Abstract

To improve the measurement accuracy of the profilometer for large optical surfaces, a new single-step spatial rotation error separation technique (SSEST) is proposed to separate the surface profile error and spindle spatial rotation error, and a novel SSEST-based system for surface profile measurement is developed. In the process of separation, two sets of measured results at the ith measurement circle are obtained before and after the rotation of error separation table, the surface profile error and spatial rotation error of spindle can be determined using discrete Fourier-transform and harmonic analysis. Theoretical analyses and experimental results indicate that SSEST can accurately separate spatial rotation error of spindle from the measured surface profile results within the range of 1–100 upr and improve the accuracy of surface profile measurements.

© 2014 Optical Society of America

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References

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  1. J. Burge, L. Kot, H. Martin, C. Zhao, and T. Zobrist, “Alternate surface measurements for GMT primary mirror segments,” Proc. SPIE 6273, 62732T (2006).
    [CrossRef]
  2. T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
    [CrossRef]
  3. D. J. Whitehouse, “Measurement techniques,” in Handbook of Surface and Nanometrology, 2nd ed. (Taylor & Francis, 2011), pp. 257–385.
  4. P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing-arm optical coordinate measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51, 043601 (2012).
    [CrossRef]
  5. P. Su, J. H. Burge, and R. E. Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Opt. 49, 21–31 (2010).
    [CrossRef]
  6. R. Grejda, E. Marsh, and R. Vallance, “Techniques for calibrating spindles with nanometer error motion,” Precis. Eng. 29, 113–123 (2005).
    [CrossRef]
  7. A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry-traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, 2006), pp. 101–105.
  8. H. Jing, C. King, and D. Walker, “Measurement of influence function using swing arm profilometer and laser tracker,” Opt. Express 18, 5271–5281 (2010).
    [CrossRef]
  9. H. Jing, C. King, and D. Walker, “Simulation and validation of a prototype swing arm profilometer for measuring extremely large telescope mirror-segments,” Opt. Express 18, 2036–2048 (2010).
    [CrossRef]
  10. R. Henselmans, L. Cacace, G. Kramer, P. Rosielle, and M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35, 607–624 (2011).
    [CrossRef]
  11. “Taylor Hobson PGI Dimension Technical reference brochure” (Taylor Hobson Ltd, 2013), retrieved http://www.taylor-hobson.com/products/10/107.html .
  12. D. Chetwynd and G. Siddall, “Improving the accuracy of roundness measurement,” J. Phys. E 9, 537–544 (1976).
    [CrossRef]
  13. W. Zhao, Z. Xue, J. Tan, and Z. Wang, “SSEST: a new approach to higher accuracy cylindricity measuring instrument,” Int. J. Mach. Tools Manuf. 46, 1869–1878 (2006).
    [CrossRef]
  14. W. Zhao, J. Tan, Z. Xue, and S. Fu, “SEST: a new error separation technique for ultra-high precision roundness measurement,” Meas. Sci. Technol. 16, 833–841 (2005).
    [CrossRef]
  15. S. Zhang, S. To, C. Cheung, and H. Wang, “Dynamic characteristics of an aerostatic bearing spindle and its influence on surface topography in ultra-precision diamond turning,” Int. J. Mach. Tools Manuf. 62, 1–12 (2012).
    [CrossRef]
  16. W. Zhao, J. B. Tan, Z. Xue, and Z. Feng, “A high precision circuit based on digital techniques for roundness measurement,” Key Eng. Mater. 295, 271–276 (2005).
    [CrossRef]
  17. W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12, 5013–5021 (2004).
    [CrossRef]
  18. W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
    [CrossRef]

2013 (1)

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

2012 (2)

S. Zhang, S. To, C. Cheung, and H. Wang, “Dynamic characteristics of an aerostatic bearing spindle and its influence on surface topography in ultra-precision diamond turning,” Int. J. Mach. Tools Manuf. 62, 1–12 (2012).
[CrossRef]

