Abstract

We present a single-shot line sensor based on spectral interferometry. Light of a broadband laser source is chromatically dispersed by a grating and focused onto a line on the surface such that each focal point on this line is formed by another wavelength. The entire height profile is obtained by applying a phase evaluation algorithm to the registered interference signal, followed by a model-based approach. The sensor concept is finally verified by experimental results.

© 2011 Optical Society of America

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References

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  1. G. Molesini, G. Pedrini, G. Poggi, and F. Quercioli, “Focus wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
    [Crossref]
  2. J. Schwider and L. Zhou, “Dispersive interferometric profilometer,” Opt. Lett. 19, 995–997 (1994).
    [Crossref] [PubMed]
  3. K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006).
    [Crossref]
  4. G. J. Tearney, R. H. Webb, and B. E. Bouma, “Spectrally encoded confocal microscopy,” Opt. Lett. 23, 1152–1154 (1998).
    [Crossref]
  5. D. Yelin, B. E. Bouma, N. Iftimia, and G. J. Tearney, “Three-dimensional spectrally encoded imaging,” Opt. Lett. 28, 2321–2323 (2003).
    [Crossref] [PubMed]
  6. D. Yelin, S. H. Yun, B. E. Bouma, and G. J. Tearney, “Three-dimensional imaging using spectral encoding heterodyne interferometry,” Opt. Lett. 30, 1794–1796 (2005).
    [Crossref] [PubMed]
  7. A. K. Ruprecht, K. Körner, T. F. Wiesendanger, H. J. Tiziani, and W. Osten, “Chromatic confocal detection for high speed micro-topography measurements,” Proc. SPIE 5302, 53–60(2004).
    [Crossref]
  8. M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” Proc. SPIE 775, 233–247 (1987).
  9. G. S. Kino and S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
    [Crossref] [PubMed]
  10. C. J. R. Sheppard and K. G. Larkin, “Effect of numerical aperture on interference fringe spacing,” Appl. Opt. 34, 4731–4734 (1995).
    [Crossref] [PubMed]
  11. E. Papastathopoulos, K. Körner, and W. Osten, “Chromatic confocal spectral interferometry,” Appl. Opt. 45, 8244–8252(2006).
    [Crossref] [PubMed]
  12. S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Lasers Eng. 47, 1125–1130 (2009).
    [Crossref]
  13. J. Novák, P. Novák, and A. Miks, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
    [Crossref]
  14. L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303 (2007).
    [Crossref]
  15. P. Hlubina, J. Lunácek, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
    [Crossref]
  16. S. Mann and S. Haykin, “The Chirplet transform: a generalization of Gabor's logon transform,” in Proceedings of Vision Interface (Canadian Information Processing Society, 1991), pp. 205–212.
  17. U. Schnell, E. Zimmermann, and R. Dandliker, “Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643–651 (1995).
    [Crossref]
  18. SiMETRICS GmbH, “Resolution standard type RS-M,” http://www.simetrics.de/pdf/RS-M.pdf.
  19. R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess. 74, 572–576 (2007).
    [Crossref]

2009 (1)

S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Lasers Eng. 47, 1125–1130 (2009).
[Crossref]

2008 (2)

J. Novák, P. Novák, and A. Miks, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[Crossref]

P. Hlubina, J. Lunácek, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[Crossref]

2007 (2)

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess. 74, 572–576 (2007).
[Crossref]

L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303 (2007).
[Crossref]

2006 (2)

K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006).
[Crossref]

E. Papastathopoulos, K. Körner, and W. Osten, “Chromatic confocal spectral interferometry,” Appl. Opt. 45, 8244–8252(2006).
[Crossref] [PubMed]

2005 (1)

2004 (1)

A. K. Ruprecht, K. Körner, T. F. Wiesendanger, H. J. Tiziani, and W. Osten, “Chromatic confocal detection for high speed micro-topography measurements,” Proc. SPIE 5302, 53–60(2004).
[Crossref]

