Abstract

Lateral optical distortion is present in most optical imaging systems. In coherence scanning interferometry, distortion may cause field-dependent systematic errors in the measurement of surface topography. These errors become critical when high-precision surfaces, e.g. precision optics, are measured. Current calibration and correction methods for distortion require some form of calibration artefact that has a smooth local surface and a grid of high-precision manufactured features. Moreover, to ensure high accuracy and precision of the absolute and relative locations of the features of these artefacts, requires their positions to be determined using a traceable measuring instrument, e.g. a metrological atomic force microscope. Thus, the manufacturing and calibration processes for calibration artefacts are often expensive and complex. In this paper, we demonstrate for the first time the calibration and correction of optical distortion in a coherence scanning interferometer system by using an arbitrary surface that contains some deviations from flat and has some features (possibly just contamination), such that feature detection is possible. By using image processing and a self-calibration technique, a precision of a few nanometres is achieved for the distortion correction. An inexpensive metal surface, e.g. the surface of a coin, or a scratched and defected mirror, which can be easily found in a laboratory or workshop, may be used. The cost of the distortion correction with nanometre level precision is reduced to almost zero if the absolute scale is not required. Although an absolute scale is still needed to make the calibration traceable, the problem of obtaining the traceability is simplified as only a traceable measure of the distance between two arbitrary points is needed. Thus, the total cost of transferring the traceability may also be reduced significantly using the proposed method.

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References

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  1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999), Chap. 5.
  2. A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
    [Crossref]
  3. P. Ekberg and L. Mattsson, “A new 2D self-calibration method with large freedom and high-precision performance for imaging metrology devices,” in Proceedings of the 15th International Conference of the European Society for Precision Engineering and Nanotechnology (Elsevier, 2015), pp. 159–160.
  4. S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
    [Crossref]
  5. P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
    [Crossref]
  6. P. de Groot, Optical Measurement of Surface Topography, R. K. Leach, ed. (Springer, 2011), Chap. 9.
  7. R. Leach, C. Giusca, D. Cox, M. Guttmann, P.-J. Jakobs, and P. Rubert, “Development of low-cost material measures for calibration of the metrological characteristics of surface topography instruments,” Ann. CIRP 64(1), 545–548 (2014).
    [Crossref]
  8. J. Haycocks and K. Jackson, “Traceable calibration of transfer standards for scanning probe microscopy,” Precis. Eng. 29(2), 168–175 (2005).
    [Crossref]
  9. R. K. Leach, C. L. Giusca, and K. Naoi, “Development and characterization of a new instrument for the traceable measurement of areal surface texture,” Meas. Sci. Technol. 20(12), 125102 (2009).
    [Crossref]
  10. P. Ekberg, L. Stiblert, and L. Mattsson, “A new general approach for solving the self-calibration problem on large area 2D ultra-precision coordinate measurement machines,” Meas. Sci. Technol. 25(5), 055001 (2014).
    [Crossref]
  11. C. L. Giusca, R. K. Leach, F. Helary, T. Gutauskas, and L. Nimishakavi, “Calibration of the scales of areal surface topography-measuring instruments: part 1. Measurement noise and residual flatness,” Meas. Sci. Technol. 23(3), 035008 (2012).
    [Crossref]
  12. M. Sutton, J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications, (Springer, 2009).
  13. C. Evans, R. Hocken, and W. Estler, “Self-calibration: reversal, redundancy, error separation, and ‘absolute testing’,” Ann. CIRP 45(2), 617–634 (1996).
    [Crossref]
  14. M. Raugh, “Absolute two-dimensional sub-micron metrology for electron beam lithography – a calibration theory with applications,” Precis. Eng. 7(1), 1–13 (1985).
    [Crossref]

2015 (1)

P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
[Crossref]

2014 (2)

R. Leach, C. Giusca, D. Cox, M. Guttmann, P.-J. Jakobs, and P. Rubert, “Development of low-cost material measures for calibration of the metrological characteristics of surface topography instruments,” Ann. CIRP 64(1), 545–548 (2014).
[Crossref]

P. Ekberg, L. Stiblert, and L. Mattsson, “A new general approach for solving the self-calibration problem on large area 2D ultra-precision coordinate measurement machines,” Meas. Sci. Technol. 25(5), 055001 (2014).
[Crossref]

2013 (1)

A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
[Crossref]

2012 (1)

