Abstract

Although coherence scanning interferometry (CSI) is capable of measuring surface topography with sub-nanometre precision, it is well known that the performance of measuring instruments depends strongly on the local tilt and curvature of the sample surface. Based on 3D linear systems theory, however, a recent analysis of fringe generation in CSI provides a method to characterize the performance of surface measuring instruments and offers considerable insight into the origins of these errors. Furthermore, from the measurement of a precision sphere, a process to calibrate and partially correct instruments has been proposed. This paper presents, for the first time, a critical look at the calibration and correction process. Computational techniques are used to investigate the effects of radius error and measurement noise introduced during the calibration process for the measurement of spherical and sinusoidal profiles. Care is taken to illustrate the residual tilt and curvature dependent errors in a manner that will allow users to estimate measurement uncertainty. It is shown that by calibrating the instrument correctly and using appropriate methods to extract phase from the resulting fringes (such as frequency domain analysis), CSI is capable of measuring the topography of surfaces with varying tilt with sub-nanometre accuracy.

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References

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  1. R. K. Leach, Characterisation of Areal Surface Texture (Springer-Verlag, 2013).
  2. A. A. G. Bruzzone, H. L. Costa, P. M. Lonardo, and D. A. Lucca, “Advances in engineered surfaces for functional performance,” CIRP Ann. Manuf. Techn. 57(2), 750–769 (2008).
    [Crossref]
  3. H. N. Hansen, K. Carneiro, H. Haitjema, and L. de Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. Manuf. Techn. 55(2), 721–743 (2006).
    [Crossref]
  4. P. de Groot, “Chapter 9. Coherence scanning interferometry,” in Optical Measurement of Surface Topography, R. K. Leach, ed. (Springer, 2011).
  5. P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
    [Crossref]
  6. K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13(4), 832–843 (1996).
    [Crossref]
  7. P. de Groot, X. Colonna de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41(22), 4571–4578 (2002).
    [Crossref] [PubMed]
  8. P. de Groot, “The meaning and measure of vertical resolution in surface metrology,” presented at the 5th International Conference on Surface Metrology, Poznan, Poland, 4–7 April 2016.
  9. F. Gao, R. K. Leach, J. Petzing, and J. M. Coupland, “Surface measurement errors using commercial scanning white light interferometers,” Meas. Sci. Technol. 19(1), 015303 (2008).
    [Crossref]
  10. P. Lehmann, “Vertical scanning white-light interference microscopy on curved microstructures,” Opt. Lett. 35(11), 1768–1770 (2010).
    [Crossref] [PubMed]
  11. M. Liu, C. F. Cheung, M. Ren, and C. H. Cheng, “Estimation of measurement uncertainty caused by surface gradient for a white light interferometer,” Appl. Opt. 54(29), 8670–8677 (2015).
    [Crossref] [PubMed]
  12. R. K. Leach, “Is one step height enough?” in Proceedings of the 30th Annual Meeting of American Society for Precision Engineering, (Austin, USA, 2015), pp. 110–113.
  13. M. R. Foreman, C. L. Giusca, J. M. Coupland, P. Török, and R. K. Leach, “Determination of the transfer function for optical surface topography measuring instruments – a review,” Meas. Sci. Technol. 24(5), 052001 (2013).
    [Crossref]
  14. J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19(7), 07010 (2008).
    [Crossref]
  15. J. Coupland, R. Mandal, K. Palodhi, and R. Leach, “Coherence scanning interferometry: linear theory of surface measurement,” Appl. Opt. 52(16), 3662–3670 (2013).
    [Crossref] [PubMed]
  16. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), 695–734.
  17. W. Xie, P. Lehmann, and J. Niehues, “Lateral resolution and transfer characteristics of vertical scanning white-light interferometers,” Appl. Opt. 51(11), 1795–1803 (2012).
    [Crossref] [PubMed]
  18. P. de Groot and X. C. de Lega, “Interpreting interferometric height measurements using the instrument transfer function,” in Proceedings of the 5th International Workshop on Automatic Processing of Fringe Patterns, W. Osten, ed. (Springer, 2005), pp. 30–37.
  19. R. Mandal, J. Coupland, R. Leach, and D. Mansfield, “Coherence scanning interferometry: measurement and correction of three-dimensional transfer and point-spread characteristics,” Appl. Opt. 53(8), 1554–1563 (2014).
    [Crossref] [PubMed]
  20. A. J. Henning, J. M. Huntley, and C. L. Giusca, “Obtaining the Transfer Function of optical instruments using large calibrated reference objects,” Opt. Express 23(13), 16617–16627 (2015).
    [Crossref] [PubMed]
  21. Zygo NewView 3D optical surface profiler, https://www.zygo.com/?/met/profilers/nexview/ .
  22. A. J. Henning and C. L. Giusca, “Errors and uncertainty in the topography gained via frequency-domain analysis,” Opt. Express 23(18), 24057–24070 (2015).
    [Crossref]