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing-arm optical coordinate measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51, 043601 (2012).
[CrossRef]

2011 (1)

R. Henselmans, L. Cacace, G. Kramer, P. Rosielle, and M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35, 607–624 (2011).
[CrossRef]

2010 (3)

2006 (2)

J. Burge, L. Kot, H. Martin, C. Zhao, and T. Zobrist, “Alternate surface measurements for GMT primary mirror segments,” Proc. SPIE 6273, 62732T (2006).
[CrossRef]

W. Zhao, Z. Xue, J. Tan, and Z. Wang, “SSEST: a new approach to higher accuracy cylindricity measuring instrument,” Int. J. Mach. Tools Manuf. 46, 1869–1878 (2006).
[CrossRef]

2005 (3)

W. Zhao, J. Tan, Z. Xue, and S. Fu, “SEST: a new error separation technique for ultra-high precision roundness measurement,” Meas. Sci. Technol. 16, 833–841 (2005).
[CrossRef]

W. Zhao, J. B. Tan, Z. Xue, and Z. Feng, “A high precision circuit based on digital techniques for roundness measurement,” Key Eng. Mater. 295, 271–276 (2005).
[CrossRef]

R. Grejda, E. Marsh, and R. Vallance, “Techniques for calibrating spindles with nanometer error motion,” Precis. Eng. 29, 113–123 (2005).
[CrossRef]

2004 (1)

2002 (1)

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

1976 (1)

D. Chetwynd and G. Siddall, “Improving the accuracy of roundness measurement,” J. Phys. E 9, 537–544 (1976).
[CrossRef]

Andersen, T.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

Ardeberg, A.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

Beckers, J.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

Burge, J.

J. Burge, L. Kot, H. Martin, C. Zhao, and T. Zobrist, “Alternate surface measurements for GMT primary mirror segments,” Proc. SPIE 6273, 62732T (2006).
[CrossRef]

Burge, J. H.

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing-arm optical coordinate measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51, 043601 (2012).
[CrossRef]

P. Su, J. H. Burge, and R. E. Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Opt. 49, 21–31 (2010).
[CrossRef]

Cacace, L.

R. Henselmans, L. Cacace, G. Kramer, P. Rosielle, and M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35, 607–624 (2011).
[CrossRef]

Callender, M.

A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry-traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, 2006), pp. 101–105.

Chetwynd, D.

D. Chetwynd and G. Siddall, “Improving the accuracy of roundness measurement,” J. Phys. E 9, 537–544 (1976).
[CrossRef]

Cheung, C.

S. Zhang, S. To, C. Cheung, and H. Wang, “Dynamic characteristics of an aerostatic bearing spindle and its influence on surface topography in ultra-precision diamond turning,” Int. J. Mach. Tools Manuf. 62, 1–12 (2012).
[CrossRef]

Efstathiou, A.

A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry-traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, 2006), pp. 101–105.

Feng, Z.

W. Zhao, J. B. Tan, Z. Xue, and Z. Feng, “A high precision circuit based on digital techniques for roundness measurement,” Key Eng. Mater. 295, 271–276 (2005).
[CrossRef]

Fu, S.

W. Zhao, J. Tan, Z. Xue, and S. Fu, “SEST: a new error separation technique for ultra-high precision roundness measurement,” Meas. Sci. Technol. 16, 833–841 (2005).
[CrossRef]

Gao, D.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

Gee, A.

A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry-traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, 2006), pp. 101–105.

Goncharova, A.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

Grejda, R.

R. Grejda, E. Marsh, and R. Vallance, “Techniques for calibrating spindles with nanometer error motion,” Precis. Eng. 29, 113–123 (2005).
[CrossRef]

Guo, J.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

Henselmans, R.

R. Henselmans, L. Cacace, G. Kramer, P. Rosielle, and M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35, 607–624 (2011).
[CrossRef]

Jing, H.

