Abstract

Freeform surface is promising to be the next generation optics, however it needs high form accuracy for excellent performance. The closed-loop of fabrication-measurement-compensation is necessary for the improvement of the form accuracy. It is difficult to do an off-machine measurement during the freeform machining because the remounting inaccuracy can result in significant form deviations. On the other side, on-machine measurement may hides the systematic errors of the machine because the measuring device is placed in situ on the machine. This study proposes a new compensation strategy based on the combination of on-machine and off-machine measurement. The freeform surface is measured in off-machine mode with nanometric accuracy, and the on-machine probe achieves accurate relative position between the workpiece and machine after remounting. The compensation cutting path is generated according to the calculated relative position and shape errors to avoid employing extra manual adjustment or highly accurate reference-feature fixture. Experimental results verified the effectiveness of the proposed method.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  1. R. K. Kimmel and R. E. Parks, ISO 10110 Optics and Optical Instruments: Preparation of Drawings for Optical Elements and Systems: A User's Guide (Optical Society of America, 2002).
  2. F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
    [Crossref]
  3. P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
    [Crossref]
  4. L. Kong, C. Cheung, S. To, B. Wang, and L. Ho, “A theoretical and experimental investigation of design and slow tool servo machining of freeform progressive addition lenses (PALs) for optometric applications,” Int. J. Adv. Manuf. Technol. 72(1-4), 33–40 (2014).
    [Crossref]
  5. J. W. Duparré and F. C. Wippermann, “Micro-optical artificial compound eyes,” Bioinspir. Biomim. 1(1), R1–R16 (2006).
    [Crossref] [PubMed]
  6. W. Lee, C. Cheung, W. Chiu, and T. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
    [Crossref]
  7. F. Niehaus, S. Huttenhuis, and A. Pisarski, “Fabrication and measurement of freeform surfaces using an integrated machining platform,” in Freeform Optics (OSA, 2013), paper FW1B.
  8. S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
    [Crossref]
  9. W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
    [Crossref]
  10. S. Moriyasu, Y. Yamagata, H. Ohmori, and S. Morita, “Probe type shape measuring sensor, and NC processing equipment and shape measuring method using the sensor,” United States Patent US6539642 B1 (April 1, 2003).
  11. F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
    [Crossref]
  12. H. Ohmori, Y. Watanabe, W. M. Lin, K. Katahira, and T. Suzuki, “An ultraprecision on-machine measurement system,” in Key Engineering Materials, Y. S Gao, S. F. Tse and W. Gao, eds. (Trans Tech Publications, 2005), pp. 375–380.
  13. W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
    [Crossref]
  14. W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
    [Crossref]
  15. S. Reichelt and H. Zappe, “Combined Twyman-Green and Mach-Zehnder interferometer for microlens testing,” Appl. Opt. 44(27), 5786–5792 (2005).
    [Crossref] [PubMed]
  16. G. W. Forbes, “Characterizing the shape of freeform optics,” Opt. Express 20(3), 2483–2499 (2012).
    [Crossref] [PubMed]
  17. F. Fang, Y. Chen, X. Zhang, X. Hu, and G. Zhang, “Nanometric cutting of single crystal silicon surfaces modified by ion implantation,” CIRP Ann.- Manuf. Tech. 60(1), 527–530 (2011).
    [Crossref]
  18. F. Z. Fang, X. D. Zhang, and X. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16(10), 7323–7329 (2008).
    [Crossref] [PubMed]
  19. Z. Dong, H. Cheng, X. Ye, and H.-Y. Tam, “Developing on-machine 3D profile measurement for deterministic fabrication of aspheric mirrors,” Appl. Opt. 53(22), 4997–5007 (2014).
    [Crossref] [PubMed]
  20. X. Zhang, F. Fang, Q. Wu, X. Liu, and H. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67(9-12), 2217–2224 (2013).
    [Crossref]
  21. R. K. Sundaram, A First Course in Optimization Theory (Cambridge University, 1996).

