Abstract

In the field of ultra-precision manufacturing, the mid-spatial-frequency (MSF) error can severely affect the performance of the optical elements, but it is rather difficult to quantitatively predict the MSF error distribution. In this paper, the piecewise-path convolution (PPC) analysis is established to investigate the characteristic and the mechanism of the MSF error. The path type, tool influence function (TIF), feed rate, movement type, etc. are all considered mathematically in the analysis. This method can quantitatively predict the MSF error distribution. The coupling relationship among the path type, TIF and the MSF error are proved through the filtering theory. Besides, the analysis reveals the mathematical relationship between the tool movement type (orbital motion, radial runout) and the MSF error; the results show that the tool motion can also introduce non-negligible MSF error. Based on the research above, two selection formulae of path type, TIF and polishing parameters are provided for low MSF error polishing, which gives the theoretical guidance for the parameter selection in deterministic polishing. Practical experiments demonstrate the validity of the analysis results and conclusions.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Fiber-based tools: material removal and mid-spatial frequency error reduction

Hossein Shahinian, Mohammed Hassan, Harish Cherukuri, and Brigid A. Mullany
Appl. Opt. 56(29) 8266-8274 (2017)

Modified subaperture tool influence functions of a flat-pitch polisher with reverse-calculated material removal rate

Zhichao Dong, Haobo Cheng, and Hon-Yuen Tam
Appl. Opt. 53(11) 2455-2464 (2014)

References

  • View by:
  • |
  • |
  • |

  1. D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
    [Crossref]
  2. Y. Xu, J. Lu, X. Xu, C. C. A. Chen, and Y. Lin, “Study on high efficient sapphire wafer processing by coupling SG-mechanical polishing and GLA-CMP,” Int. J. Mach. Tool Manufact. 130-131, 12–19 (2018).
    [Crossref]
  3. U. Satake, T. Enomoto, Y. Obayashi, and T. Sugihara, “Reducing edge roll-off during polishing of substrates,” Precis. Eng. 51, 97–102 (2018).
    [Crossref]
  4. M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
    [Crossref]
  5. F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
    [Crossref]
  6. R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16(1), 218–224 (1977).
    [Crossref]
  7. C. F. Cheung, L. B. Kong, L. T. Ho, and S. To, “Modelling and simulation of structure surface generation using computer controlled ultra-precision polishing,” Precis. Eng. 35(4), 574–590 (2011).
    [Crossref]
  8. M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
    [Crossref]
  9. G. Junkang, A. Beaucamp, and S. Ibaraki, “Virtual pivot alignment method and its influence to profile error in bonnet polishing,” Int. J. Mach. Tool Manufact. 122, 18–31 (2017).
    [Crossref]
  10. R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
    [Crossref]
  11. C. J. Wang, C. F. Cheung, L. T. Ho, M. Y. Liu, and W. B. Lee, “A novel multi-jet polishing process and tool for high-efficiency polishing,” Int. J. Mach. Tool Manufact. 115, 60–73 (2017).
    [Crossref]
  12. M. Das, V. Jain, and P. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tool Manufact. 48(3-4), 415–426 (2008).
    [Crossref]
  13. M. Chunlin, J. C. Lambropoulos, and S. D. Jacobs, “Process parameter effects on material removal in magnetorheological finishing of borosilicate glass,” Appl. Opt. 49(10), 1951–1963 (2010).
    [Crossref]
  14. W. I. Kordonski and S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10(23n24), 2837–2848 (1996).
    [Crossref]
  15. A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
    [Crossref]
  16. J. Wu, Z. Lu, H. Zhang, and T. Wang, “Dwell time algorithm in ion beam figuring,” Appl. Opt. 48(20), 3930–3937 (2009).
    [Crossref]
  17. J. M. Tamkin, W. J. Dallas, and T. D. Milster, “Theory of point-spread function artifacts due to structured mid-spatial frequency surface errors,” Appl. Opt. 49(25), 4814–4824 (2010).
    [Crossref]
  18. D. M. Aikens, A. Roussel, and M. Bray, “Derivation of preliminary specifications for transmitted wavefront and surface roughness for large optics used in inertial confinement fusion,” Proc. SPIE 2633, 350–360 (1995).
    [Crossref]
  19. X. Li, C. Wei, S. Zhang, W. Xu, and J. Shao, “Theoretical and experimental comparisons of the smoothing effects for different multi-layer polishing tools during computer-controlled optical surfacing,” Appl. Opt. 58(16), 4406–4413 (2019).
    [Crossref]
  20. D. D. Walker, W. Yu, G. Yu, H. Li, W. Zhang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
    [Crossref]
  21. T. Wang, H. Cheng, W. Zhang, H. Yang, and W. Wu, “Restraint of path effect on optical surface in magnetorheological jet polishing,” Appl. Opt. 55(4), 935–942 (2016).
    [Crossref]
  22. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008).
    [Crossref]
  23. H. Hu, Y. Dai, and X. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18(22), 22973–22981 (2010).
    [Crossref]
  24. 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.
  25. 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(5), 807–818 (2010).
    [Crossref]
  26. J. Hou, D. Liao, and H. Wang, “Development of multi-pitch tool path in computer-controlled optical surfacing processes,” J. Eur. Opt. Soc.-Rapid Publ. 13(1), 22 (2017).
    [Crossref]
  27. C. Wang, Z. Wang, and Q. Xu, “Unicursal random maze tool path for computer-controlled optical surfacing,” Appl. Opt. 54(34), 10128–10136 (2015).
    [Crossref]
  28. H. Y. Tam, H. B. Cheng, and Z. C. Dong, “Peano-like paths for subaperture polishing of optical aspherical surfaces,” Appl. Opt. 52(15), 3624–3636 (2013).
    [Crossref]
  29. Y. Dai, F. Shi, X. Peng, and S. Li, “Restraint of mid-spatial frequency error in magneto-rheological finishing (MRF) process by maximum entropy method,” Sci. China, Ser. E: Technol. Sci. 52(10), 3092–3097 (2009).
    [Crossref]
  30. F. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).
  31. S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
    [Crossref]