King, C.

Kot, L.

J. Burge, L. Kot, H. Martin, C. Zhao, and T. Zobrist, “Alternate surface measurements for GMT primary mirror segments,” Proc. SPIE 6273, 62732T (2006).
[CrossRef]

Kramer, G.

R. Henselmans, L. Cacace, G. Kramer, P. Rosielle, and M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35, 607–624 (2011).
[CrossRef]

Lewis, A.

A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry-traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, 2006), pp. 101–105.

Marsh, E.

R. Grejda, E. Marsh, and R. Vallance, “Techniques for calibrating spindles with nanometer error motion,” Precis. Eng. 29, 113–123 (2005).
[CrossRef]

Martin, H.

J. Burge, L. Kot, H. Martin, C. Zhao, and T. Zobrist, “Alternate surface measurements for GMT primary mirror segments,” Proc. SPIE 6273, 62732T (2006).
[CrossRef]

Meng, J.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

Oh, C. J.

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing-arm optical coordinate measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51, 043601 (2012).
[CrossRef]

Oldfield, S.

A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry-traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, 2006), pp. 101–105.

Owner-Petersen, M.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

Parks, R. E.

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing-arm optical coordinate measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51, 043601 (2012).
[CrossRef]

P. Su, J. H. Burge, and R. E. Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Opt. 49, 21–31 (2010).
[CrossRef]

Qiu, L.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12, 5013–5021 (2004).
[CrossRef]

Riewaldt, H.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

Rosielle, P.

R. Henselmans, L. Cacace, G. Kramer, P. Rosielle, and M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35, 607–624 (2011).
[CrossRef]

Siddall, G.

D. Chetwynd and G. Siddall, “Improving the accuracy of roundness measurement,” J. Phys. E 9, 537–544 (1976).
[CrossRef]

Snel, R.

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

Steinbuch, M.

R. Henselmans, L. Cacace, G. Kramer, P. Rosielle, and M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35, 607–624 (2011).
[CrossRef]

Su, P.

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing-arm optical coordinate measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51, 043601 (2012).
[CrossRef]

P. Su, J. H. Burge, and R. E. Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Opt. 49, 21–31 (2010).
[CrossRef]

Tan, J.

W. Zhao, Z. Xue, J. Tan, and Z. Wang, “SSEST: a new approach to higher accuracy cylindricity measuring instrument,” Int. J. Mach. Tools Manuf. 46, 1869–1878 (2006).
[CrossRef]

W. Zhao, J. Tan, Z. Xue, and S. Fu, “SEST: a new error separation technique for ultra-high precision roundness measurement,” Meas. Sci. Technol. 16, 833–841 (2005).
[CrossRef]

W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12, 5013–5021 (2004).
[CrossRef]

Tan, J. B.

W. Zhao, J. B. Tan, Z. Xue, and Z. Feng, “A high precision circuit based on digital techniques for roundness measurement,” Key Eng. Mater. 295, 271–276 (2005).
[CrossRef]

To, S.

S. Zhang, S. To, C. Cheung, and H. Wang, “Dynamic characteristics of an aerostatic bearing spindle and its influence on surface topography in ultra-precision diamond turning,” Int. J. Mach. Tools Manuf. 62, 1–12 (2012).
[CrossRef]

Vallance, R.

R. Grejda, E. Marsh, and R. Vallance, “Techniques for calibrating spindles with nanometer error motion,” Precis. Eng. 29, 113–123 (2005).
[CrossRef]

Walker, D.

H. Jing, C. King, and D. Walker, “Simulation and validation of a prototype swing arm profilometer for measuring extremely large telescope mirror-segments,” Opt. Express 18, 2036–2048 (2010).
[CrossRef]

H. Jing, C. King, and D. Walker, “Measurement of influence function using swing arm profilometer and laser tracker,” Opt. Express 18, 5271–5281 (2010).
[CrossRef]

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry-traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, 2006), pp. 101–105.

