Abstract

The task of anti-aliasing in absolute profile measurement by multi-sensor scanning techniques is considered. Simulation results are presented which demonstrate that aliasing can be highly reduced by a suitable choice of the scanning steps. The simulation results were confirmed by results obtained for interferometric measurements (Nyquist frequency 1/646 µm−1) on a specifically designed chirp specimen with sinusoidal waves of amplitude 100 nm and wavelengths from 2.5 mm down to 19 µm.

© 2009 Optical Society of America

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References

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    [Crossref] [PubMed]
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  3. J. Cohen-Sabban and D. Reolon, “Vibration insensitive 3D-profilometry: a new type of white light interferometric microscopy” Proc. SPIE 7064, (2008).
    [Crossref]
  4. D J Whitehouse, “Some theoretical aspects of error separation techniques in surface metrology,” J. Phys. E Sci. Instrum.  9, 531–536 (1976).
    [Crossref]
  5. W. Gao and S. Kiyono, “High accuracy profile measurement of a machined surface by the combined method,” Measurement  19, 55–64 (1996).
    [Crossref]
  6. C. Elster, I. Weingaertner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Prec. Eng.  30, 32–38 (2006).
    [Crossref]
  7. A. Wiegmann, M. Schulz, and C. Elster, “Absolute profile measurement of large moderately flat optical surfaces with high dynamic range,” Opt. Express  16, 11975–11986 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11975.
    [Crossref] [PubMed]
  8. µPhase Interferometer, FISBA Optik AG, CH-9016 St. Gallen and FISBA Optik GmbH, Berlin, http://www.fisba.ch/.
  9. MPLS 180, STIL - 595, rue Pierre Berthier - Domaine de Saint Hilaire - 13855 Aix en Provence Cedex 3 - FRANCE, http://www.stilsa.com/.
  10. E. Marsh, J. Couey, and R. Vallance, “Nanometer-Level Comparison of Three Spindle Error Motion Separation Techniques,” J. Manuf. Sci. Eng.  128, 180–187 (2006)
    [Crossref]
  11. V. Bakshi, EUV Lithography (John Wiley & Sons, 2009), Chap. 5.3
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    [Crossref]
  13. R. Krueger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp-Kalibriernormale fuer Obeflaechenmessgeraete”. Technisches Messen  74, 572–576 (2007).
  14. A. Wiegmann, C. Elster, M. Schulz, and M. Stavridis, “Absolute Topographievermessung gekruemmter optischer Oberflaechen mit hoher lateraler Aufloesung”, in Proceedings of the 109th DgaO, http://www.dgao-proceedings.de/download/109/109_p28.pdf.

2008 (1)

2007 (1)

R. Krueger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp-Kalibriernormale fuer Obeflaechenmessgeraete”. Technisches Messen  74, 572–576 (2007).

2006 (2)

E. Marsh, J. Couey, and R. Vallance, “Nanometer-Level Comparison of Three Spindle Error Motion Separation Techniques,” J. Manuf. Sci. Eng.  128, 180–187 (2006)
[Crossref]

C. Elster, I. Weingaertner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Prec. Eng.  30, 32–38 (2006).
[Crossref]

2005 (1)

B. Doerband and J. Hetzler, “Characterizing lateral resolution of interferometers: the Height Transfer Function (HTF),” Proc. SPIE  5878, 587806 (2005).
[Crossref]

1996 (1)

W. Gao and S. Kiyono, “High accuracy profile measurement of a machined surface by the combined method,” Measurement  19, 55–64 (1996).
[Crossref]

1994 (1)

1976 (1)

D J Whitehouse, “Some theoretical aspects of error separation techniques in surface metrology,” J. Phys. E Sci. Instrum.  9, 531–536 (1976).
[Crossref]

Bakshi, V.

V. Bakshi, EUV Lithography (John Wiley & Sons, 2009), Chap. 5.3

Bakucz, P.

R. Krueger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp-Kalibriernormale fuer Obeflaechenmessgeraete”. Technisches Messen  74, 572–576 (2007).

Cohen-Sabban, J.

J. Cohen-Sabban and D. Reolon, “Vibration insensitive 3D-profilometry: a new type of white light interferometric microscopy” Proc. SPIE 7064, (2008).
[Crossref]

Couey, J.

E. Marsh, J. Couey, and R. Vallance, “Nanometer-Level Comparison of Three Spindle Error Motion Separation Techniques,” J. Manuf. Sci. Eng.  128, 180–187 (2006)
[Crossref]

David, J.

L. Lahousse, S. Leleu, J. David, O. Gibaru, and S. Ducourtieux, “Z calibration of the LNE ultra precision coordinate measuring machine,” in Proceedings of the 9th international conference of the european society for precision engineering and nanotechnology, V 2, 348–353 (2007).

de Groot, P.

Deck, L.

Doerband, B.