C. L. Giusca, R. K. Leach, F. Helary, T. Gutauskas, and L. Nimishakavi, “Calibration of the scales of areal surface topography-measuring instruments: part 1. Measurement noise and residual flatness,” Meas. Sci. Technol. 23(3), 035008 (2012).
[Crossref]

2009 (1)

R. K. Leach, C. L. Giusca, and K. Naoi, “Development and characterization of a new instrument for the traceable measurement of areal surface texture,” Meas. Sci. Technol. 20(12), 125102 (2009).
[Crossref]

2006 (1)

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

2005 (1)

J. Haycocks and K. Jackson, “Traceable calibration of transfer standards for scanning probe microscopy,” Precis. Eng. 29(2), 168–175 (2005).
[Crossref]

1996 (1)

C. Evans, R. Hocken, and W. Estler, “Self-calibration: reversal, redundancy, error separation, and ‘absolute testing’,” Ann. CIRP 45(2), 617–634 (1996).
[Crossref]

1985 (1)

M. Raugh, “Absolute two-dimensional sub-micron metrology for electron beam lithography – a calibration theory with applications,” Precis. Eng. 7(1), 1–13 (1985).
[Crossref]

Coupland, J.

A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
[Crossref]

Cox, D.

R. Leach, C. Giusca, D. Cox, M. Guttmann, P.-J. Jakobs, and P. Rubert, “Development of low-cost material measures for calibration of the metrological characteristics of surface topography instruments,” Ann. CIRP 64(1), 545–548 (2014).
[Crossref]

de Groot, P.

P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
[Crossref]

Ekberg, P.

P. Ekberg, L. Stiblert, and L. Mattsson, “A new general approach for solving the self-calibration problem on large area 2D ultra-precision coordinate measurement machines,” Meas. Sci. Technol. 25(5), 055001 (2014).
[Crossref]

P. Ekberg and L. Mattsson, “A new 2D self-calibration method with large freedom and high-precision performance for imaging metrology devices,” in Proceedings of the 15th International Conference of the European Society for Precision Engineering and Nanotechnology (Elsevier, 2015), pp. 159–160.

Estler, W.

C. Evans, R. Hocken, and W. Estler, “Self-calibration: reversal, redundancy, error separation, and ‘absolute testing’,” Ann. CIRP 45(2), 617–634 (1996).
[Crossref]

Evans, C.

C. Evans, R. Hocken, and W. Estler, “Self-calibration: reversal, redundancy, error separation, and ‘absolute testing’,” Ann. CIRP 45(2), 617–634 (1996).
[Crossref]

Forbes, A.

A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
[Crossref]

Giusca, C.

R. Leach, C. Giusca, D. Cox, M. Guttmann, P.-J. Jakobs, and P. Rubert, “Development of low-cost material measures for calibration of the metrological characteristics of surface topography instruments,” Ann. CIRP 64(1), 545–548 (2014).
[Crossref]

A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
[Crossref]

Giusca, C. L.

C. L. Giusca, R. K. Leach, F. Helary, T. Gutauskas, and L. Nimishakavi, “Calibration of the scales of areal surface topography-measuring instruments: part 1. Measurement noise and residual flatness,” Meas. Sci. Technol. 23(3), 035008 (2012).
[Crossref]

R. K. Leach, C. L. Giusca, and K. Naoi, “Development and characterization of a new instrument for the traceable measurement of areal surface texture,” Meas. Sci. Technol. 20(12), 125102 (2009).
[Crossref]

Gutauskas, T.

C. L. Giusca, R. K. Leach, F. Helary, T. Gutauskas, and L. Nimishakavi, “Calibration of the scales of areal surface topography-measuring instruments: part 1. Measurement noise and residual flatness,” Meas. Sci. Technol. 23(3), 035008 (2012).
[Crossref]

Guttmann, M.

R. Leach, C. Giusca, D. Cox, M. Guttmann, P.-J. Jakobs, and P. Rubert, “Development of low-cost material measures for calibration of the metrological characteristics of surface topography instruments,” Ann. CIRP 64(1), 545–548 (2014).
[Crossref]

Haycocks, J.

J. Haycocks and K. Jackson, “Traceable calibration of transfer standards for scanning probe microscopy,” Precis. Eng. 29(2), 168–175 (2005).
[Crossref]

Helary, F.

C. L. Giusca, R. K. Leach, F. Helary, T. Gutauskas, and L. Nimishakavi, “Calibration of the scales of areal surface topography-measuring instruments: part 1. Measurement noise and residual flatness,” Meas. Sci. Technol. 23(3), 035008 (2012).
[Crossref]

Henning, A.

