Abstract

We built a dispersive white-light spectral interferometer for precisely measuring the dispersion properties of a multilayer thin-film structure. A novel algorithm with improved robustness to measurement errors is presented by combining a windowed Fourier transformation with wavelet-based differentiation. Compared with previously published algorithms, this method shows substantial resistance to measurement errors. The group delay dispersion properties of bulk materials and a homemade chirped mirror are measured by our apparatus, and the measurement result manifests considerable accuracy and ro bustness. The technique shows reasonable potential for the characterization of ultrabroadband chirped mirrors.

© 2011 Optical Society of America

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References

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    [CrossRef]
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2010 (2)

Z. Luo, X. Liu, and S. Zhang, “Dispersive white-light spectral interferometer for optical properties measurement of optical thin film,” Chin. Opt. Lett. 8 supplement, 94–99(2010).
[CrossRef]

H. Lei, K. Qian, P. Bing, and A. Asundia, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

2009 (3)

2008 (1)

P. Hlubina, J. Lunacek, 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 (1)

2006 (3)

2005 (1)

2000 (1)

1998 (1)

K. Alexander, F. Chau, and J. Gao, “Wavelet transform: a method for derivative calculation in analytical chemistry,” Anal. Chem. 70, 5222–5229 (1998).
[CrossRef]

Ahmad, I.

Alexander, K.

K. Alexander, F. Chau, and J. Gao, “Wavelet transform: a method for derivative calculation in analytical chemistry,” Anal. Chem. 70, 5222–5229 (1998).
[CrossRef]

Amotchkina, T. V.

Apolonski, A.

Asundia, A.

H. Lei, K. Qian, P. Bing, and A. Asundia, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

Austin, R. R.

Bai, J.

J. Luo, J. Bai, and J. Shao, “Application of the wavelet transforms on axial strain calculation in ultrasound elastography,” Prog. Nat. Sci. 16, 942–947 (2006).
[CrossRef]

Bing, P.

H. Lei, K. Qian, P. Bing, and A. Asundia, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

Brun, G.

Chau, F.

K. Alexander, F. Chau, and J. Gao, “Wavelet transform: a method for derivative calculation in analytical chemistry,” Anal. Chem. 70, 5222–5229 (1998).
[CrossRef]

Chlebus, R.

P. Hlubina, J. Lunacek, 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. Lunacek, 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]

P. Hlubina, D. Ciprian, J. Lunácek, and M. Lesnák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678–7685(2006).
[CrossRef] [PubMed]

Deng, Y.

Diddams, S. A.

Gao, J.

K. Alexander, F. Chau, and J. Gao, “Wavelet transform: a method for derivative calculation in analytical chemistry,” Anal. Chem. 70, 5222–5229 (1998).
[CrossRef]

Golubovic, B.

Gosteva, A.

Grupe, D.

Haiml, M.

Hlubina, P.

P. Hlubina, J. Lunacek, 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]

P. Hlubina, D. Ciprian, J. Lunácek, and M. Lesnák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678–7685(2006).
[CrossRef] [PubMed]

Jacquot, M.

Jones, D. J.

Keller, U.

Kong, W.

Krausz, F.

Lei, H.

H. Lei, K. Qian, P. Bing, and A. Asundia, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

Lesnák, M.

Liu, X.

Z. Luo, X. Liu, and S. Zhang, “Dispersive white-light spectral interferometer for optical properties measurement of optical thin film,” Chin. Opt. Lett. 8 supplement, 94–99(2010).
[CrossRef]

Z. Luo, S. Zhang, W. Shen, and X. Liu, “Direct measurement of group-delay properties for dispersive mirrors,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper FB4.

Lunacek, J.

P. Hlubina, J. Lunacek, 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]

Lunácek, J.

Luo, J.

J. Luo, J. Bai, and J. Shao, “Application of the wavelet transforms on axial strain calculation in ultrasound elastography,” Prog. Nat. Sci. 16, 942–947 (2006).
[CrossRef]

Luo, Z.

Z. Luo, X. Liu, and S. Zhang, “Dispersive white-light spectral interferometer for optical properties measurement of optical thin film,” Chin. Opt. Lett. 8 supplement, 94–99(2010).
[CrossRef]

Z. Luo, S. Zhang, W. Shen, and X. Liu, “Direct measurement of group-delay properties for dispersive mirrors,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper FB4.

Paschotta, R.

Pervak, V.

Qian, K.