2019 (1)

2018 (4)

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

Y. Xu, J. Lu, X. Xu, C. C. A. Chen, and Y. Lin, “Study on high efficient sapphire wafer processing by coupling SG-mechanical polishing and GLA-CMP,” Int. J. Mach. Tool Manufact. 130-131, 12–19 (2018).
[Crossref]

U. Satake, T. Enomoto, Y. Obayashi, and T. Sugihara, “Reducing edge roll-off during polishing of substrates,” Precis. Eng. 51, 97–102 (2018).
[Crossref]

R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
[Crossref]

2017 (4)

C. J. Wang, C. F. Cheung, L. T. Ho, M. Y. Liu, and W. B. Lee, “A novel multi-jet polishing process and tool for high-efficiency polishing,” Int. J. Mach. Tool Manufact. 115, 60–73 (2017).
[Crossref]

G. Junkang, A. Beaucamp, and S. Ibaraki, “Virtual pivot alignment method and its influence to profile error in bonnet polishing,” Int. J. Mach. Tool Manufact. 122, 18–31 (2017).
[Crossref]

D. D. Walker, W. Yu, G. Yu, H. Li, W. Zhang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
[Crossref]

J. Hou, D. Liao, and H. Wang, “Development of multi-pitch tool path in computer-controlled optical surfacing processes,” J. Eur. Opt. Soc.-Rapid Publ. 13(1), 22 (2017).
[Crossref]

2016 (1)

2015 (1)

2013 (1)

2011 (2)

C. F. Cheung, L. B. Kong, L. T. Ho, and S. To, “Modelling and simulation of structure surface generation using computer controlled ultra-precision polishing,” Precis. Eng. 35(4), 574–590 (2011).
[Crossref]

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

2010 (4)

2009 (2)

Y. Dai, F. Shi, X. Peng, and S. Li, “Restraint of mid-spatial frequency error in magneto-rheological finishing (MRF) process by maximum entropy method,” Sci. China, Ser. E: Technol. Sci. 52(10), 3092–3097 (2009).
[Crossref]

J. Wu, Z. Lu, H. Zhang, and T. Wang, “Dwell time algorithm in ion beam figuring,” Appl. Opt. 48(20), 3930–3937 (2009).
[Crossref]

2008 (3)

M. Das, V. Jain, and P. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tool Manufact. 48(3-4), 415–426 (2008).
[Crossref]

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008).
[Crossref]

2005 (2)

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

2002 (1)

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

1996 (1)

W. I. Kordonski and S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10(23n24), 2837–2848 (1996).
[Crossref]

1995 (1)

D. M. Aikens, A. Roussel, and M. Bray, “Derivation of preliminary specifications for transmitted wavefront and surface roughness for large optics used in inertial confinement fusion,” Proc. SPIE 2633, 350–360 (1995).
[Crossref]

1977 (1)

1927 (1)

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

Aikens, D. M.