A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
[Crossref]

Hocken, R.

C. Evans, R. Hocken, and W. Estler, “Self-calibration: reversal, redundancy, error separation, and ‘absolute testing’,” Ann. CIRP 45(2), 617–634 (1996).
[Crossref]

Jackson, K.

J. Haycocks and K. Jackson, “Traceable calibration of transfer standards for scanning probe microscopy,” Precis. Eng. 29(2), 168–175 (2005).
[Crossref]

Jakobs, P.-J.

R. Leach, C. Giusca, D. Cox, M. Guttmann, P.-J. Jakobs, and P. Rubert, “Development of low-cost material measures for calibration of the metrological characteristics of surface topography instruments,” Ann. CIRP 64(1), 545–548 (2014).
[Crossref]

Kikuta, H.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Kitagawa, A.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Kitamura, K.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Leach, R.

R. Leach, C. Giusca, D. Cox, M. Guttmann, P.-J. Jakobs, and P. Rubert, “Development of low-cost material measures for calibration of the metrological characteristics of surface topography instruments,” Ann. CIRP 64(1), 545–548 (2014).
[Crossref]

A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
[Crossref]

Leach, R. K.

C. L. Giusca, R. K. Leach, F. Helary, T. Gutauskas, and L. Nimishakavi, “Calibration of the scales of areal surface topography-measuring instruments: part 1. Measurement noise and residual flatness,” Meas. Sci. Technol. 23(3), 035008 (2012).
[Crossref]

R. K. Leach, C. L. Giusca, and K. Naoi, “Development and characterization of a new instrument for the traceable measurement of areal surface texture,” Meas. Sci. Technol. 20(12), 125102 (2009).
[Crossref]

Mandal, R.

A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
[Crossref]

Mattsson, L.

P. Ekberg, L. Stiblert, and L. Mattsson, “A new general approach for solving the self-calibration problem on large area 2D ultra-precision coordinate measurement machines,” Meas. Sci. Technol. 25(5), 055001 (2014).
[Crossref]

P. Ekberg and L. Mattsson, “A new 2D self-calibration method with large freedom and high-precision performance for imaging metrology devices,” in Proceedings of the 15th International Conference of the European Society for Precision Engineering and Nanotechnology (Elsevier, 2015), pp. 159–160.

Naoi, K.

R. K. Leach, C. L. Giusca, and K. Naoi, “Development and characterization of a new instrument for the traceable measurement of areal surface texture,” Meas. Sci. Technol. 20(12), 125102 (2009).
[Crossref]

Nimishakavi, L.

C. L. Giusca, R. K. Leach, F. Helary, T. Gutauskas, and L. Nimishakavi, “Calibration of the scales of areal surface topography-measuring instruments: part 1. Measurement noise and residual flatness,” Meas. Sci. Technol. 23(3), 035008 (2012).
[Crossref]

Raugh, M.

M. Raugh, “Absolute two-dimensional sub-micron metrology for electron beam lithography – a calibration theory with applications,” Precis. Eng. 7(1), 1–13 (1985).
[Crossref]

Rubert, P.

R. Leach, C. Giusca, D. Cox, M. Guttmann, P.-J. Jakobs, and P. Rubert, “Development of low-cost material measures for calibration of the metrological characteristics of surface topography instruments,” Ann. CIRP 64(1), 545–548 (2014).
[Crossref]

Smith, I.

A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
[Crossref]

Stiblert, L.

P. Ekberg, L. Stiblert, and L. Mattsson, “A new general approach for solving the self-calibration problem on large area 2D ultra-precision coordinate measurement machines,” Meas. Sci. Technol. 25(5), 055001 (2014).
[Crossref]

Yoneyama, S.

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Adv. Opt. Photonics (1)

P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
[Crossref]

Ann. CIRP (3)

R. Leach, C. Giusca, D. Cox, M. Guttmann, P.-J. Jakobs, and P. Rubert, “Development of low-cost material measures for calibration of the metrological characteristics of surface topography instruments,” Ann. CIRP 64(1), 545–548 (2014).
[Crossref]

A. Henning, C. Giusca, A. Forbes, I. Smith, R. Leach, J. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” Ann. CIRP 62(1), 547–550 (2013).
[Crossref]

C. Evans, R. Hocken, and W. Estler, “Self-calibration: reversal, redundancy, error separation, and ‘absolute testing’,” Ann. CIRP 45(2), 617–634 (1996).
[Crossref]

