Abstract

We describe a method that combines phase-shifting and coherence-peak-sensing techniques to permit measurements with the height resolution of phase-shifting interferometry without the interval-slope limitation of λ/4 per data sample of phase-shifting interferometry. A five-frame algorithm is used to determine both the best-focus frame position and the fractional phase from the best-focus frame of the correlogram acquired through vertical scanning. The two surface profiles retrieved from the phase and the modulation contrast of the correlograms are compared in the phase-unwrapping process to remove fringe-order ambiguity.

© 2000 Optical Society of America

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  1. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics XXVI, E. Wolf, ed. (Elsevier, Amsterdam, The Netherlands, 1988), pp. 349–393.
    [CrossRef]
  2. J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.
  3. J. Schmit, K. Creath, “Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry,” Appl. Opt. 34, 3610–3619 (1995).
    [CrossRef] [PubMed]
  4. P. de Groot, “Derivation algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
    [CrossRef]
  5. J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
    [CrossRef]
  6. Y.-Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [CrossRef]
  7. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef] [PubMed]
  8. J. C. Wyant, K. Creath, “Two-wavelength phase-shifting interferometer and method,” U.S. patent4,832,489 (filed 19March1986; issued 23May1989).
  9. P. J. de Groot, “Extending the unambiguous range of two-color interferometers,” Appl. Opt. 33, 5948–5953 (1994).
    [CrossRef] [PubMed]
  10. Rough surfaces have local steep slopes that result in narrow fringe spacings, so the condition of two detectors per fringe is easily violated. Compared with the step height, which consists of smooth surfaces and step discontinuities, the surface profile obtained by use of the two-wavelength PSI technique is less accurate.
  11. N. Balsubramanian, “Optical system for surface topography measurement,” U.S. patent4,340,306 (filed 4February1980; issued 20July1982).
  12. M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of an interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).
  13. B. S. Lee, T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990).
    [CrossRef] [PubMed]
  14. G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
    [CrossRef] [PubMed]
  15. S. S. C. Chim, G. S. Kino, “Three-dimensional image realization in interference microscopy,” Appl. Opt. 31, 2550–2553 (1992).
    [CrossRef] [PubMed]
  16. P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
    [CrossRef] [PubMed]
  17. L. Deck, P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
    [CrossRef] [PubMed]
  18. K. G. Larkin, “Effective nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832–843 (1996).
    [CrossRef]
  19. C. Ai, E. L. Novak, “Centroid approach for estimating modulation peak in broad-bandwidth interferometry,” U.S. patent5,633,715 (filed 19May1996; issued 27May1997).
  20. P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
    [CrossRef] [PubMed]
  21. R. J. Recknagel, G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
    [CrossRef]
  22. M. Hart, D. G. Vass, M. L. Begbie, “Fast surface profiling by spectral analysis of white-light interferograms with Fourier transform spectroscopy,” Appl. Opt. 37, 1764–1769 (1998).
    [CrossRef]
  23. A. Harasaki, J. C. Wyant, “Fringe modulation skewing effect in white light vertical scanning interferometry,” Appl. Opt. 39, 2101–2106 (2000).
    [CrossRef]
  24. P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
    [CrossRef]
  25. D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (filed 12June1991; issued 28July1992).
  26. P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
    [CrossRef]
  27. Please refer to Fig. 3. The interferogram is taken every 90° (270°), which corresponds to a distance of λ̅/4 (3λ̅/4). The frame position with the largest modulation contrast (the best-focus frame position) should be found to minimize the focus error, and the fractional phase is measured from the best-focus position.
  28. P. Hariharan, B. F. Oreb, E. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [CrossRef] [PubMed]
  29. K. Creath, “Calibration of numerical aperture effects in interferometric microscope objectives,” Appl. Opt. 28, 3333–3338 (1989).
    [CrossRef] [PubMed]
  30. C. J. R. Sheppard, K. G. Larkin, “Effect of numerical aperture on interference fringe spacing,” Appl. Opt. 34, 4731–4734 (1995).
    [CrossRef] [PubMed]
  31. The coherence length of the unfiltered tungsten light source is 1.2 µm, and after the 80-nm bandpass filter at the center wavelength of 600 nm the coherence length is 2.2 µm. This coherence length (2.2 µm) is limited by the NA of the 50×objective rather than by the filter’s bandwidth.14
  32. K. Hibino, B. F. Oreb, D. I. Farrany, K. G. Larkin, “Phase shifting for nonsinusoidal waveforms with shifting errors,” J. Opt. Soc. Am. A 12, 761–768 (1995).
    [CrossRef]

2000 (1)

1998 (2)

1997 (2)

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (5)

1994 (2)

1993 (1)

1992 (1)

1990 (2)

1989 (1)

1987 (2)

1984 (1)

Ai, C.

C. Ai, E. L. Novak, “Centroid approach for estimating modulation peak in broad-bandwidth interferometry,” U.S. patent5,633,715 (filed 19May1996; issued 27May1997).

