Abstract

Discrepancies between phase-shifting and white-light interferometry have been observed in step-height and surface roughness measurements. The discrepancies have a strong relation to the roughness average parameter of the surface. The skewing effect, which mainly occurs in the vicinity of peaks, valleys, and edges of the sample, causes this problem in white-light interferometry of step height. For roughness, two possible sources of the discrepancy are considered.

© 2005 Optical Society of America

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References

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  1. T. V. Vorburger, J. Fu, N. Orji, “In the rough,” oe Magazine (March)31–34 (2002).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. L. Deck, P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
    [CrossRef] [PubMed]
  6. J. Schmit, A. Olszak, “High-precision shape measurement by white-light interferometry with real time scanner correction,” Appl. Opt. 41, 5943–5950 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. B. Wang, S. P. Marchese-Ragona, T. C. Bristow, “Roughness characterization of ultrasmooth surfaces using common path interferometry,” Proc. SPIE 3619, 121–127 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. A. Olszak, J. Schmit, “High-stability white-light interferometry with reference signal for real-time correction of scanning errors,” Opt. Eng. 42, 54–59 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  19. K. G. Larkin, “Effective nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832–843 (1996).
    [CrossRef]
  20. P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
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    [CrossRef]
  22. J. F. Song, T. V. Vorburger, “Standard reference specimens in quality control of engineering surfaces,” J. Res. Natl. Inst. Stand. Technol. 96, 271–289 (1991).
    [CrossRef]
  23. Information about the specimens is available at www.rubert.co.uk .
  24. Certain commercial materials are identified in this paper to specify adequately an experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that materials are necessarily the best available for the purpose.
  25. A. Jendral, O. Bryngdahl, “Synthetic near-field holograms with localized information,” Opt. Lett. 20, 1204–1206 (1995).
    [CrossRef] [PubMed]
  26. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gayload, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
    [CrossRef]
  27. A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of submicrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
    [CrossRef]

2003

A. Olszak, J. Schmit, “High-stability white-light interferometry with reference signal for real-time correction of scanning errors,” Opt. Eng. 42, 54–59 (2003).
[CrossRef]

2002

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

J. Schmit, A. Olszak, “High-precision shape measurement by white-light interferometry with real time scanner correction,” Appl. Opt. 41, 5943–5950 (2002).
[CrossRef] [PubMed]

T. V. Vorburger, J. Fu, N. Orji, “In the rough,” oe Magazine (March)31–34 (2002).

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of submicrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

2000

1999

T. Doi, T. V. Vorburger, P. J. Sullivan, “Effects of defocus and algorithm on optical step height calibration,” Precis. Eng. 23, 135–143 (1999).
[CrossRef]

B. Wang, S. P. Marchese-Ragona, T. C. Bristow, “Roughness characterization of ultrasmooth surfaces using common path interferometry,” Proc. SPIE 3619, 121–127 (1999).
[CrossRef]

1997

1996

1995

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

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

A. Jendral, O. Bryngdahl, “Synthetic near-field holograms with localized information,” Opt. Lett. 20, 1204–1206 (1995).
[CrossRef] [PubMed]

M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gayload, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
[CrossRef]

1994

1992

1991

J. Song, T. V. Vorburger, “Stylus profiling at high resolution and low force,” Appl. Opt. 30, 42–50 (1991).
[CrossRef] [PubMed]

J. F. Song, T. V. Vorburger, “Standard reference specimens in quality control of engineering surfaces,” J. Res. Natl. Inst. Stand. Technol. 96, 271–289 (1991).
[CrossRef]

1990

1986

G. Binnig, C. F. Quate, Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930–933 (1986).
[CrossRef] [PubMed]

1985

J. C. Wyant, K. Creath, “Recent advances in interferometric optical testing,” Laser Focus Electro-Optics 21, 118–132 (1985).

Binnig, G.

G. Binnig, C. F. Quate, Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930–933 (1986).
[CrossRef] [PubMed]

Bristow, T. C.

B. Wang, S. P. Marchese-Ragona, T. C. Bristow, “Roughness characterization of ultrasmooth surfaces using common path interferometry,” Proc. SPIE 3619, 121–127 (1999).
[CrossRef]

Bruning, J. H.

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

Bryngdahl, O.

Chim, S. S. C.

Creath, K.