B. Doerband and J. Hetzler, “Characterizing lateral resolution of interferometers: the Height Transfer Function (HTF),” Proc. SPIE  5878, 587806 (2005).
[Crossref]

Ducourtieux, S.

L. Lahousse, S. Leleu, J. David, O. Gibaru, and S. Ducourtieux, “Z calibration of the LNE ultra precision coordinate measuring machine,” in Proceedings of the 9th international conference of the european society for precision engineering and nanotechnology, V 2, 348–353 (2007).

Elster, C.

A. Wiegmann, M. Schulz, and C. Elster, “Absolute profile measurement of large moderately flat optical surfaces with high dynamic range,” Opt. Express  16, 11975–11986 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11975.
[Crossref] [PubMed]

C. Elster, I. Weingaertner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Prec. Eng.  30, 32–38 (2006).
[Crossref]

A. Wiegmann, C. Elster, M. Schulz, and M. Stavridis, “Absolute Topographievermessung gekruemmter optischer Oberflaechen mit hoher lateraler Aufloesung”, in Proceedings of the 109th DgaO, http://www.dgao-proceedings.de/download/109/109_p28.pdf.

Gao, W.

W. Gao and S. Kiyono, “High accuracy profile measurement of a machined surface by the combined method,” Measurement  19, 55–64 (1996).
[Crossref]

Gibaru, O.

L. Lahousse, S. Leleu, J. David, O. Gibaru, and S. Ducourtieux, “Z calibration of the LNE ultra precision coordinate measuring machine,” in Proceedings of the 9th international conference of the european society for precision engineering and nanotechnology, V 2, 348–353 (2007).

Hetzler, J.

B. Doerband and J. Hetzler, “Characterizing lateral resolution of interferometers: the Height Transfer Function (HTF),” Proc. SPIE  5878, 587806 (2005).
[Crossref]

Jung, L.

R. Krueger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp-Kalibriernormale fuer Obeflaechenmessgeraete”. Technisches Messen  74, 572–576 (2007).

Kiyono, S.

W. Gao and S. Kiyono, “High accuracy profile measurement of a machined surface by the combined method,” Measurement  19, 55–64 (1996).
[Crossref]

Krueger-Sehm, R.

R. Krueger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp-Kalibriernormale fuer Obeflaechenmessgeraete”. Technisches Messen  74, 572–576 (2007).

Lahousse, L.

L. Lahousse, S. Leleu, J. David, O. Gibaru, and S. Ducourtieux, “Z calibration of the LNE ultra precision coordinate measuring machine,” in Proceedings of the 9th international conference of the european society for precision engineering and nanotechnology, V 2, 348–353 (2007).

Leleu, S.

L. Lahousse, S. Leleu, J. David, O. Gibaru, and S. Ducourtieux, “Z calibration of the LNE ultra precision coordinate measuring machine,” in Proceedings of the 9th international conference of the european society for precision engineering and nanotechnology, V 2, 348–353 (2007).

Marsh, E.

E. Marsh, J. Couey, and R. Vallance, “Nanometer-Level Comparison of Three Spindle Error Motion Separation Techniques,” J. Manuf. Sci. Eng.  128, 180–187 (2006)
[Crossref]

Reolon, D.

J. Cohen-Sabban and D. Reolon, “Vibration insensitive 3D-profilometry: a new type of white light interferometric microscopy” Proc. SPIE 7064, (2008).
[Crossref]

Schulz, M.

A. Wiegmann, M. Schulz, and C. Elster, “Absolute profile measurement of large moderately flat optical surfaces with high dynamic range,” Opt. Express  16, 11975–11986 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11975.
[Crossref] [PubMed]

C. Elster, I. Weingaertner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Prec. Eng.  30, 32–38 (2006).
[Crossref]

A. Wiegmann, C. Elster, M. Schulz, and M. Stavridis, “Absolute Topographievermessung gekruemmter optischer Oberflaechen mit hoher lateraler Aufloesung”, in Proceedings of the 109th DgaO, http://www.dgao-proceedings.de/download/109/109_p28.pdf.

Stavridis, M.

A. Wiegmann, C. Elster, M. Schulz, and M. Stavridis, “Absolute Topographievermessung gekruemmter optischer Oberflaechen mit hoher lateraler Aufloesung”, in Proceedings of the 109th DgaO, http://www.dgao-proceedings.de/download/109/109_p28.pdf.

Vallance, R.

E. Marsh, J. Couey, and R. Vallance, “Nanometer-Level Comparison of Three Spindle Error Motion Separation Techniques,” J. Manuf. Sci. Eng.  128, 180–187 (2006)
[Crossref]

Weingaertner, I.

C. Elster, I. Weingaertner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Prec. Eng.  30, 32–38 (2006).
[Crossref]

Whitehouse, D J

D J Whitehouse, “Some theoretical aspects of error separation techniques in surface metrology,” J. Phys. E Sci. Instrum.  9, 531–536 (1976).
[Crossref]

Wiegmann, A.

