Edge mis-figure is regarded as one of the most difficult technical issues for manufacturing the segments of extremely large telescopes, which can dominate key aspects of performance. A novel edge-control technique has been developed, based on ‘Precessions’ polishing technique and for which accurate and stable edge tool influence functions (TIFs) are crucial. In the first paper in this series [D. Walker Opt. Express 20, 19787–19798 (2012)], multiple parameters were experimentally optimized using an extended set of experiments. The first purpose of this new work is to ‘short circuit’ this procedure through modeling. This also gives the prospect of optimizing local (as distinct from global) polishing for edge mis-figure, now under separate development. This paper presents a model that can predict edge TIFs based on surface-speed profiles and pressure distributions over the polishing spot at the edge of the part, the latter calculated by finite element analysis and verified by direct force measurement. This paper also presents a hybrid-measurement method for edge TIFs to verify the simulation results. Experimental and simulation results show good agreement.

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1. D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, Paper 1: edges on processing the global surface,” Opt. Express20(18), 19787–19798 (2012). [CrossRef] [PubMed]
2. R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004). [CrossRef]
3. H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004). [CrossRef]
4. H. M. Martin, R. G. Allen, B. Cuerden, J. M. Hill, D. A. Ketelsen, S. M. Miller, J. M. Sasian, M. T. Tuell, and S. Warner, “Manufacture of the second 8.4m primary mirror for the Large Binocular Telescope,” Proc. SPIE 6273, 62730C1 (2006).
5. J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” Proc. SPIE4004, 282–289 (2000). [CrossRef]
6. R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE5494, 57–61 (2004). [CrossRef]
7. A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004). [CrossRef]
8. T. S. Mast and J. E. Nelson, “The fabrication of large optical surface using a combination of polishing and mirror bending,” Proc. SPIE1236, 670–681 (1990). [CrossRef]
9. 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. Express11(8), 958–964 (2003). [CrossRef] [PubMed]
10. H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub.6, 1104801–1104806 (2011).
11. F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol.11, 214–256 (1927).
12. R. E. Wagner and R. R. Shannon, “Fabrication of aspherics using a mathematical model for material removal,” Appl. Opt.13(7), 1683–1689 (1974). [CrossRef] [PubMed]
13. R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng.25(6), 785–790 (1986). [CrossRef]
14. A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. A. Aguilar-Chiu, J. Cuautle-Cortés, and C. Robledo-Sánchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt.43(6), 1250–1254 (2004). [CrossRef] [PubMed]
15. D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express17(7), 5656–5665 (2009). [CrossRef] [PubMed]

Appl. Opt.

• R. E. Wagner and R. R. Shannon, “Fabrication of aspherics using a mathematical model for material removal,” Appl. Opt.13(7), 1683–1689 (1974). [CrossRef] [PubMed]
• A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. A. Aguilar-Chiu, J. Cuautle-Cortés, and C. Robledo-Sánchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt.43(6), 1250–1254 (2004). [CrossRef] [PubMed]

J. Eur. Opt. Soc. Rap. Pub.

• H. Li, G. Yu, D. D. Walker, and R. Evans, “Modeling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Pub.6, 1104801–1104806 (2011).

J. Soc. Glass Technol.

• F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol.11, 214–256 (1927).

Opt. Eng.

• R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng.25(6), 785–790 (1986). [CrossRef]

Opt. Express

• D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express17(7), 5656–5665 (2009). [CrossRef] [PubMed]
• 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. Express11(8), 958–964 (2003). [CrossRef] [PubMed]
• D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, Paper 1: edges on processing the global surface,” Opt. Express20(18), 19787–19798 (2012). [CrossRef] [PubMed]

Proc. SPIE

• R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004). [CrossRef]
• H. M. Martin, J. Burge, H. B. Cuerden, S. M. Miller, B. Smith, and C. Zhao, “Manufacture of 8.4m off-axis segments: a 1/5 scale demonstration,” Proc. SPIE5494, 62–70 (2004). [CrossRef]
• J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” Proc. SPIE4004, 282–289 (2000). [CrossRef]
• R. Geyl, M. Cayrel, and M. Tarreau, “Glan Tlescope Canarias optics manufacture: progress report3,” Proc. SPIE5494, 57–61 (2004). [CrossRef]
• A. P. Semenov, M. A. Abdulkadyrov, A. N. Ignatov, V. Patrikeev, V. V. Pridnya, A. V. Polyanchikov, and Y. A. Sharov, “Fabrication of blank, figuring, polishing and testing of segmented astronomic Mirrors for SALT AND LAMOST project,” Proc. SPIE5494, 31–38 (2004). [CrossRef]
• T. S. Mast and J. E. Nelson, “The fabrication of large optical surface using a combination of polishing and mirror bending,” Proc. SPIE1236, 670–681 (1990). [CrossRef]

Other

• H. M. Martin, R. G. Allen, B. Cuerden, J. M. Hill, D. A. Ketelsen, S. M. Miller, J. M. Sasian, M. T. Tuell, and S. Warner, “Manufacture of the second 8.4m primary mirror for the Large Binocular Telescope,” Proc. SPIE 6273, 62730C1 (2006).

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