Wavelet-transform analysis of spectral shearing interferometry for phase reconstruction of femtosecond optical pulses

Yuqiang Deng; Zubin Wu; Lu Chai; Ching-yue Wang; Keisaku Yamane; Ryoji Morita; Mikio Yamashita; Zhigang Zhang

doi:10.1364/OPEX.13.002120

Wavelet-transform analysis of spectral shearing interferometry for phase reconstruction of femtosecond optical pulses

Yuqiang Deng, Zubin Wu, Lu Chai, Ching-yue Wang, Keisaku Yamane, Ryoji Morita, Mikio Yamashita, and Zhigang Zhang

Optics Express
Vol. 13,
Issue 6,
pp. 2120-2126
(2005)
•https://doi.org/10.1364/OPEX.13.002120

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Yuqiang Deng, Zubin Wu, Lu Chai, Ching-yue Wang, Keisaku Yamane, Ryoji Morita, Mikio Yamashita, and Zhigang Zhang, "Wavelet-transform analysis of spectral shearing interferometry for phase reconstruction of femtosecond optical pulses," Opt. Express 13, 2120-2126 (2005)

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- Research Papers
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Phase retrieval (100.5070)
- Wavelets (100.7410)
- Phase measurement (120.5050)
- Ultrafast lasers (320.7090)

About this Article
History
- Original Manuscript: January 13, 2005
- Revised Manuscript: February 25, 2005
- Manuscript Accepted: March 12, 2005
- Published: March 21, 2005

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Open Access

Abstract

We introduce a novel method for retrieving the phase from a spectral shearing interferogram, based on wavelet-transform technique. We demonstrate with both theoretical and experimental data that this technique provides an alternative and reliable technique for phase retrieval, particularly for highly structured pulse spectra.

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References

View by:
Article Order
|
Year
|
Author
|
Publication

K. Yamane, T. Kito, R. Morita, and M. Yamashita, “2.8-fs transform-limited optical-pulse generation in the monocycle region,” in Conf. Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2004), postdeadline paper PDC2.
M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry.” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]
C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses”, IEEE J. Quantum Electron. 35, 501–509 (1999).
[Crossref]
M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]
S. Jensen and M. E. Anderson, “Measuring ultrashort optical pulses in the presence of noise: an empirical study of the performance of spectral phase interferometry for direct electric field reconstruction,” Appl. Opt. 43, 883–893 (2004).
[Crossref] [PubMed]
B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, 1987–1989 (2003).
[Crossref] [PubMed]
C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]
K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258–2260 (2003).
[Crossref] [PubMed]
C. K. Chui ed., An introduction to wavelets (Academic Press, Boston, 1992).
B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[Crossref]
Y. Morimoto and Y. Imamoto, “Application of wavelet transform to displacement and strain measurement by grid method,” in Proc. of 1995 SEM Spring Conf. on Exp. Mech. (Society for Experimental Mechanics, MI, 1995), 898–903.
L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
[Crossref]
Y. Q. Deng, X. H. Ji, Y. W. Qin, and J. L. Chen, “Application of wavelet-transform to measurement of phase of isodyne fringe,” in Proc. SPIE - The International Society for Optical Engineering, 5286, 277–281 (2003).
J. -C. Hong and Y. Y. Kim, “Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept,” Society for Exp. Mech. 44, 387–395 (2004).
[Crossref]
D. J. Kane and R. Trebino “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18, 823–825 (1993).
[Crossref] [PubMed]
K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency- resolved optical gating with the use of second-harmonic generation”, J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

2004 (3)

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, Carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004).
[Crossref]

J. -C. Hong and Y. Y. Kim, “Determination of the optimal Gabor wavelet shape for the best time-frequency localization using the entropy concept,” Society for Exp. Mech. 44, 387–395 (2004).
[Crossref]

S. Jensen and M. E. Anderson, “Measuring ultrashort optical pulses in the presence of noise: an empirical study of the performance of spectral phase interferometry for direct electric field reconstruction,” Appl. Opt. 43, 883–893 (2004).
[Crossref] [PubMed]

2003 (2)

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28, 1987–1989 (2003).
[Crossref] [PubMed]

K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258–2260 (2003).
[Crossref] [PubMed]

2000 (1)

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

1999 (2)

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses”, IEEE J. Quantum Electron. 35, 501–509 (1999).
[Crossref]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
[Crossref]

1994 (1)

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency- resolved optical gating with the use of second-harmonic generation”, J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

1993 (1)

D. J. Kane and R. Trebino “Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating,” Opt. Lett. 18, 823–825 (1993).
[Crossref] [PubMed]

1992 (1)

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[Crossref]

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry.” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]

Anderson, M. E.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

Barnes, T. H.

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
[Crossref]

Biegert, J.

Chen, J. L.

Y. Q. Deng, X. H. Ji, Y. W. Qin, and J. L. Chen, “Application of wavelet-transform to measurement of phase of isodyne fringe,” in Proc. SPIE - The International Society for Optical Engineering, 5286, 277–281 (2003).

Couairon, A.

de Araujo, L. E. E.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

De Silvestri, S.

DeLong, K. W.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency- resolved optical gating with the use of second-harmonic generation”, J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

Deng, Y. Q.

Hauri, C. P.

Heinrich, A.

Helbing, F. W.