D. M. Aikens, A. Roussel, and M. Bray, “Derivation of preliminary specifications for transmitted wavefront and surface roughness for large optics used in inertial confinement fusion,” Proc. SPIE 2633, 350–360 (1995).
[Crossref]

Beaucamp, A.

G. Junkang, A. Beaucamp, and S. Ibaraki, “Virtual pivot alignment method and its influence to profile error in bonnet polishing,” Int. J. Mach. Tool Manufact. 122, 18–31 (2017).
[Crossref]

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Bray, M.

D. M. Aikens, A. Roussel, and M. Bray, “Derivation of preliminary specifications for transmitted wavefront and surface roughness for large optics used in inertial confinement fusion,” Proc. SPIE 2633, 350–360 (1995).
[Crossref]

Brecherb, C.

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

Chen, C. C. A.

Y. Xu, J. Lu, X. Xu, C. C. A. Chen, and Y. Lin, “Study on high efficient sapphire wafer processing by coupling SG-mechanical polishing and GLA-CMP,” Int. J. Mach. Tool Manufact. 130-131, 12–19 (2018).
[Crossref]

Chen, D.

R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
[Crossref]

Cheng, H.

Cheng, H. B.

H. Y. Tam, H. B. Cheng, and Z. C. Dong, “Peano-like paths for subaperture polishing of optical aspherical surfaces,” Appl. Opt. 52(15), 3624–3636 (2013).
[Crossref]

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(5), 807–818 (2010).
[Crossref]

Cheung, C. F.

C. J. Wang, C. F. Cheung, L. T. Ho, M. Y. Liu, and W. B. Lee, “A novel multi-jet polishing process and tool for high-efficiency polishing,” Int. J. Mach. Tool Manufact. 115, 60–73 (2017).
[Crossref]

C. F. Cheung, L. B. Kong, L. T. Ho, and S. To, “Modelling and simulation of structure surface generation using computer controlled ultra-precision polishing,” Precis. Eng. 35(4), 574–590 (2011).
[Crossref]

Cho, U.

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.

Chunlin, M.

Dai, Y.

H. Hu, Y. Dai, and X. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18(22), 22973–22981 (2010).
[Crossref]

Y. Dai, F. Shi, X. Peng, and S. Li, “Restraint of mid-spatial frequency error in magneto-rheological finishing (MRF) process by maximum entropy method,” Sci. China, Ser. E: Technol. Sci. 52(10), 3092–3097 (2009).
[Crossref]

Dallas, W. J.

Das, M.

M. Das, V. Jain, and P. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tool Manufact. 48(3-4), 415–426 (2008).
[Crossref]

Dong, Z. C.

Doubrovski, V.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Dumas, P.

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

Dunn, C.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Dunn, C. R.

Enomoto, T.

U. Satake, T. Enomoto, Y. Obayashi, and T. Sugihara, “Reducing edge roll-off during polishing of substrates,” Precis. Eng. 51, 97–102 (2018).
[Crossref]

Eom, D. G.

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.

Fan, J.

R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
[Crossref]

Forbes, G.

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

Freeman, R.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Ghoshdastidar, P.

M. Das, V. Jain, and P. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tool Manufact. 48(3-4), 415–426 (2008).
[Crossref]

Ho, L. T.

C. J. Wang, C. F. Cheung, L. T. Ho, M. Y. Liu, and W. B. Lee, “A novel multi-jet polishing process and tool for high-efficiency polishing,” Int. J. Mach. Tool Manufact. 115, 60–73 (2017).
[Crossref]

C. F. Cheung, L. B. Kong, L. T. Ho, and S. To, “Modelling and simulation of structure surface generation using computer controlled ultra-precision polishing,” Precis. Eng. 35(4), 574–590 (2011).
[Crossref]

Hou, J.

J. Hou, D. Liao, and H. Wang, “Development of multi-pitch tool path in computer-controlled optical surfacing processes,” J. Eur. Opt. Soc.-Rapid Publ. 13(1), 22 (2017).
[Crossref]

Hu, H.

Ibaraki, S.