2015 (4)

2014 (1)

2013 (2)

J. Coupland, R. Mandal, K. Palodhi, and R. Leach, “Coherence scanning interferometry: linear theory of surface measurement,” Appl. Opt. 52(16), 3662–3670 (2013).
[Crossref] [PubMed]

M. R. Foreman, C. L. Giusca, J. M. Coupland, P. Török, and R. K. Leach, “Determination of the transfer function for optical surface topography measuring instruments – a review,” Meas. Sci. Technol. 24(5), 052001 (2013).
[Crossref]

2012 (1)

2010 (1)

2008 (3)

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19(7), 07010 (2008).
[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(1), 015303 (2008).
[Crossref]

A. A. G. Bruzzone, H. L. Costa, P. M. Lonardo, and D. A. Lucca, “Advances in engineered surfaces for functional performance,” CIRP Ann. Manuf. Techn. 57(2), 750–769 (2008).
[Crossref]

2006 (1)

H. N. Hansen, K. Carneiro, H. Haitjema, and L. de Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. Manuf. Techn. 55(2), 721–743 (2006).
[Crossref]

2002 (1)

1996 (1)

Bruzzone, A. A. G.

A. A. G. Bruzzone, H. L. Costa, P. M. Lonardo, and D. A. Lucca, “Advances in engineered surfaces for functional performance,” CIRP Ann. Manuf. Techn. 57(2), 750–769 (2008).
[Crossref]

Carneiro, K.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. de Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. Manuf. Techn. 55(2), 721–743 (2006).
[Crossref]

Cheng, C. H.

Cheung, C. F.

Colonna de Lega, X.

Costa, H. L.

A. A. G. Bruzzone, H. L. Costa, P. M. Lonardo, and D. A. Lucca, “Advances in engineered surfaces for functional performance,” CIRP Ann. Manuf. Techn. 57(2), 750–769 (2008).
[Crossref]

Coupland, J.

Coupland, J. M.

M. R. Foreman, C. L. Giusca, J. M. Coupland, P. Török, and R. K. Leach, “Determination of the transfer function for optical surface topography measuring instruments – a review,” Meas. Sci. Technol. 24(5), 052001 (2013).
[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(1), 015303 (2008).
[Crossref]

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19(7), 07010 (2008).
[Crossref]

de Chiffre, L.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. de Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. Manuf. Techn. 55(2), 721–743 (2006).
[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]

P. de Groot, X. Colonna de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41(22), 4571–4578 (2002).
[Crossref] [PubMed]

P. de Groot and X. C. de Lega, “Interpreting interferometric height measurements using the instrument transfer function,” in Proceedings of the 5th International Workshop on Automatic Processing of Fringe Patterns, W. Osten, ed. (Springer, 2005), pp. 30–37.

de Lega, X. C.

P. de Groot and X. C. de Lega, “Interpreting interferometric height measurements using the instrument transfer function,” in Proceedings of the 5th International Workshop on Automatic Processing of Fringe Patterns, W. Osten, ed. (Springer, 2005), pp. 30–37.

Foreman, M. R.

M. R. Foreman, C. L. Giusca, J. M. Coupland, P. Török, and R. K. Leach, “Determination of the transfer function for optical surface topography measuring instruments – a review,” Meas. Sci. Technol. 24(5), 052001 (2013).
[Crossref]

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(1), 015303 (2008).
[Crossref]

Giusca, C. L.