2003 (1)

1998 (1)

1995 (2)

U. Schnell, E. Zimmermann, and R. Dandliker, “Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643–651 (1995).
[Crossref]

C. J. R. Sheppard and K. G. Larkin, “Effect of numerical aperture on interference fringe spacing,” Appl. Opt. 34, 4731–4734 (1995).
[Crossref] [PubMed]

1994 (1)

1991 (1)

S. Mann and S. Haykin, “The Chirplet transform: a generalization of Gabor's logon transform,” in Proceedings of Vision Interface (Canadian Information Processing Society, 1991), pp. 205–212.

1990 (1)

1987 (1)

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” Proc. SPIE 775, 233–247 (1987).

1984 (1)

G. Molesini, G. Pedrini, G. Poggi, and F. Quercioli, “Focus wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[Crossref]

Bakucz, P.

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess. 74, 572–576 (2007).
[Crossref]

Bouma, B. E.

Chim, S. S. C.

Chlebus, R.

P. Hlubina, J. Lunácek, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[Crossref]

Ciprian, D.

P. Hlubina, J. Lunácek, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[Crossref]

Cohen, F.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” Proc. SPIE 775, 233–247 (1987).

Dandliker, R.

U. Schnell, E. Zimmermann, and R. Dandliker, “Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643–651 (1995).
[Crossref]

Davidson, M.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” Proc. SPIE 775, 233–247 (1987).

Debnath, S. K.

S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Lasers Eng. 47, 1125–1130 (2009).
[Crossref]

Haykin, S.

S. Mann and S. Haykin, “The Chirplet transform: a generalization of Gabor's logon transform,” in Proceedings of Vision Interface (Canadian Information Processing Society, 1991), pp. 205–212.

Hlubina, P.

P. Hlubina, J. Lunácek, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[Crossref]

Iftimia, N.

Jung, L.

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess. 74, 572–576 (2007).
[Crossref]

Kaufman, K.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” Proc. SPIE 775, 233–247 (1987).

Kim, S.-W.

S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Lasers Eng. 47, 1125–1130 (2009).
[Crossref]

Kino, G. S.

Körner, K.

E. Papastathopoulos, K. Körner, and W. Osten, “Chromatic confocal spectral interferometry,” Appl. Opt. 45, 8244–8252(2006).
[Crossref] [PubMed]

A. K. Ruprecht, K. Körner, T. F. Wiesendanger, H. J. Tiziani, and W. Osten, “Chromatic confocal detection for high speed micro-topography measurements,” Proc. SPIE 5302, 53–60(2004).
[Crossref]

Kothiyal, M. P.

S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Lasers Eng. 47, 1125–1130 (2009).
[Crossref]

Krüger-Sehm, R.

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess. 74, 572–576 (2007).
[Crossref]

Larkin, K. G.

Li, P.

K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006).
[Crossref]

Liu, Z.

K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006).
[Crossref]

Lunácek, J.

P. Hlubina, J. Lunácek, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[Crossref]

Mann, S.

S. Mann and S. Haykin, “The Chirplet transform: a generalization of Gabor's logon transform,” in Proceedings of Vision Interface (Canadian Information Processing Society, 1991), pp. 205–212.

Mazor, I.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” Proc. SPIE 775, 233–247 (1987).

Miks, A.

J. Novák, P. Novák, and A. Miks, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[Crossref]

Molesini, G.

G. Molesini, G. Pedrini, G. Poggi, and F. Quercioli, “Focus wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[Crossref]

Nam, S. H.

K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006).
[Crossref]

Novák, J.

J. Novák, P. Novák, and A. Miks, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[Crossref]

Novák, P.

J. Novák, P. Novák, and A. Miks, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[Crossref]

Osten, W.