Hong, J. -C.

Hunter, J.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency- resolved optical gating with the use of second-harmonic generation”, J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

Iaconis, C.

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses”, IEEE J. Quantum Electron. 35, 501–509 (1999).
[Crossref]

Imamoto, Y.

Y. Morimoto and Y. Imamoto, “Application of wavelet transform to displacement and strain measurement by grid method,” in Proc. of 1995 SEM Spring Conf. on Exp. Mech. (Society for Experimental Mechanics, MI, 1995), 898–903.

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry.” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]

Jensen, S.

Ji, X. H.

Kane, D. J.

Keller, U.

Kim, Y. Y.

Kito, T.

K. Yamane, T. Kito, R. Morita, and M. Yamashita, “2.8-fs transform-limited optical-pulse generation in the monocycle region,” in Conf. Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2004), postdeadline paper PDC2.

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry.” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]

Kornelis, W.

Kosik, E. M.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

Morimoto, Y.

Morita, R.

Mysyrowicz, A.

Nisoli, M.

Oka, K.

Qin, Y. W.

Sansone, G.

Schenkel, B.

Stagira, S.

Suguro, A.

Svelto, O.

Szu, H. H.

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[Crossref]

Takeda, M.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry.” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]

Tan, S. M.

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
[Crossref]

Telfer, B.

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[Crossref]

Trebino, R.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency- resolved optical gating with the use of second-harmonic generation”, J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

Vozzi, C.

Walmsley, I. A.

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses”, IEEE J. Quantum Electron. 35, 501–509 (1999).
[Crossref]

Watkins, L. R.

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
[Crossref]

White, W. E.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency- resolved optical gating with the use of second-harmonic generation”, J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

Yamane, K.

Yamashita, M.

Zhang, Z.

Appl. Opt. (1)

Appl. Phys. B (2)

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, “The effects of noise on ultrashort-optical-pulse measurement using SPIDER,” Appl. Phys. B 70, S85–S93 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses”, IEEE J. Quantum Electron. 35, 501–509 (1999).
[Crossref]

J. Opt. Soc. Am. (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry.” J. Opt. Soc. Am. 72, 156–160 (1982).
[Crossref]

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

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency- resolved optical gating with the use of second-harmonic generation”, J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

Opt. Eng. (1)

B. Telfer and H. H. Szu, “New wavelet transform normalization to remove frequency bias,” Opt. Eng. 31, 1830–1834 (1992).
[Crossref]

Opt. Lett. (4)

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
[Crossref]

Society for Exp. Mech. (1)

Other (4)

C. K. Chui ed., An introduction to wavelets (Academic Press, Boston, 1992).

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Fig. 1. WT graphics for zero phases: (a) magnitude topography. (b) phase topography.

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Fig. 2. WT graphics for high order phases.

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Fig. 3. Measured spectral shearing interferogram.

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Fig. 4. Results of WT: (a) Magnitude topography. (b) Phase topography. (The pink colored curve represents the maximum value of the magnitude.)

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Fig. 5. (a) Spectrum and reconstructed phase with WT and FT techniques. (b) Reconstructed pulse profiles in comparison with the transform-limited pulses.

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Equations (4)

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

W (Δ ω, ω) = \frac{1}{Δ ω} \int_{- \infty}^{+ \infty} f (ω') ψ^{*} (\frac{ω - ω}{Δ ω}) d ω'

t = 2 π ⁄ Δ ω

W (t, ω) = \frac{t}{2 π} \int_{- \infty}^{+ \infty} f (ω') ψ^{*} [\frac{(ω' - ω) \cdot t}{2 π}] d ω'

ψ (ω') = e^{(- {ω'}^{2} ⁄ 2 σ^{2} + i 2 π ω')} ⁄ {(σ^{2} π)}^{\frac{1}{4}}

Abstract

References

2004 (3)

2003 (2)

2000 (1)

1999 (2)

1994 (1)

1993 (1)

1992 (1)

1982 (1)

Anderson, M. E.

Barnes, T. H.

Biegert, J.

Chen, J. L.

Couairon, A.

de Araujo, L. E. E.

De Silvestri, S.

DeLong, K. W.

Deng, Y. Q.

Hauri, C. P.

Heinrich, A.

Helbing, F. W.

Hong, J. -C.

Hunter, J.

Iaconis, C.

Imamoto, Y.

Ina, H.

Jensen, S.

Ji, X. H.

Kane, D. J.

Keller, U.

Kim, Y. Y.

Kito, T.

Kobayashi, S.

Kornelis, W.

Kosik, E. M.

Morimoto, Y.

Morita, R.

Mysyrowicz, A.

Nisoli, M.

Oka, K.

Qin, Y. W.

Sansone, G.

Schenkel, B.

Stagira, S.

Suguro, A.

Svelto, O.

Szu, H. H.

Takeda, M.

Tan, S. M.

Telfer, B.

Trebino, R.

Vozzi, C.

Walmsley, I. A.

Watkins, L. R.

White, W. E.

Yamane, K.

Yamashita, M.

Zhang, Z.

Appl. Opt. (1)

Appl. Phys. B (2)

IEEE J. Quantum Electron. (1)

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

Opt. Lett. (4)

Society for Exp. Mech. (1)

Other (4)

Cited By

Figures (5)

Equations (4)

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