G. Junkang, A. Beaucamp, and S. Ibaraki, “Virtual pivot alignment method and its influence to profile error in bonnet polishing,” Int. J. Mach. Tool Manufact. 122, 18–31 (2017).
[Crossref]

Jacobs, S. D.

Jain, V.

M. Das, V. Jain, and P. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tool Manufact. 48(3-4), 415–426 (2008).
[Crossref]

Jiang, X.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

Jones, R. A.

Junkang, G.

G. Junkang, A. Beaucamp, and S. Ibaraki, “Virtual pivot alignment method and its influence to profile error in bonnet polishing,” Int. J. Mach. Tool Manufact. 122, 18–31 (2017).
[Crossref]

Klockea, F.

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

Kong, L. B.

C. F. Cheung, L. B. Kong, L. T. Ho, and S. To, “Modelling and simulation of structure surface generation using computer controlled ultra-precision polishing,” Precis. Eng. 35(4), 574–590 (2011).
[Crossref]

Kordonski, W. I.

W. I. Kordonski and S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10(23n24), 2837–2848 (1996).
[Crossref]

Lambropoulos, J. C.

Lee, D. Y.

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.

Lee, W. B.

C. J. Wang, C. F. Cheung, L. T. Ho, M. Y. Liu, and W. B. Lee, “A novel multi-jet polishing process and tool for high-efficiency polishing,” Int. J. Mach. Tool Manufact. 115, 60–73 (2017).
[Crossref]

Li, H.

Li, S.

Y. Dai, F. Shi, X. Peng, and S. Li, “Restraint of mid-spatial frequency error in magneto-rheological finishing (MRF) process by maximum entropy method,” Sci. China, Ser. E: Technol. Sci. 52(10), 3092–3097 (2009).
[Crossref]

Li, X.

Liao, D.

J. Hou, D. Liao, and H. Wang, “Development of multi-pitch tool path in computer-controlled optical surfacing processes,” J. Eur. Opt. Soc.-Rapid Publ. 13(1), 22 (2017).
[Crossref]

Lin, Y.

Y. Xu, J. Lu, X. Xu, C. C. A. Chen, and Y. Lin, “Study on high efficient sapphire wafer processing by coupling SG-mechanical polishing and GLA-CMP,” Int. J. Mach. Tool Manufact. 130-131, 12–19 (2018).
[Crossref]

Liu, M. Y.

C. J. Wang, C. F. Cheung, L. T. Ho, M. Y. Liu, and W. B. Lee, “A novel multi-jet polishing process and tool for high-efficiency polishing,” Int. J. Mach. Tool Manufact. 115, 60–73 (2017).
[Crossref]

Lu, C.

Lu, J.

Y. Xu, J. Lu, X. Xu, C. C. A. Chen, and Y. Lin, “Study on high efficient sapphire wafer processing by coupling SG-mechanical polishing and GLA-CMP,” Int. J. Mach. Tool Manufact. 130-131, 12–19 (2018).
[Crossref]

Lu, Z.

McCavana, G.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Milster, T. D.

Morton, R.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Novitskii, N. N.

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

Obayashi, Y.

U. Satake, T. Enomoto, Y. Obayashi, and T. Sugihara, “Reducing edge roll-off during polishing of substrates,” Precis. Eng. 51, 97–102 (2018).
[Crossref]

Pan, R.

R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
[Crossref]

Park, J. O.

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.

Peng, X.

H. Hu, Y. Dai, and X. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18(22), 22973–22981 (2010).
[Crossref]

Y. Dai, F. Shi, X. Peng, and S. Li, “Restraint of mid-spatial frequency error in magneto-rheological finishing (MRF) process by maximum entropy method,” Sci. China, Ser. E: Technol. Sci. 52(10), 3092–3097 (2009).
[Crossref]

Pitschke, E.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Preston, F.

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

Rascher, R.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Riley, D.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Roussel, A.

D. M. Aikens, A. Roussel, and M. Bray, “Derivation of preliminary specifications for transmitted wavefront and surface roughness for large optics used in inertial confinement fusion,” Proc. SPIE 2633, 350–360 (1995).
[Crossref]

Satake, U.

U. Satake, T. Enomoto, Y. Obayashi, and T. Sugihara, “Reducing edge roll-off during polishing of substrates,” Precis. Eng. 51, 97–102 (2018).
[Crossref]

Schinhaerl, M.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Shao, J.

Shi, F.