E. Papastathopoulos, K. Körner, and W. Osten, “Chromatic confocal spectral interferometry,” Appl. Opt. 45, 8244–8252(2006).
[Crossref] [PubMed]

A. K. Ruprecht, K. Körner, T. F. Wiesendanger, H. J. Tiziani, and W. Osten, “Chromatic confocal detection for high speed micro-topography measurements,” Proc. SPIE 5302, 53–60(2004).
[Crossref]

Papastathopoulos, E.

Pedrini, G.

G. Molesini, G. Pedrini, G. Poggi, and F. Quercioli, “Focus wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[Crossref]

Poggi, G.

G. Molesini, G. Pedrini, G. Poggi, and F. Quercioli, “Focus wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[Crossref]

Quercioli, F.

G. Molesini, G. Pedrini, G. Poggi, and F. Quercioli, “Focus wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[Crossref]

Ruprecht, A. K.

A. K. Ruprecht, K. Körner, T. F. Wiesendanger, H. J. Tiziani, and W. Osten, “Chromatic confocal detection for high speed micro-topography measurements,” Proc. SPIE 5302, 53–60(2004).
[Crossref]

Schnell, U.

U. Schnell, E. Zimmermann, and R. Dandliker, “Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643–651 (1995).
[Crossref]

Schwider, J.

Sheppard, C. J. R.

Shi, K.

K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006).
[Crossref]

Tearney, G. J.

Tiziani, H. J.

A. K. Ruprecht, K. Körner, T. F. Wiesendanger, H. J. Tiziani, and W. Osten, “Chromatic confocal detection for high speed micro-topography measurements,” Proc. SPIE 5302, 53–60(2004).
[Crossref]

Watkins, L. R.

L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303 (2007).
[Crossref]

Webb, R. H.

Wiesendanger, T. F.

A. K. Ruprecht, K. Körner, T. F. Wiesendanger, H. J. Tiziani, and W. Osten, “Chromatic confocal detection for high speed micro-topography measurements,” Proc. SPIE 5302, 53–60(2004).
[Crossref]

Wilhelms, H.

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess. 74, 572–576 (2007).
[Crossref]

Yelin, D.

Yin, S.

K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006).
[Crossref]

Yun, S. H.

Zhou, L.

Zimmermann, E.

U. Schnell, E. Zimmermann, and R. Dandliker, “Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643–651 (1995).
[Crossref]

Appl. Opt. (3)

Opt. Commun. (4)

G. Molesini, G. Pedrini, G. Poggi, and F. Quercioli, “Focus wavelength encoded optical profilometer,” Opt. Commun. 49, 229–233 (1984).
[Crossref]

K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006).
[Crossref]

J. Novák, P. Novák, and A. Miks, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[Crossref]

P. Hlubina, J. Lunácek, D. Ciprian, and R. Chlebus, “Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals,” Opt. Commun. 281, 2349–2354 (2008).
[Crossref]

Opt. Lasers Eng. (2)

L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303 (2007).
[Crossref]

S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single-frame techniques,” Opt. Lasers Eng. 47, 1125–1130 (2009).
[Crossref]

Opt. Lett. (4)

Proc. SPIE (2)

A. K. Ruprecht, K. Körner, T. F. Wiesendanger, H. J. Tiziani, and W. Osten, “Chromatic confocal detection for high speed micro-topography measurements,” Proc. SPIE 5302, 53–60(2004).
[Crossref]

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” Proc. SPIE 775, 233–247 (1987).

Pure Appl. Opt. (1)

U. Schnell, E. Zimmermann, and R. Dandliker, “Absolute distance measurement with synchronously sampled white-light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643–651 (1995).
[Crossref]

Tech. Mess. (1)

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess. 74, 572–576 (2007).
[Crossref]

Other (2)

SiMETRICS GmbH, “Resolution standard type RS-M,” http://www.simetrics.de/pdf/RS-M.pdf.

S. Mann and S. Haykin, “The Chirplet transform: a generalization of Gabor's logon transform,” in Proceedings of Vision Interface (Canadian Information Processing Society, 1991), pp. 205–212.