Wang, H.

S. Zhang, S. To, C. Cheung, and H. Wang, “Dynamic characteristics of an aerostatic bearing spindle and its influence on surface topography in ultra-precision diamond turning,” Int. J. Mach. Tools Manuf. 62, 1–12 (2012).
[CrossRef]

Wang, Y.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing-arm optical coordinate measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51, 043601 (2012).
[CrossRef]

Wang, Z.

W. Zhao, Z. Xue, J. Tan, and Z. Wang, “SSEST: a new approach to higher accuracy cylindricity measuring instrument,” Int. J. Mach. Tools Manuf. 46, 1869–1878 (2006).
[CrossRef]

Whitehouse, D. J.

D. J. Whitehouse, “Measurement techniques,” in Handbook of Surface and Nanometrology, 2nd ed. (Taylor & Francis, 2011), pp. 257–385.

Xue, Z.

W. Zhao, Z. Xue, J. Tan, and Z. Wang, “SSEST: a new approach to higher accuracy cylindricity measuring instrument,” Int. J. Mach. Tools Manuf. 46, 1869–1878 (2006).
[CrossRef]

W. Zhao, J. B. Tan, Z. Xue, and Z. Feng, “A high precision circuit based on digital techniques for roundness measurement,” Key Eng. Mater. 295, 271–276 (2005).
[CrossRef]

W. Zhao, J. Tan, Z. Xue, and S. Fu, “SEST: a new error separation technique for ultra-high precision roundness measurement,” Meas. Sci. Technol. 16, 833–841 (2005).
[CrossRef]

Zhang, S.

S. Zhang, S. To, C. Cheung, and H. Wang, “Dynamic characteristics of an aerostatic bearing spindle and its influence on surface topography in ultra-precision diamond turning,” Int. J. Mach. Tools Manuf. 62, 1–12 (2012).
[CrossRef]

Zhao, C.

J. Burge, L. Kot, H. Martin, C. Zhao, and T. Zobrist, “Alternate surface measurements for GMT primary mirror segments,” Proc. SPIE 6273, 62732T (2006).
[CrossRef]

Zhao, W.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

W. Zhao, Z. Xue, J. Tan, and Z. Wang, “SSEST: a new approach to higher accuracy cylindricity measuring instrument,” Int. J. Mach. Tools Manuf. 46, 1869–1878 (2006).
[CrossRef]

W. Zhao, J. Tan, Z. Xue, and S. Fu, “SEST: a new error separation technique for ultra-high precision roundness measurement,” Meas. Sci. Technol. 16, 833–841 (2005).
[CrossRef]

W. Zhao, J. B. Tan, Z. Xue, and Z. Feng, “A high precision circuit based on digital techniques for roundness measurement,” Key Eng. Mater. 295, 271–276 (2005).
[CrossRef]

W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12, 5013–5021 (2004).
[CrossRef]

Zobrist, T.

J. Burge, L. Kot, H. Martin, C. Zhao, and T. Zobrist, “Alternate surface measurements for GMT primary mirror segments,” Proc. SPIE 6273, 62732T (2006).
[CrossRef]

Appl. Opt. (1)

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

W. Zhao, Z. Xue, J. Tan, and Z. Wang, “SSEST: a new approach to higher accuracy cylindricity measuring instrument,” Int. J. Mach. Tools Manuf. 46, 1869–1878 (2006).
[CrossRef]

S. Zhang, S. To, C. Cheung, and H. Wang, “Dynamic characteristics of an aerostatic bearing spindle and its influence on surface topography in ultra-precision diamond turning,” Int. J. Mach. Tools Manuf. 62, 1–12 (2012).
[CrossRef]

J. Phys. E (1)

D. Chetwynd and G. Siddall, “Improving the accuracy of roundness measurement,” J. Phys. E 9, 537–544 (1976).
[CrossRef]

Key Eng. Mater. (1)

