Abstract

By analyzing the spectral domain’s phase information, one can use spectrally resolved white-light interferometry (SRWLI) to obtain the profile with a single frame of an interferogram. We present here a two-dimensional (2D) SRWLI method that can be applied to measure narrow rectangle areas. A frequency comb is produced by using a Fabry–Perot (F-P) etalon to filter the broadband source. With the filtered frequency comb illumination, the interference patterns under adjacent wavelengths would be separated by a little distance, which enables us to obtain a 2D profile with a small width. The experimental details of measurement on a step sample are discussed in this paper.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. S. Lee and T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990).
    [CrossRef]
  2. L. Deck and P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
    [CrossRef]
  3. T. Dresel, G. Häusler, and H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
    [CrossRef]
  4. P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
    [CrossRef]
  5. A. Harasaki and J. C. Wyant, “Fringe modulation skewing effect in white-light vertical scanning interferometry,” Appl. Opt. 39, 2101–2106 (2000).
    [CrossRef]
  6. A. Pfortner and J. Schwider, “Dispersion error in white-light Linnik interferometers and its implications for evaluation procedures,” Appl. Opt. 40, 6223–6228 (2001).
    [CrossRef]
  7. P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41, 4571–4578 (2002).
    [CrossRef]
  8. C. Sainz, J. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
    [CrossRef]
  9. P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms,” J. Mod. Opt. 43, 701–708 (1996).
    [CrossRef]
  10. U. Schnell and R. Dandliker, “Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target,” Opt. Lett. 21, 528–530 (1996).
    [CrossRef]
  11. K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14, 5954–5960 (2006).
    [CrossRef]
  12. D. X. Hammer and A. J. Welch, “Spectrally resolved white-light interferometry for measurement of ocular dispersion,” J. Opt. Soc. Am. A 16, 2092–2102 (1999).
    [CrossRef]
  13. S. K. Debnath and M. P. Kothiyal, “Spectrally resolved white–light phase–shifting interference microscopy for thickness–profile measurements of transparent thin film layers on patterned substrates,” Opt. Express 4662, 8636–8640 (2006).
    [CrossRef]
  14. K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE 1162, 395–401 (1989).
    [CrossRef]
  15. K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29, 3280–3285 (1990).
    [CrossRef]
  16. D. R. Herriott, “Multiple-wavelength multiple-beam interferometric observation of flat surfaces,” J. Opt. Soc. Am. 51, 1142–1145 (1961).
    [CrossRef]
  17. J. Schwider, “Multiple beam Fizeau interferometer with frequency comb illumination,” Opt. Commun. 282, 3308–3324(2009).
    [CrossRef]
  18. P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms.” J. Mod. Opt. 43, 701–708 (1996).
    [CrossRef]
  19. J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt Laser Technol. 28, 485–489 (1996).
    [CrossRef]
  20. H. S. Suja, M. P. Kothiyal, and R. S. Sirohi, “Analysis of spectrally resolved white light interferograms: use of a phase shifting technique,” Opt. Eng. 40, 1329–36 (2001).
    [CrossRef]
  21. S. K. Debnath and M. P. Kothiyal, “Optical profiler based on spectrally resolved white light interferometry,” Opt. Eng. 44, 013606 (2005).
    [CrossRef]
  22. S. K. Debnath and M. P. Kothiyal, “Improved optical profiling using spectral phase in spectrally resolved white light interferometry,” Appl. Opt. 45, 6965–6972 (2006).
    [CrossRef]
  23. S. K. Debnath and M. P. Kothiyal, “Analysis of spectrally resolved white light interferometry by Hilbert transform method,” Proc. SPIE 6292, 62920P (2006).
    [CrossRef]
  24. J. Schwider and L. Zhou, “Dispersive interferometric profilometer,” Opt. Lett. 19, 995–997 (1994).
    [CrossRef]
  25. A. Harasaki, J. Schmidt, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt. 39, 2107–2115 (2000).
    [CrossRef]

2009 (1)

J. Schwider, “Multiple beam Fizeau interferometer with frequency comb illumination,” Opt. Commun. 282, 3308–3324(2009).
[CrossRef]

2006 (4)

S. K. Debnath and M. P. Kothiyal, “Spectrally resolved white–light phase–shifting interference microscopy for thickness–profile measurements of transparent thin film layers on patterned substrates,” Opt. Express 4662, 8636–8640 (2006).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Analysis of spectrally resolved white light interferometry by Hilbert transform method,” Proc. SPIE 6292, 62920P (2006).
[CrossRef]

