Abstract

Optical profilometers such as scanning white light interferometers and confocal microscopes provide high-resolution measurements and are widely utilized in many fields for measuring surface topography. Slope-dependent systematic errors can be present in the measurement and can be the same order of magnitude as features on the surface to be measured. We propose a self-calibration technique, the random ball test (RBT), for calibrating slope-dependent errors of such instruments. The calibration result can be used to compensate future measurements of similar spherical geometries such as profiles of refractive microlenses. A simulation study validates the approach and shows that the RBT is effective in practical limits. We demonstrate the calibration on a 50× confocal microscope and find a surface slope-dependent bias that increases monotonically with the magnitude of the surface slope and is as large as 800nm at a surface slope of 12°. The uncertainty of the calibration is smaller than the observed measurement bias and is dominated by residual random noise. Effects such as drift and ball radius uncertainty were investigated to understand their contribution to the calibration uncertainty.

© 2013 Optical Society of America

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References

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  1. X. J. Jiang and D. J. Whitehouse, “Technological shifts in surface metrology,” CIRP Ann. 61, 815–836 (2012).
    [CrossRef]
  2. Olympus LEXT OLS4000 laser scanning confocal microscopy manual.
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    [CrossRef]
  4. R. K. Leach, C. L. Giusca, and J. M. Coupland, “Advances in calibration methods for micro- and nanoscale surfaces,” Proc. SPIE 8430, 84300H (2012).
    [CrossRef]
  5. R. Mandal, K. Polodhi, J. M. Coupland, R. K. Leach, and D. Mansfield, “Applications of linear systems theory to characterize coherence scanning interferometry,” Proc. SPIE 8430, 84300T (2012).
    [CrossRef]
  6. P. de Groot and X. Colonna de Lega, “Interpreting interferometric height measurements using the instrument transfer function,” Zygo Corporation (2005).
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    [CrossRef]
  10. U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibration,” Proc. SPIE 5869, 58690S (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. Metrology Laboratory, Center for Precision Metrology, University of North Carolina, Charlotte.
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  16. K. Creath and J. C. Wyant, “Absolute measurement of surface roughness,” Appl. Opt. 29, 3823–3827 (1990).
    [CrossRef]

2012 (3)

X. J. Jiang and D. J. Whitehouse, “Technological shifts in surface metrology,” CIRP Ann. 61, 815–836 (2012).
[CrossRef]

R. K. Leach, C. L. Giusca, and J. M. Coupland, “Advances in calibration methods for micro- and nanoscale surfaces,” Proc. SPIE 8430, 84300H (2012).
[CrossRef]

R. Mandal, K. Polodhi, J. M. Coupland, R. K. Leach, and D. Mansfield, “Applications of linear systems theory to characterize coherence scanning interferometry,” Proc. SPIE 8430, 84300T (2012).
[CrossRef]

2009 (1)

P. Zhou and J. Burge, “Limits for interferometer calibration using the random ball test,” Proc. SPIE 7426, 74260U (2009).
[CrossRef]

2008 (1)

F. Gao, R. K. Leach, J. Petzing, and J. M. Coupland, “Surface measurement errors using commercial scanning white light interferometers,” Meas. Sci. Technol. 19, 015303 (2008).
[CrossRef]

2006 (1)

N. Gardner and A. Davies, “Self-calibration for microrefractive lens measurements,” Opt. Eng. 45, 033603 (2006).
[CrossRef]

2005 (1)

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibration,” Proc. SPIE 5869, 58690S (2005).
[CrossRef]

1996 (1)

1990 (1)

Burge, J.

P. Zhou and J. Burge, “Limits for interferometer calibration using the random ball test,” Proc. SPIE 7426, 74260U (2009).
[CrossRef]

Carakos, R.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibration,” Proc. SPIE 5869, 58690S (2005).
[CrossRef]

Colonna de Lega, X.

P. de Groot and X. Colonna de Lega, “Interpreting interferometric height measurements using the instrument transfer function,” Zygo Corporation (2005).

Coupland, J. M.