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Figures (7)

Fig. 1
Fig. 1 Schematic of the white light Michelson-like interferometer with a lateral chromatically dispersed focus, a plane reference, and detection in the optical frequency domain, utilizing a grating spectrometer.

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Fig. 2
Fig. 2 Schema of the whole signal evaluation process.

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Fig. 3
Fig. 3 (a) Interference signal of a resolution standard (solid line), reference signal of the SLD source (dotted). (b) Normalized interference signal by subtracting the reference signal from the measurement signal.

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Fig. 4
Fig. 4 Schema of a section of the line profile.

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Fig. 5
Fig. 5 Resolution standard RS-M, pitch 200   μm , nominal OPD 180   nm , model-based evaluation approach.

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Fig. 6
Fig. 6 Resolution standard RS-M, pitch 200   μm , nominal height 90   nm , model-based evaluation by combining five lateral-shifted measurements (offset 100   μm ).

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Fig. 7
Fig. 7 (a) Line measurement at y position 2.45   mm of a chirped calibration specimen with incrementing frequency and an approximated height of 0.9   μm . (b) Three-dimensional measurement of this chirped specimen.

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Tables (1)

Tables Icon

Table 1 Period Measurement of Chirped Calibration Specimen

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Equations (17)

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I ( z , k , ψ ) = A R 2 + A O 2 + 2 A R A O · cos ⁡ ( 2 k z ( k ) cos ⁡ ψ + δ ( k ) ︸ ) φ ,
I ( z , k ) = S ( k ) ∫ 0 π / 2 U ( ψ ) I ( z , k , ψ ) cos ⁡ ( ψ ) sin ⁡ ( ψ ) d ψ ,
d ( k ) = 2 z ( k )
φ ( k , d ) = k d ( k ) + δ ( k )
φ meas ( k , d ) = φ real mod ⁡ 2 π = k d ( k ) + δ ( k ) + 2 π m ; m ∈ N ,
φ meas ( k , d ) = ( φ real mod ⁡ 2 π ) sign ( ∂ φ real ∂ k ) .
| d | ≥ 2 l k ,
φ meas ( k , d ) = k d ( k ) + 2 π m ; m ∈ N .
γ ( k ) = ∂ φ ∂ k = d ( k ) + k ∂ d ∂ k = d ( k ) + k b ( k ) .
d j + 1 − d j = 1 2 ( k j + 1 − k j ) ( b j + 1 + b j ) = 1 2 Δ k j ( b j + 1 + b j ) .
[ 0 k 2 ⋱ ⋮ 0 1 ⋱ ⋮ ⋮ ⋱ ⋱ 0 ⋮ ⋱ ⋱ 0 0 ⋯ 0 k n 0 ⋯ 0 1 Δ k 1 Δ k 1 0 0 2 − 2 0 0 0 ⋱ ⋱ 0 0 ⋱ ⋱ 0 0 0 Δ k n − 1 Δ k n − 1 0 0 2 − 2 ] ︸ A · [ b 1 ⋮ b n d 1 ⋮ d n ︸ [ B D ] ] = [ γ 1 ⋮ γ n 0 ⋮ 0 ] .
X = ( B D ) = ( B D ) 1 + τ · ( B D ) 2 ; τ ∈ R 1 .
( φ j , 1 , k j , 1 ) , … , ( φ j , m , k j , m )
∂ φ i ∂ k | k i , j = d ( x j ) + k j , i · ∂ x ∂ k | x j , k i , j ︸ · ∂ d ∂ x | x j η ( x j , k i , j ) .
[ 1 η 1 ⋮ ⋮ 1 η m ] ︸ A · [ d ∂ d ∂ x ] = [ ∂ φ 1 ∂ k ⋮ ∂ φ m ∂ k ] .
D 1 = D 1 , 1 + τ 1 · D 2 , 1 ⋮ ⋮ D m = D 1 , m + τ m · D 2 , m ; τ 1 ⋯ τ m ∈ R .
| Δ φ | ≤ 2 π 3 .

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