Meas. Sci. Technol. (3)

R. K. Leach, C. L. Giusca, and K. Naoi, “Development and characterization of a new instrument for the traceable measurement of areal surface texture,” Meas. Sci. Technol. 20(12), 125102 (2009).
[Crossref]

P. Ekberg, L. Stiblert, and L. Mattsson, “A new general approach for solving the self-calibration problem on large area 2D ultra-precision coordinate measurement machines,” Meas. Sci. Technol. 25(5), 055001 (2014).
[Crossref]

C. L. Giusca, R. K. Leach, F. Helary, T. Gutauskas, and L. Nimishakavi, “Calibration of the scales of areal surface topography-measuring instruments: part 1. Measurement noise and residual flatness,” Meas. Sci. Technol. 23(3), 035008 (2012).
[Crossref]

Opt. Eng. (1)

S. Yoneyama, H. Kikuta, A. Kitagawa, and K. Kitamura, “Lens distortion correction for digital image correlation by measuring rigid body displacement,” Opt. Eng. 45(2), 023602 (2006).
[Crossref]

Precis. Eng. (2)

J. Haycocks and K. Jackson, “Traceable calibration of transfer standards for scanning probe microscopy,” Precis. Eng. 29(2), 168–175 (2005).
[Crossref]

M. Raugh, “Absolute two-dimensional sub-micron metrology for electron beam lithography – a calibration theory with applications,” Precis. Eng. 7(1), 1–13 (1985).
[Crossref]

Other (4)

M. Sutton, J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications, (Springer, 2009).

P. de Groot, Optical Measurement of Surface Topography, R. K. Leach, ed. (Springer, 2011), Chap. 9.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999), Chap. 5.

P. Ekberg and L. Mattsson, “A new 2D self-calibration method with large freedom and high-precision performance for imaging metrology devices,” in Proceedings of the 15th International Conference of the European Society for Precision Engineering and Nanotechnology (Elsevier, 2015), pp. 159–160.

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Figures (8)

Fig. 1
Fig. 1 Distortion correction process.
Fig. 2
Fig. 2 Extraction of 2D intensity map in CSI. a) Interferometirc image stack in CSI; b) interference signal recorded by a pixel; c) the Fourier transform of the signal, where the low frequency part corresponds to the intensity map; d) the extracted intensity map.
Fig. 3
Fig. 3 Illustration of the image correlation method. a) 9-by-9 grid of image patches defined in the 2D intensity map of the CSI measurement of a coin surface; b) the enlarged image patch (100-by-100 pixels) of which the centroid is located at (I, J) in the image coordinate; c) the correlation function, which is the result of searching for the reference image patch around (I, J) in the translated or rotated views.
Fig. 4
Fig. 4 Extraction of the 2D intensity maps from CSI measurements of a coin surface and definition of the grid. a) Photograph of the coin; b) an image slice from the 3D fringe data; c) calculated height map; d, e, f) Intensity maps of the reference, translated and rotated views, respectively; g) defined grid and image patches. The grey scales of all intensity images are normalised. The 50 × objective lens was used.
Fig. 5
Fig. 5 Measured grids from three different views. a, b, c) Resulting grids (absolute coordinates) of the repeated measurements of the reference, translated and rotated views, respectively (the errors are magnified for visualisation purpose); d, e, f) calculated drifts for the reference, translated and rotated views, respectively. The 50 × objective lens was used.
Fig. 6
Fig. 6 Measured grids from three different views. a, b, c) Resulting grids (absolute coordinates) of the repeated measurements of the reference, translated and rotated views, respectively (the errors are magnified for visualisation purpose); d, e, f) calculated drifts for the reference, translated and rotated views, respectively. The 5.5 × objective lens was used.
Fig. 7
Fig. 7 Self-calibration result. a) Input to the self-calibration algorithm and the placement scheme; b) calculated distortion of the CSI system with 50 × objective lens; c) overlay of the distortion-corrected grids.
Fig. 8
Fig. 8 Self-calibration result. a) Input to the self-calibration algorithm and the placement scheme; b) calculated distortion of the CSI system with 5.5 × objective lens; c) overlay of the distortion-corrected grids.

Tables (3)

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Table 1 Specifications of the objective lenses

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Table 2 Distortion correction result for the 50 × objective lens

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Table 3 Distortion correction result for the 5.5 × objective lens

Equations (1)

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C I,J ( p,q )= j i f( iI,jJ )g( iI+p,jJ+q ),

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