K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14, 5954–5960 (2006).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Improved optical profiling using spectral phase in spectrally resolved white light interferometry,” Appl. Opt. 45, 6965–6972 (2006).
[CrossRef]

2005 (1)

S. K. Debnath and M. P. Kothiyal, “Optical profiler based on spectrally resolved white light interferometry,” Opt. Eng. 44, 013606 (2005).
[CrossRef]

2002 (1)

2001 (2)

A. Pfortner and J. Schwider, “Dispersion error in white-light Linnik interferometers and its implications for evaluation procedures,” Appl. Opt. 40, 6223–6228 (2001).
[CrossRef]

H. S. Suja, M. P. Kothiyal, and R. S. Sirohi, “Analysis of spectrally resolved white light interferograms: use of a phase shifting technique,” Opt. Eng. 40, 1329–36 (2001).
[CrossRef]

2000 (2)

1999 (1)

1996 (4)

U. Schnell and R. Dandliker, “Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target,” Opt. Lett. 21, 528–530 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms.” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt Laser Technol. 28, 485–489 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms,” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

1994 (2)

1993 (1)

1992 (1)

1990 (3)

1989 (1)

K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE 1162, 395–401 (1989).
[CrossRef]

1961 (1)

Caber, P. J.

Calatroni, J.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt Laser Technol. 28, 485–489 (1996).
[CrossRef]

C. Sainz, J. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[CrossRef]

Dandliker, R.

de Groot, P.

de Lega, X. C.

Debnath, S. K.

S. K. Debnath and M. P. Kothiyal, “Spectrally resolved white–light phase–shifting interference microscopy for thickness–profile measurements of transparent thin film layers on patterned substrates,” Opt. Express 4662, 8636–8640 (2006).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Improved optical profiling using spectral phase in spectrally resolved white light interferometry,” Appl. Opt. 45, 6965–6972 (2006).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Analysis of spectrally resolved white light interferometry by Hilbert transform method,” Proc. SPIE 6292, 62920P (2006).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Optical profiler based on spectrally resolved white light interferometry,” Opt. Eng. 44, 013606 (2005).
[CrossRef]

Deck, L.

Dresel, T.

Escalona, R.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt Laser Technol. 28, 485–489 (1996).
[CrossRef]

Guerrero, A. L.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt Laser Technol. 28, 485–489 (1996).
[CrossRef]

Hammer, D. X.

Harasaki, A.

Häusler, G.

Herriott, D. R.

Joo, K.-N.

Kim, S.-W.

Kothiyal, M. P.

S. K. Debnath and M. P. Kothiyal, “Improved optical profiling using spectral phase in spectrally resolved white light interferometry,” Appl. Opt. 45, 6965–6972 (2006).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Spectrally resolved white–light phase–shifting interference microscopy for thickness–profile measurements of transparent thin film layers on patterned substrates,” Opt. Express 4662, 8636–8640 (2006).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Analysis of spectrally resolved white light interferometry by Hilbert transform method,” Proc. SPIE 6292, 62920P (2006).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Optical profiler based on spectrally resolved white light interferometry,” Opt. Eng. 44, 013606 (2005).
[CrossRef]

H. S. Suja, M. P. Kothiyal, and R. S. Sirohi, “Analysis of spectrally resolved white light interferograms: use of a phase shifting technique,” Opt. Eng. 40, 1329–36 (2001).
[CrossRef]

Kramer, J.

Lee, B. S.

Okada, K.

K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29, 3280–3285 (1990).
[CrossRef]

K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE 1162, 395–401 (1989).
[CrossRef]

Ose, T.

Perrin, H.

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms,” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms.” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

Pfortner, A.

Sainz, C.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt Laser Technol. 28, 485–489 (1996).
[CrossRef]

C. Sainz, J. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[CrossRef]

Sakuta, H.

Sandoz, P.

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms,” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms.” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

Schmidt, J.

Schnell, U.

Schwider, J.

Sirohi, R. S.

H. S. Suja, M. P. Kothiyal, and R. S. Sirohi, “Analysis of spectrally resolved white light interferograms: use of a phase shifting technique,” Opt. Eng. 40, 1329–36 (2001).
[CrossRef]

Strand, T. C.

Suja, H. S.

H. S. Suja, M. P. Kothiyal, and R. S. Sirohi, “Analysis of spectrally resolved white light interferograms: use of a phase shifting technique,” Opt. Eng. 40, 1329–36 (2001).
[CrossRef]

Tribillon, G.