Y. Dai, F. Shi, X. Peng, and S. Li, “Restraint of mid-spatial frequency error in magneto-rheological finishing (MRF) process by maximum entropy method,” Sci. China, Ser. E: Technol. Sci. 52(10), 3092–3097 (2009).
[Crossref]

Simms, J.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Smith, G.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Smith, L.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Sperber, P.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Stamp, R.

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Stognij, A. I.

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

Stukalov, O. M.

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

Sugihara, T.

U. Satake, T. Enomoto, Y. Obayashi, and T. Sugihara, “Reducing edge roll-off during polishing of substrates,” Precis. Eng. 51, 97–102 (2018).
[Crossref]

Tam, H. Y.

H. Y. Tam, H. B. Cheng, and Z. C. Dong, “Peano-like paths for subaperture polishing of optical aspherical surfaces,” Appl. Opt. 52(15), 3624–3636 (2013).
[Crossref]

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(5), 807–818 (2010).
[Crossref]

Tamkin, J. M.

To, S.

C. F. Cheung, L. B. Kong, L. T. Ho, and S. To, “Modelling and simulation of structure surface generation using computer controlled ultra-precision polishing,” Precis. Eng. 35(4), 574–590 (2011).
[Crossref]

Tricard, M.

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

Tuecksb, R.

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

Walker, D. D.

D. D. Walker, W. Yu, G. Yu, H. Li, W. Zhang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
[Crossref]

C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008).
[Crossref]

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Wan, S.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

Wang, C.

Wang, C. J.

C. J. Wang, C. F. Cheung, L. T. Ho, M. Y. Liu, and W. B. Lee, “A novel multi-jet polishing process and tool for high-efficiency polishing,” Int. J. Mach. Tool Manufact. 115, 60–73 (2017).
[Crossref]

Wang, H.

J. Hou, D. Liao, and H. Wang, “Development of multi-pitch tool path in computer-controlled optical surfacing processes,” J. Eur. Opt. Soc.-Rapid Publ. 13(1), 22 (2017).
[Crossref]

Wang, T.

Wang, Z.

R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
[Crossref]

C. Wang, Z. Wang, and Q. Xu, “Unicursal random maze tool path for computer-controlled optical surfacing,” Appl. Opt. 54(34), 10128–10136 (2015).
[Crossref]

Wei, C.

Wei, S.

R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
[Crossref]

Wei, X.

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

Wu, J.

Wu, W.

Xu, M.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

Xu, Q.

Xu, W.

Xu, X.

Y. Xu, J. Lu, X. Xu, C. C. A. Chen, and Y. Lin, “Study on high efficient sapphire wafer processing by coupling SG-mechanical polishing and GLA-CMP,” Int. J. Mach. Tool Manufact. 130-131, 12–19 (2018).
[Crossref]

Xu, Y.

Y. Xu, J. Lu, X. Xu, C. C. A. Chen, and Y. Lin, “Study on high efficient sapphire wafer processing by coupling SG-mechanical polishing and GLA-CMP,” Int. J. Mach. Tool Manufact. 130-131, 12–19 (2018).
[Crossref]

Yang, H.

Yu, G.

Yu, W.

Zhang, C.

R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
[Crossref]

Zhang, H.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

J. Wu, Z. Lu, H. Zhang, and T. Wang, “Dwell time algorithm in ion beam figuring,” Appl. Opt. 48(20), 3930–3937 (2009).
[Crossref]

Zhang, S.

Zhang, W.

Zhang, X.

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

Zhong, B.

R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
[Crossref]

Zunkea, R.

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

Appl. Opt. (9)

J. Wu, Z. Lu, H. Zhang, and T. Wang, “Dwell time algorithm in ion beam figuring,” Appl. Opt. 48(20), 3930–3937 (2009).
[Crossref]

M. Chunlin, J. C. Lambropoulos, and S. D. Jacobs, “Process parameter effects on material removal in magnetorheological finishing of borosilicate glass,” Appl. Opt. 49(10), 1951–1963 (2010).
[Crossref]

J. M. Tamkin, W. J. Dallas, and T. D. Milster, “Theory of point-spread function artifacts due to structured mid-spatial frequency surface errors,” Appl. Opt. 49(25), 4814–4824 (2010).
[Crossref]

H. Y. Tam, H. B. Cheng, and Z. C. Dong, “Peano-like paths for subaperture polishing of optical aspherical surfaces,” Appl. Opt. 52(15), 3624–3636 (2013).
[Crossref]

