peano-like paths for subaperture polishing of optical aspherical surfaces

Hon-Yuen Tam, Haobo Cheng, and Zhichao Dong  »View Author Affiliations

Applied Optics, Vol. 52, Issue 15, pp. 3624-3636 (2013)

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Polishing can be more uniform if the polishing path provides uniform coverage of the surface. It is known that Peano paths can provide uniform coverage of planar surfaces. Peano paths also contain short path segments and turns: (1) all path segments have the same length, (2) path segments are mutually orthogonal at the turns, and (3) path segments and turns are uniformity distributed over the domain surface. These make Peano paths an attractive candidate among polishing tool paths because they enhance multidirectional approaches of the tool to each surface location. A method for constructing Peano paths for uniform coverage of aspherical surfaces is proposed in this paper. When mapped to the aspherical surface, the path also contains short path segments and turns, and the above attributes are approximately preserved. Attention is paid so that the path segments are still well distributed near the vertex of the surface. The proposed tool path was used in the polishing of a number of parabolic BK7 specimens using magnetorheological finishing (MRF) and pitch with cerium oxide. The results were rather good for optical lenses and confirm that a Peano-like path was useful for polishing, for MRF, and for pitch polishing. In the latter case, the surface roughness achieved was 0.91 nm according to WYKO measurement.

© 2013 Optical Society of America

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.4610) Optical design and fabrication : Optical fabrication

ToC Category:
Optics at Surfaces

Original Manuscript: February 13, 2013
Revised Manuscript: April 17, 2013
Manuscript Accepted: April 19, 2013
Published: May 20, 2013

Hon-Yuen Tam, Haobo Cheng, and Zhichao Dong, "Peano-like paths for subaperture polishing of optical aspherical surfaces," Appl. Opt. 52, 3624-3636 (2013)

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  1. R. A. Jones, “Computer control for grinding and polishing,” Photon. Spectra34–39 (1963).
  2. H. B. Cheng, Z. J. Feng, K. Cheng, and Y. W. Wang, “Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors,” Int. J. Mach. Tools Manuf. 45, 1085–1094 (2005). [CrossRef]
  3. W. Kordonski and D. Golini, “Progress update in magnetorheological finishing,” Int. J. Mod. Phys. B 13, 2205–2212 (1999). [CrossRef]
  4. P. M. Shanbhag, M. R. Feinberg, G. Sandri, M. N. Horenstein, and T. G. Bifano, “Ion-beam machining of millimeter scale optics,” Appl. Opt. 39, 599–611 (2000). [CrossRef]
  5. D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11, 958–964 (2003). [CrossRef]
  6. W. Kordonski, A. Shorey, and A. Sekeres, “New magnetically assisted finishing method: material removal with magnetorheological fluid jet,” Proc. SPIE 5l80, 107–114 (2004). [CrossRef]
  7. Y. Mizugaki, M. Sakamoto, and T. Sata, “Fractal path generation for a metal-mold polishing robot system and its evaluation by the operability,” CIRP Ann. 41, 531–534 (1992). [CrossRef]
  8. U. Cho, D. G. Eom, D. Y. Lee, and J. O. Park, “A flexible polishing robot system for die and mould,” in Proceedings of the 23rd International Symposium on Industrial Robots (1992), pp. 449–456.
  9. X. Pessoles and C. Tournier, “Automatic polishing process of plastic injection molds on a 5-axis milling center,” J. Mater. Process. Technol. 209, 3665–3673 (2009). [CrossRef]
  10. M. J. Tsai and J. F. Huang, “Efficient automatic polishing process with a new compliant abrasive tool,” Int. J. Adv. Manuf. Technol. 30, 817–827 (2006). [CrossRef]
  11. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16, 18942–18949 (2008). [CrossRef]
  12. H. Hu, Y. F. Dai, and X. Q. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18, 22973–22981 (2010). [CrossRef]
  13. W. J. Deng, X. J. Zhang, X. K. Wang, and X. Wang, “Novel method for optimizing polishing tool-path in CCOS based on weighted-iterative algorithm,” Proc. SPIE 7282, 728214 (2009). [CrossRef]
  14. H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010). [CrossRef]
  15. H. B. Cheng, Y. Yam, and Y. T. Wang, “Experimentation on MR fluid using a 2-axis wheel tool,” J. Mater. Process. Technol. 209, 5254–5261 (2009). [CrossRef]

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