R. K. Leach, C. L. Giusca, and J. M. Coupland, “Advances in calibration methods for micro- and nanoscale surfaces,” Proc. SPIE 8430, 84300H (2012).
[CrossRef]

R. Mandal, K. Polodhi, J. M. Coupland, R. K. Leach, and D. Mansfield, “Applications of linear systems theory to characterize coherence scanning interferometry,” Proc. SPIE 8430, 84300T (2012).
[CrossRef]

F. Gao, R. K. Leach, J. Petzing, and J. M. Coupland, “Surface measurement errors using commercial scanning white light interferometers,” Meas. Sci. Technol. 19, 015303 (2008).
[CrossRef]

Creath, K.

Davies, A.

N. Gardner and A. Davies, “Self-calibration for microrefractive lens measurements,” Opt. Eng. 45, 033603 (2006).
[CrossRef]

Y. Zhou, A. Fard, and A. Davies, “Assessment of instrument drift using a spherical artifact,” Precis. Eng. (to be published).

de Groot, P.

P. de Groot and X. Colonna de Lega, “Interpreting interferometric height measurements using the instrument transfer function,” Zygo Corporation (2005).

Evans, C. J.

C. J. Evans and R. N. Kestner, “Test optic error removal,” Appl. Opt. 35, 1015–1021 (1996).
[CrossRef]

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” poster presented at Optical Fabrication and Testing, Kona, Hawaii (1998).

Fard, A.

Y. Zhou, A. Fard, and A. Davies, “Assessment of instrument drift using a spherical artifact,” Precis. Eng. (to be published).

Flack, D.

D. Flack, Good Practice Guide No. 42—CMM Verification (National Physical Laboratory, 2001).

Forbs, A. B.

A. B. Forbs, “Robust circle and sphere fitting by least squares,” (National Physical Laboratory, 1989).

Gao, F.

F. Gao, R. K. Leach, J. Petzing, and J. M. Coupland, “Surface measurement errors using commercial scanning white light interferometers,” Meas. Sci. Technol. 19, 015303 (2008).
[CrossRef]

Gardner, N.

N. Gardner and A. Davies, “Self-calibration for microrefractive lens measurements,” Opt. Eng. 45, 033603 (2006).
[CrossRef]

Giusca, C. L.

R. K. Leach, C. L. Giusca, and J. M. Coupland, “Advances in calibration methods for micro- and nanoscale surfaces,” Proc. SPIE 8430, 84300H (2012).
[CrossRef]

Griesmann, U.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibration,” Proc. SPIE 5869, 58690S (2005).
[CrossRef]

Jiang, X. J.

X. J. Jiang and D. J. Whitehouse, “Technological shifts in surface metrology,” CIRP Ann. 61, 815–836 (2012).
[CrossRef]

Kestner, R. N.

Leach, R. K.

R. Mandal, K. Polodhi, J. M. Coupland, R. K. Leach, and D. Mansfield, “Applications of linear systems theory to characterize coherence scanning interferometry,” Proc. SPIE 8430, 84300T (2012).
[CrossRef]

R. K. Leach, C. L. Giusca, and J. M. Coupland, “Advances in calibration methods for micro- and nanoscale surfaces,” Proc. SPIE 8430, 84300H (2012).
[CrossRef]

F. Gao, R. K. Leach, J. Petzing, and J. M. Coupland, “Surface measurement errors using commercial scanning white light interferometers,” Meas. Sci. Technol. 19, 015303 (2008).
[CrossRef]

Mandal, R.

R. Mandal, K. Polodhi, J. M. Coupland, R. K. Leach, and D. Mansfield, “Applications of linear systems theory to characterize coherence scanning interferometry,” Proc. SPIE 8430, 84300T (2012).
[CrossRef]

Mansfield, D.

R. Mandal, K. Polodhi, J. M. Coupland, R. K. Leach, and D. Mansfield, “Applications of linear systems theory to characterize coherence scanning interferometry,” Proc. SPIE 8430, 84300T (2012).
[CrossRef]

Parks, R. E.

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” poster presented at Optical Fabrication and Testing, Kona, Hawaii (1998).

Petzing, J.

F. Gao, R. K. Leach, J. Petzing, and J. M. Coupland, “Surface measurement errors using commercial scanning white light interferometers,” Meas. Sci. Technol. 19, 015303 (2008).
[CrossRef]

Polodhi, K.

R. Mandal, K. Polodhi, J. M. Coupland, R. K. Leach, and D. Mansfield, “Applications of linear systems theory to characterize coherence scanning interferometry,” Proc. SPIE 8430, 84300T (2012).
[CrossRef]

Shao, L.