Haitjema, H.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. de Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. Manuf. Techn. 55(2), 721–743 (2006).
[Crossref]

Hansen, H. N.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. de Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. Manuf. Techn. 55(2), 721–743 (2006).
[Crossref]

Henning, A. J.

Huntley, J. M.

Kramer, J.

Larkin, K. G.

Leach, R.

Leach, R. K.

M. R. Foreman, C. L. Giusca, J. M. Coupland, P. Török, and R. K. Leach, “Determination of the transfer function for optical surface topography measuring instruments – a review,” Meas. Sci. Technol. 24(5), 052001 (2013).
[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(1), 015303 (2008).
[Crossref]

R. K. Leach, “Is one step height enough?” in Proceedings of the 30th Annual Meeting of American Society for Precision Engineering, (Austin, USA, 2015), pp. 110–113.

Lehmann, P.

Liu, M.

Lobera, J.

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19(7), 07010 (2008).
[Crossref]

Lonardo, P. M.

A. A. G. Bruzzone, H. L. Costa, P. M. Lonardo, and D. A. Lucca, “Advances in engineered surfaces for functional performance,” CIRP Ann. Manuf. Techn. 57(2), 750–769 (2008).
[Crossref]

Lucca, D. A.

A. A. G. Bruzzone, H. L. Costa, P. M. Lonardo, and D. A. Lucca, “Advances in engineered surfaces for functional performance,” CIRP Ann. Manuf. Techn. 57(2), 750–769 (2008).
[Crossref]

Mandal, R.

Mansfield, D.

Niehues, J.

Palodhi, K.

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(1), 015303 (2008).
[Crossref]

Ren, M.

Török, P.

M. R. Foreman, C. L. Giusca, J. M. Coupland, P. Török, and R. K. Leach, “Determination of the transfer function for optical surface topography measuring instruments – a review,” Meas. Sci. Technol. 24(5), 052001 (2013).
[Crossref]

Turzhitsky, M.

Xie, W.

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]

Appl. Opt. (5)

CIRP Ann. Manuf. Techn. (2)

A. A. G. Bruzzone, H. L. Costa, P. M. Lonardo, and D. A. Lucca, “Advances in engineered surfaces for functional performance,” CIRP Ann. Manuf. Techn. 57(2), 750–769 (2008).
[Crossref]

H. N. Hansen, K. Carneiro, H. Haitjema, and L. de Chiffre, “Dimensional micro and nano metrology,” CIRP Ann. Manuf. Techn. 55(2), 721–743 (2006).
[Crossref]

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (3)

F. Gao, R. K. Leach, J. Petzing, and J. M. Coupland, “Surface measurement errors using commercial scanning white light interferometers,” Meas. Sci. Technol. 19(1), 015303 (2008).
[Crossref]

M. R. Foreman, C. L. Giusca, J. M. Coupland, P. Török, and R. K. Leach, “Determination of the transfer function for optical surface topography measuring instruments – a review,” Meas. Sci. Technol. 24(5), 052001 (2013).
[Crossref]

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19(7), 07010 (2008).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Other (7)

P. de Groot, “The meaning and measure of vertical resolution in surface metrology,” presented at the 5th International Conference on Surface Metrology, Poznan, Poland, 4–7 April 2016.

P. de Groot, “Chapter 9. Coherence scanning interferometry,” in Optical Measurement of Surface Topography, R. K. Leach, ed. (Springer, 2011).

R. K. Leach, “Is one step height enough?” in Proceedings of the 30th Annual Meeting of American Society for Precision Engineering, (Austin, USA, 2015), pp. 110–113.

P. de Groot and X. C. de Lega, “Interpreting interferometric height measurements using the instrument transfer function,” in Proceedings of the 5th International Workshop on Automatic Processing of Fringe Patterns, W. Osten, ed. (Springer, 2005), pp. 30–37.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), 695–734.