W. Zhao, J. B. Tan, Z. Xue, and Z. Feng, “A high precision circuit based on digital techniques for roundness measurement,” Key Eng. Mater. 295, 271–276 (2005).
[CrossRef]

Meas. Sci. Technol. (1)

W. Zhao, J. Tan, Z. Xue, and S. Fu, “SEST: a new error separation technique for ultra-high precision roundness measurement,” Meas. Sci. Technol. 16, 833–841 (2005).
[CrossRef]

Opt. Commun. (1)

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

Opt. Eng. (1)

P. Su, R. E. Parks, Y. Wang, C. J. Oh, and J. H. Burge, “Swing-arm optical coordinate measuring machine: modal estimation of systematic errors from dual probe shear measurements,” Opt. Eng. 51, 043601 (2012).
[CrossRef]

Opt. Express (3)

Precis. Eng. (2)

R. Grejda, E. Marsh, and R. Vallance, “Techniques for calibrating spindles with nanometer error motion,” Precis. Eng. 29, 113–123 (2005).
[CrossRef]

R. Henselmans, L. Cacace, G. Kramer, P. Rosielle, and M. Steinbuch, “The NANOMEFOS non-contact measurement machine for freeform optics,” Precis. Eng. 35, 607–624 (2011).
[CrossRef]

Proc. SPIE (2)

J. Burge, L. Kot, H. Martin, C. Zhao, and T. Zobrist, “Alternate surface measurements for GMT primary mirror segments,” Proc. SPIE 6273, 62732T (2006).
[CrossRef]

T. Andersen, A. Ardeberg, J. Beckers, A. Goncharova, M. Owner-Petersen, H. Riewaldt, R. Snel, and D. Walker, “The Euro50 extremely large telescope,” Proc. SPIE 4840, 214–225 (2002).
[CrossRef]

Other (3)

D. J. Whitehouse, “Measurement techniques,” in Handbook of Surface and Nanometrology, 2nd ed. (Taylor & Francis, 2011), pp. 257–385.

“Taylor Hobson PGI Dimension Technical reference brochure” (Taylor Hobson Ltd, 2013), retrieved http://www.taylor-hobson.com/products/10/107.html .

A. Lewis, S. Oldfield, M. Callender, A. Efstathiou, A. Gee, C. King, and D. Walker, “Accurate arm profilometry-traceable metrology for large mirrors,” in Proceedings of Simposio de Metrología (Academic, 2006), pp. 101–105.

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Figures (19)

Fig. 1.
Fig. 1.

Schematic of the developed SSEST-based system.

Fig. 2.
Fig. 2.

Principle of SSEST.

Fig. 3.
Fig. 3.

Relationship between P(k) and k.

Fig. 4.
Fig. 4.

Relationship between M(k) and k.

Fig. 5.
Fig. 5.

Curves of generated data sets {Pi(n)} and {Vi(n)}.

Fig. 6.
Fig. 6.

Curve of data set {Qi(n)} using SSEST.

Fig. 7.
Fig. 7.

Curve of data set {Ui(n)} using SSEST.

Fig. 8.
Fig. 8.

Curve of data set {ΔPi(n)}.

Fig. 9.
Fig. 9.

Curve of data set {ΔVi(n)}.

Fig. 10.
Fig. 10.

Curves of measured workpiece data sets {Pi(n)}.

Fig. 11.
Fig. 11.

Curves of measured workpiece data sets {Vi(n)}.

Fig. 12.
Fig. 12.

Curves of measured workpiece data sets {Pi(n)} in 2–100 upr.

Fig. 13.
Fig. 13.

Curves of measured workpiece data sets {Vi(n)} in 2–100 upr.

Fig. 14.
Fig. 14.

Curves of separated workpiece data sets {Qi(n)} and Δα=0.01°.

Fig. 15.
Fig. 15.

Curves of separated workpiece data sets {Ui(n)} and Δα=0.01°.