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms,” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms.” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

C. Sainz, J. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[CrossRef]

Tsujiuchi, J.

K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29, 3280–3285 (1990).
[CrossRef]

K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE 1162, 395–401 (1989).
[CrossRef]

Turzhitsky, M.

Venzke, H.

Welch, A. J.

Wyant, J. C.

Zhou, L.

Appl. Opt. (10)

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

K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29, 3280–3285 (1990).
[CrossRef]

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

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

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

A. Harasaki, J. Schmidt, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt. 39, 2107–2115 (2000).
[CrossRef]

T. Dresel, G. Häusler, and H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
[CrossRef]

A. Pfortner and J. Schwider, “Dispersion error in white-light Linnik interferometers and its implications for evaluation procedures,” Appl. Opt. 40, 6223–6228 (2001).
[CrossRef]

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

S. K. Debnath and M. P. Kothiyal, “Improved optical profiling using spectral phase in spectrally resolved white light interferometry,” Appl. Opt. 45, 6965–6972 (2006).
[CrossRef]

J. Mod. Opt. (2)

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms,” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, “High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms.” J. Mod. Opt. 43, 701–708 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Meas. Sci. Technol. (1)

C. Sainz, J. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[CrossRef]

Opt Laser Technol. (1)

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally-resolved white-light interferometry as a profilometry tool,” Opt Laser Technol. 28, 485–489 (1996).
[CrossRef]

Opt. Commun. (1)

J. Schwider, “Multiple beam Fizeau interferometer with frequency comb illumination,” Opt. Commun. 282, 3308–3324(2009).
[CrossRef]

Opt. Eng. (2)

H. S. Suja, M. P. Kothiyal, and R. S. Sirohi, “Analysis of spectrally resolved white light interferograms: use of a phase shifting technique,” Opt. Eng. 40, 1329–36 (2001).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Optical profiler based on spectrally resolved white light interferometry,” Opt. Eng. 44, 013606 (2005).
[CrossRef]

Opt. Express (2)

S. K. Debnath and M. P. Kothiyal, “Spectrally resolved white–light phase–shifting interference microscopy for thickness–profile measurements of transparent thin film layers on patterned substrates,” Opt. Express 4662, 8636–8640 (2006).
[CrossRef]

K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14, 5954–5960 (2006).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (2)

K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE 1162, 395–401 (1989).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, “Analysis of spectrally resolved white light interferometry by Hilbert transform method,” Proc. SPIE 6292, 62920P (2006).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Frequency comb produced with the help of F-P etalon; the wavelength difference between consecutive resonance wavelengths is about 0.298 nm, and the half width of each high-transmission peak is about 0.07 nm.

Fig. 2.
Fig. 2.

Experimental setup for 2D SRWLI.

Fig. 3.
Fig. 3.

Dispersed interferogram of 2D SRWLI.

Fig. 4.
Fig. 4.

Phase unwrapping process of one point of the surface; (a) Light intensity of one transverse line of Fig. 3; (b) shaped profile of one point’s intensity; (c) the wrapped phase map of this point.

Fig. 5.
Fig. 5.

Calculated 2D profile with batwing effect: the h axis is in the direction of the optical axis, the y axis corresponds to the height of the tested area, and the x axis corresponds to the width of the tested area.

Fig. 6.
Fig. 6.

Calculated 2-D profile after removing the batwing effect.

Equations (13)

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

δ=(2πλ)2dcosθ,
T=11+Fsin2(δ2),
Δλ=λ022d+λ0λ022d,
Ik(x,y)=IR(x,y)+I0(x,y)+2[IR(x,y)×I0(x,y)]1/2cos[4πλkh(x,y)],
δ(x,y)=4π(λk+1λk)h(x,y)λk+1λk4πh(x,y)λ02Δλ.
h(x,y)=14π(ΔϕΔσ).
ϕk(x,y)+ϕ0=4πλk×h(x,y),
Δϕk(x,y)=Δ[4πλk×h(x,y)].
hk(x,y)=Δϕk(x,y)4πλk4πλk1.
h(x,y)=k=2N{Δϕk(x,y)(4πλk4πλk1)}k=2N(4πλk4πλk1)2.
δh=[δ(Δφ)4πΔk]2+[Δφδ(Δk)4π(Δk)2]2,
δhh=[δ(Δφ)Δφ]2+[δ(Δk)Δk]2,
hmax=14(dσ)max,

Metrics