J. C. Wyant, K. Creath, “Recent advances in interferometric optical testing,” Laser Focus Electro-Optics 21, 118–132 (1985).

de Groot, P.

de Lega, X. C.

Deck, L.

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

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

Doi, T.

T. Doi, T. V. Vorburger, P. J. Sullivan, “Effects of defocus and algorithm on optical step height calibration,” Precis. Eng. 23, 135–143 (1999).
[CrossRef]

Dresler, T.

Fu, J.

T. V. Vorburger, J. Fu, N. Orji, “In the rough,” oe Magazine (March)31–34 (2002).

Gayload, T. K.

Gerber, Ch.

G. Binnig, C. F. Quate, Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930–933 (1986).
[CrossRef] [PubMed]

Grann, E. B.

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 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]

Häusler, G.

Jendral, A.

Kerwien, N.

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of submicrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

Kino, G. S.

Kramer, J.

Larkin, K. G.

Marchese-Ragona, S. P.

B. Wang, S. P. Marchese-Ragona, T. C. Bristow, “Roughness characterization of ultrasmooth surfaces using common path interferometry,” Proc. SPIE 3619, 121–127 (1999).
[CrossRef]

Moharam, M. G.

Olszak, A.

Orji, N.

T. V. Vorburger, J. Fu, N. Orji, “In the rough,” oe Magazine (March)31–34 (2002).

Pommet, D. A.

Quate, C. F.

G. Binnig, C. F. Quate, Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930–933 (1986).
[CrossRef] [PubMed]

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.

Schmit, J.

Song, J.

Song, J. F.

J. F. Song, T. V. Vorburger, “Standard reference specimens in quality control of engineering surfaces,” J. Res. Natl. Inst. Stand. Technol. 96, 271–289 (1991).
[CrossRef]

Sullivan, P. J.

T. Doi, T. V. Vorburger, P. J. Sullivan, “Effects of defocus and algorithm on optical step height calibration,” Precis. Eng. 23, 135–143 (1999).
[CrossRef]

Tavrov, A.

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of submicrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

Tiziani, H. J.

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of submicrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

Totzeck, M.

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of submicrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

Turzhitsky, M.

Venzke, H.

Vorburger, T. V.

T. V. Vorburger, J. Fu, N. Orji, “In the rough,” oe Magazine (March)31–34 (2002).

T. Doi, T. V. Vorburger, P. J. Sullivan, “Effects of defocus and algorithm on optical step height calibration,” Precis. Eng. 23, 135–143 (1999).
[CrossRef]

J. F. Song, T. V. Vorburger, “Standard reference specimens in quality control of engineering surfaces,” J. Res. Natl. Inst. Stand. Technol. 96, 271–289 (1991).
[CrossRef]

J. Song, T. V. Vorburger, “Stylus profiling at high resolution and low force,” Appl. Opt. 30, 42–50 (1991).
[CrossRef] [PubMed]

Wang, B.

B. Wang, S. P. Marchese-Ragona, T. C. Bristow, “Roughness characterization of ultrasmooth surfaces using common path interferometry,” Proc. SPIE 3619, 121–127 (1999).
[CrossRef]

Wyant, J. C.

Appl. Opt.

J. Mod. Opt.

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

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

J. Opt. Soc. Am. A

J. Res. Natl. Inst. Stand. Technol.

J. F. Song, T. V. Vorburger, “Standard reference specimens in quality control of engineering surfaces,” J. Res. Natl. Inst. Stand. Technol. 96, 271–289 (1991).
[CrossRef]

Laser Focus Electro-Optics

J. C. Wyant, K. Creath, “Recent advances in interferometric optical testing,” Laser Focus Electro-Optics 21, 118–132 (1985).

oe Magazine (March)

T. V. Vorburger, J. Fu, N. Orji, “In the rough,” oe Magazine (March)31–34 (2002).

Opt. Eng.

A. Olszak, J. Schmit, “High-stability white-light interferometry with reference signal for real-time correction of scanning errors,” Opt. Eng. 42, 54–59 (2003).
[CrossRef]

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of submicrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

G. Binnig, C. F. Quate, Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930–933 (1986).
[CrossRef] [PubMed]

Precis. Eng.