Balsubramanian, N.

N. Balsubramanian, “Optical system for surface topography measurement,” U.S. patent4,340,306 (filed 4February1980; issued 20July1982).

Begbie, M. L.

Brophy, C. P.

D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (filed 12June1991; issued 28July1992).

Bruning, J. H.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Caber, P. J.

P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
[CrossRef] [PubMed]

D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (filed 12June1991; issued 28July1992).

Cheng, Y.-Y.

Chim, S. S. C.

Cohen, D. K.

D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (filed 12June1991; issued 28July1992).

Cohen, F.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of an interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

Creath, K.

Davidson, M.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of an interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

de Groot, P.

de Groot, P. J.

Deck, L.

Devillers, R.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Eiju, E.

Farrany, D. I.

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Harasaki, A.

Hariharan, P.

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

P. Hariharan, B. F. Oreb, E. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
[CrossRef] [PubMed]

Hart, M.

Hibino, K.

Kaufman, K.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of an interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

Kino, G. S.

Larkin, K. G.

Lee, B. S.

Mazor, I.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of an interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

Notni, G.

R. J. Recknagel, G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Novak, E. L.

C. Ai, E. L. Novak, “Centroid approach for estimating modulation peak in broad-bandwidth interferometry,” U.S. patent5,633,715 (filed 19May1996; issued 27May1997).

Oreb, B. F.

Plata, A.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Recknagel, R. J.

R. J. Recknagel, G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Roy, M.

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

Sandoz, P.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
[CrossRef] [PubMed]

Schmit, J.

J. Schmit, K. Creath, “Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry,” Appl. Opt. 34, 3610–3619 (1995).
[CrossRef] [PubMed]

J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
[CrossRef]

Sheppard, C. J. R.

Strand, T. C.

Vass, D. G.

Wyant, J. C.

A. Harasaki, J. C. Wyant, “Fringe modulation skewing effect in white light vertical scanning interferometry,” Appl. Opt. 39, 2101–2106 (2000).
[CrossRef]

Y.-Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
[CrossRef]

J. C. Wyant, K. Creath, “Two-wavelength phase-shifting interferometer and method,” U.S. patent4,832,489 (filed 19March1986; issued 23May1989).

J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
[CrossRef]

Appl. Opt. (15)

J. Schmit, K. Creath, “Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry,” Appl. Opt. 34, 3610–3619 (1995).
[CrossRef] [PubMed]

P. de Groot, “Derivation algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
[CrossRef]

P. J. de Groot, “Extending the unambiguous range of two-color interferometers,” Appl. Opt. 33, 5948–5953 (1994).
[CrossRef] [PubMed]

B. S. Lee, T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990).
[CrossRef] [PubMed]

G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
[CrossRef] [PubMed]

S. S. C. Chim, G. S. Kino, “Three-dimensional image realization in interference microscopy,” Appl. Opt. 31, 2550–2553 (1992).
[CrossRef] [PubMed]

P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
[CrossRef] [PubMed]

L. Deck, P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
[CrossRef] [PubMed]

Y.-Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
[CrossRef]

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[CrossRef] [PubMed]

M. Hart, D. G. Vass, M. L. Begbie, “Fast surface profiling by spectral analysis of white-light interferograms with Fourier transform spectroscopy,” Appl. Opt. 37, 1764–1769 (1998).
[CrossRef]

A. Harasaki, J. C. Wyant, “Fringe modulation skewing effect in white light vertical scanning interferometry,” Appl. Opt. 39, 2101–2106 (2000).
[CrossRef]

P. Hariharan, B. F. Oreb, E. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
[CrossRef] [PubMed]

K. Creath, “Calibration of numerical aperture effects in interferometric microscope objectives,” Appl. Opt. 28, 3333–3338 (1989).
[CrossRef] [PubMed]

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

J. Mod. Opt. (2)

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

R. J. Recknagel, G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Opt. Lett. (1)

Other (11)

J. C. Wyant, K. Creath, “Two-wavelength phase-shifting interferometer and method,” U.S. patent4,832,489 (filed 19March1986; issued 23May1989).

C. Ai, E. L. Novak, “Centroid approach for estimating modulation peak in broad-bandwidth interferometry,” U.S. patent5,633,715 (filed 19May1996; issued 27May1997).

Rough surfaces have local steep slopes that result in narrow fringe spacings, so the condition of two detectors per fringe is easily violated. Compared with the step height, which consists of smooth surfaces and step discontinuities, the surface profile obtained by use of the two-wavelength PSI technique is less accurate.

N. Balsubramanian, “Optical system for surface topography measurement,” U.S. patent4,340,306 (filed 4February1980; issued 20July1982).

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of an interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
[CrossRef]

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics XXVI, E. Wolf, ed. (Elsevier, Amsterdam, The Netherlands, 1988), pp. 349–393.
[CrossRef]

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Please refer to Fig. 3. The interferogram is taken every 90° (270°), which corresponds to a distance of λ̅/4 (3λ̅/4). The frame position with the largest modulation contrast (the best-focus frame position) should be found to minimize the focus error, and the fractional phase is measured from the best-focus position.

