Abstract

A laser differential confocal radius measurement system with high measurement accuracy is developed for optical manufacturing and metrology. The system uses the zero-crossing point of the differential confocal intensity curve to precisely identify the cat’s-eye and confocal positions and uses an interferometer to measure the distance between these two positions, thereby achieving a high-precision measurement for the radius of curvature. The coaxial measuring optical path reduces the Abbe error, and the air-bearing slider reduces the motion error. The error analysis indicates the theoretical accuracy of the system is up to 2 ppm, and the experiment shows that the system has high focusing sensitivity and is little affected by environmental fluctuations; the measuring repeatability is between 4 and 12 ppm.

© 2012 Optical Society of America

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References

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  1. T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
    [CrossRef]
  2. R. A. Nicolaus and G. Bönsch, “A novel interferometer for dimensional measurement of a silicon sphere,” IEEE Trans. Instrum. Meas. 46, 563–565 (1997).
    [CrossRef]
  3. P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
    [CrossRef]
  4. D. Malacara, “Radius of curvature measurement,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley Interscience, 1991), Chap. 18, pp. 728–735.
  5. L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1967 (1992).
    [CrossRef]
  6. J. Lin, D. Su, F. Yin, and D. Sha, “Research on a high-precision measuring technique for the curvature radius of a concave spherical surface,” Proc. SPIE 2536, 489–497 (1995).
  7. T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
    [CrossRef]
  8. W. Zhao, J. Tan, and L. Qiu, “Confocal bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12, 5013–5021 (2004).
    [CrossRef]
  9. W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal radius measurement,” Opt. Express 18, 2345–2360 (2010).
    [CrossRef]
  10. Z. Jianhuan and Z. Junxian, “Effect of tilt angle of surface to be measured on differential confocal microscope pointing signal,” Acta Opt. Sin. 26, 1363–1366 (2006) (in Chinese).
  11. A. Davies and T. L. Schmitz, “Defining the measurand in radius of curvature measurements,” in Recent Developments in Traceable Dimensional Measurements II, Proceedings of the 18th ASPE Annual Meeting (CD) (American Society for Precision Engineering, 2003).
  12. A. Davies and T. L. Schmitz, “Correcting for stage error motions in radius measurements,” Appl. Opt. 44, 5884–5893 (2005).
    [CrossRef]
  13. T. L. Schmitz, N. Gardner, M. Vaughn, K. Medicus, and A. Davies, “Improving optical bench radius measurements using stage error motion data,” Appl. Opt. 47, 6692–6700 (2008).
    [CrossRef]
  14. X. Ding, R. D. Sun, F. Li, W. Zhao, and W. Liu, “Experimental research on radius of curvature measurement of spherical lenses based on laser differential confocal technique,” Proc. SPIE 8201, 82011W (2011).

2011 (1)

X. Ding, R. D. Sun, F. Li, W. Zhao, and W. Liu, “Experimental research on radius of curvature measurement of spherical lenses based on laser differential confocal technique,” Proc. SPIE 8201, 82011W (2011).

2010 (1)

2009 (1)

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

2008 (1)

2006 (1)

Z. Jianhuan and Z. Junxian, “Effect of tilt angle of surface to be measured on differential confocal microscope pointing signal,” Acta Opt. Sin. 26, 1363–1366 (2006) (in Chinese).

2005 (1)

2004 (1)

2002 (1)

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

2001 (1)

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

1997 (1)

R. A. Nicolaus and G. Bönsch, “A novel interferometer for dimensional measurement of a silicon sphere,” IEEE Trans. Instrum. Meas. 46, 563–565 (1997).
[CrossRef]

1995 (1)

J. Lin, D. Su, F. Yin, and D. Sha, “Research on a high-precision measuring technique for the curvature radius of a concave spherical surface,” Proc. SPIE 2536, 489–497 (1995).

1992 (1)

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1967 (1992).
[CrossRef]

Becker, P.

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Bönsch, G.

R. A. Nicolaus and G. Bönsch, “A novel interferometer for dimensional measurement of a silicon sphere,” IEEE Trans. Instrum. Meas. 46, 563–565 (1997).
[CrossRef]

Davies, A.