Fig. 16.
Fig. 16.

Curve of separated data set Q3(n) in 2–100 upr.

Fig. 17.
Fig. 17.

Curve of separated data set U3(n) in 2–100 upr.

Fig. 18.
Fig. 18.

Curves of data sets {P1(n)} and {Q1(n)} using SSEST.

Fig. 19.
Fig. 19.

Curve of {ΔP1(n)} using SSEST.

Equations (28)

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Sai(θ)=Pi(θ)+Vi(θ).
Pi(θ)=P0+k=1(aikcoskθ+biksinkθ)
Vi(θ)=V0+k=1(cikcoskθ+diksinkθ),
Sbi(θ)=Pi(θ+α)+Vi(θ).
Pi(θ+α)=P0+k=1[aikcosk(θ+α)+biksink(θ+α)]=P0+k=1[(aikcoskα+biksinkα)coskθ+(bikcoskαaiksinkα)sinkθ].
Ri(θ)=Sai(θ)Sbi(θ)=Pi(θ)Pi(θ+α)=P0+k=1S1[(aik(1coskα)biksinkα)coskθ+(aiksinkα+bik(1coskα))sinkθ],
Ri(n)=P0+k=1S1[(aik(1coskα)biksinkα)cos(2nπkN)+(aiksinkα+bik(1coskα))sin(2nπkN)],
Ri(n)=r0+k=1S1[eikcos(2nπk/N)+fiksin(2nπk/N)],
{eik=aik(1coskα)biksinkαfik=aiksinkα+bik(1coskα).
{aik=12eik+sinkα2(1coskα)fikbik=sinkα2(1coskα)eik+12fik.
Pi(n)=P0+k=1[(12eik+sinkα2(1coskα)fik)cos(2nπkN)+(sinkα2(1coskα)eik+12fik)sin(2nπkN)].
Vi(n)=Sai(n)Pi(n).
Pi(n)=k=1S1[aikcos(2nπkN)+biksin(2nπkN)].
Sai(n)=S02+k=1S1[hikcos(2nπkN)+liksin(2nπkN)],
Sai(n)=Sai(n)S0.
etotal=Max{Pi(n)}Min{Pi(n)}.
Cik(n)=[aikcos(2nπkN)+biksin(2nπkN)],
P(k)=sinkα2(1coskα).
α=9×360°/10243.164°.
{Δak=k2fk(coskα1coskαsin2kα(1coskα)2)ΔαΔbk=k2ek(coskα1coskαsin2kα(1coskα)2)Δα.
M(k)=k2(coskα1coskαsin2kα(1coskα)2).
Sai(n)=Pi(n)+Vi(n),(i=1,2,,M;n=0,1,N1).
Sbi(n)=Pi(n+n1)+Vi(n),(i=1,2,,M;n=0,1,N1).
ΔPi(n)=Qi(n)Pi(n),(i=1,2,,M;n=0,1,N1).
RMS(Pi)={[n=1N(Qi(n)Pi(n))2]/N}1/2.
δ(Pi)=|[ΔPi(n)]Max[ΔPi(n)]Min||[Pi(n)]Max[Pi(n)]Min|×100%.
Pi(n)=cos[2(2nπ1024)]+cos[3(2nπ1024)]+0.1cos[5(2nπ1024)]+0.1cos[10(2nπ1024)]+cos[13(2nπ1024)]+cos[15(2nπ1024)]+cos[25(2nπ1024)]+0.1cos[43(2nπ1024)]+cos[49(2nπ1024)]+0.1cos[50(2nπ1024)].
Vi(n)=cos[2(2nπ1024)]+cos[3(2nπ1024)]+cos[7(2nπ1024)]+0.1cos[10(2nπ1024)]+cos[15(2nπ1024)]+cos[17(2nπ1024)]+cos[23(2nπ1024)]+0.1cos[30(2nπ1024)]+0.1cos[41(2nπ1024)]+cos[50(2nπ1024)]

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