D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (filed 12June1991; issued 28July1992).

The coherence length of the unfiltered tungsten light source is 1.2 µm, and after the 80-nm bandpass filter at the center wavelength of 600 nm the coherence length is 2.2 µm. This coherence length (2.2 µm) is limited by the NA of the 50×objective rather than by the filter’s bandwidth.14

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Figures (11)

Fig. 1
Fig. 1

Surface profiles of the 460-nm height standard (VLSI, SHS 4600 Å) processed by (a) the centroid algorithm,19 (b) from the centroid of the recovered modulation contrast by the Fourier transform algorithm,14 (c) from the centroid of the recovered modulation contrast by the Hilbert transform algorithm,15 (d) from the phase slope in the Fourier domain.17,22

Fig. 2
Fig. 2

Typical correlograms and their coherence envelopes obtained by use of the Mirau interference microscope: (a) Positioned far from the step edge. The peak position is 48.77, and the centroid position is 48.75. (b) Positioned on or close to the step edge. The peak position is 50.80, and the centroid position is 50.91.

Fig. 3
Fig. 3

Correlogram and its retrieved phase information obtained while the optical path difference is scanned. The filled circles indicate five consecutive intensity data points separated by a 90° phase shift (the scanning step is Δ = λ̅/8); the open circles indicate five consecutive intensity data points separated by a 270° phase shift (the scanning step is Δ = 3λ̅/8). The term Δϕ is the relative phase from the best-focus position, and Nα is the absolute best-focus position.

Fig. 4
Fig. 4

Processed surface profile of a 460-nm height standard (VLSI, SHS 4600 Å): (a) The energy distribution along the pixel positions. (b) The surface profile obtained by use of Eq. (7). (c) The surface profile obtained by use of Eq. (5). (d) The resultant unwrapped surface profile.

Fig. 5
Fig. 5

Experimental setup with the Mirau interference microscope (Veeco, Model WYKO NT-2000). A broadband light source with a center wavelength of 600 nm and a bandwidth of 80 nm is used. PZT, piezoelectric transducer.

Fig. 6
Fig. 6

Surface profile of a ball bearing obtained by use of 90° white-light phase shifting: (a) Determined with the coherence-peak-sensing technique with Eq. (7). (b) Determined with Eq. (5). (c) Final result after 2π phase correction.

Fig. 7
Fig. 7

Surface profile of a ball bearing obtained by use of 270° white-light phase shifting: (a) Determined with the coherence-peak-sensing technique with Eq. (7). (b) Determined with Eq. (5). (c) Final result after 2π phase correction.

Fig. 8
Fig. 8

Camera image of the step-height standard (VLSI, SHS 4600 Å). Note the structure close to the step edge.

Fig. 9
Fig. 9

Processed surface profile of the step-height standard (VLSI, SHS 4600 Å). The measurement was performed with an 80-nm bandpass filter at the center wavelength of 600 nm: (a) The profile obtained by use of the regular coherence-peak-sensing algorithm.18 (b) The profile obtained by use of the proposed white-light phase-shifting algorithm.

Fig. 10
Fig. 10

Processed surface profile of the step-height standard (VLSI, SHS 4600 Å). The measurement was performed with an unfiltered tungsten light source: (a) The profile obtained by use of the regular coherence-peak-sensing algorithm.18 (b) The profile obtained by use of the proposed white-light phase-shifting algorithm.

Fig. 11
Fig. 11

Processed surface profile of the step-height standard (VLSI, SHS 4600 Å). The measurement was performed with an 80-nm bandpass filter at the center wavelength of 600 nm: (a) The x profile and (b) the y profile of the hole close to the step edge at position (346, 69). (c) The x profile and (d) the y profile of a small bump at position (104, 96) far toward the left-hand side of Fig. 8.

Tables (1)

Tables Icon

Table 1 Surface-Roughness Parameters of a Ball Bearing for Two Algorithms

Equations (13)

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

λeq=λ1λ2|λ1-λ2|.
M2  I2-I42-I1-I3I3-I5.
tanΔϕ=2 sin α I2-I42I3-I5-I1,
sin2 α=4I2-I42-I1-I524I2-I42.
zphasex, y=Δstep number+f2Δϕλ¯2π,
zphasex, y=Δstep number+f2Δϕ+2kπλ¯2π,
zenvelopex, y=Δstep number+Δz,
Δz=0.4Δ L1+3L2-3L4-L5L1-2L3+L5
|zphasei-zenvelopei+offset|f4 λ¯.
|zenvelopei-zenvelopei-1|<f4 λ¯,|zphasei-zphasei-1|>f4 λ¯,
|zenvelopei-zenvelopei-1|<f4 λ¯,|zphasei-zphasei-1|<f4 λ¯.
Ra=1Ni=1N |zi-zfiti|,
Rq=1Ni=1Nzi-zfiti21/2,

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