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” poster presented at Optical Fabrication and Testing, Kona, Hawaii (1998).

Soons, J.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibration,” Proc. SPIE 5869, 58690S (2005).
[CrossRef]

Wang, Q.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibration,” Proc. SPIE 5869, 58690S (2005).
[CrossRef]

Whitehouse, D. J.

X. J. Jiang and D. J. Whitehouse, “Technological shifts in surface metrology,” CIRP Ann. 61, 815–836 (2012).
[CrossRef]

Wyant, J. C.

Zhou, P.

P. Zhou and J. Burge, “Limits for interferometer calibration using the random ball test,” Proc. SPIE 7426, 74260U (2009).
[CrossRef]

Zhou, Y.

Y. Zhou, A. Fard, and A. Davies, “Assessment of instrument drift using a spherical artifact,” Precis. Eng. (to be published).

Appl. Opt. (2)

CIRP Ann. (1)

X. J. Jiang and D. J. Whitehouse, “Technological shifts in surface metrology,” CIRP Ann. 61, 815–836 (2012).
[CrossRef]

Meas. Sci. Technol. (1)

F. Gao, R. K. Leach, J. Petzing, and J. M. Coupland, “Surface measurement errors using commercial scanning white light interferometers,” Meas. Sci. Technol. 19, 015303 (2008).
[CrossRef]

Opt. Eng. (1)

N. Gardner and A. Davies, “Self-calibration for microrefractive lens measurements,” Opt. Eng. 45, 033603 (2006).
[CrossRef]

Proc. SPIE (4)

R. K. Leach, C. L. Giusca, and J. M. Coupland, “Advances in calibration methods for micro- and nanoscale surfaces,” Proc. SPIE 8430, 84300H (2012).
[CrossRef]

R. Mandal, K. Polodhi, J. M. Coupland, R. K. Leach, and D. Mansfield, “Applications of linear systems theory to characterize coherence scanning interferometry,” Proc. SPIE 8430, 84300T (2012).
[CrossRef]

P. Zhou and J. Burge, “Limits for interferometer calibration using the random ball test,” Proc. SPIE 7426, 74260U (2009).
[CrossRef]

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibration,” Proc. SPIE 5869, 58690S (2005).
[CrossRef]

Other (7)

Metrology Laboratory, Center for Precision Metrology, University of North Carolina, Charlotte.

Y. Zhou, A. Fard, and A. Davies, “Assessment of instrument drift using a spherical artifact,” Precis. Eng. (to be published).

P. de Groot and X. Colonna de Lega, “Interpreting interferometric height measurements using the instrument transfer function,” Zygo Corporation (2005).

D. Flack, Good Practice Guide No. 42—CMM Verification (National Physical Laboratory, 2001).

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” poster presented at Optical Fabrication and Testing, Kona, Hawaii (1998).

A. B. Forbs, “Robust circle and sphere fitting by least squares,” (National Physical Laboratory, 1989).

Olympus LEXT OLS4000 laser scanning confocal microscopy manual.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the RBT calibration configuration. Upper right, profilometer; lower right, phase shift interferometer (PSI).

Fig. 2.
Fig. 2.

Simulated sphere with base radius of R=0.595mm and a radial RMS error of 100nm. The parameter Δρ is the ball error in the radial direction.

Fig. 3.
Fig. 3.

Two types of ball error spatial distributions. (Left) Ball with a (exaggerated) symmetric ball error distribution. (Right) Ball with an (exaggerated) asymmetric ball error distribution.

Fig. 4.
Fig. 4.

Difference in the best-fit radius to the RBT result compared to the base radius used to generate the ball, for balls with different error distributions.

Fig. 5.
Fig. 5.

Residual RMS of RBT as a function of 1/N; N is the number of measurements.

Fig. 6.
Fig. 6.

RBT calibration result for a LSCM configured with a 50× objective.

Fig. 7.
Fig. 7.

Residual RMS of RBT as a function of 1/N. N is the number of measurements.

Equations (5)

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

W=Wball+εnoise+εbias,
W=Wbase+Wball error+εnoise+εbias.
Wn=Wbase+εbias.
A(θ,ϕ)=l,malmYlm(θ,ϕ)=l,malm2l+14π(lm)!(l+m)!Plm(cosθ)eimϕ,
A(x2+y2+z2)+Bx+Cy+Dz+E=0,

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