H. Lei, K. Qian, P. Bing, and A. Asundia, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

Reed, M. K.

Reolon, D.

Shao, J.

J. Luo, J. Bai, and J. Shao, “Application of the wavelet transforms on axial strain calculation in ultrasound elastography,” Prog. Nat. Sci. 16, 942–947 (2006).
[CrossRef]

Shen, W.

Z. Luo, S. Zhang, W. Shen, and X. Liu, “Direct measurement of group-delay properties for dispersive mirrors,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper FB4.

Steiner-Shepard, M. K.

Tao, J.

Tikhonravov, A. V.

Trubetskov, M. K.

Van Engen, A. G.

Veillas, C.

Verrier, I.

Wang, X.

Yang, W.

Zeng, H.

Zhang, S.

Z. Luo, X. Liu, and S. Zhang, “Dispersive white-light spectral interferometer for optical properties measurement of optical thin film,” Chin. Opt. Lett. 8 supplement, 94–99(2010).
[CrossRef]

Z. Luo, S. Zhang, W. Shen, and X. Liu, “Direct measurement of group-delay properties for dispersive mirrors,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper FB4.

Zhang, Z.

Zhong, J.

Zhou, C.

Anal. Chem. (1)

K. Alexander, F. Chau, and J. Gao, “Wavelet transform: a method for derivative calculation in analytical chemistry,” Anal. Chem. 70, 5222–5229 (1998).
[CrossRef]

Appl. Opt. (2)

Chin. Opt. Lett. (1)

Z. Luo, X. Liu, and S. Zhang, “Dispersive white-light spectral interferometer for optical properties measurement of optical thin film,” Chin. Opt. Lett. 8 supplement, 94–99(2010).
[CrossRef]

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

Opt. Commun. (1)

P. Hlubina, J. Lunacek, 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. Express (4)

Opt. Lasers Eng. (1)

H. Lei, K. Qian, P. Bing, and A. Asundia, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

Opt. Lett. (1)

Prog. Nat. Sci. (1)

J. Luo, J. Bai, and J. Shao, “Application of the wavelet transforms on axial strain calculation in ultrasound elastography,” Prog. Nat. Sci. 16, 942–947 (2006).
[CrossRef]

Other (1)

Z. Luo, S. Zhang, W. Shen, and X. Liu, “Direct measurement of group-delay properties for dispersive mirrors,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2010), paper FB4.

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Figures (9)

Fig. 1
Fig. 1

Schematics of the white-light spectral interferometer.

Fig. 2
Fig. 2

Windowed Fourier transform results for the measured spectral interferogram.

Fig. 3
Fig. 3

Demonstration of the wavelet denoising method: (a) the noisy sine curve and (b) comparison of results by wavelet differentiation and direct differentiation.

Fig. 4
Fig. 4

Process of the Fourier transform: (a) intensity interferogram, (b) Fourier transform and filtering, (c) retrieved spectral phase, and (d) retrieved GD properties.

Fig. 5
Fig. 5

(a) Presentation of wavelet transform and its ridge. (b) Measured GD and the smoothed GD.

Fig. 6
Fig. 6

(a) Retrieved GD properties with the common Fourier method, our method, and the theoretical GD. (b) Retrieved GDD properties with our method and the theoretical GDD.

Fig. 7
Fig. 7

(a), (c), (e) Measured spectral interferograms and (b), (d), (f) the retrieved GD at three different OPDs.

Fig. 8
Fig. 8

Measured GDD at three different OPDs.

Fig. 9
Fig. 9

Measured GDD at different times at the same OPD.

Equations (7)

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F ( ω , ξ ) = + I ( ω ) g ( ω ω ) exp ( j ξ ω ) d w ,
F ( ω , ξ ) ¯ = { F ( ω , ξ ) if | F ( ω , ξ ) | > thr esh old 0 oth erw ise .
I ( ω ) ¯ = 1 2 π + + F ( ω , ξ ) ¯ g ( ω ω ) exp ( j ξ ω ) d ξ d ω .
φ ( ω ) = unw rap ( angle ( I ( ω ) ¯ ) ) .
G D ( w n ) = φ ( w n + 1 ) φ ( w n ) w n + 1 w n
CWT ( ω , ϖ ) = + φ ( ω ) 1 ϖ ψ ( ω ω ϖ ) d ω ,
lim ϖ 0 CWT ( ω , ϖ ) K ϖ 3 / 2 | w = w = d φ ( ω ) d ω = GD ( ω ) .

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