T. L. Schmitz, N. Gardner, M. Vaughn, K. Medicus, and A. Davies, “Improving optical bench radius measurements using stage error motion data,” Appl. Opt. 47, 6692–6700 (2008).
[CrossRef]

A. Davies and T. L. Schmitz, “Correcting for stage error motions in radius measurements,” Appl. Opt. 44, 5884–5893 (2005).
[CrossRef]

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

A. Davies and T. L. Schmitz, “Defining the measurand in radius of curvature measurements,” in Recent Developments in Traceable Dimensional Measurements II, Proceedings of the 18th ASPE Annual Meeting (CD) (American Society for Precision Engineering, 2003).

Davies, A. D.

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Ding, X.

X. Ding, R. D. Sun, F. Li, W. Zhao, and W. Liu, “Experimental research on radius of curvature measurement of spherical lenses based on laser differential confocal technique,” Proc. SPIE 8201, 82011W (2011).

Estler, W. T.

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

Evans, C. J.

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Friedrich, H.

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Fujii, K.

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Gardner, N.

Giardini, W.

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Jianhuan, Z.

Z. Jianhuan and Z. Junxian, “Effect of tilt angle of surface to be measured on differential confocal microscope pointing signal,” Acta Opt. Sin. 26, 1363–1366 (2006) (in Chinese).

Junxian, Z.

Z. Jianhuan and Z. Junxian, “Effect of tilt angle of surface to be measured on differential confocal microscope pointing signal,” Acta Opt. Sin. 26, 1363–1366 (2006) (in Chinese).

Li, F.

X. Ding, R. D. Sun, F. Li, W. Zhao, and W. Liu, “Experimental research on radius of curvature measurement of spherical lenses based on laser differential confocal technique,” Proc. SPIE 8201, 82011W (2011).

Lin, J.

J. Lin, D. Su, F. Yin, and D. Sha, “Research on a high-precision measuring technique for the curvature radius of a concave spherical surface,” Proc. SPIE 2536, 489–497 (1995).

Liu, W.

X. Ding, R. D. Sun, F. Li, W. Zhao, and W. Liu, “Experimental research on radius of curvature measurement of spherical lenses based on laser differential confocal technique,” Proc. SPIE 8201, 82011W (2011).

Malacara, D.

D. Malacara, “Radius of curvature measurement,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley Interscience, 1991), Chap. 18, pp. 728–735.

Mana, G.

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Medicus, K.

Nicolaus, R. A.

R. A. Nicolaus and G. Bönsch, “A novel interferometer for dimensional measurement of a silicon sphere,” IEEE Trans. Instrum. Meas. 46, 563–565 (1997).
[CrossRef]

Picard, A.

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Pohl, H. J.

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Qiu, L.

Riemann, H.

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Schmitz, T. L.

T. L. Schmitz, N. Gardner, M. Vaughn, K. Medicus, and A. Davies, “Improving optical bench radius measurements using stage error motion data,” Appl. Opt. 47, 6692–6700 (2008).
[CrossRef]

A. Davies and T. L. Schmitz, “Correcting for stage error motions in radius measurements,” Appl. Opt. 44, 5884–5893 (2005).
[CrossRef]

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

A. Davies and T. L. Schmitz, “Defining the measurand in radius of curvature measurements,” in Recent Developments in Traceable Dimensional Measurements II, Proceedings of the 18th ASPE Annual Meeting (CD) (American Society for Precision Engineering, 2003).

Selberg, L. A.

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1967 (1992).
[CrossRef]

Sha, D.

W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal radius measurement,” Opt. Express 18, 2345–2360 (2010).
[CrossRef]

J. Lin, D. Su, F. Yin, and D. Sha, “Research on a high-precision measuring technique for the curvature radius of a concave spherical surface,” Proc. SPIE 2536, 489–497 (1995).

Su, D.

J. Lin, D. Su, F. Yin, and D. Sha, “Research on a high-precision measuring technique for the curvature radius of a concave spherical surface,” Proc. SPIE 2536, 489–497 (1995).

Sun, R.

Sun, R. D.

X. Ding, R. D. Sun, F. Li, W. Zhao, and W. Liu, “Experimental research on radius of curvature measurement of spherical lenses based on laser differential confocal technique,” Proc. SPIE 8201, 82011W (2011).