2014 (2)

L. Kong, C. Cheung, S. To, B. Wang, and L. Ho, “A theoretical and experimental investigation of design and slow tool servo machining of freeform progressive addition lenses (PALs) for optometric applications,” Int. J. Adv. Manuf. Technol. 72(1-4), 33–40 (2014).
[Crossref]

Z. Dong, H. Cheng, X. Ye, and H.-Y. Tam, “Developing on-machine 3D profile measurement for deterministic fabrication of aspheric mirrors,” Appl. Opt. 53(22), 4997–5007 (2014).
[Crossref] [PubMed]

2013 (2)

X. Zhang, F. Fang, Q. Wu, X. Liu, and H. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67(9-12), 2217–2224 (2013).
[Crossref]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

2012 (1)

2011 (1)

F. Fang, Y. Chen, X. Zhang, X. Hu, and G. Zhang, “Nanometric cutting of single crystal silicon surfaces modified by ion implantation,” CIRP Ann.- Manuf. Tech. 60(1), 527–530 (2011).
[Crossref]

2010 (3)

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

2008 (1)

2007 (2)

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

2006 (1)

J. W. Duparré and F. C. Wippermann, “Micro-optical artificial compound eyes,” Bioinspir. Biomim. 1(1), R1–R16 (2006).
[Crossref] [PubMed]

2005 (1)

2004 (1)

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

2000 (1)

W. Lee, C. Cheung, W. Chiu, and T. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Alvarez, J. L.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

Aoki, J.

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

Arai, Y.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

Araki, T.

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

Benitez, P.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

Blen, J.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

Chaves, J.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

Chen, F.

F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Chen, Y.

F. Fang, Y. Chen, X. Zhang, X. Hu, and G. Zhang, “Nanometric cutting of single crystal silicon surfaces modified by ion implantation,” CIRP Ann.- Manuf. Tech. 60(1), 527–530 (2011).
[Crossref]

Cheng, H.

Cheung, C.

L. Kong, C. Cheung, S. To, B. Wang, and L. Ho, “A theoretical and experimental investigation of design and slow tool servo machining of freeform progressive addition lenses (PALs) for optometric applications,” Int. J. Adv. Manuf. Technol. 72(1-4), 33–40 (2014).
[Crossref]

W. Lee, C. Cheung, W. Chiu, and T. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Chiu, W.

W. Lee, C. Cheung, W. Chiu, and T. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Damm, C.

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Dong, Z.

Dross, O.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

Duparré, J. W.

J. W. Duparré and F. C. Wippermann, “Micro-optical artificial compound eyes,” Bioinspir. Biomim. 1(1), R1–R16 (2006).
[Crossref] [PubMed]

Evans, C.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

Falicoff, W.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

Fan, Y.

F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Fang, F.

X. Zhang, F. Fang, Q. Wu, X. Liu, and H. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67(9-12), 2217–2224 (2013).
[Crossref]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

F. Fang, Y. Chen, X. Zhang, X. Hu, and G. Zhang, “Nanometric cutting of single crystal silicon surfaces modified by ion implantation,” CIRP Ann.- Manuf. Tech. 60(1), 527–530 (2011).
[Crossref]

Fang, F. Z.

Forbes, G. W.

Gao, H.

X. Zhang, F. Fang, Q. Wu, X. Liu, and H. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67(9-12), 2217–2224 (2013).
[Crossref]

Gao, W.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

Gebhardt, A.

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Hernandez, M.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

Ho, L.

L. Kong, C. Cheung, S. To, B. Wang, and L. Ho, “A theoretical and experimental investigation of design and slow tool servo machining of freeform progressive addition lenses (PALs) for optometric applications,” Int. J. Adv. Manuf. Technol. 72(1-4), 33–40 (2014).
[Crossref]

Holota, W.

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Hu, X.

F. Fang, Y. Chen, X. Zhang, X. Hu, and G. Zhang, “Nanometric cutting of single crystal silicon surfaces modified by ion implantation,” CIRP Ann.- Manuf. Tech. 60(1), 527–530 (2011).
[Crossref]

Hu, X. T.

Huang, H.

F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Hwang, J. H.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

Ju, B.-F.

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

Kiyono, S.

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

Kong, L.

L. Kong, C. Cheung, S. To, B. Wang, and L. Ho, “A theoretical and experimental investigation of design and slow tool servo machining of freeform progressive addition lenses (PALs) for optometric applications,” Int. J. Adv. Manuf. Technol. 72(1-4), 33–40 (2014).
[Crossref]

Lee, J. C.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

Lee, W.