R. K. Leach, Characterisation of Areal Surface Texture (Springer-Verlag, 2013).

Zygo NewView 3D optical surface profiler, https://www.zygo.com/?/met/profilers/nexview/ .

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Figures (12)

Fig. 1
Fig. 1 Calibration of the 3D TF of a CSI system by measuring a spherical object. Cross-sectional views of a) the CSI fringe data (0.55 NA, λ0 = 0.58 μm and Δλ = 0.08 μm); b) foil model of the surface (sphere radius of 50 µm); c) normalised MTF (note the phase term is zero); d) flattened MTF; e) original PSF and f) filtered PSF.
Fig. 2
Fig. 2 Schema of the signal modelling, TF calibration and inverse filtering process for CSI.
Fig. 3
Fig. 3 Schema of the signal modelling and inverse filtering of CSI measurement of surfaces.
Fig. 4
Fig. 4 Cross-sectional CSI signal of the calibration sphere (R0 = 21.5 μm) and the signal profile through the top of the sphere, of the experiment (a) and simulation (b).
Fig. 5
Fig. 5 Surface height profiles (a) of the calibration sphere (R0 = 50 μm and ΔR0 = 0, profiles offset by 10 μm for display purpose; black curve shows the nominal surface), and height error of the simulated (solid blue) and the inverse filtered (dashed red) sphere calculated using the direct phase method (b) and FDA method (c).
Fig. 6
Fig. 6 Effect of noise on CSI measurement of a sphere (R0 = 50 μm and the TF is correctly calibrated as ΔR0 = 0); The height errors of the simulated (a) and inverse filtered (b) spheres with 1% RMS noise relative to the fringe modulation peak, and the height errors of the simulated (c) and inverse filtered (d) spheres with 4% noise. The direct phase algorithm is used.
Fig. 7
Fig. 7 CSI measurement of a sinusoidal surface with λG = 5 μmand AG = 0.3 μm; a) cross-sectional surface profiles; b) the simulated CSI fringes; c) the inverse filtered fringes; d) the height errors calculated from the simulated (solid blue) and filtered fringes (solid red) by the direct phase algorithm; e) the height errors calculated from the simulated (solid blue) and inverse filtered fringes (solid red) by the FDA algorithm; f), g) and h) show the height errors calculated by the FDA algorithm for the fringes with noise levels of 1%, 2% and 4%, respectively.
Fig. 8
Fig. 8 Schema of geometrical errors of a sphere: a) asymmetrical error; b) symmetrical error; c) radius error.
Fig. 9
Fig. 9 The normalised magnitude (a) and the phase (b) of the measured TF with the radius error ΔR0 = 1 μm.
Fig. 10
Fig. 10 Height error of CSI measurement of a sphere (R0 = 50 μm) after the phase inverse filtering (without the gain function) based on the correct (solid blue) and incorrect (dashed red) calibrations of the TF for ΔR0 = 0.01 μm, 0.1 μm, 0.5 μm and 1 μm, respectively. The FDA algorithm is used.
Fig. 11
Fig. 11 Additional height error as a function of ΔR0 and the surface slope angle.
Fig. 12
Fig. 12 Profiles (upper) of CSI measurements of sinusoidal grating surfaces a) S1, b) S2 and c) S3, and the corresponding height errors (lower) after the inverse filtering. The red and blue curves show the height errors of the filtered surfaces with and without the radius error of the calibration sphere, respectively; the dashed and solid curves show the inverse filtering with and without the flattening of the MTF, respectively. The FDA algorithm is used.

Tables (1)

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Table 1 Sinusoidal surfaces parameters

Equations (6)

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F( k )=H( k )×O( k ).
o( x,y,z )=4πjRw( x,y )δ[ zs(x,y) ],
δ(z)= lim σε 1 2π σ exp[ z 2 2 σ 2 ],
H(k)=( | k | 2 2k o ^ ) G NA ( k i , k 0 ) G NA ( k k i , k 0 ) d 3 k i S( k 0 )d k 0 ,
G NA ( k, k 0 )= j 4π k 0 2 δ( | k | k 0 )step( k o ^ 1 A n 2 ),
H( k )= F( k ) O( k ) ,

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