C. Wang, Z. Wang, and Q. Xu, “Unicursal random maze tool path for computer-controlled optical surfacing,” Appl. Opt. 54(34), 10128–10136 (2015).
[Crossref]

T. Wang, H. Cheng, W. Zhang, H. Yang, and W. Wu, “Restraint of path effect on optical surface in magnetorheological jet polishing,” Appl. Opt. 55(4), 935–942 (2016).
[Crossref]

D. D. Walker, W. Yu, G. Yu, H. Li, W. Zhang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
[Crossref]

X. Li, C. Wei, S. Zhang, W. Xu, and J. Shao, “Theoretical and experimental comparisons of the smoothing effects for different multi-layer polishing tools during computer-controlled optical surfacing,” Appl. Opt. 58(16), 4406–4413 (2019).
[Crossref]

R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16(1), 218–224 (1977).
[Crossref]

Int. J. Mach. Tool Manufact. (5)

Y. Xu, J. Lu, X. Xu, C. C. A. Chen, and Y. Lin, “Study on high efficient sapphire wafer processing by coupling SG-mechanical polishing and GLA-CMP,” Int. J. Mach. Tool Manufact. 130-131, 12–19 (2018).
[Crossref]

G. Junkang, A. Beaucamp, and S. Ibaraki, “Virtual pivot alignment method and its influence to profile error in bonnet polishing,” Int. J. Mach. Tool Manufact. 122, 18–31 (2017).
[Crossref]

R. Pan, B. Zhong, D. Chen, Z. Wang, J. Fan, C. Zhang, and S. Wei, “Modification of tool influence function of bonnet polishing based on interfacial friction coefficient,” Int. J. Mach. Tool Manufact. 124, 43–52 (2018).
[Crossref]

C. J. Wang, C. F. Cheung, L. T. Ho, M. Y. Liu, and W. B. Lee, “A novel multi-jet polishing process and tool for high-efficiency polishing,” Int. J. Mach. Tool Manufact. 115, 60–73 (2017).
[Crossref]

M. Das, V. Jain, and P. Ghoshdastidar, “Fluid flow analysis of magnetorheological abrasive flow finishing (MRAFF) process,” Int. J. Mach. Tool Manufact. 48(3-4), 415–426 (2008).
[Crossref]

Int. J. Mod. Phys. B (1)

W. I. Kordonski and S. D. Jacobs, “Magnetorheological finishing,” Int. J. Mod. Phys. B 10(23n24), 2837–2848 (1996).
[Crossref]

J. Eur. Opt. Soc.-Rapid Publ. (1)

J. Hou, D. Liao, and H. Wang, “Development of multi-pitch tool path in computer-controlled optical surfacing processes,” J. Eur. Opt. Soc.-Rapid Publ. 13(1), 22 (2017).
[Crossref]

J. Mater. Process. Technol. (1)

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(5), 807–818 (2010).
[Crossref]

J. Soc. Glass Technol. (1)

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

Opt. Express (2)

Precis. Eng. (5)

S. Wan, X. Zhang, H. Zhang, M. Xu, and X. Jiang, “Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces,” Precis. Eng. 51, 415–425 (2018).
[Crossref]

U. Satake, T. Enomoto, Y. Obayashi, and T. Sugihara, “Reducing edge roll-off during polishing of substrates,” Precis. Eng. 51, 97–102 (2018).
[Crossref]

F. Klockea, C. Brecherb, R. Zunkea, and R. Tuecksb, “Corrective polishing of complex ceramics geometries,” Precis. Eng. 35(2), 258–261 (2011).
[Crossref]

C. F. Cheung, L. B. Kong, L. T. Ho, and S. To, “Modelling and simulation of structure surface generation using computer controlled ultra-precision polishing,” Precis. Eng. 35(4), 574–590 (2011).
[Crossref]

M. Schinhaerl, R. Rascher, R. Stamp, L. Smith, G. Smith, P. Sperber, and E. Pitschke, “Utilisation of time-variant influence functions in the computer controlled polishing,” Precis. Eng. 32(1), 47–54 (2008).
[Crossref]

Proc. SPIE (3)

M. Tricard, P. Dumas, and G. Forbes, “Subaperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[Crossref]

D. D. Walker, A. Beaucamp, V. Doubrovski, C. Dunn, R. Freeman, G. McCavana, R. Morton, D. Riley, J. Simms, and X. Wei, “New results extending the precessions process to smoothing ground aspheres and producing freeform parts,” Proc. SPIE 5869, 58690E (2005).
[Crossref]