W. Lee, C. Cheung, W. Chiu, and T. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Leung, T.

W. Lee, C. Cheung, W. Chiu, and T. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Liu, X.

X. Zhang, F. Fang, Q. Wu, X. Liu, and H. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67(9-12), 2217–2224 (2013).
[Crossref]

Miñano, J. C.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

Mohedano, R.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

Noh, Y. J.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

Ohmori, H.

F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Park, C. H.

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

Peschel, T.

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Reichelt, S.

Risse, S.

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Scheiding, S.

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Tam, H.-Y.

Tano, M.

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

To, S.

L. Kong, C. Cheung, S. To, B. Wang, and L. Ho, “A theoretical and experimental investigation of design and slow tool servo machining of freeform progressive addition lenses (PALs) for optometric applications,” Int. J. Adv. Manuf. Technol. 72(1-4), 33–40 (2014).
[Crossref]

Tünnermann, A.

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Wang, B.

L. Kong, C. Cheung, S. To, B. Wang, and L. Ho, “A theoretical and experimental investigation of design and slow tool servo machining of freeform progressive addition lenses (PALs) for optometric applications,” Int. J. Adv. Manuf. Technol. 72(1-4), 33–40 (2014).
[Crossref]

Wang, Y.

F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Weckenmann, A.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

Wippermann, F. C.

J. W. Duparré and F. C. Wippermann, “Micro-optical artificial compound eyes,” Bioinspir. Biomim. 1(1), R1–R16 (2006).
[Crossref] [PubMed]

Wu, Q.

X. Zhang, F. Fang, Q. Wu, X. Liu, and H. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67(9-12), 2217–2224 (2013).
[Crossref]

Ye, X.

Yin, S.

F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Zappe, H.

Zhang, G.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

F. Fang, Y. Chen, X. Zhang, X. Hu, and G. Zhang, “Nanometric cutting of single crystal silicon surfaces modified by ion implantation,” CIRP Ann.- Manuf. Tech. 60(1), 527–530 (2011).
[Crossref]

Zhang, X.

X. Zhang, F. Fang, Q. Wu, X. Liu, and H. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67(9-12), 2217–2224 (2013).
[Crossref]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

F. Fang, Y. Chen, X. Zhang, X. Hu, and G. Zhang, “Nanometric cutting of single crystal silicon surfaces modified by ion implantation,” CIRP Ann.- Manuf. Tech. 60(1), 527–530 (2011).
[Crossref]

Zhang, X. D.

Zhu, Y.

F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

Appl. Opt. (2)

Bioinspir. Biomim. (1)

J. W. Duparré and F. C. Wippermann, “Micro-optical artificial compound eyes,” Bioinspir. Biomim. 1(1), R1–R16 (2006).
[Crossref] [PubMed]

CIRP Ann.- Manuf. Tech. (2)

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann.- Manuf. Tech. 62(2), 823–846 (2013).
[Crossref]

F. Fang, Y. Chen, X. Zhang, X. Hu, and G. Zhang, “Nanometric cutting of single crystal silicon surfaces modified by ion implantation,” CIRP Ann.- Manuf. Tech. 60(1), 527–530 (2011).
[Crossref]

Int. J. Adv. Manuf. Technol. (2)

L. Kong, C. Cheung, S. To, B. Wang, and L. Ho, “A theoretical and experimental investigation of design and slow tool servo machining of freeform progressive addition lenses (PALs) for optometric applications,” Int. J. Adv. Manuf. Technol. 72(1-4), 33–40 (2014).
[Crossref]

X. Zhang, F. Fang, Q. Wu, X. Liu, and H. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67(9-12), 2217–2224 (2013).
[Crossref]

Int. J. Mach. Tools Manuf. (2)

W. Gao, J. C. Lee, Y. Arai, Y. J. Noh, J. H. Hwang, and C. H. Park, “Measurement of slide error of an ultra-precision diamond turning machine by using a rotating cylinder workpiece,” Int. J. Mach. Tools Manuf. 50(4), 404–410 (2010).
[Crossref]

F. Chen, S. Yin, H. Huang, H. Ohmori, Y. Wang, Y. Fan, and Y. Zhu, “Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement,” Int. J. Mach. Tools Manuf. 50(5), 480–486 (2010).
[Crossref]