Tan, J.

Valkiers, S.

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Vaughn, M.

Yin, F.

J. Lin, D. Su, F. Yin, and D. Sha, “Research on a high-precision measuring technique for the curvature radius of a concave spherical surface,” Proc. SPIE 2536, 489–497 (1995).

Zhao, W.

X. Ding, R. D. Sun, F. Li, W. Zhao, and W. Liu, “Experimental research on radius of curvature measurement of spherical lenses based on laser differential confocal technique,” Proc. SPIE 8201, 82011W (2011).

W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal radius measurement,” Opt. Express 18, 2345–2360 (2010).
[CrossRef]

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

Acta Opt. Sin. (1)

Z. Jianhuan and Z. Junxian, “Effect of tilt angle of surface to be measured on differential confocal microscope pointing signal,” Acta Opt. Sin. 26, 1363–1366 (2006) (in Chinese).

Appl. Opt. (2)

CIRP Ann. (1)

T. L. Schmitz, C. J. Evans, A. Davies, and W. T. Estler, “Displacement uncertainty in interferometric radius measurements,” CIRP Ann. 51, 451–454 (2002).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

R. A. Nicolaus and G. Bönsch, “A novel interferometer for dimensional measurement of a silicon sphere,” IEEE Trans. Instrum. Meas. 46, 563–565 (1997).
[CrossRef]

Meas. Sci. Technol. (1)

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H. J. Pohl, H. Riemann, and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 092002 (2009).
[CrossRef]

Opt. Eng. (1)

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1967 (1992).
[CrossRef]

Opt. Express (2)

Proc. SPIE (3)

X. Ding, R. D. Sun, F. Li, W. Zhao, and W. Liu, “Experimental research on radius of curvature measurement of spherical lenses based on laser differential confocal technique,” Proc. SPIE 8201, 82011W (2011).

J. Lin, D. Su, F. Yin, and D. Sha, “Research on a high-precision measuring technique for the curvature radius of a concave spherical surface,” Proc. SPIE 2536, 489–497 (1995).

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Other (2)

A. Davies and T. L. Schmitz, “Defining the measurand in radius of curvature measurements,” in Recent Developments in Traceable Dimensional Measurements II, Proceedings of the 18th ASPE Annual Meeting (CD) (American Society for Precision Engineering, 2003).

D. Malacara, “Radius of curvature measurement,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley Interscience, 1991), Chap. 18, pp. 728–735.

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Figures (9)

Fig. 1.
Fig. 1.

Differential confocal radius measurement principle.

Fig. 2.
Fig. 2.

Light path with adjustment bias of the DUT.

Fig. 3.
Fig. 3.

Instrument design of differential confocal radius measurement.

Fig. 4.
Fig. 4.

Light path with different offsets of VPHs.

Fig. 5.
Fig. 5.

Differential confocal radius measurement system.

Fig. 6.
Fig. 6.

Spherical components under test.

Fig. 7.
Fig. 7.

Single measurement result of DUT1.

Fig. 8.
Fig. 8.

Repeatability measurement data.

Fig. 9.
Fig. 9.

Reproducibility measurement data.

Tables (2)

Tables Icon

Table 1. ROC Measurement Range (mm)

Tables Icon

Table 2. Results of Reproducibility Experiments (mm)

Equations (12)

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

I(u,uM)=|201ejρ2(2u+uM)/2ρdρ|2|201ejρ2(2uuM)/2ρdρ|2=(sinc2u+uM4)2(sinc2uuM4)2,
u=π2λ(Df)2z,
M=10.42λπ(fcD)2.
{I(uA,uM)=(sinc2uA+uδ+uM4)2(sinc2uAuM4)2=0I(uB,uM)=(sinc2uB+uδ+uM4)2(sinc2uBuM4)2=0.
uA=uB=uδ/4.
σaxial=r(1cosβ·cosγ).
σaxial=r(1cosγ)=r(1cos0.0005)r×0.12ppm.
σz=1.18λSNR·(D/f)2,
σL=0.5×rppm.
σrσaxial2+2·σz2+σL2.
σrσL2+2·σz2+σaxial2=(0.012)2+2×(0.17)2+(0.05)20.24μm.
σrr=0.241000002ppm.

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