A. Wiegmann, M. Schulz, and C. Elster, “Absolute profile measurement of large moderately flat optical surfaces with high dynamic range,” Opt. Express  16, 11975–11986 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11975.
[Crossref] [PubMed]

A. Wiegmann, C. Elster, M. Schulz, and M. Stavridis, “Absolute Topographievermessung gekruemmter optischer Oberflaechen mit hoher lateraler Aufloesung”, in Proceedings of the 109th DgaO, http://www.dgao-proceedings.de/download/109/109_p28.pdf.

Wilhelms, H.

R. Krueger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp-Kalibriernormale fuer Obeflaechenmessgeraete”. Technisches Messen  74, 572–576 (2007).

Appl. Opt. (1)

J. Manuf. Sci. Eng. (1)

E. Marsh, J. Couey, and R. Vallance, “Nanometer-Level Comparison of Three Spindle Error Motion Separation Techniques,” J. Manuf. Sci. Eng.  128, 180–187 (2006)
[Crossref]

J. Phys. E Sci. Instrum. (1)

D J Whitehouse, “Some theoretical aspects of error separation techniques in surface metrology,” J. Phys. E Sci. Instrum.  9, 531–536 (1976).
[Crossref]

Measurement (1)

W. Gao and S. Kiyono, “High accuracy profile measurement of a machined surface by the combined method,” Measurement  19, 55–64 (1996).
[Crossref]

Opt. Express (1)

Prec. Eng. (1)

C. Elster, I. Weingaertner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Prec. Eng.  30, 32–38 (2006).
[Crossref]

Proc. SPIE (1)

B. Doerband and J. Hetzler, “Characterizing lateral resolution of interferometers: the Height Transfer Function (HTF),” Proc. SPIE  5878, 587806 (2005).
[Crossref]

Technisches Messen (1)

R. Krueger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp-Kalibriernormale fuer Obeflaechenmessgeraete”. Technisches Messen  74, 572–576 (2007).

Other (6)

A. Wiegmann, C. Elster, M. Schulz, and M. Stavridis, “Absolute Topographievermessung gekruemmter optischer Oberflaechen mit hoher lateraler Aufloesung”, in Proceedings of the 109th DgaO, http://www.dgao-proceedings.de/download/109/109_p28.pdf.

µPhase Interferometer, FISBA Optik AG, CH-9016 St. Gallen and FISBA Optik GmbH, Berlin, http://www.fisba.ch/.

MPLS 180, STIL - 595, rue Pierre Berthier - Domaine de Saint Hilaire - 13855 Aix en Provence Cedex 3 - FRANCE, http://www.stilsa.com/.

V. Bakshi, EUV Lithography (John Wiley & Sons, 2009), Chap. 5.3

L. Lahousse, S. Leleu, J. David, O. Gibaru, and S. Ducourtieux, “Z calibration of the LNE ultra precision coordinate measuring machine,” in Proceedings of the 9th international conference of the european society for precision engineering and nanotechnology, V 2, 348–353 (2007).

J. Cohen-Sabban and D. Reolon, “Vibration insensitive 3D-profilometry: a new type of white light interferometric microscopy” Proc. SPIE 7064, (2008).
[Crossref]

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Figures (8)

Fig. 1.
Fig. 1.

Sketch of the used absolute profile measurement method. The thick red horizontal lines represent the line sensor array in different measurement positions. The blue vertical lines represent the systematic sensor errors εj.

Fig. 2.
Fig. 2.

Transfer functions of the interpolation scheme used in the reconstruction algorithm for different degrees of interpolation in comparison to the ideal sinc interpolation.

Fig. 3.
Fig. 3.

Dense topography sampling with a line sensor consisting of N equidistant sensors.

Fig. 4.
Fig. 4.

Root mean square errors of the reconstructed topographies in dependence on the frequency of the simulated topography (ftopo) for dense and fore sparse sampling.

Fig. 5.
Fig. 5.

Local wavelength λ of the manufactured chirp specimen as function of the distance to the center of the specimen.

Fig. 6.
Fig. 6.

Lateral high-resolution reconstruction of the entire chirp specimen utilizing all pixels of the compact interferometer (orange) and aliasing free reconstruction (blue) for dense sampling with the reduces sensor array. The red vertical lines mark the positions where the chirp specimen has a local frequency corresponding to the Nyquist frequency of the reduced sensor array.

Fig. 7.
Fig. 7.

Detailed view on the reconstructed chirp specimen for sparse topography sampling.

Fig. 8.
Fig. 8.

Fig. 8. Detailed view on the reconstructed chirp specimen for dense topography sampling.

Equations (3)

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mi,j=Σk=floor(x˜ds)ο12ceil(x˜ds)+ο12ck(X˜)f(xk)+εj+ai+bis(j)
ck(x˜)=i=floor(x˜ds)ο12ceil(x˜ds)+ο12x˜xixkxi.
ik

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