J. Mater. Process. Technol. (1)

W. Lee, C. Cheung, W. Chiu, and T. Leung, “An investigation of residual form error compensation in the ultra-precision machining of aspheric surfaces,” J. Mater. Process. Technol. 99(1-3), 129–134 (2000).
[Crossref]

Opt. Express (2)

Precis. Eng. (2)

W. Gao, M. Tano, T. Araki, S. Kiyono, and C. H. Park, “Measurement and compensation of error motions of a diamond turning machine,” Precis. Eng. 31(3), 310–316 (2007).
[Crossref]

W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precis. Eng. 31(3), 304–309 (2007).
[Crossref]

Proc. SPIE (2)

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 506857 (2004).
[Crossref]

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra-precisely manufactured mirror assemblies with well-defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Other (5)

H. Ohmori, Y. Watanabe, W. M. Lin, K. Katahira, and T. Suzuki, “An ultraprecision on-machine measurement system,” in Key Engineering Materials, Y. S Gao, S. F. Tse and W. Gao, eds. (Trans Tech Publications, 2005), pp. 375–380.

R. K. Kimmel and R. E. Parks, ISO 10110 Optics and Optical Instruments: Preparation of Drawings for Optical Elements and Systems: A User's Guide (Optical Society of America, 2002).

S. Moriyasu, Y. Yamagata, H. Ohmori, and S. Morita, “Probe type shape measuring sensor, and NC processing equipment and shape measuring method using the sensor,” United States Patent US6539642 B1 (April 1, 2003).

F. Niehaus, S. Huttenhuis, and A. Pisarski, “Fabrication and measurement of freeform surfaces using an integrated machining platform,” in Freeform Optics (OSA, 2013), paper FW1B.

R. K. Sundaram, A First Course in Optimization Theory (Cambridge University, 1996).

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Figures (11)

Fig. 1
Fig. 1 Shape deviations caused by the angle errors. (a) Depth map of shape deviation for freeform surface z = sin(kπx)cos(kπy) where k = 0.1 and there are 0.1° errors respectively in roll, pitch and yaw. (b) Deviation change plot of peak to valley (PV) for different k values.
Fig. 2
Fig. 2 Relative position between the remounted workpiece and the reference model measured by on-machine profilometer.
Fig. 3
Fig. 3 Alignment errors by the probe gauge along the cylinder side contour in one adjustment process.
Fig. 4
Fig. 4 Process flow of the proposed method.
Fig. 5
Fig. 5 Matching relation between the measured points and the reference model.
Fig. 6
Fig. 6 Evaluation results of form error by (a) Panasonic UA3P-5 and (b), (c) the proposed optimization method. (b) 3D view and (c) YZ view of evaluated of result.
Fig. 7
Fig. 7 Design and form error of the experimental saddle surface. (a) Depth map for design model and (b) Shape error distribution by off-machine measurement.
Fig. 8
Fig. 8 Experiment setup of fabrication and on-machine measurement.
Fig. 9
Fig. 9 Step measurement results of (a) step signals and (b) step deviation plot.
Fig. 10
Fig. 10 Consistency between the measured profile after remounting and reference model. (a) Measurement data and reference model, and (b) the deviation distribution.
Fig. 11
Fig. 11 Related data for the compensation process. (a) The source and compensated cutting path. (b) Shape error distribution after compensation.

Tables (5)

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Table 1 Transformation Parameters for the Simulated Measured Points

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Table 2 Relative Positions Calculated from the Simulated Measured Points using the Proposed Method.

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Table 3 Remounting Errors for Different Numbers of Sampled Points.

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Table 4 Remounting Errors for Different Errors in Measurement.

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Table 5 Relative Position Calculated from the Measured Points

Equations (3)

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F o b j = min R , T R p i + T q i 2 = min R , T p i q i 2
F c o n = ( r 2 1 + r 2 4 + r 2 7 1 ) 2 + ( r 2 2 + r 2 5 + r 2 8 1 ) 2 + ( r 2 3 + r 2 6 + r 2 9 1 ) 2 + ( r 1 r 2 + r 4 r 5 + r 7 r 8 ) 2 + ( r 1 r 3 + r 4 r 6 + r 7 r 9 ) 2 + ( r 2 r 3 + r 5 r 6 + r 8 r 9 ) 2
F c o n = t 1 2 + t 2 2 + t 3 2

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