T. Doi, T. V. Vorburger, P. J. Sullivan, “Effects of defocus and algorithm on optical step height calibration,” Precis. Eng. 23, 135–143 (1999).
[CrossRef]

Proc. SPIE

B. Wang, S. P. Marchese-Ragona, T. C. Bristow, “Roughness characterization of ultrasmooth surfaces using common path interferometry,” Proc. SPIE 3619, 121–127 (1999).
[CrossRef]

Other

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

Information about the specimens is available at www.rubert.co.uk .

Certain commercial materials are identified in this paper to specify adequately an experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that materials are necessarily the best available for the purpose.

“Surface texture, surface roughness, waviness, and lay,” (American Society of Mechanical Engineers, 2003), pp. 6–12.

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Figures (11)

Fig. 1
Fig. 1

Graph of the calculated heights with PSI and WLI of the seven specimens calculated with a two-sided algorithm. The numbers along the x axis are the step-height specimen numbers shown in Table 2. Sd, standard deviation.

Fig. 2
Fig. 2

Measured profiles of a sinusoidal grating with (a) PSI and (b) WLI. The test sample is Rubert 529.

Fig. 3
Fig. 3

Measured profiles of a sinusoidal grating with (a) PSI and (b) WLI. The test sample is Rubert 528.

Fig. 4
Fig. 4

Measured profiles of a random specimen with (a) PSI and (b) WLI. The test sample is Rubert 501.

Fig. 5
Fig. 5

WLI deviation from PSI in Ra value. Test samples include five random specimens: Veeco smooth mirror (smallest Ra) and Rubert 501, 502, 503, 504 (largest Ra); four sinusoidal gratings: sample 3 (smallest Ra), Rubert 529, SRM2071, Rubert 528 (largest Ra); and one periodic cusp shape specimen: No. 00635. Details are in Table 3.

Fig. 6
Fig. 6

WLI deviation from PSI in Ra value with different instruments.

Fig. 7
Fig. 7

(a) PSI and (b) WLI deviation from the stylus readings.

Fig. 8
Fig. 8

Model configuration of (a) an imaging system and (b) imaged area.

Fig. 9
Fig. 9

Configuration of a Mirau interferometer.

Fig. 10
Fig. 10

Simulated WLI readings with a virtual sine shape. The virtual sample was generated with a 330 nm peak–valley value and 10 μm surface spatial wavelength.

Fig. 11
Fig. 11

Second diffraction model: (a) broad intensity distribution from a rough surface, (b) sharp intensity distribution from a smooth surface, (c) intensity distribution from a surface whose Ra is approximately between 50 and 150 nm. In each model, the intensity distribution might be a part of a Gaussian profile.

Tables (3)

Tables Icon

Table 1 Specifications of Two Optical Instruments

Tables Icon

Table 2 Step-Height Results for Seven Samples Obtained after Masking Spikes Produced by the Skewing Effecta

Tables Icon

Table 3 Specifications of Specimens

Equations (8)

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

u ( x , z ) = - u i ( x 0 , z 0 ) u p ( x - x 0 , z - z 0 ) d x 0 ,
u p ( x - x 0 , z - z 0 ) = - 1 2 π z [ exp ( i k r ) r ] .
u ( x , z ) = FT - 1 [ U ( ξ , z ) ] = - U ( ξ , z ) exp ( 2 π i ξ x ) d ξ ,
U ( ξ , z ) = U i ( ξ , z 0 ) FT [ u p ( x - x 0 , z - z 0 ) ] = U i ( ξ , z 0 ) exp [ - 2 π i ( z - z 0 ) 1 λ 2 - ξ 2 ] ,
U test ( ξ , z ) = FT [ u test ( x , z ) ] = S U ( ξ , z ) H ( x ) d x = S U i ( ξ , z 0 ) exp [ - 2 π i ( z - z 0 ) 1 λ 2 - ξ 2 ] H ( x ) d x ,
S = P M + 1.22 λ NA ,
u test ( x , z , λ ) = FT - 1 [ U test ( ξ , z , λ ) ] = - 1 / λ 1 / λ S U i ( ξ , z 0 , λ ) exp [ - 2 π i ( z - z 0 ) 1 λ 2 - ξ 2 ] H ( x ) d x exp ( 2 π i ξ x ) d ξ .
I ( x , z ) = λ 1 λ 2 u test ( x , z , λ ) + u reference ( x , z + Δ z , λ ) 2 F ( λ ) d λ ,

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