D. M. Aikens, A. Roussel, and M. Bray, “Derivation of preliminary specifications for transmitted wavefront and surface roughness for large optics used in inertial confinement fusion,” Proc. SPIE 2633, 350–360 (1995).
[Crossref]

Sci. China, Ser. E: Technol. Sci. (1)

Y. Dai, F. Shi, X. Peng, and S. Li, “Restraint of mid-spatial frequency error in magneto-rheological finishing (MRF) process by maximum entropy method,” Sci. China, Ser. E: Technol. Sci. 52(10), 3092–3097 (2009).
[Crossref]

Tech. Phys. Lett. (1)

A. I. Stognij, N. N. Novitskii, and O. M. Stukalov, “Nanoscale ion beam polishing of optical materials,” Tech. Phys. Lett. 28(1), 17–20 (2002).
[Crossref]

Other (1)

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.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1.
Fig. 1. The diagram of the sampling points distribution and the TIF measurement.
Fig. 2.
Fig. 2. Shortages of traditional calculation methods.
Fig. 3.
Fig. 3. Flow chart of the PPC analysis and the schematic diagram of the dual rotation tool.
Fig. 4.
Fig. 4. The shapes of the TIFs and the paths in simulation.
Fig. 5.
Fig. 5. Simulation results based on the PPC method.
Fig. 6.
Fig. 6. The PSD curve of the PPC method simulation results.
Fig. 7.
Fig. 7. The Fourier spectra of different paths.
Fig. 8.
Fig. 8. The Fourier spectra of the TIFs and the orbital circle path.
Fig. 9.
Fig. 9. Simulation results of No. 1-5 based on the PPC method.
Fig. 10.
Fig. 10. Simulation results of No.6-8 based on the PPC method.
Fig. 11.
Fig. 11. Simulation results of No. 6-8 based on the PPC method.
Fig. 12.
Fig. 12. Schematic diagram of the MSF error generated by orbital motion or radial runout.
Fig. 13.
Fig. 13. Dual-rotation polishing machine.
Fig. 14.
Fig. 14. The static TIFs measured by the interferometer.
Fig. 15.
Fig. 15. The comparisons between the experimental results and the modeling results.

Tables (3)

Tables Icon

Table 1. Processing parameters and conditions of the simulation.

Tables Icon

Table 2. Processing parameters and conditions of the simulation.

Tables Icon

Table 3. Experimental conditions of PPC method validation.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

d z ( x , y ) = k P ( x , y ) V ( x , y ) d t
z ( x , y ) = i = 1 n T I F ( i Δ t ) { L ( t ) | ( i 1 ) Δ t t < i Δ t } Δ t = T n = i = 1 n F 1 ( F ( T I F ( i Δ t ) ) × F { L ( t ) | ( i 1 ) Δ t t < i Δ t } )
P ( x , y ) = P 0 ( x , y ) with ( x y ) = ( cos ω 1 t sin ω 1 t sin ω 1 t cos ω 1 t ) ( x y ) V ( x , y ) = | | ( y ω 1 ρ ω 2 sin ( θ 0 + ω 2 t ) x ω 1 + ρ ω 2 cos ( θ 0 + ω 2 t ) ) | | 2
L ( t ) : { x = L 0 j ( x , t ) + ρ cos ( θ 0 + ω 2 t ) y = L 0 j ( y , t ) + ρ sin ( θ 0 + ω 2 t )
e r r N o r m a l ( x , y ) = e r r a c t u a l ( x , y ) / z ( x , y )
z ( x , y ) = i = 1 n T I F ( i Δ t ) L ( t ) { | ( i 1 ) Δ t t < i Δ t } T I F L o r b L 0 = F 1 ( F ( T I F ) × F ( L o r b ) × F ( L 0 ) ) with L o r b : x 2 + y 2 = ρ 2
f > f c , | F ( T I F ; f ) × F ( L o r b ; f ) × F ( L 0 ; f ) | < | F ( e r r i n i t i a l ; f ) |
{ Δ d < S Δ d < ρ , Δ d = v m 2 π ω 1 , when ρ S > 0.1 v m ω 1 < 1 2 π min ( S , ρ ) when ρ S > 0.1
k P ( x , y ) = medfilter ( T I F V ( x , y ) )

Metrics